JANAS 39 2 2007

Volume 39(2) Journal of the Arizona-Nevada Academy of Science Special Issue: Psychology – Analysis and Measurement Golden Anniversary Meeting University of Arizona,Tucson, AZ April 7, 8, 9, 2006 CONTENTS Foreword ............................................................................................................................................. iii Assortative Mating in the Jewel Wasp: 1. Female Matching of Eye-Color Genotype, Not Host-Feeding Phenotype Aurelio José Figueredo and Rebecca M. S. Sage ........................................................................... 51 Assortative Mating in the Jewel Wasp: 2. Sequential Canonical Analysis as an Exploratory Form of Path Analysis Aurelio José Figueredo, and Richard L. Gorsuch .......................................................................... 59 Differential Parental Investment in the Southwestern United States Melinda F. Davis, Cordelia B. Guggenheim, Aurelio José Figueredo, and Catherine J. Locke ... 65 Sons Or Daughters: A Cross-Cultural Study Of Sex Ratio Biasing And Differential Parental Investment Cordelia B. Guggenheim, Melinda F. Davis, and Aurelio José Figueredo ................................... 73 Sexual Risk Behavior Among Kenyan University Students Mary B. Adam and Mike Mutungi ................................................................................................ 91 Likelihood-Evidential Support And Bayesian Analysis On A Prospective Cohort Of Children And Adolescents With Mild Scoliosis Under Chiropractic Management J. Michael Menke, Gregory Plaugher, Christina A. Carrari, Roger R. Coleman, Luca Vannetiello, and Trent R. Bachman, .................................................................................................................. 99 2007 Published by the ARIZONA-NEVADA ACADEMY OF SCIENCE i ARIZONA-NEVADA ACADEMY OF SCIENCE OFFICERS FOR 2007-2008 CARLETON “BUCK” JONES, Midwestern University CARLETON “BUCK” JONES, Midwestern University INGRID NOVODVORSKY, University of Arizona ELIZABETH HULL, Midwestern University WILLIAM PERRY BAKER, University of Arizona KAREN CONZELMAN, Glendale Community College WILLIAM PERRY BAKER, University of Arizona MICHAEL W. DIEHL, Desert Archaeology, Inc., Tucson ROBERT REAVIS, Glendale Community College AREGAI TECLE, Northern Arizona University J-PETRINA MCCARTY-PUHL, Robert McQueen High School, Reno President President-Elect Membership Secretary Recording Secretary Permanent Secretary Treasurer Editor Director/Southern Arizona Director/Central Arizona Director/Northern Arizona Director/Nevada ASSOCIATE EDITORS AREGAI TECLE, Northern Arizona University JIM DEVOS, Arizona Game and Fish Department GORDON JOHNSON, Northern Arizona University LINDA SMITH, Glendale Community College HENRI GRISSINO-MAYER, Valdosta State University ROBERT REAVIS, Glendale Community College CINDY D. ZISNER, Arizona State University Hydrology/Geography Conservation/Biology Education/General Science Anthropology Geology Advertising Editor Production Editor Subscription rates for institutions and libraries within the United States is $35.00 per year; institutions and libraries outside the United States subscribe at the rate of $45.00 per year. To subscribe please address correspondence to: Ingrid Novodvorsky, Membership Secretary - ANAS, Physics Department, 1118 E 4th St, University of Arizona, Tucson, AZ 85721. Individual memberships to the Academy (which includes a subscription to the Journal) are $35.00 per year within the United States and $45 per year for foreign members. Student membership is $15.00 per year (requires proof of student status). Family and patron memberships are also available. For membership information, please see our web site at http://www.geo.arizona.edu/anas or contact the membership secretary at the address listed above. Single copies of the Journal are $6.00; special issues are $10. For a list of previous issues see our web site at http://www.geo.arizona.edu/anas/publicatons.html. EDITORIAL POLICY The Journal of the Arizona-Nevada Academy of Science (ISSN 1533-6085) is published principally by and for the members of the Arizona-Nevada Academy of Science. It is the intention of the Editorial Board that the Journal shall serve all members, and publications are not restricted to formal, original scientific papers. The Editorial Board will decide the material to be included in each issue and will use its prerogative to edit all published items. The Arizona-Nevada Academy of Science is a nonprofit organization, and publication costs for its journal are subsidized in part by page charges. Page charges for ANAS members are $15 per page up to eight pages and $30 per page for each additional page. Page charges for nonmembers are $30 per page. Contributors without grant support may request waiver of page charges. ii FOREWORD There have now been four psychology sessions at the ANAS annual meetings, and this issue of JANAS is an introduction to psychological research in Arizona for ANAS members. This issue has several themes; measurement, data analysis, and evolutionary psychology. The first four articles demonstrate an analytical approach that is intended for studies with multiple, correlated dependent variables that can be implemented using common statistical packages. The first two articles are likely to be of interest to biologists and science educators, because they use this novel approach to tease out the genetic and developmental factors influencing assortative mating in insects. While there is some overlap between Jewel Wasp 1 and Jewel Wasp 2, they are designed for different readers. Jewel Wasp 1 addresses the study hypotheses, and Jewel Wasp 2 focuses on the data analytic approach. The next two articles in this issue apply the same analytic approach to examine the differential allocation of parental investment in humans according to the sex of the offspring; in a sample of Arizona babies, and in a secondary analysis of a multinational dataset. The availability of high quality datasets will undoubtedly be increasingly useful for researchers and educators. The final articles are health related, examining sexual risk behavior in university students, and demonstrating an application of Bayesian techniques to the measurement of scoliosis. The authors are all members of the Evaluation Group for the Analysis of Data (EGAD), led by Lee Sechrest, in the Psychology Department at the University of Arizona, where A. J. Figueredo is also the Director of the Graduate Program in Ethology and Evolutionary Psychology. Contributions to this issue were primarily selected from presentations at the Psychology Session at the 50th Anniversary meeting of the Arizona Nevada Academy of Sciences, held in Tucson in 2006. The most relevant contributions from that session are included in this publication. All submissions received external peer reviews. Melinda Davis, Chair, Psychology Section, Owen Davis, Past-President and Michael Menke, editors iii iv ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE 51 ASSORTATIVE MATING IN THE JEWEL WASP: 1. FEMALE MATCHING OF EYE-COLOR GENOTYPE, NOT HOST-FEEDING PHENOTYPE AURELIO JOSÉ FIGUEREDO and REBECCA M. S. SAGE, Department of Psychology, University of Arizona, Tucson, AZ 85721 ABSTRACT An experiment was performed to test the influence of two factors on assortative mating in the Jewel wasp (Nasonia vitripennis): (1) inherited eye-color genotype, and (2) conditioned foraging phenotype. To determine the female choice of sires, genetically marked wasps were used of two recessive mutant eye-color genotypes: white or red. Each female (of independently crossed eye-color and juvenile host) was given a choice of two males, one of each eye-color, counterbalanced for juvenile host: blowfly (Sarcophaga bullata) or housefly (Musca domestica) pupae. Blowflyreared females produced more total offspring, indicating higher fertility. Red-eyed females produced more offspring sired by red-eyed males, indicating assortative mating by eye color. Blowfly-reared females, however, did not produce more offspring sired by blowfly-reared males, indicating no assortative mating by juvenile host. INTRODUCTION The Jewel wasp (Nasonia vitripennis) is a beneficial parasitoid insect which may feed on a variety of species of two-winged flies (Diptera), such as blowflies (Sarcophaga bullata) and houseflies (Musca domestica). Like certain other insects, the Jewel wasp is behaviorally predisposed in adulthood to feed its own offspring (by selective oviposition) on the particular host species that it fed on as a juvenile, or larva (Figueredo 1987, 1989). For such insects, it has been proposed that such behavioral feeding traditions may lead to mutual reproductive isolation between divergent feeding types, and thus to sympatric speciation, which is the splitting of one parent species into two or more daughter species without the benefit of geographical isolation (e.g., Bush 1969, Futuyma and Mayer 1980, Berlocher and Feder 2002). In fact, host-specific reproductive isolation has been specifically proposed as a potential mechanism for sympatric speciation in the Jewel wasp (Smith and Cornell 1979). In the absence of geographical barriers, reproductive isolation can only occur by some form of assortative mating. Assortative mating is the tendency for phenotypically similar individuals to mate. This tendency may be based on either one or several phenotypic variations and may include both physical characteristics and behavioral characteristics. Assortative mating can be distinguished from inbreeding in that inbreeding involves mating with individuals which are genetically similar at all or most variable loci whereas assortative mating minimally involves similarity only at those loci affecting variation in the traits for which the assortment occurs. In nature, most assortative mating is positive, favoring similarity over dissimilarity (Partridge 1983). Although positive assortment can theoretically lead to sympatric speciation (Bush 1969, Tauber and Tauber 1977a, 1977b), this potential consequence is believed to be epiphenomenal and not is hypothesized to represent its evolved adaptive function. Assortative mating may be passive or active. Passive assortative mating can occur as a result of any persistent habitat preferences among individuals with different host-plant feeding experience that might cause them to breed in the same habitats in which they developed (Papaj and Prokopy 1988, Feder et al. 1994), as in the case of the Apple Maggot fly (Rhagoletis pomonella). This habitat preference might be mediated by differential attraction to volatile host-specific semiochemicals, as in the case of the Apple Maggot Fly (Forbes et al. 2005), the Apple fruit moth (Argyresthia conjugella) (Bengtsson et al. 2006), and the pea aphid (Acyrthosiphon pisum) (Del Campo et al. 2003). Segregation of host-specific phenotypes can also occur in time as well as in space, as in the case of the European Corn Borer (Ostrinia nubilalis Hübner), in which moths feeding on different host plants emerge at different times (Bethenod et al. 2005, Malausaet et al. 2005), or in the case of Enchenopa treehoppers, in which eggs hatch at different times on different host plants and therefore have asynchronous life histories and temporal mating windows (Wood and Keese 1990). In the latter case, cohorts of treehoppers that were experimentally synchronized in the laboratory showed no behavioral tendencies towards assortative mating by host plant of origin. On the other hand, active assortative mating can occur when individuals seek out sexual partners that are genetically similar to themselves by phenotype matching (Rushton 1989, Rushton and Bons 2005). For example, behavioral male preferences have been shown to produce positive assortative mating based on genetically distinct female pheromone strains in the Cabbage Looper moth (Trichoplusia ni) (Zhu, Chastain, Spohn, FIGUEREDO, A. J., AND R. M. S. SAGE. 2007. ASSORTATIVE MATING IN THE JEWEL WASP: 1. FEMALE MATCHING OF EYE-COLOR GENOTYPE, NOT HOST-FEEDING PHENOTYPE. JOURNAL OF THE ARIZONA-NEVADA ACADEMY OF SCIENCE 39(2):51-57. ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE and Haynes 1997). In addition, active assortative mating may also be based on traits that are not necessarily genetic in origin. For example, behaviorally-mediated assortative mating based on adult size has been shown in water striders (Heteroptera: Gerridae) (Rowe and Arnqvist 1996) and in meloid beetles (Lytta magister) (Snead and Alcock 1985). Furthermore, active assortative mating may be based upon acquired characteristics that are host-specific and based upon feeding experience. For example, in the case of the cactophilic fruit fly (Drosophila mojavensis), assortative mating is based on the distinct cuticular hydrocarbon compositions acquired as adults by larvae raised on different hosts, producing behaviorally-mediated reproductive isolation (Etges 1992, Brazner and Etges 1993, Etges and Ahrens 2001). The development of host-specific cuticular hydrocarbons has also been documented in the case of the bethylid wasp (Cephalonomia tarsalis Ashmead) (Howard 1998). Thus, assortatively mating individuals are sometimes able to discriminate potential sexual partners based on host-specific chemosensory cues. In the case of parasitoid feeding traditions, we need to pay close attention to the proximate behavioral mechanisms presumably involved. Because of the observed plasticity in foraging behavior, the putative mechanism or behavioral predisposition for assortative mating are not likely to be under direct genetic control because there might be no simple correspondence between an individual’s genotype and its host-feeding phenotype. For the same reason, philopatric patterns of dispersal (Shields 1982), the tendency to remain in the natal area through adulthood, might be similarly ineffective mechanisms for assortative mating. The major candidate for a proximate behavioral mechanism therefore appears to be phenotype matching, as has been documented in the monarch butterfly (Norton-Griffiths 1968). There are several theoretical considerations to be taken into account when proposing assortative mating hypotheses for the Jewel wasp. There are ecological factors which might mitigate against assortative mating for host specificity. For example, the population densities of different species of hosts may vary significantly and behaviorally-inflexible daughters might then suffer, and the foraging opportunity costs of not finding a preferred host might exceed the benefits of increased offspring fecundity associated with ovipositing on the preferred host. For the Jewel wasp, it has been found that adult foraging experience may modify the behavioral effects of juvenile feeding experience to track the relative local abundance of alternative host species (Figueredo 1987, 1989). Thus, it was concluded that sympatric speciation based on host-specific assortative mating was an unlikely result of such a lifelong learning mechanism. On the other hand, the influence of juvenile feeding experience on adult mate choice, per se, was not determined. Because adult experience might modify foraging behavior without altering any sexual preferences im- 52 printed earlier, reproductive isolation by differential juvenile feeding experience — affecting mate choice directly, rather than indirectly through diet — was still technically possible. It remained possible that Jewel wasps might mate assortatively based on juvenile feeding experience. Alternatively, because blowfly-reared females were found to be significantly more fecund (Figueredo 1987, 1989), one might instead hypothesize a possible species-typical disposition for mate choice to favor males that were blowfly-reared to maintain that host predisposition. Finally, there is also the possibility of assortative mating for other phenotypic characteristics reflecting genetic differences that are unrelated to feeding experience. This paper reports the results of an experiment which was designed to test the effects of juvenile feeding experience on adult mate choice in the Jewel wasp. The principal hypothesis was that adult female Jewel wasps, when given a choice of males as sires for their offspring, would assortatively mate with males reared on the same juvenile host as themselves. This hypothesis was tested in the context of an alternative hypothesis that adult female Jewel wasps would assortatively mate, given the same choice conditions, on the basis of an unrelated and purely genetically determined phenotypic trait, such as eye color. The latter finding would instead support assortative mating based on genetic similarity (e.g., Rushton 1989, Rushton and Bons 2005). METHODS Subjects A total of 85 adult female and 170 adult male Jewel wasps (Nasonia vitripennis) were used in this mate choice experiment. To accurately determine female choice of male wasps as sires for their offspring, genetically marked male and female wasps were used. Two recessive mutant genotypes were used, one for white eyes and one for red eyes (technically called “oyster” eyes and “scarlet” eyes), which, when crossed, produce hybrids with brown eyes (called the “wild” phenotype). Female wasps of both eye-color genotypes were randomly assigned to oviposit on pupae of either the carrion blowfly (Sarcophaga bullata) or the common housefly (Musca domestica). These initial ovipositing exposures were carried out in 32x102 mm plastic culture vials stoppered with foam plugs. All host fly pupae used were three to five days old as pupae and were used directly after one day of preconditioning in the incubator at LD 12:12, 25C +/- 2C, and 80%RH +/- 10%RH. Both the male and female offspring of the originally ovipositing female Jewel wasps were used as experimental subjects for this study. Cultures of all three species, including both mutant eye-color genotypes of Jewel wasp, were originally obtained from Carolina Biological Supply Company. 53 ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE The experimental offspring were reared to maturity in the incubator at the photoperiods, temperatures, and humidities specified for host fly pupae. To obtain virgin females for this study, male and female subjects had to be separated from each other while they were still within the pupal stage. This was necessary because the males typically eclose a day or two earlier than their sisters, and are known to sometimes successfully inseminate female pupae. Separation of the wasp pupae was performed by carefully dissecting the pupal cases of the host flies that they had developed in and then extracting and sexing the individual wasp pupae under a microscope. This was a very delicate procedure which sometimes damaged the soft bodies of the immature wasp subjects. Moreover, housefly pupae are generally much smaller than blowfly pupae, and female Jewel wasps reared on housefly hosts are also generally smaller than those reared on blowfly hosts. The necessary handling therefore caused a certain amount of differential mortality between subjects reared on different juvenile host species. After eclosion, all adult wasps were separately housed in 15x85 mm borosilicate glass tubes stoppered with cotton plugs and fed on honey until the controlled mating and ovipositing exposures to eliminate any effects of prior feeding experience on pupae other than the larval rearing host. PROCEDURE All mating exposures were conducted for a standard period of 24 hours in separate 15x85 mm borosilicate glass tubes stoppered with cotton plugs under the controlled environmental conditions specified above. Adult male and female wasps were refrigerated at 6C for about 6 minutes each to facilitate handling without chemical anaesthesia and then transferred into these tubes by camel’s hair brush. After the mating exposures, separate ovipositing exposures were conducted for another standard period of 24 hours in separate 32x102 mm plastic culture vials stoppered with foam plugs under the same controlled environmental conditions. Each adult female wasp was separately transferred by camel’s hair brush into an individual culture vial, each of which contained one blowfly pupa for oviposition. All offspring of the experimental females were reared to maturity in these vials and then counted and classified as described below. Experimental design Within each test tube, every adult female was given a choice of two adult males for mating, one of each eyecolor genotype, which were counterbalanced for the particular host species, either blowfly or housefly, that they had been reared on as larvae. The basic idea was that one of these males would be blowfly-reared and that the other would be housefly-reared, but that their eventual offspring could only be distinguished from each other by the particular eye-color genotype that was randomly associated with each individual sire. Because the different mutant eye-color genotypes used might themselves influence female mate choice, however, the experiment was ultimately designed to test the relative influence of two separate factors on assortative mating in the Jewel wasp: (1) inherited eye-color genotype, and (2) conditioned foraging phenotype. Each adult male wasp in this study therefore had both an eye-color genotype and an independently assigned rearing-host phenotype. Females of independently crossed eye-color genotype and juvenile feeding experience were also used. Data encoding The critical information in this study was provided by the paternity of the female offspring produced by the experimental matings, but had to be statistically controlled for various related and causally prior reproductive outcomes. Because these outcomes represented the effects of various interdependent reproductive decisions made by the ovipositing females, they were not amenable to experimental control. Therefore, several dependent variables were recorded for hierarchical statistical analysis. Because female Jewel wasps reared on housefly hosts are significantly less fertile than those reared on blowfly hosts (Figueredo 1987), we could expect significantly different total numbers of offspring (TOT), regardless of paternity, from subjects reared on different juvenile hosts. Second, a variable number of Jewel wasp offspring remain immature in a dormant condition, called diapause, for up to six months past the normal fourteen days (and, thus, the end of our experiment). The total number of such dormant immature offspring (TIO) is known to vary with certain environmental factors, such as ambient temperatures and photoperiods, but might also be affected in some unknown way by the local mating conditions experienced by the mother. Because these dormant larvae had not yet developed eyes of either color, it was not possible to determine their paternity without costly genetic analysis, perhaps producing nonrandomly missing data. Third, male Jewel wasps are always produced asexually by the mother (by parthenogenesis, or “virgin birth”) and, therefore, have no biological father at all. Thus, a female Jewel wasp that does not mate with either of the males provided might produce a clutch of all male offspring. The total number of male offspring (TMO) could not be simply ignored in this study because it might have indicated female rejection of both males, and perhaps constituted more nonrandomly missing data. These first three dependent variables, although of lesser theoretical interest, were modeled hierarchically as causally prior to the last two to be able to statistically control any effect that they might have on the remaining two dependent variables. The two dependent variables of principal interest were the total number of female offspring sired by red- ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE eyed, rather than white-eyed, males (TRFO), and the total number of female offspring sired by blowfly-reared, rather than housefly-reared, males (TBFO). Of course, the specified eye colors and juvenile hosts referred to are those of the fathers, rather than those of the daughters, because all genetic hybrids had brown eyes, and all posttest offspring were reared on the larger blowfly hosts for convenience (given the greater number of offspring typically produced therein). Because paternal genotypes and juvenile hosts were also slightly correlated, by the postoperative mortality described above, eye color was modeled hierarchically as causally prior to juvenile host in these two dependent variables (TRFO and TBFO). For the same reasons, eye color was modeled hierarchically as causally prior to juvenile host in the two corresponding independent variables (FG and FJ). Consistently in direction with TRFO and TBFO, female eyecolor genotype (FG) was coded 1 for red-eyed females and 0 for white-eyed females; female juvenile rearing host (FJ) was coded 1 for blowfly-reared females and 0 for housefly-reared females. Statistical Analyses Although the experiment seemed superficially quite simple, there were several nontrivial complications. Due to the differential mortality by rearing host alluded to above, we wound up with somewhat more blowflyreared than housefly-reared female subjects. This also produced a slight, though nonsignificant, negative correlation between the independent variables, female genotype (FG) and female juvenile host (FJ), due to the random subject mortality across the two eye colors. Such correlated independent variables are easily modeled by hierarchical regression. To be conservative in our testing of the effects of female host, however, we assigned causal priority to female genotype. Moreover, we did not hypothesize an interaction between these two factors. The multiple dependent variables, however, presented problems that could not be handled by unaided Multiple Regression/Correlation (MRC) techniques (Cohen and Cohen 1983). Sequential canonical analysis (SEQCA) was selected as the optimal analytical model for the present data because it partitions the covariance among multiple dependent variables sequentially, as a hierarchical regression does, while maintaining their separate identity (Gorsuch 1991, Gorsuch and Figueredo 1991). This method isolates the direct effects of the independent variables, or interventions, sequentially on each of the dependent variables or outcomes, controlling for all indirect effects through the prior dependent variables or outcomes. The only theoretical guidance required is a tentative specification of the causal order between the dependent variables (Figueredo and Gorsuch 2007). Because the two model predictor variables were binary in form, this SEQCA can also be conceptualized as mathematically equivalent to a “Step-Down” (i.e., 54 hierarchical) Multivariate Analysis of Variance (MANOVA). This statistical method has been used previously in the study of oviposition in parasitoid wasps (Henneman et al. 1995). A full theoretical consideration of the merits and limitations of this statistical method in comparison with related methods is provided in Figueredo and Gorsuch (2007). RESULTS Descriptive Statistics A total of 1072 offspring were produced by the experimental wasps. Of these, 15 were diapausing larvae at the end of the experiment and 313 were adult males. Both of these offspring categories were of indeterminate paternity and the diapausing larvae were also of undetermined sex. Of the remaining 744 adult female offspring, 256 were sired by red-eyed males and 488 were sired by white-eyed males. Inferential Statistics Sequential canonical analysis was performed using UNIMULT (Gorsuch 1991). All that was required for running this multivariate model was the specification of two hierarchies of causal priority, one for the two independent variables and another for the five dependent variables. The theoretical justifications for these hierarchies of causal priority were detailed above. The PillaiBartlett “V” Statistic (PBV) for the whole model was .21, F(10,158)= 1.86 (p=.05), which provided an overall protected test of statistical significance. Table 1 displays the overall tests of the proportions of the variance of each of the five dependent variables accounted for by the linear combinations of the two independent variables. The SEQCA or “Step-Down” MANOVA also provided hierarchical significance tests for the separate effects of each of the two independent variables on each of the five dependent variables, as shown in Table 2. Tabl e 1. Mult iple Correlat ions and Associat ed Test s of Signif icance f or Each Dependent Variable in t he Mult iv ariat e Model. Variable Effect Size PBV F(2,158) p TOT R = . 25 0. 0 6 2. 6 8 0. 0 7 TIO R = .14 0. 0 3 1.31 0. 3 TMO R = . 08 0. 0 2 0. 6 5 n.s. TRFO R = .32 0. 1 5 7. 0 6 < 0.005 TBFO R = .12 0. 0 2 0. 7 3 n.s. ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE 55 Tabl e 2. Semipart ial Correlat ions and Associat ed Test s of Signif icance f or Each Independent Variable in t he Mult iv ariat e Model. Variable Effect Size PBV F(1,158) p Tabl e 3. St andardized Regression C oef f icient s f or E a c h In d e p e n d e n t Va r ia b le in t h e Mu lt iv a r ia t e Model. TOT = - .105*FG + .217*FJ TIO = - .144*FG + .004*FJ TMO = - .080*FG + .016*FJ TRFO = .300*FG - .092*FJ TBFO = .121*FG + .012*FJ Dependent variable: TOT FG r =- .13 0.02 1.43 0.2 FJ r = .22 0.05 3.93 0.05 Dependent variable: TIO FG r =- .14 0.03 2.62 0.1 FJ r = .00 0 0 n.s. Dependent variable: TMO FG r =- .08 0.02 1.25 0.3 FJ r = .02 0 0.05 n.s. Dependent variable: TRFO FG r = .31 0.14 13 <.001 FJ r =- .09 0.01 1.12 0.3 Dependent variable: TBFO FG r = .12 0.02 1.44 0.2 FJ r = .01 0 0.02 n.s. The standardized regression coefficients (“betaweights”) obtained by SEQCA are shown in Table 3. Thus, controlling for all the prior dependent variables, there were only two statistically significant effects of the independent variables on the dependent variables. These significant effects were: (1) the predicted effect of female juvenile rearing host (FJ) on total number of offspring (TOT), and (2) the effect of female genotype (FG) on total number of female offspring sired by redeyed males (TRFO). These findings indicate that: (1) blowfly-reared experimental females produced more offspring in general than did housefly-reared females (beta=.217), and (2) red-eyed experimental females produced more female offspring sired by red-eyed males than did whiteeyed females (beta=.300). The former is a previously documented effect of rearing host (Figueredo 1987, 1989) and the latter constitutes evidence for positive assortative mating for eye color. The mean number of offspring in all categories combined produced by blowfly-reared females was 14.52 and that produced by housefly-reared females was only 6.81, both regardless of eye-color genotype. The mean number of female offspring sired by red-eyed males produced by red-eyed females was 4.46 and that produced by white-eyed females was only 1.14, both regardless of juvenile rearing host. When these means are statistically adjusted for the effects of all prior dependent variables, they are 4.90 and 1.36, respectively, which represent an even larger difference. The most important negative result of this analysis is that female juvenile rearing host (FJ) had no significant effect on the total number of female offspring sired by blowfly-reared males (TBFO). This latter result represents empirical evidence against the hypothesis that there is positive assortative mating for juvenile rearing host in the Jewel wasp. When these means are statistically adjusted for the effects of all prior dependent variables, they are 4.09 and 4.15, respectively, which would hardly indicate a difference of any consequence even had it reached statistical significance. DISCUSSION Our study revealed no evidence of assortative mating by juvenile feeding experience in the Jewel wasp. It is therefore unlikely that differential juvenile feeding experience can lead to sympatric speciation in this particular species by either of the mechanisms that have been proposed. The requisite reproductive isolation can apparently not be produced by differential juvenile feeding experience either indirectly by permanently differentiated foraging behavior or directly by differentially imprinted sexual preferences. Instead, assortative mating was shown to be greatly influenced by genetic markers, such as eye color. Like many other species, the Jewel wasp does assortatively mate. Although the mutant eye-color genotypes used in this experiment were artificially selected laboratory strains, assortment by eye color was probably indicative of a preference for the greater set of genetic similarities that presumably existed between the members of the same recessive mutant strains. The selective breeding of these two recessive mutant strains was likely to have resulted in homozygosity on a variety of other ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE traits as well as on eye color. It is therefore possible that eye color, per se, was not even directly perceived or used as markers by the wasps as proximate cue for mate discrimination, but that the relevant genetic information regarding relatedness was carried instead by other indicators of phenotypic similarity, such as olfactory cues. Assortative mating is thought to function in the wild to maintain specific homozygous genotypic adaptations and reduce the costs of mating (Bateson 1983). Assortative mating tracks local selective forces and thus allows local populations to become genetically better adapted to local circumstances in which surviving genotypes have been successful (see also Kawecki 1994 for other genetic benefits). Why, then, do Jewel wasps not assortatively mate by host-feeding experience? Should not similar benefits accrue? The advantage of specialization to a single host species is that the parasitoid can maximize its adaptations to that particular host’s physiology and lifecycle and thus reduce its competition with generalists. The disadvantage is that complete dependence on a single fluctuating host population may indirectly result in the occasional extinction of local parasitoid populations. The most likely reason for the absence of either natural or sexual selection for more restricted host specificity in the Jewel wasp might therefore reside in the nature of the host fly life histories. Because the host flies feed on ephemeral resources, such as animal carcasses, fly populations are locally unstable. As colonizers, the first pioneering fly species to find a favorable microenvironment temporarily becomes the locally predominant species. When these ephemeral resources are exhausted, however, the local population of that host species then precipitously crashes. Proverbially, they breed like flies and they die like flies (Figueredo 1987, 1989). Any parasitoid specializing on such a host species will experience large shifts in host abundance. If there were any genetic variance in the restrictedness of host selection by the parasitoid, this fluctuating food supply could result in the elimination of any more restricted feeding genotypes and the survival of any less restricted feeding genotypes which were able to utilize any of a variety of fly species that colonized the local area. As demonstrated in adult foraging behavior (Figueredo 1987, 1989), Jewel wasps display a lifelong conditional feeding strategy based on the relative abundances of alternative host species. The host species on which an individual wasp was reared influences but does not permanently limit its foraging options as an adult. A more restricted host preference, whether environmental or genetic in origin, would force the wasp to search until a host of a specific type is found, even in cases where acceptable substitutes were available in the immediate vicinity. Assortative mating for host-feeding phenotype would therefore impose an additional foraging cost on the offspring that is evidently suboptimal in the adult. In the absence of lifelong host fidelity in the adult (which 56 could lead to some microgeographic segregation and, thus, to passive assortative mating), the most plausible mechanism remaining for sympatric speciation was thus active assortative mating for prior host-feeding experience. This hypothesis was disconfirmed. Although Jewel wasp females were found to be mating assortatively based on manipulated markers of genetic relatedness (presumably indicated by phenotypic similarity), they were not found to be mating assortatively based on hostfeeding phenotype. We can only conclude that both of the plausible mechanisms proposed for reproductive isolation leading to sympatric speciation, passive assortative mating by permanently differentiated foraging behavior and active assortative mating by differentially imprinted sexual preferences, are absent in the Jewel wasp. Behaviorally flexible parasitoid species like the Jewel wasp are thus likely to remain polyphagous. 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Deep geographic variation in epicuticular hydrocarbons among isolated populations. American Naturalist 158:585–598. 57 ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE FEDER, J. L., S. B. OPP, B. WLAZLO, K. REYNOLDS, W. GO, AND S. SPISAK. 1994. Host fidelity is an effective premating barrier between sympatric races of the apple maggot fly. Proceedings of the National Academy of Sciences 91:79907994. FIGUEREDO, A. J. 1987. The statistical measurement, developmental mechanisms, and adaptive ecological functions of conditioned host selection in the parasitoid Jewel wasp. Dissertation, University of California, Riverside, CA. FIGUEREDO, A. J. 1989. Host-cue information processing by foraging Jewel wasps: Response-bias tracking of expected host-species encounter rates, not modified profitabilities. Psychobiology 17:435-444. FIGUEREDO, A. J. AND R. GORSUCH. 2007. Assortative mating in the jewel wasp: 2. Sequential canonical analysis as an exploratory form of path analysis. Journal of the Arizona Nevada Academy of Sciences, 39:59-64. FORBES, A. A., J. FISHER, AND J. L. FEDER. 2005. Habitat avoidance: Overlooking an important aspect of hostspecific mating and sympatric speciation? Evolution 59(7):1552–1559. FUTUYMA, D. J., AND G. C. MAYER. 1980. Non-allopatric speciation in animals. Systematic Zoology 29(3):254-271. GORSUCH, R. L., and A. J. FIGUEREDO. 1991. Sequential canonical analysis as an exploratory form of path analysis. Paper. American Evaluation Association Conference, Chicago, Illinois. GORSUCH, R. L. 1991. UniMult: For univariate and multivariate data analysis. UniMult, Altadena, CA. HENNEMAN, M. L., D. R. PAPAJ, A. J. FIGUEREDO, AND L. E. M. VETT. 1995. Egg-laying experience and acceptance of parasitized hosts by the parasitoid, Leptopilina heterotoma (Hymenoptera: Eucoilidae). Journal of Insect Behavior 8:331-342. HOWARD, R. W. 1998. Ontogenetic, reproductive, and nutritional effects on the cuticular hydrocarbons of the hostspecific ectoparasitoid Cephalonomia tarsalis (Hymenoptera: Bethylidae). Annals of the Entomological Society of America 91(1):101-112. KAWECKI, T. J. 1994. Accumulation of deleterious mutations and the evolutionary cost of being a generalist. The American Naturalist 144(5):833-838. MALAUSA, T., M. T. BETHENOD, A. BONTEMPS, D. BOURGUET, J. M. CORNUET, AND S. PONSARD. 2005. Assortative mating in sympatric host races of the European corn borer. Science 308(5719):258-260. NORTON-GRIFFITHS, M. 1968. The feeding behavior of the Oystercatcher, Haematatopus ostralegus. D. Phil. Thesis. University of Oxford. PAPAJ, D. R., AND R. J. PROKOPY. 1988. The effect of prior adult experience on components of habitat preference in the apple maggot fly (Rhagoletis pomonella). Oecologia 76(4):538-543 PARTRIDGE, L. 1983. Non-random mating and offspring fitness. Pp. 227-256 in P. Bateson ed., Mate choice. Cambridge University Press, London, UK. ROWE, L., AND G. ARNQVIST. 1996. Analysis of the causal components of assortative mating in water striders. Behavioral Ecology and Sociobiology 38:279–286. RUSHTON, J. P. 1989. Genetic similarity, human altruism, and group selection. Behavioral and Brain Sciences 12:503559. RUSHTON, J. P., AND T. A. BONS. 2005. Mate Choice and Friendship in Twins: Evidence for Genetic Similarity. Psychological Science 16:555-559. SHIELDS, W. M. 1982. Philopatry, inbreeding, and the evolution of sex. State University of New York Press, Albany, NY. SMITH, M. A., AND H. V. CORNELL. 1979. Hopkins host-selection in Nasonia vitripennis and its implications for sympatric speciation. Animal Behavior 27:365-370. SNEAD, J. S., AND J. ALCOCK. 1985. Aggregation formation and assortative mating in two meloid beetles. Evolution 39(5):1123-1131. TAUBER, C. A., AND M. J. TAUBER. 1977a. Sympatric speciation based on allelic changes at three loci: Evidence from natural populations in two habitats. Science 197:12981299. TAUBER, C. A., AND M. J. TAUBER. 1977b. A genetic model for sympatric speciation through habitat diversification and seasonal isolation. Nature 268:702-705. WOOD, T. K., AND M. C. KEESE. 1990. Host-plant-induced assortative mating in Enchenopa treehoppers. Evolution 44(3):619-628. ZHU, J., B. B. CHASTAIN, B. G. SPOHN, AND K. F. HAYNES. 1997. Assortative mating in two pheromone strains of the cabbage looper moth, Trichoplusia ni. Journal of Insect Behavior 10(6):805-817. ASSORTATIVE MATING IN THE JEWEL WASP 1 ! FIGUEREDO AND SAGE 58 ASSORTATIVE MATING IN THE JEWEL WASP 2 ! FIGUEREDO AND GORSUCH 59 ASSORTATIVE MATING IN THE JEWEL WASP: 2. SEQUENTIAL CANONICAL ANALYSIS AS AN EXPLORATORY FORM OF PATH ANALYSIS AURELIO JOSÉ FIGUEREDO, Department of Psychology, University of Arizona, Tucson, AZ 85721; and RICHARD L. GORSUCH, Graduate School of Psychology, Fuller Theological Seminary, Pasadena, CA 91182 ABSTRACT This paper discusses the conceptual and mathematical relationships between three statistical models: 1) traditional, or “Simultaneous”, Canonical Analysis, 2) hierarchical, or “Sequential”, Canonical Analysis, and 3) Structural Equations Modeling, or confirmatory path analysis. The advantages of Sequential over Simultaneous Canonical Analysis are reviewed. The relationships between Sequential Canonical Analysis and Path Analysis are explored. The need for a legitimate exploratory form of path analysis, analogous to existing exploratory forms of both multiple regression and factor analysis, is discussed. A logical extension of Sequential Canonical Analysis is proposed as adequately serving the function of an exploratory path analysis. Empirical data from psychological research is used to illustrate and qualitatively compare and contrast the results of these three approaches. INTRODUCTION It is often the case that the multiple outcomes of an experimental treatment or manipulation need to be assessed. Moreover, these dependent variables are often selected to measure the impact of the treatment on several conceptually distinct outcomes, rather than converge upon a single construct. Thus, multivariate data reduction methods, such as common factor modeling, may not be appropriate. On the other hand, because the intervention may exert a common causal influence on these outcomes, the dependent variables are likely to be at least spuriously correlated with each other. In addition, the multiple outcomes may also subsequently exert various causal influences on each other. Thus, separate causal analyses for each of these dependent variables may also not be appropriate. Fortunately, there exist several statistical procedures for the analysis of multiple correlated dependent variables. One of these is structural equations modeling (SEM), or confirmatory path analysis, in which the hypothesized causal network between outcomes can be fully specified, estimated, and tested (Bentler 1989). This method, however, requires the guidance of a strong causal theory which is often not available. Another multivariate method is simultaneous canonical analysis (SIMCA), which requires little theory. This method, however, produces empirically-derived linear composites of dependent variables, or “canonical variates”, which are often difficult to interpret pragmatically in terms of the concrete outcomes that we are interested in. The linear composites are statistically defined, but are dependent upon the exact data set and so may not be replicated if the next study uses a slightly different set of variables. A third alternative is sequential canonical analysis (SEQCA), which combines some of the advantages of both (Gorsuch 1991, Gorsuch and Figueredo 1991). Rather than combining all dependent variables into uninterpretable linear composites, as a simultaneous regression does for independent variables, it partitions their covariance sequentially, as a hierarchical regression does, while maintaining their separate identity. This method isolates the direct effects of the independent variables, or interventions, sequentially on each of the dependent variables, or outcomes, controlling for all indirect effects through the prior dependent variables, or outcomes. Because the only theoretical guidance required is a tentative specification of a meaningful order among the dependent variables, we propose that this sequential method can be developed into an exploratory form of path analysis. The purpose of this paper is to explore the properties of sequential canonical analysis both in relation to those of confirmatory path analysis and simultaneous canonical analysis, and as a potential model for exploratory path analysis. To do this, we will use an example from insect psychobiology which has the advantage of clearly illustrating these principles with very concrete, “brass tacks”, numbers. ASSORTATIVE MATING IN THE JEWEL WASP The natural history of the Jewel wasp and the psychobiological rationale for this study is described in Figueredo and Sage (2007). Basically, this experiment was designed to test the effects of juvenile feeding experience on adult mate choice in the Jewel wasp. To FIGUEREDO, A. J., AND R. GORSUCH. 2007. ASSORTATIVE MATING IN THE JEWEL WASP: 2. SEQUENTIAL CANONICAL ANALYSIS AS AN EXPLORATORY FORM OF PATH ANALYSIS. JOURNAL OF THE ARIZONA-NEVADA ACADEMY OF SCIENCE 39(2):59-64. ASSORTATIVE MATING IN THE JEWEL WASP 2 ! FIGUEREDO AND GORSUCH accurately determine the female choice of male wasps as sires for their offspring, genetically marked wasps were used. Two recessive mutant genotypes were used, one for white eyes and one for red eyes, which, when crossed, produce hybrids with brown eyes. Each female was given a choice of two males, one of each eye-color genotype (which were counterbalanced for the particular prey species, either housefly or blowfly, that they had been fed on as larvae). Females of independently crossed eye-color genotype and juvenile feeding experience were also used. Because these different genotypes might themselves influence mate choice, the experiment was designed to test the relative influence of two factors, 1) inherited eye-color genotype, and 2) conditioned foraging phenotype, on assortative mating in the Jewel wasp. We wound up with a slight, though nonsignificant, negative correlation between the independent variables, female genotype (FG) and female juvenile host (FJ), due to postoperative differential subject mortality. Such correlated independent variables are easily modeled by hierarchical partitioning of variance. To be conservative in our testing of the effects of female host, we assigned causal priority to female genotype. Moreover, we did not hypothesize an interaction between these two factors. The dependent variables, however, presented problems that could not be handled by unaided multiple regression. First, female Jewel wasps that feed on housefly hosts are significantly less fertile than those that feed on blowfly hosts (Figueredo 1987, 1989). This means that we could expect significantly different total numbers of offspring (TOT), regardless of paternity, from subjects reared on different juvenile hosts. Second, a variable number of Jewel wasp offspring remain immature in a dormant condition, called diapause, for up to six months past the normal fourteen days (and, thus, the end of our experiment). The total number of such dormant immature offspring (TIO) is known to vary with certain environmental factors, such as ambient temperatures and photoperiods, but might also be affected in some unknown way by the local mating conditions experienced by the mother. Because these dormant larvae had not yet developed eyes of either color, it was not possible to determine their paternity, perhaps producing nonrandom missing data. Third, male Jewel wasps are always produced asexually by the mother and, therefore, have no biological father at all. Thus, a female Jewel wasp that does not mate with either of the males provided might produce a clutch of all male offspring. The total number of male offspring (TMO) could not be simply ignored in this study because it might have indicated female rejection of both males, and perhaps constituted more nonrandom missing data. Finally, the critical information in this study was provided by the paternity of the female offspring, but had to be controlled for all of the above causally prior offspring outcomes. Thus, the two dependent variables of principal interest were the total number of female 60 offspring sired by red-eyed, rather than white-eyed, males (TRFO), and the total number of female offspring sired by blowfly-reared, rather than housefly-reared, males (TBFO). In the interests of brevity, these female offspring were, respectively, referred to as “red-sired female offspring”, “white-sired female offspring”, “blowflysired female offspring”, and “housefly-sired female offspring”. Of course, the specified eye colors and juvenile hosts referred to are those of the fathers, rather than those of the daughters, because all genetic hybrids had brown eyes, and all posttest offspring were reared on the larger blowfly hosts for convenience. Because paternal genotypes and juvenile hosts were also slightly correlated, by the postoperative mortality noted above, eye color was modeled as causally prior to juvenile host in these two dependent variables, for the same reasons that they were in the two corresponding independent variables. ALTERNATIVE METHODS OF ANALYSIS The question then becomes, precisely how do we accomplish the requisite feats of multivariate statistical control? To expedite our discussion, we report the results of the most uninformative statistical model first, namely, simultaneous canonical analysis (SIMCA). This analysis was performed using PROC CANCORR in SAS (SAS Institute 1989). SIMCA constructed two pairs of canonical variates, V1 and W1, and V2 and W2, to represent our manifest variables. Pillai’s Trace for the whole model was .21, F(10,158)= 1.856, p= .055. Furthermore, V1 was correlated to W1 by a canonical correlation of .42, which was statistically significant (F(10,156)= 1.89, p= .05); V2, however, was correlated to W2 by a canonical correlation of .17, which was statistically nonsignificant (F(4,79)= 0.61, p= .66). Presumably, we could therefore proceed to interpret V1 and W1, and forget about V2 and W2. Fortunately, V1 and W1 were defined by the following linear equations, using the standardized canonical coefficients, as seen in Table 1 above. Using SIMCA, we were also helpfully provided with the resulting indirect correlations between W1 and the independent manifest variables (FG and FJ) and between V1 and the dependent manifest variables (TOT through TBFO), as well as all the corresponding estimates for the nonsignificant pair of canonical variates, V2 and W2, in both their raw and standardized forms. Unfortunately, in spite of this apparent wealth of information, we still had some trouble understanding what any of this meant for the results of our experiment. How did some linear combination of female genotype and female juvenile host somehow produce some other linear combination of the total numbers of various types of offspring? A more informative approach was structural equations modeling (SEM), or confirmatory path analysis. This analysis was done using EQS (Bentler 1989). Be- ASSORTATIVE MATING IN THE JEWEL WASP 2 ! FIGUEREDO AND GORSUCH 61 Tabl e 1. Linear equat ions f or dependent canonical v ariat es V1 and W1. V1 = W1 = - 1.015*TOT - 0.082*TIO + .046*TMO + .919*TRFO 0.864*FG - 0. 41 3 * F J - . 1 05 * F G +.218*FJ - .117*FG +.004*FJ - .054*FG +.012*FJ + .263*FG - .090*FJ + .123*FG +.004*FJ + 0.274*TBFO Tabl e 2. St andardized pat h coef f icient s f or sat urat ed st ruct ural model. TOT = TIO = .579*TOT TMO = .760*TOT - .022*TIO TRFO = .856*TOT - .255*TIO - .241*TMO TBFO = .753*TOT - .103*TIO - .307*TMO - .083TRFO Tabl e 3. St andardized pat h coef f icient s f or rest rict ed model wit h non-signif icant pat hways omit t ed. TOT = +.230*FJ TIO = .595*TOT TMO = .756*TOT TRFO = .646*TOT TBFO = .630*TOT - .247*TIO +.281*FG - .296*TMO cause we had no strong causal theory to specify the structural relations between the multiple dependent variables, a fully saturated structural model was run, freely estimating every causal pathway possible between every dependent variable, specifying only the presumed causal priority. This method has also been referred to as the cascade model in cognitive psychology (e.g., Mouyi 2006, Demetriou et al. 2002). This specification produced a saturated structural model perfectly reproducing the data, with a residual chi-squared of zero, based on zero degrees of freedom. The standardized path coefficients are summarized in Table 2 above. Using the statistical tests reported in the EQS output, we tested each of these path coefficients against zero. We then eliminated nonsignificant causal pathways to develop a more restricted model in which all the remaining pathways were statistically significant. Not surprisingly, this model was statistically acceptable: the chi-squared was 11.06 based on 14 degrees of freedom (p = .68). The standardized path coefficients for this model are described in Table 3. Such brazenly exploratory use of SEM, however, is technically inappropriate. The probability of the model chi-squared reported, for example, no longer represented a prior probability under the null hypothesis, due to the many empirical model respecifications. Another disadvantage was that SEM did not provide for performing hierarchical tests of significance, except through such nested model comparisons, which required running multiple causal models. Of course, such results could be obtained by running a series of separate hierarchical regressions, as specified by the structural equations written above. This piecemeal method had the disadvantage of requiring a separate regression model for each of the dependent variables and, thus, still providing no valid overall protective test of significance. This alternative procedure was performed first using PROC GLM in SAS (SAS Institute 1989), and then using UNIMULT (Gorsuch 1991, Gorsuch and Figueredo 1991), and, in spite of the algorithmic differences in parameter estimation, both produced nearly identical results to each other. Furthermore, this alternative procedure has the practical advan- ASSORTATIVE MATING IN THE JEWEL WASP 2 ! FIGUEREDO AND GORSUCH tage of not requiring any specialized software to perform. Any standard software package (such as SAS or SPSS) that can estimate hierarchical multiple regressions (using Type I sums of squares) can be used. In spite of all these limitations, at least SEM provided us with some clue as to what is going on. Controlling for all significant prior dependent variables, it appeared that there were only two significant causal effects of our two independent variables. As indicated by the positive effect of FJ on TOT, blowfly-reared females produced more total offspring than housefly-reared females, indicating their generally higher fertility, as was expected. As indicated by the positive effect of FG on TRFO, red-eyed females produced more red-sired female offspring than white-eyed females, indicating assortative mating by eye color. Contrary to the principal experimental hypothesis, however, blowfly-reared females apparently produced no more blowfly-sired female offspring than housefly-reared females, indicating no assortative mating by juvenile host. This was indicated by the lack of a significant causal effect of FJ on TBFO. The third multivariate method used on this data was sequential canonical analysis (SEQCA). This analysis was performed using UNIMULT (Gorsuch 1991). All that was required for running this model was the specification of two hierarchies of causal priority, one for the two independent variables and another for the five dependent variables. The Pillai-Bartlett V for the whole model was .21, F(10,158)= 1.86, p= .05, which was the same, within rounding error, as the corresponding SIMCA results. In addition, we also obtained overall tests of the proportions of the variance of each of the five dependent variables accounted for by the linear combinations of the two independent variables, which are shown in Table 4. SEQCA also provided the following hierarchical significance tests for the separate effects of each of the two independent variables on each of the five dependent variables and these are shown in Table 5. Tabl e 4. Mult iple Correlat ions and Associat ed Test s of Signif icance f or Each Dependent Variable in t he Mult iv ariat e Model. Variable Effect Size PBV F(2,158) p TOT R = . 25 0. 0 6 2.68 0.07 TIO R = .14 0.03 1.31 0. 3 TMO R = . 08 0.02 0.65 n.s. TRFO R = .32 0. 1 5 7.06 < 0.005 TBFO R = .12 0. 0 2 0.73 n.s. 62 Tabl e 5. Semipart ial Correlat ions and Associat ed Test s of Signif icance f or Each Independent Variable in t he Mult iv ariat e Model. Variable Effect Size PBV F(1,158) p Dependent variable: TOT FG r =- .13 0.02 1 . 43 0.2 FJ r = .22 0.05 3.93 0.05 Dependent variable: TIO FG r =- .14 0.03 2.62 0. 1 FJ r = .00 0 0 n.s. Dependent variable: TMO FG r =- .08 0.02 1.25 0.3 FJ r = .02 0 0. 05 n.s. Dependent variable: TRFO FG r = .31 0. 1 4 13 <.001 FJ r =- .09 0.01 1.12 0.3 Dependent variable: TBFO FG r = .12 0.02 1.44 0. 2 FJ r = .01 0 0.02 n.s. Note that the two statistically significant effects of the independent variables on the dependent variables were the same as those identified by SEM. Controlling for all the prior dependent variables, the standardized regression coefficients obtained by SEQCA were also very similar to those produced by SEM, but tended to become somewhat higher as one stepped sequentially down the causal hierarchy of dependent variables. These slightly higher parameter estimates were a systematic property of the current UNIMULT implementation of SEQCA, not an artifact of slightly different estimation algorithms. Recall that when the separate multiple regressions for the structural equations model were performed by UNIMULT, nearly identical parameter estimates were obtained. The SEQCA estimates were systematically higher because UNIMULT currently uses what Cohen and Cohen (1983) referred to as the “partial” rather than the “semipartial” residual correlations used by SEM. In the current version of UNIMULT, SEQCA residualized the denominator, or total variance to be explained (including the error), as well as the numerator, or portion of variance actually explained, of each of the sequential dependent variables on all the prior ones. This affected significance testing, as well as parameter estimation, by increasing the power of the tests. For com- ASSORTATIVE MATING IN THE JEWEL WASP 2 ! FIGUEREDO AND GORSUCH 63 Tabl e 6. St andardized Regression Coef f icient s f or E a c h In d e p e n d e n t Va r ia b le in t h e Mu lt iv a r ia t e Model. TOT = - . 1 05 * F G + .217*FJ TIO = - . 1 44* F G + .004*FJ TMO = - . 08 0* F G + .016*FJ TRFO = . 3 00* F G - .092*FJ TBFO = . 1 21 * F G + .012*FJ parison with those obtained by SEM, the SEQCA standardized estimates are reported in Table 6. The UNIMULT implementation of SEQCA does not explicitly provide estimates of the sequential effects of the dependent variables upon each other. Doing so would provide an alternative implementation of SEQCA that would be fully equivalent to an exploratory path analysis by explicitly including estimates of sequential effects between dependent variables. Such a model would restore the status of hierarchically residualized correlations as the “semipartials” (Cohen and Cohen 1983) typically estimated in SEM. This new model would have the added advantages of both hierarchical partitioning of variance and protective overall tests of significance, such as the Pillai-Bartlett V statistic, so important to exploratory data analysis. It would also help legitimize an alternative path analytic model for empirically-assisted theory development, instead of perpetuating the widespread abuse of available structural models that are clearly intended exclusively for theory confirmation. As it stands, as illustrated by our Jewel wasp example, SEQCA represents a useful diagnostic tool for isolating and identifying the direct effects of independent variables on a multiplicity of correlated dependent variables, if not for estimating the magnitudes of these effects in the conventional way. In either case, parameter estimation should never be based on the initially saturated model used for data exploration because the probable inclusion of nonsignificant variables substantially reduces the efficiency of estimation. Superior estimates can be obtained by running the various final structural equations, as respecified by protected and hierarchical significance testing, as separate multiple regressions after the initial exploration of the data, as was briefly described above. One potential disadvantage of SEQCA in relation to the alternative methods is that it requires the specialized UNIMULT software (Gorsuch 1991) to perform. Armed with the basic theory behind SEQCA, however, one may use the more commonly available SAS software (SAS Institute 1989), or even SPSS, to perform a series of hierarchical regressions in which multiple dependent criterion variables are analyzed sequentially according to a hypothesized causal order. These dependent criterion variables can be entered sequentially into a system of multiple regression equations with each hierarchically prior criterion variable entered as the first predictor for the next, as we did in the SEM cascade model presented above. Each successive dependent variable can be predicted from an initial set of ordered predictor variables, each time entering the immediately preceding dependent variable hierarchically as the first predictor, then entering all the ordered predictors from the previous regression equation. Thus, each successive regression enters all of the preceding dependent variables in reverse causal order to statistically control for any indirect effects that might be transmitted through them. Within this analytical scheme, as with SEQCA, the estimated effect of each predictor is limited to its direct effect on each of the successive dependent variables. The general format for this system of hierarchical multiple regressions is as shown in Table 7 below. Tabl e 7. G eneral f orm at f or m ult iple dependent crit erion v ariables analyzed sequent ially according t o a hypot hesized causal order. β 1X1 +β 2X2 +β 3X3 β 4Y4 +β 1X1 +β 2X2 +β 3X3 +β 4Y4 +β 1X1 +β 2X2 +β 3X3 Y4= Y5= Y6= β 5Y5 Where X1, X2 and X3 are the ordered predictor variables and Y4, Y5, and Y6 are the ordered criterion variables, numbered consecutively after the predictors to avoid confusion among the subscripts. What is lost by using this method, as opposed to SEQCA, is the protective overall test of significance. What is gained by this method, as opposed to SEQCA, is obtaining estimates of the sequential effects among dependent variables. Thus, this is superior to merely including all the prior dependent variables as “covariates”. What is gained as opposed SEM is the ability to perform hierarchical partitioning of variance and hypothesis testing, as in SEQCA. In addition, one avoids compromising the purely confirmatory nature of the SEM tests of whole-model goodness-of-fit. SUBSTANTIVE AND METHODOLOGICAL CONCLUSIONS To finish our story, our study revealed no evidence of assortative mating by juvenile feeding experience in the Jewel wasp. It is therefore unlikely that differential juvenile feeding experience can lead to sympatric speciation in this particular species by either of the mecha- ASSORTATIVE MATING IN THE JEWEL WASP 2 ! FIGUEREDO AND GORSUCH nisms that have been proposed. The requisite reproductive isolation can apparently not be produced by differential juvenile feeding experience either indirectly by permanently differentiated foraging behavior or directly by differentially imprinted sexual preferences. Instead, assortative mating was shown to be greatly influenced by genetic markers, such as eye color. Converging evidence for these conclusions was variously obtained by hierarchical multiple regression, conventional path analysis, and sequential canonical analysis. Finally, the methodological implications of these findings for research are as follows. It was shown how the separate direct effects of the experimental manipulations on a set of seemingly hopelessly interdependent outcomes could be readily discriminated by sequential canonical analysis, producing results very similar to those obtainable by confirmatory path analysis without requiring the stronger theoretical assumptions of that model. This was done directly on the variables of practical interest, without altering the basic nature of the research question by constructing either inappropriate common factors or uninterpretable canonical variates. The statistical results were readily interpretable and directly relevant to the experimental hypotheses that motivated the study. LITERATURE CITED BENTLER, P. M. 1989. EQS, Structural Equations, Program Manual, Program Version 3.0. BMDP Statistical Software, Inc., Los Angeles, CA. COHEN, J., AND P. COHEN. 1983. Applied multiple regression/ correlation analysis for the behavioral sciences. Lawrence Erlbaum, Hillsdale, NJ. DEMETRIOU, A., C. CHRISTOU, G. SPANOUDIS, AND M. PLATSIDOU. 2002. The development of mental processing: Efficiency, working memory, and thinking. Monographs of the Society of Research in Child Development 67(1, Serial No. 268):1-154. FIGUEREDO, A. J. 1987. The statistical measurement, developmental mechanisms, and adaptive ecological functions of conditioned host selection in the parasitoid Jewel wasp. Dissertation, University of California, Riverside, CA. FIGUEREDO, A. J. 1989. Host-cue information processing by foraging Jewel wasps: Response-bias tracking of expected host-species encounter rates, not modified profitabilities. Psychobiology 17:435-444. FIGUEREDO, A. J., AND R. S. S. SAGE. 2007. Assortative mating in the Jewel wasp: 1. Female matching of eye-color genotype, not host-feeding phenotype. Journal of the Arizona-Nevada Academy of Science, 39:51-57. GORSUCH, R. L. 1991. UniMult: For univariate and multivariate data analysis. UniMult, Altadena, CA. GORSUCH, R. L., AND A. J. FIGUEREDO. 1991. Sequential canonical analysis as an exploratory form of path analysis. Paper. American Evaluation Association Conference, Chicago, Illinois. MOUYI, A. 2006. Untangling the cognitive processes web. Paper. Seventh Annual Conference of the International Society for Intelligence Research, San Francisco, California. 64 SAS INSTITUTE, INC. 1989. SAS Language and Procedures: Usage, Version 6, First Edition. SAS Institute, Cary, NC. Differential Parental Investment! Davis Et Al. 65 Differential Parental Investment in the Southwestern United States MELINDA F. DAVIS, CORDELIA B. GUGGENHEIM, AURELIO JOSÉ FIGUEREDO, & CATHERINE J. LOCKE*, University of Arizona, PO Box 245073 Tucson, Arizona 85724-5073 *Deceased ABSTRACT The Trivers-Willard model (1973) predicts differential parental investment in children by sex and income; wealthier families will invest more in boys, while poorer families will invest more in girls. We investigated the TW Hypothesis in a sample of 103 six month old Tucson babies and their mothers. Hierarchical multiple regression equations were used entering baby’s age, baby’s sex, mother’s age, male paternal commitment, a dichotomous poverty measure, per capita income, and four interaction terms, baby’s sex by 1) mother’s age 2) mother’s education, 3) male paternal commitment, 4) poverty, and 5) per capita income. We included three dependent variables in successive regression equations; mother’s attitudes towards ideal baby size for boy versus girl babies, weeks breast fed and the baby’s weight at six months. These variables measure attitude, behavior, and physical outcomes. Poverty was a significant predictor of differential preference in ideal body size for boys versus girls; poor mothers preferred bigger baby girls. There was no evidence of differential preference in breast feeding. Education was also a significant predictor; but in the opposite direction than predicted by the TWH. Mothers with higher levels of education had heavier baby girls. Within Hispanics only, poverty was a significant predictor of sex-biased weight; poor mothers had heavier baby girls. This effect was not seen in Caucasians. These results provide mixed evidence for the TriversWillard model in a resource rich environment for humans. INTRODUCTION 'In species with a long period of parental investment after birth of young, one might expect biases in parental behavior toward offspring of different sex, according to parental condition; parents in better condition would be expected to show a bias toward male offspring.' (Trivers and Willard, 1973) The Trivers-Willard Hypothesis (TWH) proposes sex-biased resource allocation by parents in order to maximize the reproductive success of their offspring. The hypothesis is salient in species where variations in parental condition (either prenatally or after birth) contribute to the differential reproductive success by their offspring. When reproductive variance is higher for males than for females (an intrinsic function of polygyny), mothers in optimal condition (defined here by plentiful resources) will be more likely to invest in male offspring, while mothers in poor condition (defined by scarce resources), will be more likely to invest in female offspring. The TWH suggests that parents will differentially invest in the sex with the greatest chance for reproductive success. Since 1973, the Trivers-Willard Hypothesis (TWH) has been the focus of hundreds of plant and animal studies that have examined both the sex ratio at birth and differential parental investment throughout the life cycle. The results of these studies have been mixed, as have been the result of several meta-analyses. Brown and Silk (2002) examined sex ratios in nonhuman primates, and did not find support for the TW Hypothesis. “Our analyses indicate that the data are distributed much as we would expect by chance and that maternal rank is not associated consistently with biased birth sex ratios in this data set on nonhuman primates.” In a subsequent meta-analysis, Schino (2004) replicated Brown and Silk’s overall results, but also found support for the TW Hypothesis in conditions with high resource availability and low sexual dimorphism. Cameron (2004) performed a meta-analysis of 381 studies examining sex ratios in mammals (excluding humans); only a third provided support for the TW Hypothesis. However, there was considerable heterogeneity in the dataset. When the data were examined within indicator of maternal condition and timing, there was a consistent effect of maternal body condition around the time of conception and the TW Hypothesis was supported nearly 90% of the time. Sheldon and West (2004) found the same results in a meta-analysis of ungulate mammals. Within humans, there is evidence for sex-biased infanticide and differential mortality. However, the evidence for differential parental investment is not uniform; with half of the studies showing evidence consistent with the TW hypothesis and the other half rejecting it. This ambiguity may be due to the heterogeneity of indicators used in human studies, or to the absence of a TW effect. Unfortunately, the number of studies testing the TW Hypothesis in humans remains limited, particularly for resource rich environments, and existing work in the United States has provided conflicting results. In a DAVIS, M. F., C. B. GUGGENHEIM, A. J. FIGUEREDO, AND C. J. LOCKE. 2007. DIFFERENTIAL PARENTAL INVESTMENT IN THE SOUTHWESTERN UNITED STATES. JOURNAL OF THE ARIZONA-NEVADA ACADEMY OF SCIENCE 39(2)65-72. Differential Parental Investment ! Davis Et Al. heterogeneous set of studies using national samples in the United States, Gaulin and Robbins (1991), Kanazawa (2005), and Hopcroft (2005) all found evidence for the TW Hypothesiss, while others (Freese and Powell 1999, Keller et al. 2001) found no indication of sex-biased investment. It is our intention to investigate the Trivers-Willard Hypothesis in a resource-rich sample in the Southwestern United States. Our measures of parental investment are infant weight at six months, weeks breastfed, and discrepancies in the mother’s preferred infant size for boys and girls at six months. These outcomes are on a continuum from attitude, behavior, to physical outcomes and each is intended to measure the underlying construct of parental investment. Our approach follows that of Donald Campbell’s work on acquired behavioral dispositions. Rather than viewing behavior as different from attitude, Campbell viewed them as a continuum, noting that “. . there has been a stubborn confusion of the fact that verbal behaviors and overt behaviors have different situational thresholds with the fact of consistency. . . From the dispositional perspective, the supposed absence of relationship between attitudes and behavior disappears” (1963). In this framework, an attitude can be considered a behavior that is not yet observable because it has not passed the threshold into action. Further along the continuum are rare and infrequent behaviors, those that occur with fair regularity, and finally behaviors that are ingrained habits. Discrepancies in perception of the best baby size for baby boys and girls is an indicator of the mother’s attitude that she may not be consciously aware of. It is difficult, if not impossible to get candid answers to the question “Do you think that girl babies should be smaller than boy babies?” A common measure of attitudes regarding body size are the figural drawings pioneered by Stunkard et al. (1983). In this approach, respondents rate silhouettes of body size that correspond to standard height and weight percentiles. Discrepancy scores between ideal and current body size (current – desired) are used as measures of body dissatisfaction. In this study, discrepancy scores are used as a covert measure of maternal investment. In a summary of breast feeding studies in humans, Quinlan et al. (2005) found inconsistent results across countries irrespective of resource level. Likewise, Margulis et al. (1993) reported no support for the TW hypothesis in a sample of Hutterites, while Gaulin and Robbins (1991) found evidence for the TW Hypothesis in length of breastfeeding in the United States. We tested the TW Hypothesis in a sample of six month old babies, using several indicators of parental investment; maternal preference for baby size, months breastfed, and infant weight at 6 months. Differential preference for baby size is a measure of attitude; breast feeding is a measure of behavior, and infant weight is a physical outcome. Measures of parental condition in- 66 clude maternal age, education, male parental commitment, poverty, and per capita household income. Poverty and per capita household income are direct measures of resources, as is male parental commitment (measured by presence of a spouse or boyfriend in the household). The age of the mother and her education are proxies for rank and increased resources. We hypothesized that 1) mothers with greater resources will prefer larger baby boys than girls and mothers with few resources will prefer larger baby girls. 2) Mothers with greater resources will breastfeed boys longer, and those with few resources will breastfeed girls longer than boys. 3) Mothers with greater resources will have heavier baby boys, and mothers with few resources will have heavier baby girls. METHODS Subjects The women were drawn from a number of pediatric clinics throughout a metropolitan area in Arizona, in order to include women from a wide range of backgrounds. Eligible subjects were mothers of infants between five and eight months old who were attending a pediatric clinic for their child’s six-month well baby visit and spoke English. Exclusion critera included attendance at the clinic for a sick child visit, and children brought to clinic by someone other than their mother. Mother-infant pairs were approached in pediatric waiting rooms, the sample was stratified by income and ethnicity, and 110 women completed the interview. The child’s weight was recorded from the medical records after the visit. Weight was not collected for six of the babies, and these mother-child pairs were not included in the analyses. Two mother-child pairs were not included in the analyses; one child was adopted, and the other child had a birth defect that resulted in a very low weight. Approximately half of the babies were male, and their ages ranged from 23 to 37 weeks, and their weight ranged from 4554 to 10700 grams. The mothers’ ages ranged from 17 to 39 years (Table 1). Procedure Potential subjects were identified by the clinic staff and were approached by the research staff member and invited to participate in the study. The purpose of the study was explained, and written consent obtained from women who agreed to participate in the study. The mothers were interviewed while at the pediatric clinic for their baby’s 6 month well baby exam. The interview elicited the mothers’ opinions on body size for themselves and their child, current feeding practices, and demographic questions. The interviews took approximately twenty minutes to complete. In order to compensate the mother for her time and effort, each mother was given a toy for her baby. Actual weight was recorded Differential Parental Investment! Davis Et Al. 67 Tabl e 1. Demographics Mother’s age Mother’s education Household size Total income Baby’s age Baby’s weight Discrepancy score Weeks breastfed Poverty Mother’s ethnicity Baby’s sex Male paternal commitment Mean (SD) 27.2 (6.0) 13.6 (2.6) 4.3 (1.5) $28,214 (16,037) 28.5 weeks (4.0) 7966 gr. (1079) 0.0 (0.70) 11.72 (10.17) N (%) < $15,000 27 (26.2) = $15,000 76 (73.8) Anglo 61 (59.2) Hispanic 42 (40.8) Male 52 (50.5) Female 51 (49.5) Does not live with 23 (22.3) partner Lives with boyfriend 11 (10.7) Lives with spouse 69 (67.0) from the child’s medical record. The study was approved by the Human Subjects Com-mittee of the University of Arizona. Body Image The measures for infant body size followed the figural approach developed by Stunkard, Sørensen and Schulsinger (1983). Figure rating scales have been widely used in body image research to measure attitudes and perceptions, and discrepancy scores between ideal and current body size (current – desired) have often been employed as measures of body dissatisfaction (Sørensen et al. 1983, Fallon and Rozin 1985, Beebe et al. 1999, McArthur et al. 2005). Seven line drawings for infants were developed based on photographs of actual infants at different points on the weight-for-length chart. The babies were between six and eight months old ± 2 weeks. The middle drawing (#4) represents infants at the 50th percentile on this chart, e.g. their weight is average for all infants of a similar length. Drawings #3 and #5 represent the 25th and 75th percentiles, drawings #2 and #6 the 10th and 90th percentiles, and drawings #1 and #7 correspond to <10th and > 90th percentiles (Figure 1). The figural approach has demonstrated reliability and validity (Sørensen et al. 1983, Stunkard 2000, Bulik et al. 2001). In this study, mothers were shown drawings of infants and were told that these were six month olds of the same sex as the mother’s own child. The mothers were asked to indicate the ideal body size, as well as the range of acceptable body sizes. Mothers were then asked to imagine that the drawings represented six month old infants of the opposite sex, and were asked to rate the drawings on the same criteria. To prevent any systematic bias resulting from the order presentation, the infant drawings were presented in a prespecified random order. Discrepancy scores The difference between current body size and desired body size has been frequently used as a measure of body dissatisfaction. Our measure of sex-biased parental investment was the mother’s discrepancy between ideal body size for males minus the ideal body size for females. Overall, the mothers endorsed the silhouette 4 (the 50th percentile) for baby boys, and silhouette 4 for girls, with an average discrepancy score of 0.0. However, nearly half of the women chose either a heavier boy picture or a heavier girl picture. Parental condition Measures of parental resources included the mother’s age, her years of education, male parental Figural Drawings for six month old babies Figure 1. Figural stimuli for 6 month old babies. The numbers 1-7 represent the following points on the weigh- for-length charts: 1 < 10%, 2 = 10%, 3 = 25%, 4 = 40%, 5 = 75%, 6 = 90%, 7 > 90%. Differential Parental Investment ! Davis Et Al. commitment (scored 1 for no partner, 2 for boyfriend, and 3 for spouse), poverty (<$15,000 and > $15,000) and per capita household income. The mother’s ethnicity (Hispanic or Caucasian) and the baby’s sex were also collected during the interview. Multivariate imputation was used for the few cases with missing predictors. Parental investment Measures included maternal preference in baby body size (discrepancy scores), the number of weeks the mother breastfed her baby (adjusted to 24 weeks for babies who were still being breastfed), and the baby’s weight as recorded by the medical staff. 68 statistically for any indirect effects of the predictors through the causally prior dependent variables. In this analysis, we followed a theoretically pre-specified order for the indicators of parental invest-ment: Maternal preference for baby body size was assumed to precede the length of breast feeding, given the causal priority of attitude over behavior. In turn, weeks breastfed was assumed to be causally prior to the baby’s actual weight at six months. The causal order for the dependent variables is illustrated in Figure 2. Hypotheses There are three specific hypotheses for this study. 1) Mothers with greater resources will prefer larger baby boys than girls; mothers with fewer resources will prefer larger baby girls. Greater resources include increased maternal age, education, male parental commitment, and income. 2) Mothers with greater resources will breastfeed boys longer than girls; mothers with fewer resources will breastfeed girls longer than boys. 3) Mothers with greater resources will have heavier baby boys than girls; mothers with few resources will have heavier baby girls. Data Analysis A series of sequential hierarchical regressions was executed in which the multiple dependent variables were analyzed according to a prespecified causal order. Because the dependent criterion variables were expected to influence each other, they were entered sequentially in a causal order in a series of multiple regression equations with each hierarchically prior criterion variable entered as the first predictor for the next. Each successive dependent variable was therefore predicted from the initial set of ordered predictor variables, and the immediately preceding dependent variable was entered hierarchically as the first predictor, followed by all of the ordered predictors from the previous regression equation. Each successive regression therefore entered all of the preceding dependent variables in reverse causal order to statistically control for the indirect effects that might be transmitted through them. Within this analytical approach, the estimated effect of each predictor was therefore limited to its direct effect on each of the successive dependent variables. The general format for these hierarchical multiple regressions is as follows: Y1 = Y2 = Y3 = Y1 + Y2 + Y1 + X1 + X1 + X1 + X2 + X2 + X2 + X3 X3 X3 This procedure is conceptually equivalent to a sequential canonical analysis (Gorsuch and Figueredo 1991, Figueredo and Gorsuch, 2007), which controls Figure 2. Theoretical and empirical model for parental investment. The independent variables and their order of entry for the dependent variables were 1) mother’s age, 2) mother’s education, 3) male parental commitment, 4) poverty (above or below $15,000), and 5) per capita household income. Each of these is an indicator of maternal condition, or socioeconomic resources. Ethnicity was entered next to examine possible differences in feeding practices in Hispanics versus Caucasians. The baby’s sex and interaction terms with sex were entered last. The interaction terms test the TW hypothesis for weight and for breastfeeding. A significant sex by condition interaction in the appropriate direction is regarded as support for the hypothesis; “wealthy” mothers will invest more in sons and poor mothers will invest more in daughters. For preference, the dependent variable is already a measure of differential parental investment, and the main effects test the TW hypothesis. 69 Differential Parental Investment! Davis Et Al. RESULTS Tabl e 3. Hypot hesis Test s f or Predict ors of Breast f eeding. The relationships between the three measures of parental investment and the five measures of maternal condition were examined for colinearity. Correlations between the maternal condition measures ranged from .26 to .59. Correlations between the measures of parental investment ranged from -.13 to .15 and were not significant. Preference 50th On average, the mothers chose picture #4 (the percentile) for the ideal baby boy and #4 for the ideal baby girl; resulting in an average discrepancy score of zero and a standard deviation of .7. While the average was zero, there was considerable variation; nearly half of the mothers chose either a bigger baby boy or baby girl picture. Table 3 shows the results of a hierarchical regression examining predictors of differential preference (best baby boy size minus best baby girl size). Because preference is already a difference score, the main effects test the TW Hypothesis. Predictor Preference Mother’s age F(1,102) 2.10 p 0.151 19.07 <0.001 Mother’s education 4.91 0.029 Male parental commitment 1.23 0.271 Poverty 0.99 0.332 Per capita household income 0.44 0.510 Hispanic ethnicity 1.19 0.278 Baby’s sex 0.12 0.725 Ethnicity * poverty 5 . 04 0.027 Sex * preference 0.15 0.698 Sex * mother’s age 0.02 0.881 Sex * mother’s education 7.16 0.009 Interactions T a b l e 2 . H y p o t h e s i s T e s t s f o r P re d i c t o r s o f P ref erence. Sex * male parental commitment 0.17 0.682 Sex * poverty 0.01 0.944 Predictor Sex * per capita household income 0.01 0.938 F(1,102) p Mother’s age 0.92 0. 3 3 9 Sex * ethnicity 0.07 0.794 Mother’s education 0. 8 0 0.372 Sex * ethnicity * poverty 4.62 0.034 Male parental commitment 1.00 0.321 Pove rty 9.68 0.003 Per capita household income 0.08 0.773 Hispanic ethnicity 0.21 0.645 Baby’s sex 4.38 0.039 Of the five indicators of parental condition, one was significant and is bolded. Mothers whose incomes were below the poverty level preferred larger baby girls, with a standardized beta weight (β) of 0.28. This provides support for the TW Hypothesis. The last two main effects do not test the TW Hypothesis and are included for consistency because they are used in subsequent analyses. There was no difference in body size by ethnicity. Mothers of girls preferred larger baby girls, and mothers of boys preferred larger baby boys (β= -0.21). Breast feeding Two indicators of maternal condition were associated with longer breast feeding (Table 3). Older mothers breastfed their babies longer (β=0.32), and mothers with more education breastfed longer (β= 0.21). For each additional year of mother’s age, breastfeeding increased by .5 of a week; each additional year of education increased breastfeeding by .8 of a week. These differences provide evidence for the validity of education and age as indicators of maternal condition. There were no interactions by sex, and therefore no support for the TW Hypothesis for this outcome. Weight The hypothesis tests for predictors of babies’ weight are in Table 4. Only one main effect was significant, baby boys were heavier than baby girls (β= 0.57). This term adjusts for normal sex differences in weight, and the first two interaction terms; sex * breastfeeding and sex * preference are included to control for the effect of previous dependent variables. Mothers of boys who preferred larger boys had larger boys, similarly, mothers of girls who pre-ferred larger girls had larger girls (β= 0.16). This effect may provide evidence for the link between weight preference and the actual weight of the baby. Or, mothers may simply prefer the size of the child that they have. Differential Parental Investment ! Davis Et Al. The remainder of the interaction terms with sex test the TW Hypothesis for weight; only one test was significant; mothers with more education had heavier baby girls (β= -0.40). For each additional year of the mother’s education, the baby girls were 61 grams heavier. This effect does not provide support for the TW Hypothesis because it was in the opposite direction. Inspection of the data indicated a more complex relationship between income and weight that appear-ed to be associated with ethnicity. We therefore tested the interaction between ethnicity, poverty, and child’s sex. Hispanic mothers in poverty had larger baby girls than Hispanic mothers with greater resources; in fact, their daughters were larger than baby boys born to Hispanic mothers in poverty (β= 0.11). This was not seen in Caucasian mothers. Power analysis With a sample size of 103 and 16 predictors in a multiple regression analysis, this study had the power to detect a small effect size (R2 =.02) 10% of the time, and a medium effect size (R2=.15) 60% of the time. A standardized effect size of .22 would be detected approximately 80% of the time. DISCUSSION We examined the TW Hypothesis in a resource rich metropolitan environment in the southwestern United States using three indicators of parental investment; maternal attitude, behavior, and baby’s weight. This study was specifically designed to elicit information regarding feeding practices in mothers of young children. In these analyses, we included five measures of parental condition; mother’s age, education, male parental commitment, a dichotomous measure of poverty, and per capita household income. Poverty appeared to be the only maternal condition that was associated with a TW effect in this resource rich environment, and the effect appeared to be more pronounced in Hispanic mothers. Mothers showed a differential preference for baby body size by poverty and sex. This effect was not observed for income, but only when the dichotomous variable for poverty (<15,000) was used. Poorer mothers preferred heavier girl babies, and mothers with more resources preferred heavier boy babies. This is consistent with the TW Hypothesis. For breast feeding, there was no evidence of differential parental investment. This is consistent with Gaulin and Robbins (1999) who found no effect for breast feeding in a United States sample. For weight, mothers with more education had heavier girl babies, which was an effect that was in the opposite direction. Interestingly, we observed a differential patternby ethnicity; a TW effect was observed only in poor Hispanic mothers and not in poor Caucasian mothers. This result is puzzling. Why would a TW effect be active in 70 Hispanics, but not in Caucasians? We speculate that the difference could be due to the study protocol. The sample was stratified by income and considerable effort was taken to ensure the same percentages of Hispanics and Anglos were included in each income bracket. This resulted in an oversampling of affluent Hispanics in the study, when compared to the US Census (2005). The use of discrepancy scores as a subtle measure of body satisfaction is a common use of figural drawings, and rating others with these drawings is also fairly typical. This is an example of a disguised method (Campbell 1950, Davis 2001), and is useful in a setting where the individual either may not be consciously aware of their belief, or may not be willing to share it. There was no effect of parental condition on breastfeeding in this study, and the results are variable in other countries (Quinlan et al. 2005). Breast feeding information is problematic as a measure of parental investment, and variations in duration may be attributable to cultural, socioeconomic, or reporting error. An additional issue concerns a mother’s inability to provide breast milk. Were the measures we chose for parental condition valid in this sample and setting? In order to evaluate the effectiveness of the measures of parental condition we examined all main effects and interactions. Associations with parental investment, either for all children (main effect), or for some children (an interaction effect by sex) provide support for the value of each measure of condition. The study showed significant main effects for mothers’ education and age, and significant interaction effects for poverty, providing evidence for the validity of three indicators of parental condition in a resource rich setting. However, only poverty was associated in a Trivers Willard effect. Results from existing investigations of the TW Hypothesis are highly variable, and a meta-analytic approach will undoubtedly be required to tease out the effects of parental condition in humans. The benefits of meta-analysis in this area of research have been demonstrated in ungulates (Sheldon and West 2004), nonhuman primates (Shino 2004) and mammals (Cameron 2004). In each case, subtle effects were found based on either type of maternal condition or timing. To our knowledge, a meta-analysis in humans has not been attempted, and we await the results of such an endeavor with great interest. Contrary to the TW Hypothesis, we found that the weights of baby girls at six months increased in tandem with the education of their mothers. Guggenheim (2004) also found a number of regional effects that were not consistent with the TW Hypothesis. Overall, this study provides ambiguous results for the TWH. It may well be that timing effects for the TWH in humans are consistent with other mammals, and any effect of the Trivers Willard Hypothesis takes place well before birth. 71 Other approaches, such as Life History Theory or Local Resource Competition may offer additional explanatory power. We recommend the use of multiple working hypotheses (Chamberlin 1890) in future studies. There were several limitations to this study. The mothers were approached during their child’s six month well baby visit and the sample was therefore restricted to mothers who were already investing resources in their children; in essence, the data were collected at the watering hole. The study was powered to detect a standardized effect size of .22 approximately 80% of the time. Such a sample size would detect some, but not all of the hypothesized differences. These analyses provide a novel test of the TriversWillard Hypothesis in a resource-rich environment. We examined the effect of the TW Hypothesis on weight, breastfeeding, and differential preference; and found mixed support for the hypothesis in humans. Only poverty was associated with sex-biased maternal investment in both the mother’s preference in baby size and for actual weight. ACKNOWLEDGEMENTS This research was supported by the US Department of Health and Human Services, Administration on Developmental Disabilities - 90DD0315. Our appreciation to Anne Wright who reviewed an earlier version of this manuscript, Barbara Altimari for project management, and Britt Robertson for parent interviews. LITERATURE CITED BEEBE, D. W, G. N. HOLMBECK, AND C. GRZESKIEWICZ. 1999. 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MARGULIS, S. W., J. ALTMANN, AND C. OBER. 1993. Sex-biased lactation duration in a human population and its reproductive costs. Behavioral Ecology and Sociobiology 32:41-45. MCARTHUR, L. H., D. HOLBERT, AND M. PEÑA. 2005. An exploration of the attitudinal and perceptual dimensions of body image among male and female adolescents from six Latin American cities. Adolescence 40:801-816. QUINLAN, R. J., M. B. QUINLAN, AND M. B. FLINN. 2005. Local resource enhancement and sex-biased breastfeeding in a Caribbean community. Current Anthropology 46:471-480. SCHINO, G. 2004. Birth sex ratio and social rank: Consistency and variability within and between primate groups. Behavioral Ecology 15:850-856. SHELDON, B. C., AND S. A. WEST. 2004. Maternal dominance, maternal condition, and offspring sex ratio in ungulate mammals. American Naturalist 163:40-54. SØRENSEN, T., A. STUNKARD, T. TEASDALE, AND M. HIGGINS. 1983. The accuracy of the reports of weight: Children’s recall of their parents’ weights 15 y earlier. International Journal of Obesity 7:155-122. STUNKARD, A. 2000. Old and new scales for the assessment of body image. Perceptual and Motor Skills 90:(3 Pt 1): 930. STUNKARD, A., T. SØRENSEN, AND F. SCHULSINGER. 1983. Use of the adoption registry for the study of obesity and thinness. Pp. 115-120 in S. Kety, L. Roland, R. Sidman, and S. Matthysse, eds., The Genetics and Neurological and Psychiatric Disorders. New York, Raven Press. TRIVERS, R. L., AND D. E. WILLARD. 1973. Natural selection of parental ability to vary the sex ratio of offspring. Science, 179:90-92. U.S. CENSUS BUREAU, HOUSING AND HOUSEHOLD ECONOMIC STATISTICS DIVISION. 2005. Historical Income Inequality Tables. http://www.census.gov/ hhes/www/income/histinc/ ineqtoc.html Accessed 18 Dec 2006. Differential Parental Investment ! Davis Et Al. 72 SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 73 SONS OR DAUGHTERS: A CROSS-CULTURAL STUDY OF SEX RATIO BIASING AND DIFFERENTIAL PARENTAL INVESTMENT CORDELIA B. GUGGENHEIM, MELINDA F. DAVIS, AND AURELIO JOSÉ FIGUEREDO, UNIVERSITY OF ARIZONA, TUCSON, AZ 85721 ABSTRACT Survivorship of children is dependent upon numerous variables, including the role that preferential treatment may play in biasing the birth and survival of sons and daughters across cultures. This study draws upon an evolutionary approach by examining a theory referred to as the “Trivers-Willard hypothesis” concerning condition-dependent sex allocation and differential parental investment. Previous research on humans concerning this hypothesis tends to be restricted to one cultural group and thereby limited in sample size. For this study, nationally representative household survey data collected by the Demographic and Health Surveys (DHS+) program across 35 countries was used to test biological, resource-oriented, and behavioral aspects affecting maternal condition, sex allocation, and parental investment in humans. The units of analysis for this study were the mothers and their lastborn child (N = 128,039 woman-child pairs). A series of hierarchical regressions were executed to empirically investigate the TW hypothesis in humans. Scales were developed for maternal socioeconomic resources (MSR), maternal biological condition (MBC), prenatal care for the lastborn child (PCL), and health-seeking for the lastborn child (HSL). MSR was measured by relative household economic status, woman’s and partner’s education, and residence in an urban/rural setting. MBC was defined by body mass index, pregnancy status and duration, and breast-feeding status. PCL was an index for type of prenatal care received, number of prenatal visits, and assistance during delivery of the lastborn child. Lastly, HSL measured indicators of treatment for diarrhea and immunizations received by the lastborn child. Across the 35 countries, the analyses did not support the Trivers-Willard hypothesis. However, there is evidence of regional and country level differences. INTRODUCTION “Once you’ve learned to think of a herring gull as an equal, the rest is easy.” – William Drury (Trivers 2002, p. 57) While there are academic endeavors that can wrap themselves neatly around a circle of concepts, sex ratio research is certainly not one of them. Explorations of what drives any sexual species to produce one of merely two potential outcomes – a daughter or a son – has garnered remarkable attention for several centuries. Indeed, sex determination or adjustment has been attributed to timing of ovulation, maternal hormones, parental chromosomes, sexual positions, phases of the moon, mating opportunities, available nutritional resources, environmental stressors (e.g., drought, famine, flood), temperature changes (viz., across reptilian species), presence of kin and non-kin, the probability of infant survivorship, and even stochastic variation (Andersson 1994, Brewis 1993, Brown and Silk 2002, Cameron 2004, Ciofi and Swingland 1997, CluttonBrock and Iason 1986, Grant 1998, Hamilton 1967, Hardy 1997, Hardy 2002, Hrdy 1987, Hrdy 1988, James 1987). Sex ratio differences – what causes them and what maintains them – have been studied in a wide spectrum of species, ranging from spinach to whales (e.g., Freeman et al. 1994, Wiley and Clapham 1993). What is noteworthy is the extent to which research has attempted to account for such variations in elements of gestation, survivorship, and parenting style. Such research has crossed the domains of anthropology, sociology, psychology, biology, and evolutionary theory. The evolutionary angle from which academics tend to approach the topics of conception, gestation, survivorship, and parenting is understandably from an evaluation of reproductive fitness and the adaptations that are predicted to come into play in order to maximize it. The heart of the theory reviewed in this paper is embedded in the notion that nonhuman and human animals actually do behave in a manner so as to optimize reproductive success (i.e., number of viable offspring produced), measured not only in parity but also in post-parturition investment in the survivorship of offspring. Richard Alexander once wrote: “My own view of the optimal outcome would be for the significance of evolution to become so widely known and so thoroughly embedded in the understanding of all those working in human-oriented disciplines, that its tenets can be employed, without fanfare, when they are useful, and ignored or discarded when they are not” (1988, p. 339). A model concerning sex-biased parental investment is evaluated in this light, drawing upon evolutionary and cultural approaches in order to appreciate not only how evolutionary adaptations operate within cultures but also how humans cross-culturally may be GUGGENHEIM, C. B., M. F. DAVIS, AND A. J. FIGUEREDO. 2007. SONS OR DAUGHTERS: A CROSS-CULTURAL STUDY OF SEX RATIO BIASING AND DIFFERENTIAL PARENTAL INVESTMENT. JOURNAL OF THE ARIZONA-NEVADA ACADEMY OF SCIENCE 39(3):73-90. SONS OR DAUGHTERS ! GUGGENHEIM ET AL. outrightly invoking an evolutionary strategy in the treatment of their children. As Cronin points out, the acceptance of natural selection and sexual selection as forces of evolution are thankfully, at this point, “...for modern Darwinism...a storm in a teacup” (1991, p. 236). This study focuses on a theory referred to as the “Trivers-Willard hypothesis” concerning conditiondependent sex allocation and differential parental investment in humans (Trivers and Willard 1973). The central idea is that within a polygynous social mating structure, where reproductive variance is higher for males than for females as an intrinsic function of polygyny, mothers in optimal condition (defined by high status, good health, and abundant resources) are more likely to produce and invest in male offspring whereas mothers in poor condition (defined by low status, poor health, and resource deprivation) are more likely to produce and invest in female offspring. Although the Trivers-Willard hypothesis has been demonstrated in many animal species, its application and explanation for sex ratio determination across taxa have been notably inconsistent, sometimes even within species (e.g., Cockburn 1994, Cockburn et al. 2002). For example, animals exhibiting condition-dependent sex allocation and differential parental investment include: fur seals, elephant seals, opossums, red deer, mule deer, zebras, spider monkeys, horses, humpbacked whales, chimpanzees, zebra finches, reindeer, hamsters, rats, coypus, mouse lemurs, and wood rats. Species where the theory has demonstrated less applicability include sea lions and chickens with inconsistent support evident across studies on bison, lion tamarins, certain species of ungulates, pigs, mice, rhesus monkeys, and baboons1. In one study, food-restricted hamster mothers produced smaller, female-biased litters and by the 15th day of the study, they had reduced their litters by half, whereas no such mortality pattern was present in the other food conditions (Huck et al. 1986). Moreover, of the food-restricted pups, males and females weighed less than all others by the 25th day of the study. Similar tests of maternal condition and its impact on the sex ratio of litters have yielded moderate support for the TW hypothesis (e.g., coypu; Gosling 1986). In the wild boar, for example, mothers apparently adjust their litter size and sex ratio in that maternal condition, as measured by weight and size, was associated with litter size 1 For good reviews of studies addressing sex ratio variation and differential parental investment across various species (including humans) refer to any of the following: Anderson and Crawford 1993, Brown 2001, Clutton-Brock and Iason 1986, Caley and Nudds 1987, Cameron 2004, Carranza 2002, Cockburn et al. 2002, Hamilton 1967, Hardy 1997, Hewison and Gaillard 1999, Hrdy 1988, James 1987, Lazarus 2002, Pedersen 1991, Rosenfeld and Roberts 2004, Sheldon and West 2004, and van Hooff 1997. 74 (Fernández-Llario et al. 1999). A study on house mice by Krackow (1993) examined fitness differentials based on body weight variation and found a positive effect for males but not for females. Yet in others, support is absent on account of social variables purported to influence the sex ratio (e.g., yellow-bellied marmots; Armitage 1987; spotted hyaenas; Hofer and East 1997). Nonetheless, several studies seem to suggest that the TW hypothesis finds its strongest support in ungulates such as reindeer and red deer (Kojola 1997). For example, Kucera (1991) demonstrated that heavier and fatter (as measured by kidney-fat index) female mule deer produced male-biased litters. In fact, Hewison and Gaillard (1999) argue that the predictions are supported in species such as red deer, reindeer, bighorn sheep, and fallow deer because these species most satisfy the assumptions of the theory. Its applicability to humans is just as open to debate. While several studies on humans have found support for the Trivers-Willard hypothesis, others have provided inconclusive results on account of differences in measuring evidence of sex ratio biasing and parental resource allocation biasing (Keller et al. 2001). For example, several studies have indicated a weak to moderate Trivers-Willard effect for lower status groups but no real effect in the higher status groups, regardless of how status (or maternal condition) was actually measured (e.g., Borgerhoff Mulder 1998, ChaconPuignau and Jaffe 1996, Webster 2004). On the other hand, Freese and Powell (1999) were not able to support the TW hypothesis in humans in that sex-biased differences in socioeconomic investment were absent in their study while Mealey and Mackey (1990) showed that, among 19th century Mormons, higher order wives produced higher sex ratios. Interestingly, they also make note that a threshold effect may exist in humans in that the TW hypothesis “…cannot by itself predict which species will exhibit sex ratio biases under which conditions, or whether sex ratios will exhibit continuous variations or respond to some environmental threshold” (1990, p. 92). The data required for such an analysis in humans has often been unavailable or problematic in its measurement, and differences across cultures – for example, the practice of selective neglect and/or infanticide – may confound otherwise potentially ethologically comparative analyses. As a result, there is a theoretical and practical need for additional examination of condition-dependent sex allocation and differential parental investment in humans. The main objective of this study is to extend the application of the animal model to include human reproductive and parental behavior thereby revealing how humans produce and enhance the survival of their male and female offspring based on an evolutionary principle concerning reproductive success. Essentially, what might a cross-cultural test of the hypothesis yield for our species? The idea is to under- 75 stand the “survival of those who survive” (Trivers 2002, p. 64) and how or why their mothers let them live. This study tests the Trivers-Willard hypothesis1 by pursuing two specific aims. First, it will evaluate the significance of condition-dependent sex allocation of offspring among humans. The working hypothesis is that the sex of the child is predicted by maternal condition such that a mother who is “healthy and wealthy” will be more likely to have a son. A woman in suboptimal condition regarding health and resources will, instead, more likely be the mother of a daughter. Secondly, the significance of differential parental investment among humans will be examined with the following working hypothesis in mind: Females of high status, abundant resources, and good health will be more likely to invest more resources in their male offspring than in their female offspring. Females at the other end of the condition continuum will tend to invest more in their female offspring. These questions will be examined in a multi-sample analysis spanning 35 developing countries from four regions around the world. This study will present an analysis of the TW hypothesis in humans by testing variables that may predict the sex allocation of the lastborn child and the parental behaviors differentially directed toward that child, thereby comparing the human model to patterns found in other animals. As such, central assumptions of the theory concerning natural deviations from a 50/50 sex ratio in nature are the following: (a) the condition of the mother during the period of parental investment serves as a predictor of the condition of the offspring at the end of the parental investment period; (b) differences in offspring condition at the end of the period of parental investment persist through adulthood; and (c) in species where males exhibit less parental investment than females, males are expected to exhibit higher variance in reproductive success. In summary, according to Trivers and Willard, “...under certain well-defined conditions, natural selection favors systematic deviations from a 50/50 sex ratio at conception.…other things being equal, species showing especially high variance in male [reproductive success] (compared to variance in female RS) should show, as a function of differences in maternal condition, especially high variance in sex ratios produced” (1973, p. 90). Interestingly, most tests of the TW hypothesis tend to focus on an abbreviated version without necessarily 2 Note that, in the research literature, the central hypothesis is sometimes interchangeably referred to as the “Trivers-Willard model” or as the “Trivers-Willard hypothesis” and thus abbreviated as TWM or TWH, respectively. In some cases it is cited as the “Trivers-Willard effect” when referring to particular predictions of the hypothesis. For the sake of clarity in this paper, the guiding theoretical framework is referred to as the “TW hypothesis” while the term “model” will indicate the analytical approach used to test the hypothesis, as measured in this study. SONS OR DAUGHTERS ! GUGGENHEIM ET AL. including – or at least, demonstrably excluding – some of the underlying predictions. While many studies readily focus on “good-condition mothers invest in sons,” it should not be overlooked that the following parameters were also included: (a) the theory is expected to apply to species with small brood sizes, given cited empirical evidence – yet less so to species with larger litters; (b) compensatory growth, in response to malnutrition or maternal effects, for example, is deemed trivial in effect; (c) sex ratio at birth is assumed to be an indicator of parental investment; (d) and reproductive success of males is free to vary on account of “negligible” paternal care (Trivers and Willard 1973, p. 91). Which is to say that several central assumptions must be met in order for analysis to address the actual Trivers-Willard hypothesis, as outlined in the original paper. The role of polygyny and minimal parental investment by males is central to the assumptions of the theory. In fact, variance in reproductive success is explained as “all or nothing” for males within a polygynous mating system whereas the contrast in reproductive success for females is of smaller disparity in that a female is more likely than not to successfully secure mating opportunities at some point. Although she will never be able to produce as many potential grandchildren as a male could, it is at least more probable that she will at least have the opportunity to try. In truly socially polygynous mating systems – such as those seen among herding or harem species – not all males are so fortunate. Hence, the greater disparity between the males who are outcompeted by other males in their access to females. While Clutton-Brock and Iason pronounce that “...the firmest conclusion that can be drawn from the distribution of observed trends in the sex ratio is that the distribution does not conform to the predictions of any single adaptive hypothesis” (1986, p. 367), it is all the more reason to apply an empirical test of one such as that provided by the Trivers-Willard hypothesis. Precisely when parental investment begins and ends can be problematic in terms of measurement; most definitely, depending on the species in question. Nonetheless, it has been defined as “...any investment by the parent in an individual offspring that increases the offspring’s chance of surviving (and hence reproductive success) at the cost of the parent’s ability to invest in other offspring” (Trivers 1972, p. 139). Despite all their efforts and intentions, or because of all the variance in parental behaviors, not all parents watch their children grow up and produce grandchildren; there is also “the darker side of parenting” (Scheper-Hughes and Sargent 1998, p. 21). Indeed, the impact of parental under-investment – or disinvestment – ranges from passive neglect to active infanticide (Scrimshaw 1984). While 9% of all world cultures practice sex-selective infanticide (Hrdy 1999), most cases where human children do not survive would be more appropriately classified as selective neglect (Larme 1997). SONS OR DAUGHTERS ! GUGGENHEIM ET AL. Extensive research has accumulated in the last years addressing what adaptive mechanisms may be driving the practice of infanticide as well as how cultural sanctions may be merely providing the framework in which “evolved decision rules” can operate (Hrdy 1999). In fact, much of the research on infanticide seems to support the Trivers-Willard hypothesis in that infanticidal trends are most evident where females have the smaller chance of reproductive success comparable to males (Beise and Voland 2002, Daly and Wilson 1984, Dickemann 1979, Gosden et al. 1999, Jeffery et al. 1984, Miller 1987). For example, Hrdy describes the role of the “daughter destroyers” within elite clans in India (1999, p. 326) and cites research revealing that among lower castes, genetic markers crossing caste boundaries serve as an indicator of females engaging in “marrying up” (i.e., hypergamy; Hrdy 1999, p. 340) in that the lower caste females have higher reproductive variance than their male counterparts. Among the elites, however, daughters are at a distinct disadvantage. As such, countries known to practice sex-selective infanticide are included in the analyses. METHODS Data source The study population was drawn from 134,257 women in 35 countries who were interviewed between 1992 and 1998 as part of the Demographic and Health Surveys (DHS+) with funding from the US Agency for International Development1. DHS+ surveys are nationally representative samples by country and usually use multistage cluster sampling techniques. We selected all countries in the DHS+ datasets that collected complete data for maternal nutritional status, socioeconomic resources, and parental investment. These 35 countries are in the least developed and developing categories. Sub-Saharan Africa is represented by 21 countries, South Asia and the Near East/North Africa by three countries each, and the Caribbean/Latin America by eight countries. A list of all countries selected for this study and survey collection dates is presented, by region, in Appendix Table 1. Sample The youngest child for each mother was selected for the analyses and cases with missing data (4.6%) were excluded, leaving a final sample size of 128,039 mother-child pairs (weighted N = 124,371). The sample size per country ranged from 732 for Comoros to 5,361 for Guatemala, with an average of approximately 3,000 mother-child pairs. The exception was India, with a sample size of 21,839 (Appendix Table 1). 3 Dataset access can be initiated at the MEASURE DHS+ website: http://www.measuredhs.com/ 76 Note that the sampling techniques employed in the DHS+ surveys are designed to maximize the retrieval of information representing 100% of the population surveyed. DHS+ emphasizes the use of nonzero probability sampling. When this is not the case and a sample is not self-weighting, calculation of sample weights should be included in any inferential analyses of DHS+ data (Macro International Inc. 1996). That is, individual weights in almost all of the surveys are normalized so that if all of the women within a sample are included, the weighted and unweighted numbers of women should be equal. If selecting a sub-sample, then the weighted and unweighted sample sizes will differ. In order to ensure that analysis is representative of the entire population – and not just of the sample population – sample weights are provided with all data sets for proper parameter estimation; their significance being that they "...are often interpreted as the number of population units represented by each unit of the sample" (Häder and Gabler 2003, p. 124). Therefore, sample weights were included in the analyses. Procedure Women between the ages of 15-49 were interviewed by trained personnel using structured questionnaires. Response rates were generally above 95%. In each country, households were selected using a multistage clustering procedure. The surveys included questions related to maternal resources, biological condition, medical care, and health-seeking behavior. Data collection procedures are described in detail in ORC Macro (2005). Scales Four scales were developed relating to the biological, resource-oriented, and behavioral aspects affecting maternal condition, sex allocation, and parental investment in humans. Selection of the final set of variables are presented in Appendix Table 2 , along with brief descriptions and coding schemes. Stringent decision rules were applied to enhance the cross-species comparative focus of this study, and these are briefly reviewed here. Maternal socioeconomic resources (MSR) The four dimensions of household economic status were drawn from a previous study by Smith et al. (2003). Economic status was defined by level of basic needs met and number of assets owned. Basic needs are measured by whether the household has a finished floor, toilet facility, or access to piped or bottled water. Cheap assets include a radio, a television, or a bicycle; expensive assets include a refrigerator, motorcycle, or car. Households were classified as “destitute” if they have one or none of the basic needs and none of the assets. Households classified as “poor” have no more 77 than two of the basic needs and cheap assets. “Rich” households have at least two basic needs met and at least one expensive asset. Urban households received a higher score because urban living tends to provide women with more efficient access to resources (Madzingira 1993). The woman’s level of education was included as a resource, and male contribution was measured by presence in the household and educational status. Maternal biological condition (MBC) Body mass index (BMI) was used as an indicator of the continuum of maternal condition. Higher BMI is used as an indicator of good condition, along with a categorical variable for under-nourished, healthy, or overweight. Current pregnancy and breast-feeding status were also included in order to differentiate between women on several important elements that constitute the mammalian female reproductive life cycle. Breast-feeding was predicted to have a negative effect on a mother’s condition by placing a drain on her energy and nutrient intake (Brown 2001). Length of pregnancy (as opposed to pregnancy status by itself) was used as a positive indicator of maternal condition in that the very fact that a woman is able to be pregnant and especially to be able to maintain a pregnancy for any length of time are considered indicators of good condition (Haig 1999). Although any pregnancy naturally deprives a woman of necessary energy reserves (i.e., maternal depletion; Ellison 2001), the very fact that she is able to be pregnant and especially to be able to maintain a pregnancy for any length of time are considered indicators of good condition, especially given that malnourished and/or stressed women are more likely to miscarry (Kerr 1971). For this reason, current pregnancy duration was selected for the maternal health scale whereby women who were not pregnant were coded as zero for pregnancy duration. Prenatal care for lastborn child (PCL) This scale measured protective, risk-avoidance behaviors. Central to this scale is access to care and initial parental effort directed toward the maintenance of maternal and child health. Type of prenatal care was measured by amount and provider (none, non-medically trained, or medically trained provider). Measures for birth assistance included delivery at a medical facility and type of provider. Health-seeking for lastborn child (HSL) The overall HSL scale is not a measure of the child’s health, but the parental response and prevention strategy experienced by the child. It serves as a direct measure of parental-initiated investment per lastborn child. Receipt of immunizations and age-relative compliance with immunization completion were included SONS OR DAUGHTERS ! GUGGENHEIM ET AL. to provide each child with a score comparable to all other children, regardless of age. Note, though, that all eight vaccinations should ideally be given before the first birthday has been reached such that by the time they are 4 months old, children should have received five of the eight vaccinations (Smith et al. 2003). Furthermore, diarrhea in the developing world is particularly dangerous for children and the risk of dehydration cannot be underplayed; as such, the scale was coded to emphasize treatment-seeking. The highest score was assigned to children who received treatment and the lowest score assigned to those who did not receive treatment for a reported case of diarrhea. Scale construction Composite scores were created by standardizing and averaging the variables, and scale scores were standardized again for the hierarchical regressions; the specific means (M) and standard deviations (SD) should, by definition, tend toward a mean of zero and a standard deviation of 1. Listwise deletion was used in scale construction. Final determination of scales was based on a Cronbach’s alpha > .60. The inter-item reliabilities for the four scales ranged from .63 for MBC to .85 for HSL. Internal consistency – a measure of scale reliability – serves as evidence of construct validity. For scale confirmation, the indicators were then correlated with the scales. The results of these correlations are presented in Table 1. While the diarrhea treatment variable did not correlate strongly with the scale to which it was assigned (r = .24, p < .01), the item was retained for theoretical considerations. It was necessary to include a measurement for diarrhea treatment-seeking behavior given that diarrhea is one of the main causes of mortality in children in developing countries. In this case, theoretical considerations overrode the weaker statistical justification for retaining that variable in the healthseeking behavior scale. Zero-order correlations between the scales ranged from .2 to .6. Detailed information regarding scale construction is in Guggenheim (2005). Statistical analyses A hierarchical cluster analysis involving Ward’s linkage method was used to determine the pattern of association between cases based on discrepancies between the national at-birth sex ratio and the sex ratios within the current data. The cluster analysis utilized a composite score for each country using national estimates from the CIA and survey research data to measure similarities and differences in individual countries’ deviation from their estimated at-birth sex ratio among children under five years of age. A series of hierarchical regressions was performed in which multiple dependent criterion variables were analyzed sequentially according to a hypothesized causal SONS OR DAUGHTERS ! GUGGENHEIM ET AL. Table 1. Pearson correlations between scales and indicators. MSR MBC PCL HSL Whether woman lives in urban area .715 Household economic status .778 Woman’s education .802 Male’s educational value .738 78 them. Within this analytical scheme, the estimated effect of each predictor was limited to its direct effect on each of the successive dependent variables. The general format for these hierarchical multiple regressions was therefore as follows: Y1 = X1 + X2 + X3 Y2 = Y1 + X1 + X2 + X3 Y3 = Y2 + Y1 + X1 + X2 + X3 Woman’s BMI .785 Woman is malnourished/ healthy/overweight .775 Duration of current pregnancy, if pregnant .544 Woman currently breast-feeding (reversed) .655 Whether prenatal care received & care type .770 Number of prenatal care visits .788 Delivery assistance .808 Delivery took place at a medical facility .824 This procedure was conceptually equivalent to a sequential canonical analysis (Gorsuch and Figueredo 1991, Figueredo and Gorsuch 2007), which controls statistically for any indirect effects of the predictors through the causally prior dependent variables. In this study, the causal order of the dependent variables was: 1) maternal socioeconomic resources (MSR), 2) maternal biological condition (MBC), 3) prenatal care for the lastborn child (PCL), 4) sex of lastborn child (SEX), and 5) health-seeking for lastborn child (HSL). The causal order for the dependent variables is presented in Figure 1. Note, however, that this figure is simplified as it does not include the successive main effects and interaction terms. The order for the general linear models was: Child’s diarrhea: untreated, absent, or received treatment in last 2 wks .243 Whether child received BCG vaccination .799 Whether child received measles vaccination .742 Total number of DPT vaccinations received .916 Total number of polio vaccinations received .894 Percent recommended vaccinations received .922 order. Because these dependent criterion variables were expected to causally influence each other, they were entered sequentially as criterion variables into a system of multiple regression equations with each hierarchically prior criterion variable entered as the first predictor for the next. Thus, each successive dependent variable was predicted from an initial set of ordered predictor variables, each time entering the immediately preceding dependent variable hierarchically as the first predictor, then entering all the ordered predictors from the previous regression equation. Thus, each successive regression entered all of the preceding dependent variables in reverse causal order to statistically control for any indirect effects that might be transmitted through MSR = REGION + COUNTRY MBC = MSR + REGION + COUNTRY PCL = MBC + MSR + REGION + COUNTRY SEX = PCL + MBC + MSR + REGION + COUNTRY HSL = SEX + PCL + MBC + MSR + REGION + COUNTRY The effect of region and country on maternal socioeconomic resources (MSR) were examined first, given the prediction that they precede the measure for maternal condition (MBC) in explanatory power. That is, socioeconomic factors are predicted to be region- and country-specific. Resources available to each mother are, in turn, predicted to influence her biological condition (as measured by MBC). The next relationship examined is the effect of MSR and MBC in influencing levels of prenatal care for each lastborn child (PCL). The frequency and type of prenatal care are, in turn, predicted to determine the sex of that same child (SEX). Lastly, degree of health-seeking for the lastborn child (HSL) is hypothesized to be predicted by the sex of that child. The analyses also assess the residual effects of each previous variable in the analysis along with interactions by region and country. These interaction terms have been included to measure whether the effect of any of the central predictors (MSR, MBC, PCL, SEX, and HSL) on the dependent variable of any given regression are moderated by REGION or COUNTRY. For example, if an interaction between REGION and MSR is significant and large in predicting PCL, this would indicate that the manner in which maternal resources impacts prenatal care varies SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 79 Figure 1. Causal order for the dependent variables. as a function of regional or country differences. For this study, the conditional associations – as measured by the interaction terms – are crucial in determining to what extent cultural variance is at play here in addressing an evolutionary theory that has been difficult to demonstrate reliably in human populations. In essence, if the Trivers-Willard hypothesis applies to humans over and above what cultural differences may exist, then results from interaction terms in the forthcoming analyses should be nonsignificant or minimal. Additionally, as referenced earlier, sample weights were used in the analyses to ensure representative samples within each country. RESULTS Thirty-five countries were sampled across four regions: South Asia, Sub-Saharan Africa, the Caribbean/Latin America, and the Near East/North Africa. For the mothers across all four regions: 91% reported a male partner present, 13% were living in female-headed households at the time of the interview, 14% were malnourished, 10% were pregnant at the time of sampling, and 63% were breast-feeding. The mean age of the women across all regions was 27.8 years, with the average age at first marriage being 17.7 years and education averaging 3.8 years. For the 22% of the sample reporting information for more than one child, the maximum number of children currently residing at home with the mother and under the age of five years was 4. The mean age of the lastborn child across all women was 19.7 months. Virtually all of the children (99%) were reported to have been breast-fed at some point. Additionally, 79% received the BCG vaccination, 53% received the measles vaccination, the average number of DPT and polio vaccinations was 2, and the mean percent of agerecommended vaccinations received was 72%. Variations by region and country are discussed in Guggenheim (2005). Sex ratio of lastborn children The number of males (65,190) to females (62,849) across all regions in the final sample selected for analysis yields a sex ratio of 1.037 (51% boys, 49% girls). Estimated sex ratios by country at birth and in the current sample are presented in Appendix Table 3. Preliminary interpretation of the discrepancy in the national at-birth sex ratios from the sex ratios of the current data was suggestive of interesting trends. Certain countries apparently deviate from the secondary sex ratio by becoming unusually female-biased (e.g., Uganda) while others deviate by becoming unusually male-biased (e.g., Turkey). Noteworthy, also, is that all three Near Eastern/North African countries yield malebiased trends as well as India; notwithstanding, these are the countries with prevalent son preference and significantly high infanticide rates. SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 80 Figure 2. Results of cluster analysis. Results reveal a distinctive pattern of three clusters, with the first break (Euclidean distance = 0.593) across two groups separating countries by those that decreased (or remained unchanged) in the number of males relative to females and those that decreased in the number of females relative to males within the underfive age group. The former group contains countries with male and female-biased sex ratios while the latter contains only male-biased countries. The second break (Euclidean distance = .343) distinguishes between a group that decreased in the number of males proportional to females, thereby producing female-biased sex ratios, and a group that either decreased or did not decrease in the number of males relative to females, thereby producing male-biased sex ratios. The cluster tree yields three distinctive groups (see Figure 2). The top cluster, in italics, includes the female-biased countries that reflect a loss of males relative to females within the under-five age group. The center of the tree identifies the male-biased countries that did or did not decrease in number of males relative to females. And the bottom group, in bold, contains the countries that demonstrate a loss of females relative to males. The cluster analysis implies a proportional decrease over time from the estimated at-birth sex ratio in almost all countries. Overview of modeling Analyses involved a system of hierarchical regressions testing for the interaction and main effects of region, country and the four scales: maternal socioeconomic resources, maternal biological condition, prenatal care for lastborn child, sex of lastborn child, and health-seeking for lastborn child. Results are presented for each dependent variable as it is predicted by each set of independent variables and interactions following the sequence depicted in Figure 1. Maternal socioeconomic resourcesIn the first general linear model, region and country together account for 22.6% of the variance in maternal socioeconomic resources (see Table 2). In fact, region accounted for 13.8% while country accounted for almost 12%, as indicated by R2 for each variable. Additionally, SubSaharan Africa had the lowest mean for the maternal socioeconomic resources scale (M = -.32, SD = .82), and Latin America and the Caribbean had the highest mean (M = .50, SD = 1.05) Maternal biological conditionIn the second general linear model, maternal socioeconomic resources accounts for 11.6% of the variance in maternal biological condition. In fact, across all regions, increasing maternal socioeconomic resources contributes toward SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 81 Tabl e 2. Predicting Maternal Socioeconomic Resources. Tabl e 3. Predict ing Mat ernal Biological Condit ion F p R2 Source 4 4983.65 .000 .138 MSR COUNTRY 31 5 28 . 3 1 .000 .116 REGION Model 35 1037.49 .000 .226 COUNTRY Source REGION df Error 124336 Total 124371 increased maternal biological condition but not all that powerfully, as indicated by the small, positive standardized regression coefficient for the maternal socioeconomic resources scale (β = .066). The main effect for region is large, with almost 18% of the variance in maternal biological condition explained by systematic differences between regions regarding maternal condition (Table 3). Although significant, the interaction between maternal socioeconomic resources and region, as well as the interaction between maternal socioeconomic resources and country, are trivial in effect. Maternal socioeconomic resources by region accounts for 0.1% of the variance in maternal biological condition, while the interaction of country with maternal socioeconomic resources accounts for 0.3% of the variance in maternal biological condition. Small interactions such as these merely demonstrate that the effect of maternal resources in explaining maternal biological condition does not vary much – if at all – as a function of regional or country differences but that in this case, some degree of conditional variation by country and region is present for this scale. This trend of trivial explanatory power is evident through almost all of the conditional relationships tested within the sequence of regressions. Moreover, that the main effect for region is so large, in comparison, indicates that almost 18% of the variance in maternal biological condition is explained by systematic differences between regions regarding maternal condition. What is interesting, on the other hand, is that South Asia (β = -.566) differs from the other three regions in the direction of its coefficient in this regression: Sub-Saharan Africa (β = .097), Latin America/Caribbean (β = .461), and the Near East/ North Africa (β= .768). In fact, Bangladesh ranks the lowest (M = -.72 , SD = .85) in maternal biological condition while Turkey has the highest mean (M = .82, SD = .94) on that scale. Furthermore, of all the regions, South Asia has the lowest mean maternal biological condition (M = -.67, SD = .83) while the Near East/North African region has the highest (M = .73, SD = 1.0). p R2 1 15391.32 .000 .110 4 6697.18 .000 .177 31 44.00 .000 .011 3 51.53 .000 .001 COUNTRY *MSR 31 10.79 .000 .003 Model 70 629.05 .000 .262 df REGION *MSR F Error 124301 Total 124371 Prenatal care for lastborn child Table 4 reveals that maternal biological condition accounts for 9% of the variance in prenatal care with a small, yet positive, effect (β= .061). Maternal socioeconomic resources has the largest effect (37.1%) in predicting prenatal care for the lastborn child. Indeed, increased maternal socioeconomic resources predicts increased prenatal care (β= .706) across all countries. Region, on the other hand, only predicts 5.5% of prenatal care, while country is the second strongest predictor by explaining 13% of the variance (Table 4). Here it Tabl e 4. Predicting Prenatal Care for Lastborn Child. Source df F p R2 MBC 1 12222.63 .000 .090 MSR 1 73307.83 .000 .371 REGIO N 4 1802.21 .000 .055 31 600.21 .000 .130 3 2. 8 0 .038 .000 31 6.28 .000 .002 3 22.18 .000 .001 31 92.02 .000 .022 105 1090.17 .000 .479 CO UN TRY REGIO N *MBC CO UN TRY *MBC REGIO N *MSR CO UN TRY *MSR Model Error 124266 Total 124371 SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 82 variance with almost all of the predictive power being explained by region. In fact, maternal socioeconomic resources only accounts for 0.1% of the variance in predicting the sex of the lastborn child while region explains 49.1% of the variance. Yet, MSR has a small, positive effect such that higher levels of resources predict lastborn daughters across all regions (β = .040). Prenatal care is not significant in predicting the sex of the lastborn child. Moreover, maternal biological condition does not contribute any detectable predictive power to the sex of the lastborn child, given that R2 equals zero for this predictor as well. should be noted that the interaction of country with maternal socioeconomic resources represents the largest proportion – with only 2.2% predictive power – of all the interactions in the entire set of regressions for the interaction model, thereby demonstrating their minimal explanatory contribution overall. Hence, 2.2% of the variance in prenatal care is explained by maternal socioeconomic resources varying as a function of country differences. Nonetheless, in its entirety, the model testing the effects of maternal condition, resources, region, and country captures 47.9% of the variance in prenatal care for the lastborn child. Across the four regions, South Asia has the lowest mean prenatal care for the lastborn child (M = -.28, SD = 1.0), while the Latin American/ Caribbean region has the highest mean (M = .44, SD = 1.0) across all countries once again. Note, however, that the Near East/North African region is similar (M = -.27, SD = 1.0) to South Asia concerning mean levels of prenatal care. The final regression in this series examines the effect of region, country, the three scales, and the sex of the lastborn child in determining health-seeking for that child (Table 6) . Results show that, overall, male lastborn children are more likely to receive treatment and immunizations; however, this effect is very small both Sex of the lastborn child in explanatory power (R2 = 0.1%) and magnitude (β = -.050). The largest contribution (16.7%) in predicting The next regression in this series tests for the effect of country, region, maternal socioeconomic resources, maternal biological condition, and prenatal care in predicting the sex of the lastborn child. As Table 5 shows, the overall model accounts for 49.2% of the Tabl e 5. Predict ing Sex of Last born Child. Source df F p R2 PC L 1 2. 1 7 . 1 41 . 000 MBC 1 11.63 . 001 . 000 MSR 1 8 4. 3 1 . 000 .001 REGION 4 30004.76 . 000 .491 COUNTRY 31 1.33 . 1 03 .000 REGION* PC L 3 . 75 .521 .000 COUNTRY *P C L 31 1 . 23 . 1 79 .000 REGION* MBC 3 5 . 62 .001 .000 COUNTRY *MBC 31 1.76 . 006 .000 REGION* MSR 3 . 93 .424 .000 COUNTRY *MSR 31 . 99 . 479 . 000 1 40 8 5 9. 3 1 .000 .492 Model Error 124231 Total 124371 Health-seeking for lastborn child health-seeking across all four regions lies in prenatal care for the lastborn child (β = .041), suggesting that higher rates of prenatal care for the mother predict higher rates of health-seeking for the lastborn child. Furthermore, maternal biological condition has a small, yet significant, positive predictive effect (β = .233) in explaining 4.2% of the variance in health-seeking behaviors. Maternal socioeconomic resources account for only 1.1% of the variance in health-seeking (β = .254); such that, as resources increase, health-seeking for the lastborn child increases. Region accounts for 0.8% of the variance in health-seeking whereby the second strongest predictor is country, accounting for 7.2% of the variance. Note also that the conditional relationships between prenatal care with region (1.6%) and prenatal care with country (1.7%) are significant, albeit also small, indicating that a small proportion of explanatory power in predicting health-seeking is contingent upon variations in how country- and region-specific differences determine prenatal care. Conditional relationships between maternal biological condition and maternal socioeconomic resources with country and region are even smaller (ranging from 0.1 to 0.5%). Furthermore, conditional relationships between sex of the lastborn child with prenatal care, maternal biological condition, maternal socioeconomic resources, region, and country were either nonsignificant or trivially small in predicting healthseeking for the lastborn child. As such, the entire model accounts for 27.9% of the variance in health-seeking for the lastborn child. What is more, South Asia has the lowest average level of investment in health-seeking behaviors (M = -.19, SD = 1.05) whereas mothers within the Near East/North African region (M = .30, SD = .85) demonstrate, on average, higher levels of preventative behaviors toward their lastborn children. SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 83 Tabl e 6. Predicting Health-seeking for Lastborn Child Source df F p R2 SEX 1 68.45 . 000 .001 PC L 1 24943.67 .000 . 1 67 MBC 1 5 3 78 . 3 0 .000 . 042 MSR 1 1428.27 .000 .011 MBC*SEX 1 .03 . 8 72 . 000 MSR*SEX 1 .51 .475 . 000 REGIO N 4 257.06 . 000 . 008 31 3 08 . 99 .000 . 072 3 14.82 . 000 .000 31 1 . 76 .006 .000 3 68 9 . 04 . 000 . 01 6 31 68.47 . 000 .017 3 66.96 .000 .002 31 5.30 .000 .001 3 48 . 3 6 .000 .001 31 20 . 06 .000 . 005 3 2 . 73 .042 .000 31 1.15 . 25 8 .000 3 1.54 .202 .000 CO UN TRY* MBC*SEX 31 1.08 . 3 47 .000 REGIO N * MSR* SEX 3 .32 .813 .000 CO UN TRY* MSR*SEX 31 .77 .811 . 000 28 0 171.27 .000 .279 CO UN TRY REGIO N * SEX CO UN TRY* SEX REGIO N * PC L CO UN TRY* PC L REGIO N * MBC CO UN TRY* MBC REGIO N * MSR CO UN TRY* MSR REGIO N * PCL* SEX CO UN TRY* PCL* SEX REGIO N * MBC*SEX Model Error 124231 Total 1 243 7 1 DISCUSSION Region and country predicted nearly 25% of the variability in maternal socioeconomic resources (MSR) and were significant predictors in each successive general linear model. That there are differences in resources across regions and countries is unsurprising, and the amount of variance that region and country accounted for in each GLM ranged from less than 10% for HSL to nearly 50% for sex of the lastborn child. MSR predicted 11% of maternal biological condition (MBC), which in turn accounted for 9% of prenatal care for the lastborn child (PCL). Neither MSR, MBC or PCL had any meaningful explanatory power for sex of the lastborn child. Health-seeking for the lastborn child (HSL), however, was predicted by PCL, MBC, and to a lesser extent, by MSR and SEX of the lastborn child. Interactions with region and country were generally small, indicating that the main effects of the predictor variables are relatively stable across geographic areas. The exceptions were regarding health-seeking behavior, whether prenatally or after birth. Namely, MSR*country accounted for 2.2% of the variance in PCL, and PCL*region and PCL*country accounted for 1.6% and 1.7% of the variance in HSL respectively. Essentially, women who can obtain healthcare are doing so at differential rates by country and region. Across the 35 countries there are two small effects that provide minimal support for the TW hypothesis. That is, MSR has a small, positive effect such that higher levels of resources predict lastborn daughters across all regions. Furthermore, male lastborn children are more likely to receive treatment and immunizations. Both are small effects, each accounting for 0.1% of the variance in the analyses. However, the role of polygyny and minimal parental investment by males is central to the assumptions of the theory, and this condition may be differentially met within the four regions. And, in fact, interaction terms for HSL by region and country account for .8% and 7.2% of the variance, respectively. Note, however, that the lack of conditional relationships between sex of the lastborn child and prenatal care, maternal biological condition, maternal socioeconomic resources, region, and country in predicting health-seeking limit any additional support for the TW hypothesis. As well-established by previous research, males are born at a higher frequency, with the average sex ratio in humans estimated to be 1.06 males born for every female (Cartwright 2000). However, variations across countries exist and a comparison of the current sample sex ratio with national estimates thereof, yielded three evident patterns: one where there is a drop in the number of males but they continue to outnumber females; one where males decrease so drastically within the first five years of life, that the sex ratio becomes female-biased; and one where males initially predominate in number and increase, due to what can only be attributed to a loss of females. The observation that good condition mothers in male-biased countries show a tendency toward producing daughters and that there are not enough daughters in these regions to account for this pattern, is an important point of contrast. All things considered, though, while the descriptive characteristics initially presented confirm foreseeable demographic differences, the system of SONS OR DAUGHTERS ! GUGGENHEIM ET AL. regressions used in this research places those differences and similarities into perspective regarding an evolutionary framework as provided by the TW hypothesis. Namely, the fact that Sub-Saharan Africa deviates somewhat from the pattern found for the other three regions is potentially explained by the higher degree of polygyny, on average, across those countries. That is, polygyny may afford more autonomy to wives than monogamy does and the husband’s influence is even more denounced the higher the women’s education is (Dodoo 1998). Indeed, there is substantial variation in the degree of polygyny across these countries. According to DHS+ information, almost 51% of women in Burkina Faso report having two or more co-wives present and 46% of women from Senegal report having one other wife present. In contrast, 96% of women in Madagascar are not in a polygynous union and the same for 75% of women in Comoros. Furthermore, of those 25% who have a co-wife, 71% only had one co-wife, according to another study (Althaus 1997). It would seem that polygyny can leave almost half of its male population without a mate. As such, the trend for the African countries in this data would suggest a mild Trivers-Willard effect in that if mothers have the resources, they produce sons. Otherwise, even when in good physical condition, they invest in the production of daughters. Note, however, that the effect for the resources was somewhat greater than that of the effect for physical condition. As such, this is the closest this analysis seems to come in supporting the TW hypothesis across thirty-five countries. Anderson and Crawford (1993) as well as Carranza (2002) provide critical reviews of how predictions stemming from the TW hypothesis require modification in order to be appropriately applied to humans. Freese and Powell (1999) did not find support for the TW hypothesis in humans either, i.e., no sex-biased differences in socioeconomic investment, but failed to mention paternal care as a potential confound. They conclude with: “...the evidentiary burden would now seem to fall upon those who might attribute our findings to the exceptional character of American society rather than to the more fundamental limitations of the theory” (p. 1737), citing sociologists’ “professional obligation... to test [sociobiological] hypotheses fairly and rigorously” (p. 1738). It is hoped that was accomplished here. However, this research used self-report data and, as such, is prone to typical biases and errors common to such methodologies. For example, standardization, whether in technique or measurement, limits the possibilities of responses and can create demand characteristics. While selection of the lastborn child may capitalize on enhanced memory recall, a focus on the oldest child might serve as a better source for measuring parental investment. In addition, previous studies 84 on birth order indicate that selection of the lastborn child may be confounded by the possibility that the favored child is being studied (Rohde et al. 2003). While no noticeable sex-biased differences were apparent across diarrhea treatment-seeking behaviors, this could in fact be due to reporting error alone. In addition, particularly relevant information concerning polygynous pairings was missing from the data at hand. Finally, definitions of parenting can vary across both monogamous social structures and in settings where alloparenting is normative. These analyses would have been more informative if child nutritional status as a measure of parental investment were included, along with indicators of maternal condition at preconception rather than postnatally. Analysis of reproductive success of offspring would also enable a more representative test of the original theory. It would also be interesting to test the sex ratio against expected averages at the primary and secondary levels; namely, 3 months post-conception (1.2:1) vs. at birth (1.06:1) sex ratios (from Cartwright 2000) to examine the juncture at which sex ratio manipulation might be occurring. The foremost issue is the notion of condition – what exactly did Trivers and Willard mean, and why have so many different interpretations been applied to it? If they meant weight and body size for polygynous animals where parental care is trivial, then the theory can be tested on those species and probably should not be expected to fit others. Which is to say, with so many constraints involved in terms of “well-defined conditions” (Trivers and Willard 1973, p. 90) is it really that surprising that there is so much variation not only in the results that have been revealed across species but in the extent to which this theory has been applied? To the extent that other studies recommend that a true analysis of the TW hypothesis would have to test for whether maternal condition predicts offspring reproductive success and then examine the variance of reproductive success between siblings, it is slightly odd that more studies have not actually done this; that is to say, on species where reproductive success can be tracked. To test for sex of offspring alone, in the absence of the predicted covariates, may actually omit parts of the theory. Ultimately, there is something inherently poetic in the original theory of Trivers and Willard. That is, the idea that maternal effects are retained from development into adulthood is reminiscent of a comment by the poet Rainer Maria Rilke: “Perhaps we are our childhood still, for as St. Augustine said, ‘Whither should it have gone?” Yet, at the end of the day, the specific relevance of the Trivers and Willard hypothesis to humans may be, after all, just another storm in a teacup and better relegated to species that satisfy most, if not all, of the assumptions laid out in the original paper. 85 ACKNOWLEDGEMENTS Our appreciation to MEASURE DHS+ for their assistance during this project and to Dr. Lisa Smith for access to data drawn from the demographic and health surveys of thirty-five countries. The original survey data referenced in this article can be obtained through www.measuredhs.com. LITERATURE CITED ALEXANDER, R. D. 1988. 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Applied Animal Behaviour Science 51:293-306. SONS OR DAUGHTERS ! GUGGENHEIM ET AL. WEBSTER, G. D. 2004. Risk, reproductive variance, and the Trivers-Willard effect: A non-linear approach. Paper presented at the annual conference of the Human Behavior and Evolution Society, Berlin, Germany. WILEY, D. N., AND P. J. CLAPHAM. 1993. Does maternal condition affect the sex ratio of offspring in humpback whales? Animal Behaviour 46:321-324. SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 88 Appendi x Tabl e 1. Final sam ple size by region and count ry. Year of collection South Asia Sub- Saharan Africa Latin America & Caribbean N ear East & N orth Africa Unweighted Bangladesh 1997 3,730 India 1998 21,839 N epal 1996 3,246 Weighted (by sample weight) 3,505 21,487 3,292 Total = 28,815 Total = 28,284 Benin 1996 2,037 2,037 Burkina Faso 1993 2,887 1 ,8 3 1 Cameroon 1998 1,411 1,411 Central African Republic 1995 1,967 1,967 Chad 1996 3,789 3,789 Comoros 1996 732 732 Cote d'Ivoire 1994 3,025 3,025 Ghana 1998 1,467 1 ,3 5 6 K enya 1998 2,474 2,386 Madagascar 1997 2,510 2,431 Malawi 1992 2,230 1,953 Mali 1996 3,933 3,619 Mozambique 1997 2,539 2,218 N amibia 1992 1,750 1,543 N iger 1998 3,443 3,762 Senegal 1997 2,615 2,615 Tanzania 1996 3,518 3,820 Togo 1998 3,076 3,249 Uganda 1995 3,290 3,079 Zambia 1996 3,834 3,827 Zimbabwe 1994 1,860 1,997 Total = 54,387 Total = 52,647 Bolivia 1998 3,073 2,874 Brazil 1996 3,034 2,873 Columbia 1995 3,368 3,517 Dominican Republic 1996 2,211 1,890 Guatemala 1995 5,361 5,471 Haiti 1995 1,805 1,805 N icaragua 1998 4,728 5,137 Peru 1996 10,741 9,960 Total = 34,321 Total = 33,527 Egypt 1995 5,049 4,371 Morocco 1992 3,116 3,116 Turkey 1993 2,351 2,426 Total = 10,516 Total = 9,913 SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 89 Appendi x Tabl e 2. List of v ariables used in scales. Scale name & code Maternal Socioeconomic Resources (MSR) Description of variables & coding scheme * Whether woman lives in urban or rural residence rural=0, urban=1 * Household economic status destitute=0, poor=1, middle=2, rich=3 * Woman’s years of education Male partner’s educational value * measured in years if partner present, otherwise equals 0 if no male partner present or if male partner has 0 years of education Maternal Biological Condition (MBC) * Woman’s body mass index (BMI) weight in kg/square of height in meters * Whether woman is malnourished, healthy, or overweigth malnourished=0, healthy=1, overweight=2 * Duration of current pregnancy (if pregnant) not pregnant=0, otherwise recorded as months (max=10) Whether woman is currently breast- feeding * not breast- feeding=0, currently breast- feeding=1 note: reverse- coded for predicted negative effect Prenatal Care for Lastborn Child (PCL) Whether woman received prenatal care & type of care did not receive prenatal care=0, received prenatal care but not * from medically trained person=1, received prenatal care from medically trained person=2 * N umber of prenatal care visits no visits=0, otherwise equals number of visits recorded Whether delivery was assisted & type of assistance * delivery was not assisted=0, delivery was assisted=1, delivery was assisted by medically trained person2 * Health- seeking for Lastborn Child (HSL) Whether delivery took place at a medical facility delivery not at medical facility=0, delivery at medical facility=1 Child’s diarrhea in last 2 weeks * child had diarrhea and was not treated=0, no diarrhea=1, had diarrhea and was treated=2 * Whether child received BCG vaccination no=0, yes=1 * Whether child received measles vaccination no=0, yes=1 * Total number of DPT vaccinations ranges from none=0 to max=3 * Total number of polio vaccinations ranges from none=0 to max=3 * Percent of age- recommended vaccinations child received ranges from 0 to 100 SONS OR DAUGHTERS ! GUGGENHEIM ET AL. 90 A ppendi x Tabl e 3. Sex rat ios by region and count ry. South Asia Sub- Saharan Africa Latin America & C aribbean N ear East & N orth Africa N ational est. sex ratio (at birth) C urrent sample (lastborn child <5 yrs) Bangladesh 1 . 06 1.04 India 1 . 05 1.12 N epal* 1.05 1.07 Benin 1 . 03 1.02 Burkina Faso 1 . 03 1.03 C ameroon 1 . 03 1.04 C entral African Republic 1 . 03 1.02 C had 1 . 04 0.99 C omoros 1 . 03 1.11 C ote d'Ivoire 1 . 03 1.02 Ghana 1.03 0.99 K enya 1.03 0.99 Madagascar 1.03 1.03 Malawi 1.03 0.99 Mali 1.03 0.95 Mozambique 1.03 0.97 N amibia 1.03 0.99 N iger 1.03 1.09 Senegal 1.03 0.95 Tanzania 1 . 03 1 . 03 Togo 1 . 03 0.99 Uganda 1.03 0.93 Zambia 1 . 03 0.97 Zimbabwe 1 . 03 0.97 Bolivia 1 . 05 1.02 Brazil 1 . 05 1.00 C olumbia 1 . 03 1.05 Dominican Republic 1.05 1.05 Guatemala 1.05 1.02 Haiti 1.05 1.07 N icaragua 1.05 0.98 Peru 1.05 1 . 03 Egypt 1 . 05 1.11 Morocco 1.05 1.11 Turkey 1 . 05 1.14 * Indicates the only country where female infant mortality exceeds male infant mortality (72.27 deaths/ 1,000 live births to 68.95 deaths/1,000 live births). N ote: Information for sex ratios based on 2003 estimates posted at C IA website for "Worldbook of Facts." SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI 91 SEXUAL RISK BEHAVIOR AMONG KENYAN UNIVERSITY STUDENTS M ARY B. A DAM , University of Arizona Departments of Pediatrics & Psychology, Tucson, Arizona 85721 M IKE M UTUNGI , I Choose Life – Africa, P.O. Box 5166, Nairobi 00100, Kenya ABSTRACT Previous HIV/AIDS assessments in Kenya have focused on the sexual risk behaviors of the general population and the HIV serostatus of women of childbearing age. No data are available for Kenyan university students. Baseline surveillance data were obtained from a representative sample of 1917 university students at Moi University in Eldoret, Kenya. Both qualitative (focus group discussions) and quantitative (self-administered questionnaire) data were collected. Students were asked about their HIV knowledge, perceptions, and sexual risk behaviors. Seventy-one % of males and 47.6% of females reported having had sex. Only 49% of university students reported any HIV/AIDS education. Of those who reported having ever had sex, 76% reported ever using a condom: only 18% of males and 14% of females reported using a condom every time they had sex in the last month. Eighty-nine% of students reported thinking they were at risk for HIV infection, but only 28% of subjects had been tested for HIV. Qualitative data suggest the issue of HIV testing remains very controversial among students, in large part because of societal stigma. The results of this study emphasize the vulnerability of university students to HIV infection. Most university students have not had access to accurate HIV/AIDS information. Sexual activity on campus is high and many students consider themselves at risk. Conversely, consistent condom use and rates of voluntary counseling and testing are low. INTRODUCTION Sub-Saharan Africa contains only 10% of the world's population but accounts for more than two thirds of the worlds HIV infected people (DeCock et al. 2002). Of the more than 25 million people who have died from AIDS worldwide, more than 14 million are from Africa. Transmission of HIV in Kenya and all of sub Saharan Africa is primarily heterosexual (Hayes and Weiss 2006). Tracking the epidemic has been important for program and policy development (Mertens and LowBeer 1996, Hayes and Weiss 2006). Monitoring HIV prevalence and sexual behaviors has grown from sentinel surveillance toward representative household surveys (Rugg, et al. 2004, Gouws et al. 2006, Garcia-Calleja et al. 2006). The World Health Organization used sentinel surveillance to estimate that HIV seroprevalence rates for Kenya ranged from 4.7%9.6%, with HIV prevalence in pregnant women in some cities as high as 30% (World Health Organization 2004). The use of household surveys has made it possible to more closely link HIV prevalence to specific risk behaviors. A 2002 Kenyan population based survey of persons age 15-49 from randomly selected households in Mombasa reports an overall HIV seroprevalence of 10.8%. Eighty-eight% of men and 83% of women reported they had ever had sex (Hawken et al. 2002). HIV-1 prevalence in the 20-24 age groups was 1.2% for men and 15.6% for women. This rises dramatically in the 25-29 age groups where rates are 8.4% for men and 20.7% for women. Forty five percent of men and 22% of women who were sexually experienced reported ever using a con- dom. Men aged 20-24 reported the highest rate of ever using a condom at 59%. However, consistent condom use was substantially lower. Only 0.2% of men ages 1549 reported consistent condom use with their regular partner. Condom use rates increased to 10% with steady partners and to 36% with casual partners (Hawken et al., 2002). Low rates of consistent condom are also found in many other countries (Hearst and Chen 2004). These data, while informative for the general population, have limited usefulness in assessing the impact of interventions for specifically targeted sub-populations (Rehle et al. 2004, Peersman and Rugg 2004). Data from university students in other countries are available but may not be sufficiently sensitive to local contextual and cultural factors to serve as a baseline to evaluate Kenyan interventions (Terry et al. 2006, Baggaley et al. 1997, Uwalaka and Matsuo 2002). Since university students represent the future business, educational, and government leaders they are an important target group for HIV interventions. The potential to multiply the impact of an effective intervention in university students is high because will they will graduate and move into all regions of the country. In response to the needs for HIV prevention in this strategically important target group, ICL began providing HIV prevention services for University students in 2003. ICL uses a theoretical framework to develop interventions with the goal of training students to (1) have accurate knowledge about HIV/AIDS, (2) implement strategies to personally reduce or eliminate their risk of HIV/AIDS acquisition, (3) implement interventions among their peers to reduce or eliminate an individuals' risk of HIV/AIDS acquisition, (4) strategically influence organizations and institutions to implement ADAM, M. B., AND M. MUTUNGI. 2007. SEXUAL RISK BEHAVIOR AMONG KENYAN UNIVERSITY STUDENTS. JOURNAL OF THE ARIZONA-NEVADA ACADEMY OF SCIENCE 39(2)91-98 SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI policies which reinforce sexual health and reduce sexual violence, and (5) organize events to promote voluntary testing and counseling and testing (VCT). The objectives of the quantitative and qualitative survey were to (1) examine current levels of knowledge of HIV/AIDS, (2) assess the perceptions of university students toward HIV testing and people living with HIV/AIDS, (3) assess risky sexual behaviors among university students, (4) examine experience with HIV/AIDS education especially as it relates to VCT, and (5) identify strategic areas for future intervention. 92 Tabl e 1. Dem ographics. Sample Characteristics Gender Age Religious Affiliation METHODS Procedure Moi University students from the Main and Chepkoilel campuses, in Eldoret, completed a confidential, anonymous questionnaire regarding their HIV knowledge, perceptions and sexual risk behaviors. The questionnaire is included in the Appendix. Almost all students live in dormitories. Since dormitories are grouped by gender, year, and field of study, recruitment procedures utilized this grouping. Dormitories were selected to ensure a representative sample. Trained study personnel collected data over a 5-day period. Data were recorded on standard forms and then entered into SPSS 11.5. Data were entered using the SPSS 11.5. Trained facilitators conducted eight focus groups that were either all male or all female and were composed of seven to ten persons. Participants were identified by number rather than by name to ensure confidentiality. Sessions were conducted in English, lasted 1.5 hours, and were recorded. Transcriptions of the sessions were reviewed and primary themes were extracted and paired with illustrative quotations from students. The study was approved by the Moi University research council. Participation was voluntary. Informed consent was obtained by all participants. The survey was publicly supported by the University administration. Since there was strong administration support almost none of those students invited to participate refused (estimated fewer than 5%). Major N Males 945 49.3 Females 972 50.7 Less than 20 22 2 11.6 21 - 22 994 51.9 23- 24 552 28 . 8 O ver 25 149 7. 8 Christian 1 8 28 94.2 Muslim 75 5.2 O ther 14 0. 4 Science & Engineering 693 36.2 Education 511 26.7 Arts 331 17.3 Medicine 210 11.0 78 4.1 Law O ther Year of Study 93 4.7 First year 586 30.6 Second year 456 23 . 8 Third year 46 9 24.5 Fourth year 400 20.9 6 0.2 1752 91.4 Fifth year Marital Status Single Married 92 4. 8 O ther 73 3.8 years. Males reported earlier sexual debut than females; with 26% of males and 10% of females reporting sexual debut in secondary school (Figure 1). Thirty-seven percent of first year females reported previous sexual experience compared with 63% of males. For both genders rates of sexual activity varied with their year at the university and the highest rate of RESULTS Quantitative Results Of the 1,917 students surveyed, 51% were female, 52% were age 21-22, and 31% were first year students. Almost all (94%) reported Christian religious affiliation, and 91% reported being single (Table 1). Seventy one percent of males and 47.6% of females reported having had sexual intercourse. Thirty percent of students reported their first sexual experience during secondary school, 26% during the years between secondary school and joining the university (typically two years), and 19% during their university % Figure 1. Gender and age at first sex. SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI 93 sexual activity in the last 12 months was for second year students (Table 2). Of those who reported having ever had sex, 76% reported ever using a condom. Eighteen percent of males and 14% of females reported using a condom every time they had sex in the last month, indicating that consistent condom use is uncommon (Figure 2). Tabl e 2. Sex ual act iv it y in t he last 12 mont hs by gender and year of st udy. Year Male (%) Female (%) First 62.9 37.3 Second 67.2 51 . 0 Third 78 . 6 55.2 Forth 75.3 5 2. 4 HIV/AIDS Knowledge Fewer than half of University students reported previous HIV/AIDS training. Of those who had received previous training, 77.1% reported training on HIV transmission, 69.1% reported training on effects of HIV, but only 28.8% reported receiving information on treatment of HIV. Many students reported significant knowledge of someone who had died of AIDS. Over half knew of a neighbor who had died of AIDS and nearly one third had a family member who had died of AIDS. HIV Risk Perception and Testing Eighty-nine percent of students reported personally believing they were at risk for HIV infection; with 38% thinking their risk for HIV infection was high or moderate. Students were asked, "Which of the follow- ing are ways that you personally feel you could become infected with HIV?" More than three-fourths reported they could become infected through intercourse without a condom, unsterilized instruments in dental work, and sharing of needles in piercing or tattooing. Nearly two thirds believed they were at risk from deep mouth kissing and about one third from sexual intercourse with a condom (Table 3). Behaviors that put one at risk for HV include sexual intercourse with an infected person, contact with HIV contaminated medical or dental instruments due to improper sterilization technique, and IV drug use with HIV contaminated needles. Tabl e 3 . Personal belief s on suscept ibilit y t o inf ect ion. Ways you feel you might become infected with HIV % Sexual intercourse without a condom 88 Unsterilized instruments in dental work 86 Sharing of needles in piercing or tattooing 76 Deep mouth kissing 59 Sexual intercourse with a condom 37 Sharing a meal with an infected person 6 Only 28.2% of subjects reported having been tested for HIV. Of those who had been tested, 67.7% had been tested at VCT centers, 21.1% at hospitals, 8.4% in private clinics, and 2.9% used self-test kits. Of those tested, 2.6% did not return for their results. Having been tested for HIV correlated somewhat with knowing someone who died of AIDS (r=0.24, p<.001). Having been tested for HIV correlated more highly (r= 0.45, p<.001) with recommending abstinence to a friend than with recommending condom use to a friend (r=0.18, p<.001). Qualitative Results Figure 2. Frequency of condom use in last month The qualitative data provide information about the context in which sexual decision-making occurs. Specific quotes from students are used to highlight prominent themes, such as condom use, relational context of sexual decisions, and concerns about HIV testing. Campus relationships are viewed as transient as opposed to marriage relationships. That observation has important implications for sexual decision-making. Also, new students were viewed as being naive. "And then the nature of relationships in campus most of them are not very long lasting. So one person may enter into one thinking it may last long then after some time or after having sex he/she is ditched." (3rd SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI year male) Coercion in the form of gift giving was a fairly prominent theme in the focus groups discussions. If you accept what they are giving you, like she said, something expensive, then straight away, there's something hidden, so you don't want to feel indebted to someone (cough), so people shy from debts, you know according to how they do something for you, you have to pay back for what they have done for you, so that's the mistake they (women) make. (2nd year female) Students also reported concern about sexual relationships between female students and male faculty, with the exchange of sex for grades, or struggles to avoid certain faculty who have a reputation for putting female students in difficult situations. It is an occurrence we have even in some courses. Some ladies have had to dodge some lecturers. You know if there is an option you can do without some other lecturers. We have heard some ladies moving away, drifting drastically from some particular lecturers who are known that after spotting a female student, she must first of all see him in the office then she can proceed with the course. (4th year male) In addition, several groups reported hearing rumors of female students who were supporting themselves at the University through prostitution. According to focus group participants, abstinence was viewed as a difficult choice, but was not perceived as "Western." Choosing abstinence was often viewed as a religious choice. In contrast, being sexually active was viewed as a type of fashion statement, the "in" thing to do. "Not only students but everybody should be told that premarital sex is not in order. I have seen it. When addressing the issue of abstinence, it's presented as if it is because of AIDS. But I think people should be told that it is not in order. It is not because of AIDS that we are told to abstain. It is in order for you to avoid premarital sex." (2nd year male) Condom use is not a straightforward issue among university students. The question students had was, "if all condoms are effective, how come some are cheaper than others?" This led to mistrust of some of the condoms on the market. A 1st year male student touched on this issue saying: But usually condoms are perceived as not usually reliable because when you find the same condom brand like Trust, there are different names and texture and you wonder if I use the one for 10 cents is it really reliable like that of 30 cents or if I use the one that I was given free of charge at the clinic (laughter) will I really be sure that I am protected or will it work? (1st year male) It also appeared that condoms from dispensers were less respected than those purchased from shops or pharmacists. One female student commented: A campus chick wouldn't hold a guy in high esteem if he uses those from the dispensers, (laughter), "he just 94 passes by one dispensary and picks — (laughter), it's true." (3rd year female) The issue of HIV testing remains very controversial among students in large part because of tremendous societal stigma. Students comment on feeling significant fear and helplessness related to HIV diagnosis. Females voice fear related to a woman's unique vulnerability. Students also express fear about lack of confidentiality for testing provided on campus. "Some people don't want to know their status. If people get to know that they are HIV positive, they have a negative attitude towards life, they think they are going to die the next minute. So they give up, that's why they don't like going to know their status that is if they doubt themselves." (1st year female) DISCUSSION These data provide interesting insight into Kenyan university students' knowledge, perceptions, and behavior. Fewer than half of university students reported any previous HIV/AIDS education. Most students (89%) reported thinking they were at risk for HIV infection, but less than a third of subjects (28%) reported having been tested for HIV. Qualitative data suggest the issue of HIV testing remains very controversial among students in large part because of tremendous societal stigma. Clearly, even for the most elite students-those admitted to university, prior HIV training had some significant gaps. Only half had previous HIV training. This demonstrates the need for HIV prevention programs at the university level as well as much earlier. Interventions with demonstrated effectiveness aimed at students in the university as well as effective interventions for primary and secondary school students would be of benefit (Wegbreit et al. 2006). More interventions for the secondary school age group have been carefully evaluated (Eke et al. 2002, Erulkar et al 2004, Jewkes et al. 2006, Klepp and Lugoe 1999, Magmami et al. 2005, Obasi et al. 2006, Stanton et al. 1998). This study highlights the importance of population specific information on risk behavior. Kenyan university students report less risk behavior than the general population. Women at the university are more likely to delay sex. Sixty-three percent of Kenyan first year female students report no sexual experience as compared to 52% of women ages 15-19 in the population based survey (Hawken et al. 2002). The qualitative results indicate that first year females represent a vulnerable population in regard to coercion and harassment. This identifies a strategic opportunity to structure interventions aimed at reducing coercion and encouraging risk avoidance and reduction in this group. Kenyan and American university students also report important similarities and differences that em- 95 phasize the value of population specific information. Kenyan university students differ from US students in a variety of ways that may influence how an intervention works. Kenyan university students are older on average than students entering college in the US because there is a two-year wait after graduation from secondary school before the admitted class is allowed to matriculate. Kenyans uniformly graduate in four years, and are much more likely to delay sexual debut. Kenyan and American university students report having been tested for HIV at about the same rate (28%), but Kenyans are at far greater risk of acquiring HIV due to the incidence and prevalence of the infection (American College Health Association 2006, World Health Organization 2004). Over three fourths of sexually active students reported some experience with using a condom. Experience with condoms is substantially higher among university students (76%) than the highest subset of the national sample, men age 20-24 (56%). However, consistent condom use was still rare. The trustworthiness of condoms was a concern identified in the qualitative data and 37.4% of students reported that having sexual intercourse with a condom could infect them. It is possible this perception is related to an accurate understanding of risk reduction methods like condoms and the role of cumulative risk for HIV infection. Correct and consistent condom use has been shown to reduce risk of HIV transmission in the range of 85% in serodiscordant couples (Davis and Weller 1999, NIAID 2001). It is also possible that this reflects a perception that only expensive name brand condoms reduce risk. The perception that the quality of the condom was related to price and place of purchase showed lack of knowledge about condoms and their ability to reduce risk for transmission. The ability of latex condoms to form a mechanical barrier does not depend on price or place of purchase. Improved knowledge of the reliability of condoms is easy to address with accurate information and is a necessary first step toward behavioral change. Over 89% of students thought they were at risk for HIV but relatively few had received VCT. Hopelessness was identified as a barrier to VCT. Interventions that promote hope by providing information about antiretroviral treatment and how to access treatment resources could be effective in increasing VCT. Studies have demonstrated that effective antiretroviral treatment can be delivered in resource poor settings (Kumarasary et al. 2005). CONCLUSION University students represent a strategic and vulnerable population, and there is a large need for effective HIV prevention interventions among university students. In our sample, over half of the students report SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI no training on HIV/AIDS prior to entering the university. Most had never been tested for HIV despite knowing they might have been exposed. The data indicate students have high levels of personal knowledge of someone who has HIV/AIDS and this knowledge could be harnessed and incorporated to promote changing risk perceptions and behavior (Macintyre et al. 2001). Programs that emphasize modes of HIV transmission should help to alleviate fear of casual contact, dispel irrational myths, and reduce societal stigma. We recommend that interventions for university students need to include the full spectrum of HIV prevention including risk avoidance (i.e. delay of sexual debut and faithfulness to one lifelong sexual partner), risk reduction (i.e. partner reduction and correct and consistent use of condoms), voluntary counseling and testing. Information about the care and support of HIV infected individuals may also help to encourage VCT by alleviating the hopelessness associated with HIV infection. ACKNOWLEDGEMENTS We wish to thank the entire I Choose Life-Africa team with special appreciation to Jackie Njagah and Juma Warria, and Dr. Amuyunzu-Nyamonogo, the Moi University administration and research team including Professors Mathentge, Kibos, Drs. Kiplagat, Mrs. Sewe and the postgraduate research assistants. 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WEGBREIT, J., S. BERTOZZI, L. M. DEMARIA, AND N. S. PADIAN. 2006. Effectiveness of HIV prevention in resource-poor settings: tailoring the intervention to the context. AIDS 20:1217-1235. WORLD HEALTH ORGANIZATION. 2004. WHO report 2004: Changing history. http://whqlibdoc.who.int/icd/hq/ 2004/9241592281_Kenya.pdf Accessed 10 Nov 2006. UWALAKA, E. AND MATSUO H. 2002. Impact of knowledge, attitude and beliefs about AIDS among college students in Nigeria: The case of the University of Nigeria, Nsukka. West Africa Review 3(2): http:/ /www.westafricareview.com Accessed 10 Nov 2006. 97 SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI APPENDIX. Moi University Survey. 1. Age: a. below 20 b. 21-22 c. 23-24 d. 25 and over 2. Gender: a. male b. female 3. Religion: a. Christian b. Muslim c. Buddhist d. Hindu e. Other 4. Year of Study: a. First b. Second c. Third d. Fourth e. Fifth 5. Field of Study: a. Art b. Education c. Medicine d. Law e. Engineering f. BcS g. Information Science h. Other 6. Marital Status: a. Single b. Married c. Divorced d. Separated e. Cohabitating f. Widowed g. Other 7a. Have you ever attended any training on HIV/AIDS? a. Yes b. No 7b. If yes above, what was the subject or subjects of the training. Circle all that apply. a. Effects of HIV/AIDS b. HIV/AIDS transmission c. Treatment of AIDS d. Counseling e. Home Based Care for HIV/AIDS f. other (specify) __________ 8. Do you think you are at risk of contracting HIV/AIDS? a. Yes b. No 9. How would you rank your chances of getting HIV infected? a. high b. moderate c. low d. no risk at all WHICH OF THE FOLLOWING ARE WAYS THAT YOU PERSONALLY FEEL YOU COULD BECOME INFECTED WITH HIV? 10. Sharing of needles in ear piercing and tattooing a. I could become infected b. I could not become infected 11. Un-sterilized instruments used in dental work a. I could become infected b. I could not become infected 12. Deep mouth kissing a. I could become infected b. I could not become infected 13. Sexual intercourse without a condom a. I could become infected b. I could not become infected 14. Sharing a meal with an infected person a. I could become infected b. I could not become infected 15. Sexual intercourse with a condom a. I could become infected b. I could not become infected TO WHAT EXTENT DO YOU AGREE WITH THE FOLLOWING STATEMENTS? 16. Without sex a relationship has no meaning. a. totally disagree b. partially agree/disagree c. totally agree 17. I can tell my partner, “No sex without a condom”. a. totally disagree b. partially agree/disagree c. totally agree 18. If all my friends and age mates are having sex, I will too. a. totally disagree b. partially agree/disagree c. totally agree 19. Using a condom shows that I care about my partner and myself. a. totally disagree b. partially agree/disagree c. totally agree 20. I cannot make right decisions about sex under the influence of alcohol/drugs. a. totally disagree b. partially agree/disagree c. totally agree 21. Condoms can’t be trusted to protect you against HIV. a. totally disagree b. partially agree/disagree c. totally agree 22. Sex should wait until marriage. a. totally disagree b. partially agree/disagree c. totally agree 23. If I suggest we use a condom my partner will suspect I have HIV. a. totally disagree b. partially agree/disagree c. totally agree 24. If a man gives a woman a gift he expects her to have sex with him in return. a. totally disagree b. partially agree/disagree c. totally agree 25. If a woman takes a gift from a man she should have sex with him in return. a. totally disagree b. partially agree/disagree c. totally agree 26. Have you ever had intercourse? a. Yes b. No IF NO PROCEED TO QUESTION 36. 27. Have you had sex in the last 12 months a. Yes b. No 28. At what level did you have sex for the first time? a. Primary b. Secondary c. Post secondary d. College/university 29. Why did you have sex for the first time? a. Forced b. Wanted to c. Cheated d.Other (specify)__________ 30. How many sexual partners have you had in the last 12 months? a. None b. One c. Two d. Three e. Four or more 31. Have you had sex in the last one month? a. Yes b. No 32. Do you currently have a sexual partner? a. Yes b. No 33. What type of sexual relationship do you have? a. Dating/Regular b. Casual c. Cohabitating d. Married e. Engaged f. Other 34. Have you ever used a condom when you had sex? a. Yes b. No 35. In the past one month how often did you use a condom when having sex? a. Every time b. Most of the time c. Some of the time d. Not at all SEXUAL RISK BEHAVIOR t ADAM AND MUTUNGI APPENDIX (CONTINUED) 36. Would you recommend the use of condoms to your friends? a. Yes b. No 37. Would you recommend to a friend that they abstain from sexual intercourse until marriage? a. Yes b. No 38. Have you ever had a Sexually Transmitted Infection? a. Yes b. No 39. Have you ever been tested for HIV/AIDS? a. Yes b. No IF NO PROCEED TO QUESTION 43. 40. If yes above, when did you undergo the last test? a. 1 month b. 3 months c. 6 months d. 12 months or more 41. Where did you undergo the test? a. Hospital b. VCT Center c. Private Clinic d. Self test kit 42. Did you find out the results of your test? a. Yes b. No 43. Have you been to a VCT Center a. Yes b. No 44. Would you be willing to go to a VCT Test at this University a. Yes b. No 45a. Do you know someone personally who has died of AIDS? a. Yes b. No 45b. How were you related to this person? a. Family member b. Friend c. University d. Other (specify) _________ TO WHAT EXTENT DO YOU AGREE WITH THE FOLLOWING STATEMENTS? 46. If a student is suffering from AIDS, they should be removed from the halls of residence. a. totally disagree b. partially agree/disagree c. totally agree 47. If I knew that a shopkeeper or food seller had the HIV virus, I would not buy food from them. a. totally disagree b. partially agree/disagree c. totally agree 48. A student, who has the HIV virus but is not sick, should be allowed to continue at the University. a. totally disagree b. partially agree/disagree c. totally agree 49. If a member of my family became infected with the HIV virus, I would want it to remain a secret. a. totally disagree b. partially agree/disagree c. totally agree 50. A student who is found HIV+ should not be supported by the university ARVs. a. totally disagree b. partially agree/disagree c. totally agree 98 BAYESIAN ANALYSIS OF SCOLIOSIS ! MENKE ET AL. 99 LIKELIHOOD-EVIDENTIAL SUPPORT AND BAYESIAN ANALYSIS ON A PROSPECTIVE COHORT OF CHILDREN AND ADOLESCENTS WITH MILD SCOLIOSIS UNDER CHIROPRACTIC MANAGEMENT J. MICHAEL MENKE, EVALUATION GROUP FOR ANALYSIS OF DATA, University of Arizona, Tucson, AZ 85721; GREGORY PLAUGHER, Private practice of chiropractic, Alameda, CA; CHRISTINA A. CARRARI, Private practice of chiropractic, Italy; ROGER R. COLEMAN, Adjunct Research Faculty, Life Chiropractic College West, Hayward, CA; and Private practice of chiropractic, Othello, WA; LUCA VANNETIELLO, Private Practice Of Medicine And Chiropractic, Nola, Italy; and TRENT R. BACHMAN, Private practice of chiropractic, Fremont, CA ABSTRACT A previous study using frequentist analytic methods on a single cohort showed no difference in forty-one patients under chiropractic management for mild or early stage scoliosis. The grantor requested a re-analysis. Plain film radiographs of 41 children and adolescents were re-measured by Risser-Ferguson and Cobb methods. Three magnitudes and three types of change were constructed to cover various notions of scoliosis change: magnitudes of 1°, 3°, or 5°, and types that alternatively included or omitted no change as a possible successful outcome (arrested progression). Improvement was assessed from using three filters across three definitions of progression: 1) curve improved or stable, 2) improved only, and 3) those that either improved or progressed. Data were then analyzed by evidential support methods and Bayesian analyses at each filter and type of progression to establish whether improvement was likely attributable to treatment or spine characteristics. Intra-class correlation for intra-examiner stability was 0.73 by Cobb method. Reliability between the new and the previous examiner was 0.59 for pre- and 0.69 for post-treatment Cobb angles. Reliability increased dramatically when end vertebrae were specified. Ratio of number improved to those progressed to was at least 2:1 for all three levels of filter: 1°, 3°, and 5°. Number of treatments or duration of care were not associated with improvement. However, the number of vertebral segments below the scoliosis curve apex – a measure of curve compression û and bone age accounted for 49% of adjusted R2 in Cobb angle changes. Initial Cobb angle as a clinical predictor was not supported. One treating chiropractor experienced a greater rate of improvement at the highest level of change (5°) in his patients. Results here could not be attributed to management, but could be from a type of scoliosis resolving spontaneously, or a subgroup of scoliosis cases that responded to chiropractic management or manipulation. INTRODUCTION This paper summarizes a re-analysis of data previously submitted to standard frequentist testing methods for significant differences between means first published in 2001 (Lantz and Chen 2001). Occasionally, the sine qua non cardinal of random selection and random assignment cannot be implemented due to financial and time constraints. Nonetheless, data is still a precious, expensive, and time-intensive asset; and in many cases quasi-experimental methodology can still reveal response to care within the limitations of measurement and collection. Field trials such as the one represented here are an enormous undertaking; often confronting limits in available subjects or the ethical dilemmas in delaying care for proper statistical control. Without a true experimental design, analysts can match statistical tools to study limitations. For example, null hypothesis significance testing (NHST) is familiar or seems to be the de facto research standard for clinical research. But NHST has several severe limitations: 1) simple significance does not measure the strength of an effect, 2) NHST test data as a match for a given hypothesis, rather than testing the hypothesis, and 3) by distilling data into point estimates considerable information is lost, leading to 4) a compromise of statistical power and increased likelihood of Type II error. ôOne size fits allö is as unlikely for data as for shoes. Furthermore, for some questions, clinical trials are only incrementally more informative than cohort or case-control studies. Or, such quasi-experimental designs may answer some questions and pose others that require a randomized clinical trial to refine care outcomes. Even the privileges and responsibilities of exploring new knowledge domains, and the expense of data acquisition, only the most sensitive instruments for the task at hand should be used. MENKE J. M., G. PLAUGHER, C. A. CARRARI. R. R. COLEMAN, L. VANNETIELLO, AND T. R. BACHMAN. LIKELIHOOD-EVIDENTIAL SUPPORT AND BAYESIAN RE-ANALYSIS ON A PROSPECTIVE COHORT OF CHILDREN AND ADOLESCENTS WITH MILD SCOLIOSIS UNDER CHIROPRACTIC MANAGEMENT. JOURNAL OF THE ARIZONA-NEVADA ACADEMY OF SCIENCE 39(2):99-111 BAYESIAN ANALYSIS OF SCOLIOSIS! MENKE ET AL. Cause and efficacious care of patients with scoliosis have been elusive (Burwell et al. 2000). This is just as true for mild curves (i.e., < 20o). The assessment and prognostic tools used to evaluate scoliosis angles and any putative consequences are not supported in welldesigned clinical trials (Dickson 1999). Despite this lack of evidence, Dickson and Weinstein (Weinstein et al. 2003) discuss the need to treat patients (i.e., bracing, surgery) with late onset (around puberty) of AIS, if it is to only address appearance concerns, since the organic complications of cardiopulmonary failure are related only to the early onset cases and in those with more severe angles > 50o. To the authors' knowledge the four-part Ste-Justine hospital “Comparative Retrospective Cohort Study of Scoliosis Patients” is the largest cohort study and includes a population-based control group (Goldberg et al. 1994a, Goldberg et al. 1994b, Mayo et al 1994, Poitras et al 1994). Some studies have defined scoliosis as a curve greater than 10o (e.g., Scoliosis Research Society). Others have used 5o as the minimum threshold (Goldberg et al. 1994a). In allopathic management, most such cases merit "cautious observation" as the primary management strategy, rather than comprehensive treatment. Curve progression is the alarming consequence of scoliosis and indicates the treatment rationale, including surgery and external bracing. Weinstein (1999) reviewed several studies where scoliosis progression was observed throughout the entire life, especially if the curve was 20o or more after skeletal maturity. They, contrary to the Ste-Justine series’ authors, concluded that the “incidence of LBP in patients with scoliosis is comparable to the incidence in the general population” and state that an increased diagnostic awareness about the topic has led to over-referring and over-screening of children. A Medline search from the period 1966 through 2003, using the key phrase “randomized controlled trial AND scoliosis,” yielded no studies in relation to younger subjects with late onset idiopathic scoliosis that evaluated Cobb angle outcomes. Howard et al. (1998), in a non-randomized study, concludes that TLSO brace is superior to others (Milwaukee and Charleston). There is a relative dearth of evidence for surgical and chiropractic treatments. Since periodic observation is the typical medical management protocol for curves under 20 degrees, it would seem reasonable to test chiropractic care (i.e., high velocity low amplitude (HVLA) adjustments, postural advice, heel lifts, etc.) approach to patients with this disorder (Lantz and Chen 2001). Lantz and Chen (2001) reported on the effect of chiropractic intervention for subjects with small scoliotic curves in younger subjects. The original authors concluded from the singlegroup analysis of 42 subjects over the course of a year that full-spine chiropractic adjustments with heel lifts, 100 and postural and lifestyle counseling, were not effective in reducing the severity of scoliotic curves. An interim preliminary analysis of some subjects from the above trial suggested that curve magnitudes were decreasing, albeit slightly (Lantz and Chen 1996). This conference report, although preliminary and based on fewer subjects, had results that contrast with the results reported in the final paper. One of us (TRB) was a member of the original study investigation team, participating as a treating chiropractor. He provided the impetus to further explore the original study’s data (i.e., plain film radiographs), and to deepen the inquiry first reported by Lantz and Chen in 2001. METHODS The principal investigator of the original study (Dr. Lantz) provided 41 complete sets of spine radiographs used to measure Cobb angle in the original published study of 42 patients. The time between the initial and comparative radiographs was approximately one year. We also had access to and reviewed subject records, progress reports, and trial protocols. Subjects were recruited from a variety of sources including local physicians' patients and health fair screenings. Primarily two different doctors provided care to the subjects; the clinicians were not randomly assigned to subjects. One approach was the diversified chiropractic technique (n=26). In the diversified technique implemented, all adjustments were high velocity and low amplitude in nature and were based on a combination of palpatory findings of movement restriction as well as intersegmental and postural alignment (full-spine A-P and sectional lateral films). Adjustments were also directed medialward at the apex of the scoliosis. Postural and exercise advice and heel lifts if a short leg was present were adjunctive to the adjustive care. The other technical approach was Gonstead technique (Plaugher 1993) (n=15). Gonstead spinal examination analyses including temperature differentials (Plaugher et al. 1991, Ebrall et al. 1994) and segmental adjusting procedures were utilized throughout the entire spine and pelvis of each subject at sites of subluxation (Simpson and Weiner 1999). Posterior to anterior full spine x-rays were analyzed using both the Cobb and Risser-Ferguson methods by a practicing doctor of chiropractic with over 27 years of clinical experience, who was blinded to subject information (e.g. subject identification, clinical status, etc.), and whether the films were pre or post intervention/time. In the Cobb method, two end-vertebrae were chosen, one at the superior aspect of the curve and the other at the inferior aspect of the curve. These two vertebrae were the ones which were most angulated (rotated on the z-axis) toward the concavity of the curve as judged by visual inspection on a standard 14 X 36-inch radio- 101 BAYESIAN ANALYSIS OF SCOLIOSIS ! MENKE ET AL. graphic light box (Plaugher and Lopes 1993, Panjabi et al. 1974). Standard lines were drawn in accordance with the Cobb method. In the Risser-Ferguson method the end-vertebrae used were the same ones that had been used in the Cobb method. In addition, a middle segment, the most laterally displaced (i.e. the vertebra at the apex of the curve) was identified. On each of these three vertebrae, diagonal lines were drawn from the opposing vertebral body corners, such that they crossed near the middle of the vertebral body. The angle formed by lines drawn from the superior and inferior bodies intersecting in the middle vertebral body, is the Risser-Ferguson angle (Rowe and Yochum 1987). Risser’s sign of each of the 41 pretreatment x-rays measured skeletal maturity of the patients, as this is a commonly used prognosticator in the trajectory of scoliosis (Lonstein and Carlson 1984). Analytic Strategy The original report (Lantz and Chen 2001) did not support effectiveness of chiropractic management of scoliosis, as tested by comparisons of pre-post treatment measures. However, the study was underpowered (1- β) = 0.46 at α = 0.05; 80 subjects were needed for 80% power) and lacked a control group and methodology to confidently conclude that no change had occurred. Potential behaviors may have been missed from using tools not sensitive enough to detect them. The main objective was to re-assess the data with scientific tools more appropriate to these research hypotheses and data. The analysis proceeded from simple description, measuring reliability, formulating new hypotheses based on observations, isolating factors and estimating predictors' variance contribution to outcomes, then testing each factor for its likelihood in contributing to outcome. Inconsistent and isolated behaviors were not accepted as plausible. Lack of a comparison control group impedes attempts to separate chiropractic management from the natural history of scoliosis. Other potential sources of error include placebo effects, radiographic positioning, and normal variance in postural differences. We assumed that these sources of variance were not systematic (biases), but were true residual (error). The objective was to assess potential contributions to knowledge and identify hypotheses to test or refine in future research. At least three relevant vectors were identified: (Lantz and Chen 2001) magnitude and direction of change, (Burwell et al. 2000) level of clinically important change, and (Dickson 1999) alternatively including no curve as successes (stabilization) and then as failures (did not respond) in analysis. Vector one is the magnitude and direction of change. Vector two was minimum acceptable clinical change as 1o, 3o or 5o called filters, designated f. Vector three had 3 levels, including no change as a good clinical outcome (filters of Improvement + No Change, fINC), improved only as a good clinical outcome (filters of Improvement Only, fIO), and bilateral (fBL for Bilateral change) movement only under all 3 three filter levels. Simple visual inspection of radiographs followed by general linear models identified associated factors. These were then tested by evidential support methods after logistic regression, and Bayesian analysis on the three magnitudes and types of success. Logistic regressions were computed with R statistical software (R Development Core Team 2004) and were applied across fIO versus fINC coded datasets. Variance contributions, likelihood ratios, and evidential support were also computed. Finally, factors were combined in hierarchical linear models to generate a prediction equation. All programs were run on Apple 867 MHz PowerBook G4 (OS 10.3.8), with Emacs text editor with ESS for "R" analysis. Natural logarithms of the likelihood ratios were computed from "R" logistic regressions (R Development Core Team 2004). Since we are dealing with logarithms of ratios, the more negative the resulting number, the higher the likelihood the factor contributes to outcomes, and the less likely the finding was an erroneous. Support numbers 0 or greater suggest no evidence; -1 is weak evidence; -2 is moderate evidence; -3 is strong evidence; and -4 is extremely strong evidence (Goodman and Royall 1988). These analyses were executed across the three definitions of improvement and three filters described above. Specific hypotheses Initial Cobb angle is an often-cited predictor of scoliosis progression, as used in the Lonstein nomogram (Lonstein and Carlson 1984). Was the initial Cobb angle predictive of outcome in this sample? What measured aspects of treatment or adjustive technique could have been effective in producing an outcome? In the course of re-measuring x-rays, an additional hypothesis emerged based on observations that more compressed scoliotic curves seemed to improve more over the course of the study. Thus, could a characteristic or characteristics of the scoliosis curve be related, or even predictive of outcome? RESULTS Table 1 summarizes descriptive statistics of the patients in this study. For α = 0.05 (2-tailed), number of subjects 41, and mean and standard deviation of the prepost difference scores of 0.56 and 5.31, respectively, statistical power (1 - β) for this study was calculated to be 0.46. The sample size needed to detect a 5 degree change, with 80% power and n= .05 should be 80 in a BAYESIAN ANALYSIS OF SCOLIOSIS! MENKE ET AL. 102 Table 1. Patient characteristics. SE=Standard Error. n=41 for all variables except bone age (n=36). Variable Age (years) Mean SE 95% CI 11.9 0.44 10.99- 12.81 Boys/Girls 26/15 Bone age 12.24 0.54 11.15- 13.33 Cobb angle at intake 1 0. 3 7 0.77 8.81- 11.94 7.71 0.70 6. 3 1 - 9. 1 3 Treatment duration 1 4. 2 9 0. 5 7 13.14- 15.44 # of visits 41.41 3.43 34.48- 48.35 3.12 0. 3 1 2.48- 4.05 Risser- Ferguson Average visits per month Reliability pre-post study. Intercorrelations of the primary measures revealed several interesting relationships (Table 2): reliability between the Cobb and Risser Ferguson (RF) methods, the relationship of the change in curve (the primary outcome measure, ∆ Cobb) with Cobb 1, age, months of treatment number of visits, rate of visits, and bone age. Note in particular the relationship of ∆ Cobb to the number of segments in the curve (named span), and the number of segments below the apex of the curve (named Apex) Patients with a greater degree of initial Cobb angle received more visits, though more visits was not associated with a greater reduction in scoliosis. Interestingly, greater chronological age was unrelated to outcome (∆ Cobb), but greater bone age correlated with curve improvement. Improvement and progression were assessed as at least 1o, 3o or 5o of change in the analysis algorithms. The correlation in change scores (pre-post) between first and second analyses was r = 0.44 (p<0.01), though both analyses concluded only 0.5o overall difference in pre to post measures. Intraclass correlation coefficients were 0.59 for pre-measures, and 0.69 post treatment measures. These low correlations may indicate differences in marking techniques such as undesignated end vertebrae in marking. Intra-rater reliability of markings in the second analysis by one of us (RRC) for initial Cobb was r = 0.81 for a randomly chosen set of 23 without end vertebrae specified. Reliability increased to over 0.91 when end vertebrae were designated. Risser Ferguson measures were 0.70 without and 0.81 with end vertebrae designation. We used the Cobb angle measures for all the analyses of outcome. Reliability of scoliosis vertebra choice (see Table 3, next page) was accomplished by converting thoracic and lumbar vertebrae to a numerical sequence from 1 to 17 (for T1 to L5), then correlating among pre- and post-treatment radiographs. Cephalic vertebrae selection correlated moderately r = 0.44 (p < 0.05, 95% CI: 0.161 to 0.654); and bottom vertebrae correlated a mere r = 0.22 (NS, 95% CI: -0.094 to 0.494). Kappa coefficients computed by intra-rater concordance analyses were virtually identical 0.44 for the cephalic and 0.21 for caudal segment selection. This suggests a major source of scoliosis measurement error could be inconsistencies in end vertebrae choice, if a rater is blinded to pretreatment and comparative radiographs. Table 2. Intercorrelations among subject variables. Cobb1 = initial Cobb angle; Cobb2 = final Cobb angle; D Cobb = change in Cobb angle; RF1 = Initial Risser Ferguson angle; Span = number of vertebral segments in the scoliosis; Apex = number of segments below the apex of scoliosis curve; Age = age of patients; Months = months under care; Visits = number of visits during care; Rate = average number of visits per month (Visits/ Months). Significant correlations are designated: * = 0.05, ** = 0.01; *** = 0.001. Cobb1 Cobb2 ∆ Cobb RF1 Span Apex Age Months Visits Rate Bone age Cobb1 Cobb2 ∆ Cobb RF1 Span Apex Age Months Visits Rate 0.56*** 0.28 0.74*** -0.07 -0.17 0.30* 0.04 0.47** 0.48*** -0.09 -0.63*** 0.50*** 0.36** 0.37** 0.13 -0.14 0.29 0.39** -0.42** 0.11 -0.49*** -0.59*** 0.13 0.21 0.10 0.00 0.42** 0.02 0.03 0.36* 0.12 0.33* 0.31* 0.01 0.87*** 0.02 0.06 -0.23 -0.22 -0.33* -0.07 -0.06 -0.26 -0.19 -0.35* 0.13 0.10 0.02 -0.07 0.02 -0.45** 0.09 0.86*** 0.17 0.11 BAYESIAN ANALYSIS OF SCOLIOSIS ! MENKE ET AL. 103 Table 3. Inter-rater and intra-rater reliability of vertebrae choice and m easured Cobb angles. Inter- rater reliability Cobb1 Sample size, n Intra- rater reliability w/o end vertebrae specified Cobb 2 Cobb 1 Intra- rater segment selection reliability Intra- rater with end vertebrae specified Cobb 2 RisserFerguson Top segment Bottom segment Cobb 1 Cobb 2 RisserFerguson 41 41 23 19 24 41 41 41 N/A 41 Pearson’s r 0.39 0.58 0.81 0.68 0.70 0.44 0.22 0.91 N/A 0.81 p value for r 0.01 0.001 0.001 0.001 0.001 0.01 N/S 0.001 N/A 0.001 ICC 0.59 0.69 0.79 0.66 0.70 0.44 0.22 0.91 N/A 0.81 0.47° 0.40° 1.31° 1.55° 0.73° 0.28 segments 0.45 segments 0.04° N/A 0.23° Mean difference Estimating clinical change The sum of initial angles was 425.5o versus a sum of 373o at the end of the one-year observation period, an overall reduction of 12.34%. Summaries of scoliosis curve characteristics are included in Table 4. The median value of the initial Cobb measurement was 10o. The change score mean was 0.55o (n=41), with a standard error of 0.83 in the current analysis. Gonstead (n=15) showed an average improvement of 1.43o, while the diversified technique (n=26) averaged 0.06. As the filter was increased, naturally the number of patients observed to change necessarily increased. A minimum 5o change on those with an initial angle of 4 degrees had 10 of 39 (26%) improve, while 9 (23%) progressed. Mean change for the second analysis was 0.56o (RRC). When the proportion of those improving versus those progressing is graphed as a function of initial angle and filter size, it is apparent that overall improving outpaced progression and monotonically increased with initial Cobb angles and filter size, by as much as 3 times (Figure 1) at higher levels of initial Cobb angle and filter size. (n=26) averaged 0.06. As the filter was increased, naturally the number of patients observed to change necessarily increased. A minimum 5o change on those with an initial angle of 4 degrees had 10 of 39 (26%) improve, while 9 (23%) progressed. Mean change for the second analysis was 0.56¦ (RRC). When the proportion of those improving versus those progressing is graphed as a function of initial angle and filter size, it is apparent that overall improving outpaced progression and monotonically increased with initial Cobb angles and filter size, by as much as 3 times (Figure 1) at higher levels of initial Cobb angle and filter size. Visual inspection of radiographs and data suggested three candidate variables that contributed to outcome variance in curve improvers versus progressors: initial Cobb angle (Cobb 1), number of infra-apex segments (Apex), span, the number of segments in the major scoliosis curve, and bone age. Both Apex and span were highly correlated and collinear û they describe the same phenomenon and were thus interchangeable in analysis. As seen below, the variable Apex consistently accounted for more variance than the span variable. The Apex variable was noticed during radiographic coding as cases more likely to improve had more compression in the scoliotic curve. Specifically, compression under the apex of the curve seemed most highly associated with or predictive of improvement. The concept of compression under the scoliotic apex is illustrated in Figure 2. In all three of the Figure 2 scenarios, Cobb angles are equal. The only differences are the apexes of the scoliosis which start at T12, then progress through L1, and L2, left to right. The ratio of patients improving to those whose curve progressed ranged from 1.5:1 to 3.5:1 for patients with at least 8? of scoliosis, with a 1o to 5o filter. Patients with 4 or fewer infra-apex segments had about 2:1 odds for improvement under a 1o filter, 2:1 ratio for a 3o filter, and 1.8:1 ratio with a 5o filter. Figures 3, 4 and 5 Table 4. Summary of Subjects’ Scoliosis Characteristics. Variable Mean, n SE 95% CI Initial Cobb angle Final Cobb angle Segments in curve Segments below apex ∆ Cobb ∆ Risser 10.38, 41 0.77 8.88-11.94 9.82, 41 0.96 7.88-11.76 7.32, 41 0.46 6.39-8.62 4.07, 41 0.24 3.58-4.56 0.55, 41 0.64, 41 0.83 0.88 -1.12-2.24 -1.14-2.43 BAYESIAN ANALYSIS OF SCOLIOSIS! MENKE ET AL. 104 Figure 2. Same 30° scoliosis with three distinct apices: T12, L1, and L2, distributing compressive forces more laterally and inferiorward. determination) was accounted for in the equation: Cobb.change = - 2*Apex + 0.32*bone age +5.1 Figure 1. The proportion (odds ratios, OR) of subjects who improved vs. those who did not (top), and those who improved or were stable as compared to those who did not (bottom). More patients improved than progressed in all cases. graphically illustrate the dominance of improvement over progression of scoliosis in this sample. In the next analysis, identified factors were used as predictors in logistic regression for estimating likelihood ratios for computation and evidential support (R Development Core Team 2004). Evidential support is the natural logarithm of the likelihood ratio (LR) of a result expected in a null hypothesis versus an alternative hypothesis of a factor having an effect in the results seen. Positive LR numbers suggest the factor did not affect clinical outcome, since result is explained by the null hypothesis for that variable (the variable had no measurable effect). Negative numbers support a factor's role in influencing outcome, since the denominator – the alternative hypothesis that the factor tested is making a contribution to the outcome – is supported as contributing to the outcome to a much greater degree than the null hypothesis. Table 5 lists each of the top four factors and their levels of variance contribution, significance, and likelihood ratio. All factors except initial Cobb angle, were strong contributors to predictability of scoliosis improvement. The greatest support was evident in the Apex and bone age factors, with the highest degree of support in all three categories of filter. Figure 6 graphically represents this finding. When the two factors, Apex and bone age were loaded into multiple regression against the change in scoliosis during the observation period, 49% of the variance (adjusted coefficient of Negative scores represent a progression, or worsening of scoliosis in this model. The above equation explains 49% of the outcome variance, or likelihood, of patients' scoliosis progressing in this study. The Apex factor, a measure of inferior Cobb angle compression is weighted most heavily (times a factor of -2) and added to bone age as assessed by wrist x-ray (times 0.32). These numbers are added to 5.1o to give an estimate of direction and degree of mild scoliosis change over the course of a year. This change cannot be confidently attributed to treatment or natural history, because of the lack of a control group. In brief, lower Apex scores (number of segments under the curve apex) predict the scoliosis will improve. When Apex exceeds 3, the overall equation becomes positive, indicating a progression of scoliosis. Bayesian analysis Bayesian analysis estimates probabilities of a clinical event prior to and after treatment û after we look at the information provided by the new study. Significance testing is unnecessary, since the clinicians may interpret these probabilities and choose treatments according to perceived clinical utility. Further, the Bayesian analysis has intuitive appeal in that these types of probabilities estimate chances the alternative hypothesis is true for given data, or P(H|D); whereas null hypothesis significance testing compares the likelihood of data given the hypothesis, or P(D|H). A final crucial point is that Bayesian statistical analysis builds upon earlier research in that results in earlier research (posterior probabilities) are the new prior probabilities in later research, leading to a refining of hypotheses, increasing predictability and clinical confidence. As there are no clinical trials on the treatment and management of mild scoliosis, there were no data to inform prior probabilities. There are thus two prior BAYESIAN ANALYSIS OF SCOLIOSIS ! MENKE ET AL. 105 Figure 3. Graphic representation of scoliosis curve changes, including improvement or progression and no change as observed through 1o, 3o, and 5o levels. of change. probabilities: a calculated naive prior probability and a prior probability of, equipoise, or neutral expectation of 50% chance of improvement or progression. Since the ratio of those who improved to those that progressed was at least 2:1 with each filter and with or without the inclusion of the no-changers, the variance for overall improvement had to be partitioned from the contributing factors. The contribution of the Apex variable contribution was within an overall trend to- Figure 4. Raw counts of patients who progressed and those who improved by categories of initial Cobb angles and observed minimum degree of improvement. wards improvement, and its unique contribution had to be separated from this overall trend. This was accomplished by the Bayesian analysis. Appendix A details the results of the Bayesian analysis and number needed to treat (NNT) analyses for filters 1o, 3o, and 5o on the fINC-coded data that considered ôstabilizedö scoliosis as a clinical success. The fIO and fBL sets could not be included because they had empty cells at filter 5o, which would erroneously inflate Table 5. Summary of evidential support analysis by variables derived from log likelihood ratios. As LR approaches 0, the corresponding log approaches infinity. Any number greater than zero indicates no support for an alternative hypothesis that the factor affected outcome. Tested Deviance Factor Initial Cobb angle Likelihood ratio, LR Probability Level of support, loge LR Improve Only Improve + N/C Filter1 Filter3 Filter5 Improve or Progress Filter1 Filter3 Filter5 Filter1 Filter3 Filter5 2.13 0.14 -0.76 2.82 0.1 -1.04 0.63 0.43 0.46 3.39 0.07 -1.22 4.08 0.04 -1.41 0.01 0.93 >> 01 0.32 0.57 1.14 1.45 0.23 -0.37 0.97 0.32 0.03 6.16 0.01 -1.82 5.1 0.02 -1.63 4.58 0.03 -1.52 7.19 0.01 -1.97 9.5 0.002 -2.25 4.016 0.05 -1.39 7.13 16.1 15.67 0.01 0.00001 0.00001 -1.96 -2.78 -2.75 8.49 0.004 -2.14 11.77 0.001 -2.47 6.9 0.01 -1.93 10.8 13.55 0.001 0.0002 -2.38 -2.61 8.08 0.004 -2.09 9.17 0.002 -2.22 17.32 0.0001 -2.85 18.11 0.0001 -2.90 2.8 0.09 -1.03 1.28 0.26 -0.25 0.02 0.89 >>01 6.12 0.01 -1.81 10.85 0.001 -2.38 1.56 0.21 -0.44 5.56 0.02 -1.72 7.33 0.007 -1.99 Span of primary scoliosis Likelihood ratio, LR Probability Level of support, loge LR Segments below curve apex Likelihood ratio, LR Probability Level of support, loge LR Bone age Likelihood ratio, LR Probability Level of support, loge LR 8.58 0.003 -2.15 BAYESIAN ANALYSIS OF SCOLIOSIS! MENKE ET AL. Figure 5. Number of patients exhibiting no change as a classification of initial Cobb angle and size of measurement filter. probability estimates. The fIO and fBL data supported Apex as a factor in filters 1o, 3o, or 5o in logistic regression analysis and log likelihood ratios (evidential support estimates). For fINC, the number of Apex segments three or fewer improved posterior probabilities from 0.10 (at filter 1o) to 0.19 (at filter 3o) over the naive prior probabilities; and 0.26 to 0.39 over the equipoise prior probabilities. For fIO filters 1o and 3o, posterior probabilities were increased by 0.04 and 0.18 respectively over computed priors and 0.19 and 0.16 over equipoise (50-50) prior probabilities. In summary, physician effects were null when combined, but closer inspection showed differential contributions at higher filter levels. 106 Primary treatment attributes were the two chiropractic techniques. Ancillary treatments such as heel lifts were used, but were not systematically implemented nor was patient adherence recorded. In aggregate, an average of 0.5o change was observed in the group. A subgroup improved and another progressed. Overall, twice as many improved as progressed at all filters. The improving subgroup had three or fewer segments in the subapical area in the scoliosis curve variable (Apex = 3). The contribution of each chiropractor cannot be separated from his technique by partitioning variance components, since care is nested within the chiropractor. Logistic regression and likelihood ratios did not support an overall association by treatment or clinician (Appendix A), but Bayesian analysis on the fINC data (the fIO and fBL had empty cells) revealed an underlying complexity between treaters (or technique). The chiropractic physician posterior probability (after observing data changes during study) for clinical outcome increased by 0.03, 0.10, and 0.13 for filters 1o, 3o, and 5o over the calculated nanve prior probabilities; and 0.18, 0.24, and 0.40 in an equipoise state. For the fINC set, one chiropractor (Gonstead technique) experienceda higher level of clinical success at filter 5o with 14:1 ratio of improvement (for n=15). The other clinician experienced a ratio of patient improvement at 18:7 at filter 5o. If technique, and not personal style of the chiropractor, or a unique subset of patients, were responsible for the difference, then a 14 times more improvers for Gonstead versus 2.57 times for the diversified technique would be remarkable. However, this question remains for future research to investigate. If a chiropractic or medical doctor is faced with recommending care or not in a young adolescent with a mild scoliosis, then this study may provide some Figure 6. Evidential support by change filter and each source of deviance from the null hypothesis 107 BAYESIAN ANALYSIS OF SCOLIOSIS ! MENKE ET AL. preliminary guidance. Doing nothing at all (cautious observation) could result in a 50/50 chance of the curve progressing. On the other hand, if diversified or Gonstead care is provided, then the odds are much greater (18:7 to 14:1) that the patient will experience an improvement in the scoliosis. Prospective and controlled studies are needed to further test this question. Number needed to treat The calculation of number needed to treat, NNT, is the reciprocal of posterior probabilities of clinical failure subtracted from success: 1/(improvement – not improved). NNT indicates how many patients must be treated to obtain one clinical success of improvement or "stabilization." NNT's ranged from 1.6 to 1.2 for naive priors and 1.9 to 1.3 for prior probabilities under the equipoise assumption for filters 1o, 3o, and 5o. For every 1 to 2 people seen with mild scoliosis, 1 improved. This finding was associated with Apex rather than treatment characteristics, since treatment variance components were not associated with outcome. DISCUSSION Recruitment of sufficient numbers of qualified patients is one of the most challenging aspects in clinical and field research. Under frequentist analyses, underpowered studies become a limiting factor, and missing responses to interventions increasingly likely. If statistical significance is achieved, results are suspect when sample sizes are inadequate. Fortunately, null hypothesis significance testing is not the only tool in the clinical researcher's toolbox. For a largely ill-defined domain such as scoliosis with lots of unproven treatments, other measures such as pain, quality of life, disability, satisfaction, and associated costs may point to other reasons to seek chiropractic management than just curve reduction. Also, other measures allow critical multiplism methods to assess change from various independent perspectives (Houts, Cook, and Shadish 1986). Here though, is verisimilitude to the modern chiropractic or medical practice, caring for a patient with scoliosis, where thecurve is the primary concern, and the ultimate objective is to at least not observe progression. So this studyrepresents clinical fidelity in concerns and outcomes of scoliosis. Including patients who did not change over the course of observation or treatment in with the clinical success group, at least twice as many improved as progressed. At higher filters of 5o , this ratio approached 3 to 1. Omitting the clinically indeterminate values in the middle does naturally increase the distance between outlying group means. But that expected difference was not tested here; the observation that twice as many improved at each level of filter. Analyses were done to identify which patient factors could discriminate improvers from progressors, measure their impact on outcome, and finally calculatetheir support as opposed to a null hypothesis of no effect. We identified factors consistent in contribution across the three vectors, and with moderate to strong evidential support in clinical contribution: bone age, a natural progression; and infra-apex segment count, which was associated strongly with outcome, but less so with time or treatment. Initial Cobb angle, a commonly used predictor in the prognosis of scoliosis was not supported. Initial span of scoliosis segments, correlated with outcome, but not with initial Cobb angle, and negatively with bone age. Span correlated with Apex, which in turn correlated more highly than span to the curve change. As span and Apex were collinear, both could not serve as regression predictors. Likelihood ratios and evidential support calculations favored Apex over Span, so Apex was chosen for regression and Bayesian analysis. The role of bone age as an outcome predictor was more complex and interesting. Initial bone age correlated with the change in Cobb angle at r = 0.42 (p < 0.01), about 15% of the outcome variance. That physiologically older kids had better outcomes is likely a snapshot of the later course of scoliosis which is consistent with younger children being more at risk for progression. Bone age was the second hierarchical predictor for the scoliosis in this study, though its contribution was not as consistent across analyses as Apex. Again, the equation: Cobb.change = 5.1 - 2*Apex + 0.32*bone age models the progression of scoliosis under the few parameters collected here. We expect further testing and refining in future studies. Apex and bone age predictors may only have been unique to this small sample with mild scoliosis, but only future research will tell. Attempts at critical multiplism were thwarted due to the limited number and kind of dependent measures originally collected. But even with the conservative analyses and inferences performed here, this sample of 41 patients with mild scoliosis could provide directions for future research. The objectives of equation modeling here are to build useful empirical tools for the practicing clinician. Science can and should inform better clinical decision-making, rather than simply reject hypotheses of no difference, which adds little to patient knowledge and management. The greatest changes were among those with over 10o in initial Cobb angle. This pattern may echo regression to the mean, though in the scoliosis literature greater angles are at higher risk for progression. More patients improved than progressed, but this too may be the natural history of mild AIS, which is unknown. Predicting regression to the mean is just as valuable as BAYESIAN ANALYSIS OF SCOLIOSIS! MENKE ET AL. predicting response to a treatment. If most kids with AIS regress to the mean, then clinicians should be apprised of this as yet another description of natural history. Many clinicians however think that AIS should be followed with at least one comparative radiograph due to a perceived risk for progression. These findings are suggestive enough to warrant future hypothesis testing. Is no change in scoliosis curvature a positive outcome? Despite many different studies over the past two decades (Montgomery and Willner 1988, Pecina et al. 1992, Bunnell 1988, Brooks et al. 1988, Rogala et al. 1978) that have looked at the natural history of lateonset scoliosis no summary conclusions can be made. The empirically chosen predictive factors (Apex and bone age) held up in both datasets –with both no change as a successful outcome and no change as an unsuccessful outcome. In the past a variety of different criteria have been used to assess the course of scoliosis, including the definition of scoliosis change (e.g. > 5 degrees or > ten degrees), and inclusion criteria of patients in treatment and discrepancies in follow-up (Soucacos et al. 1998). A characteristic of curve compression appears to be a better clinical prognosticator than bone age in the clinical trajectory of mild scoliosis. Those with three or fewer infra-apex segments improved twice as often as those with more than 4 segments. Apex and bone age accounted for 49% of the adjusted variance, an impressive value on the face of it, but interpreted cautiously for the given study constraints. However, the value of Apex as an outcome predictor, meditated by treatment or time was supported consistently via logistic regression, likelihood ratios, evidential support analysis, and Bayesian analysis. And though recorded treatment number, frequency, or duration did not contribute as a "main effect" to clinical outcome, a slight decrease in uncertainty contributed by the difference between the clinicians does not allow us to rule out care as contributing to outcome. CONCLUSION End vertebrae must be specified to reduce measurement error and to allow for a shared method to measure change of scoliosis. All patients in this studyimproved at a ratio of 2:1 in all three filter or observations levels and across improvement only (fIO) and improvement plus no change (fINC) analyses. Degree and direction of improvement was best predicted by number of infra-apex segments (a measure of curve compression), and bone age. Patients with three or fewer infra-apex segments had approximately 2:1 odds for improvement over one year, regardless of initial curve angle. Logistic regression likelihood ratio and Bayesian analysis supported a predictive role for Apex, and to lesser extents bone age and span of the 108 scoliotic curve in number of segments; but initial Cobb angle had no apparent contribution to results. The regression equation predicting change from Apex should be tested and refined in future scoliosis research. Other indicators of health should be recorded in future studies to fully assess the impact of conservative management on more signs and symptoms of scoliosis, including quality of life and pain. Probabilistic models can serve to reduce clinical uncertainty. To the extent that attributes of a patient's presentation can help improve clinical decisions, improve prognosis, and reduce costs, is a promising direction for health care. Calculating odds for improvementunder a certain management or treatment can be enormously informative and helpful for patient management and public policy. Attribution and attachment to a single cause or cure can lead a patient lead into excessive and expensive treatment or excessively delayed proper treatment. Though single-cause determinism is attractive, it is oversimplified and unpredictable. The most important aspect of treatment is properly identifying the problem. Only then may treatment commence. Since potentially valuable information was obscured in this study by the design and conventional frequentist methods, we suggest that all future studies carefully consider nomothetic estimation rather than automatically adopt frequentist null hypothesis significance testing. Models of health and disease are stochastic, not deterministic. Odds for recovery are increased under certain circumstances, and reduced under others. No one cause leads to one specific effect. Given the state of today's health care system and population health, one obvious place to decrease risks, costs, and side effects is in improved predictability. Informed consent procedures should give patients odds for success in addition to risks and side effects for any given procedure and management protocol. The aim of clinical science is to enhance individual predictability in patients. We believe that the non-frequentist methods used herein uncovered information overlooked by the typical null hypothesis significance testing. Whether these findings are ultimately of use in improving doctor prognostications remains for future research to support or refute. To this end, we support and recommend Bayesian and evidential support methodology. LITERATURE CITED BROOKS H. L., S. P. AZEN, E. GERBERG, R. BROOKS, AND L. CHAN. 1975. Scoliosis: A prospective epidemiological study. Journal of Bone and Joint Surgery 57A:968-972. BUNNELL W. P. 1988. The natural history of idiopathic scoliosis. Clinical Orthopedics 229:20-25. BURWELL R. G., P. H. DANGERFIELD, T. G. LOWE, AND J. Y. MARGULIES. 2000. 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