Variation among populations of the sailfin molly in the rate of concurrent multiple paternity and its implications for mating-system evolution

Behav Ecol Sociobiol (1997) 40: 297±305 Ó Springer-Verlag 1997 Joel C. Trexler á Joseph Travis á Andrea Dinep Variation among populations of the sail®n molly in the rate of concurrent multiple paternity and its implications for mating-system evolution Received: 6 May 1996 / Accepted in revised form: 5 December 1996 Abstract We examined patterns of concurrent multiple mating in a live-bearing poeciliid ®sh, the sail®n molly (Poecilia latipinna). We tested whether the probability of multiple paternity was related to female body size or fertility and whether the rate of multiple paternity varied among four populations that di€ered in their distributions of female body size and fertility. We analyzed data on mother and o€spring genotypes for three polymorphic allozymes by three techniques, including a maximum-likelihood estimator that accounts for sampling error in both parental and o€spring allele frequencies. The estimated rate of multiple paternity varied between 0.09 and 0.85, and the rate in one population varied seasonally between 0.33 (spring) and 0.85 (autumn). The variation in these rates was not associated with variation in body-size distributions among populations but was closely associated with variation in size-speci®c fertility: populations with greater variation in female fertility had higher multiple-paternity rates. Within two populations, logistic regression revealed that individual females of larger body size and greater size-speci®c fertility were more likely to carry multiply sired broods. This result is consistent with observations made in one of the populations 5 years earlier. In general, the results strongly suggest that the mating system varies markedly among conspeci®c populations of sail®n mollies and that larger, more fertile females are the objects of intermale competition. Key words Poecilia latipinna á Mating system á Multiple paternity á Fertility á Allozymes Joel C. Trexler (&) Department of Biological Science, Florida International University, Miami, FL 33199, USA Fax: 305-348-1986; e-mail: trexlerj@servax.®u.edu Joseph Travis Department of Biological Science, Florida State University, Tallahassee, FL 32306-2043, USA Andrea Dinep P.O. Box 1347, Mississippi State, MS 39762-1347, USA Introduction High rates of concurrent multiple paternity, multiple siring of o€spring within a single brood, have become a routine expectation in studies of natural populations (Travis et al. 1990). With the development of sensitive genetic markers, these observations have been extended to social systems once thought highly monogamous (e.g., Yezerinac et al. 1995) or strongly polygynous without polygamy (e.g., Westneat 1993; Weatherhead and Boag 1995). Such extensions have provoked reexaminations of these mating systems and, in some cases, led to revisions in the prevailing hypotheses for their evolution (Weatherhead and Boag 1995). The converse is now also true; the discovery of low rates of concurrent multiple paternity is deemed noteworthy and provokes reexamination of what were once thought to be polygamous mating systems (e.g., Poldmaa et al. 1995). Speci®c cases of low rates have been attributed to speci®c characteristics of mating systems such as mate guarding by males (Ritchison et al. 1994; Freeland et al. 1995), low movement rates of males (Hasselquist et al. 1995; Stadler et al. 1995), or high costs of travel or searching for females by males (Singer and Riechert 1995). Thus, studies of concurrent multiple paternity have revealed unsuspected variation in both presumptively polygamous and monogamous mating systems. Interspeci®c variation in concurrent multiple paternity rates and variation in mating systems appear to be associated. For example, lower levels of polyandry in eusocial Hymenoptera are associated with multiple foundresses (Keller and Reeve 1994), and higher rates of extra-pair paternity in passerine birds are associated with increased plumage brightness and greater sexual dimorphism in plumage brightness (MoÈller and Birkhead 1994). Even when broad associations are not fully delineated, signi®cant interspeci®c variation in rates of concurrent multiple paternity or polyandry is known in many taxa (Wiklund and Forsberg 1991; Oldroyd et al. 1995; Moritz et al. 1995). 298 It is unclear whether conspeci®c populations exhibit substantial variation in the rate of concurrent multiple paternity. Two studies (Darling et al. 1980; Levine et al. 1987) found no such variation. Two others (Schwartz et al. 1989; Poldmaa et al. 1995) also reported little variation, but each was limited by a small sample size of broods in one of the two populations under scrutiny. Greene and Brown (1991) failed to detect any seasonal variation within a single population. On the other hand, Tilley and Hausman (1976) presented statistical estimates of concurrent multiple-paternity rates that varied widely among four populations of salamanders. However, the rates estimable from direct counts of broods in which three paternal alleles were observed were comparable among the populations, and Tilley and Hausman (1976, p. 740) were unwilling to accept the variation in statistical estimates as real because of the sampling problems involved. There are two reasons to expect signi®cant variation among populations in rates of multiple paternity and concomitant variation in mating system. First, variation among populations in sexual and mating behaviors is proving widespread, perhaps as much so as distinctions in life-history or morphological traits (Breden and Stoner 1987; Houde and Endler 1990; Endler and Houde 1995; Ptacek and Travis 1996). Second, and more important, in many studies of concurrent multiple paternity in single populations, marked phenotypic distinctions have been found between females producing singly sired broods and those producing multiply sired broods (Borowsky and Kallman 1976; Borowsky and Khouri 1976; Darling et al. 1980; Travis et al. 1990; Greene and Brown 1991). If the distribution of those phenotypic traits varies from one population to another, or if the variance among females in those traits di€ers from one population to another, then we might expect concomitant variation in the rate of multiple paternity. Such an intraspeci®c pattern would represent a prime candidate system for testing whether ®ne-scale matingsystem variation is a product of adaptive evolution (Reznick and Travis 1996). The sail®n molly, Poecilia latipinna, a live-bearing ®sh in the poeciliid family, is an excellent species in which to explore this phenomenon. Populations exhibit extensive variation in male and female body-size distributions, various life-history traits (Travis and Trexler 1987), and size-speci®c male sexual behaviors (Ptacek and Travis 1996). In previous work (Travis et al. 1990) we found that approximately half of the females in a single population could be diagnosed as carrying multiply sired broods; these ®sh are socially polygamous, although male-male interactions and female predilections appear to favor enhanced mating success for larger males (M. Ptacek and J. Travis, unpublished work; reviewed by Travis 1994). However, the females with multiply sired broods were much larger in size and higher in size-speci®c fertility than females who could not be diagnosed as carrying multiply sired broods. We interpreted this result to indicate that larger, more fertile females were the primary foci for male-male interactions, which was consistent with behavioral observations (Travis 1994). Given that populations vary in the bodysize distributions of females and in the distribution of size-speci®c fertility (Travis and Trexler 1987), it seems likely that the rate of concurrent multiple paternity varies as well and would indicate associated variation in the mating system of these ®sh. In this paper we report the results of a more extensive examination of concurrent multiple paternity rates in ®ve samples from four natural populations that vary in their distributions of female body size and size-speci®c fertility. These results indicate that the rates are quite variable; the pattern of this variation suggests that the level of variation among females in size-speci®c fertility is responsible for signi®cant variation in the mating system of these ®shes from one location to another. Methods Sampling We obtained allozyme frequency data for three polymorphic loci from pregnant sail®n mollies and their embryos collected at four locations in Wakulla County, Florida. These data permitted us to identify the likely paternal allelic contribution to each o€spring and estimate the minimum number of males necessary to account for the genetic diversity of each brood. We chose study populations to represent a range of body size distributions; Lighthouse Pond (LHP) and Mounds Pond (MDS) harbored relatively small mollies, and Wakulla Beach (WKB) and Live Oak Island (LO) relatively large ones (Table 1). We collected ®sh from all four locations in May 1990 and made an additional collection at LO in September 1990 (LOF refers to the fall, September 1990, LO sample and LOS refers to the spring, May 1990, sample). At each site we collected as many pregnant females as possible, usually more than 20, along with a sample of males and nongravid females. In cases where many females were collected, we chose to analyze broods from a sample of individuals that represented the full size range in that population. Genetic analysis Protein samples from gravid females and up to 25 embryos from each brood were electrophoresed in horizontal starch gels. We examined no more than 25 embryos from any brood to minimize any bias toward enhancing the probability of detecting multiple paternity from larger, more fertile females as a result of the larger sample size of o€spring available. For such large broods, the mass of embryos was removed and embryos were chosen haphazardly from all parts of the ovary. Females from three populations averaged more than 25 o€spring (Table 1). Standard length (the distance from the mouth to the base of the caudal peduncle measured dorsally) was measured on all adult ®sh, and brood size was recorded for all females. Eye- and muscle-tissue samples were pooled and homogenized, whereas the liver and embryos were homogenized individually in 0.5 ll of cold grinding solution (0.01 M TRIS, 0.001 M EDTA, 0.00005 M NADP, pH ˆ 7:0). Samples were run in 10% horizontal starch gels (Connaught starch) with tris-citrate bu€er (0.687 M TRIS, 0.157 M citric acid, pH ˆ 8:0), for about 15 h. We scored three presumptive loci: Gpi-2 (glucose phosphate isomerase, E.C. no. 5.3.1.9); Pgm-3 (phosphoglucomutase, E.C. no. 5.4.2.2); and Icd-2 (isocitric dehydrogenase, E.C. no. 1.1.1.42). Staining followed Harris and Hopkinson (1976) with the omission of agar from stain solutions. 299 Statistical analysis We used a variety of methods to infer a minimum number of sires for each brood, given the mother's genotype (Levine et al. 1980). The simplest method is the direct one: observation of three or more paternal alleles at a locus. This method has the virtue of simplicity but lacks power; it cannot detect multiple paternity when multiple sires share the same genotype or when sires contribute two or fewer alleles distinct from those of the mother. These disadvantages re¯ect a problem in the statistical sampling of parental genotypes. In some cases, the progeny being assayed may fail to re¯ect the diversity of sperm genotypes stored by a female, and thus some informative combinations are not seen; this is a problem in the statistical sampling of progeny (Akin et al. 1984). Various methods can be employed to use allele frequency data to overcome those limitations and re®ne the estimated rate of concurrent multiple paternity. The simplest of these is to analyze the ratio of o€spring genotypes in broods with only one or two apparent paternal alleles for unlikely genotypic ratios under a hypothesis of single paternity (Travis et al. 1990). For homozygous females, assuming a single sire, there are two possible genotypic ratios of o€spring (1:1 for a heterozygous sire or all the same for a homozygous one). The broods of heterozygous females and a single sire could, analogously, produce three di€erent ratios, depending upon the sire's genotype (1:1, 1:2:1, or 1:1:1:1). If no Mendelian genotypic ratio describing the array of a single male was consistent with the observed progeny array, the brood is diagnosed as multiply sired. This is a simple way to compensate for the parental sampling problem if brood sizes are large enough to preclude an o€spring sampling problem. This method carries no implicit assumption about how many sires contribute to a brood, nor does it assume that each sire contributes equally to the brood for an unlikely genotypic ratio to be detected. The additional multiply sired broods diagnosed from this procedure can be added to those diagnosed by direct observation of three or more paternal alleles to provide a more or less direct estimate of the rate of concurrent multiple paternity. We refer to this estimate as method 1. A second way to overcome the limitations of using only observations of at least three paternal alleles is to estimate the probability of not detecting multiple siring because of the parental sampling problem and to adjust the minimal rate (estimated from observation of three or more paternal alleles) for this probability. The simplest way to calculate the probability of nondetection is to equate it to the probability that two sires would contribute less than three di€erent paternal alleles between them. This probability is estimable by the product, across loci, of the cumulative frequency of the germane genotypic combinations at each locus (cf. Birdsall and Nash 1973; Merritt and Wu 1975; Tilley and Hausman 1976; McCauley and O'Donnell 1984; Travis et al. 1990). The true number of multiply sired broods is then estimated by division of the number of multiply sired broods detected by observation of three or more paternal alleles by 1 ) Pnd, where Pnd is the estimated probability of nondetection. This method, which we denote method 2, will estimate the rate of concurrent multiple paternity accurately if mating is at random, only two sires contribute to multiply sired broods, each sire in a multiply sired brood contributes equally, and there is no appreciable progeny sampling problem. A third, more complicated way to overcome the limitations of direct observations of three or more paternal alleles is to use the maximum likelihood methods of Akin et al. (1984) or Williams and Evarts (1989) to account for both parental and progeny sampling problems. These methods use more of the information available in the data and allow standard errors of the estimates to be calculated. Both techniques calculate likelihoods of brood composition under alternative presumptions of single or dual siring and assume random mating, no sperm precedence, and no sperm selection. Each maximum likelihood method employs a di€erent premise to calculate the likelihood of multiple paternity, and as a result, each is more suitable for di€erent types of data. Akin et al. (1984) use the presence and absence of distinct genotypes in a brood, while Williams and Evarts (1989) use unlikely progeny ratios. The method of Akin et al. (1984) is more ecient (smaller standard errors) for highly polymorphic loci (four or more alleles with intermediate frequency), whereas Williams and Evarts' technique is more ecient for loci with low allelic diversity (two or three alleles with intermediate frequency; see Williams and Evarts 1989 for more detailed criteria identifying conditions favoring one or the other technique). In our data, only Icd-2 proved suciently polymorphic to favor analysis by the technique of Akin et al. (1984), and then only clearly so for one population. An additional advantage to the Williams-Evarts method is that their estimator can be combined across loci, even when those loci vary in allelic diversity, and thereby yield lower standard errors. In all cases, the Williams-Evarts method yielded smaller con®dence intervals than the technique of Akin et al. (1984) from our data, and the estimates from the method of Akin et al. (1984) were within the Williams and Evarts-derived con®dence intervals. With these considerations we chose the Williams-Evarts method, which we denote method 3. We used logistic regression to examine the relationship of female size and fecundity to multiple paternity. Logistic regression was chosen because it employs a log-linear model to elucidate the relationship of a binary dependent variable (presence or absence of multiple paternity) with continuous independent variables (Trexler and Travis 1993). The analysis requires ®tting a series of models to the data, starting with a ``full model'' that includes all independent variables and their interactions, and repeating the procedure with models sequentially eliminating one independent variable at a time. The di€erence in the log likelihood of each sequential model, multiplied by )2, is a v2 statistic with 1 df that indicates the contribution of the term eliminated. All analyses using embryo number and female size were performed after these variables were subjected to the natural-log transformation. Results Female body size varied widely among the populations (Table 1). Average female body size in the population with the largest females was 50% higher than that in the population with the smallest females. On the other hand, the relative variation in female size within a population, as measured by the coecient of variation in size (CV), was comparable across populations. Male size also varied signi®cantly among populations (Table 1) and the rank order of the male and female size was concordant. Average brood size varied greatly among the four study populations, spanning an order of magnitude from 7.4 to 75.7. Only the LOS and WKB populations did not di€er from all others in average brood size, before adjusting for inter-population di€erences in female size (Table 1). Brood size increased as female size increased [analysis of covariance: ln (brood size) vs. ln (female size), slope di€erent from zero, F1;116 ˆ 133:3; P < 0:001] and the slopes did not di€er among populations (population by female size interaction: F4;116 ˆ 0:16; P ˆ 0:127). The average size-speci®c fertility, estimated at the grand mean female standard length of 38.7 mm, varied from 14.9 at MDS to 27.7 at LOF, a di€erence of 86%. For this size female, all populations but one had similar brood sizes; LOF females displayed greater size-adjusted brood size than all other populations, including the same population in spring (LOS; Table 1). 300 Table 1 Description of the ®sh populations studied. CV is the coecient of variation, n is the sample size (for female standard length including all sexually mature females, pregnant and not so). Mean brood sizes, adjusted to grand mean of female size by ANCOVA, are reported in parentheses. CD indicates the coecient of Population Female Male Standard length MDS LHP WKB LOS LOF determination for the regression of brood size on female size. Superscript numbers indicate means that di€er at the P ˆ 0:05 level by Tukey's HSD multiple comparisons test. Only two sexually mature males were collected in the LOF sample Brood size n mean CV(%) n mean 126 117 35 66 27 32.41 26.82 48.03 43.34 48.43 14 8 13 14 14 22 42 16 28 18 14.01 7.42 41.93 41.73 75.74 The precision with which brood size could be predicted from female body size within a population was highly variable from one population to another (Table 1; coecients of determination for the regression of brood size on female body size ranged from 0.21 to 0.72). The level of predictability was unrelated to the average female body size or to the level of relative variation in size (CV) found there. For example, the regressions of brood size on female size from the two locations with the smallest females, MDS and LHP, had the least and greatest precision respectively. Allelic diversity varied among the three loci examined; ®ve alleles were observed at Icd-2, four at Gpi-2, and three at Pgm-3 (Table 2). Although allele frequencies were broadly comparable across the ®ve populations, there were notable distinctions in levels of genetic variance. There was more allelic diversity for Icd-2 at LOF than MDS, and greater diversity for Gpi-2 at WKB than at LOS. Only Icd-2 was consistently out of Hardy-Weinberg frequencies in the adult populations, displaying signi®cant heterozygote de®ciencies in three of the ®ve samples (LHP, MDS, WKB; see Dinep 1991). These deviations probably arose from misclassi®cation of a small number of the rare genotypes. The Pgm-3 locus exhibited a similar pattern of heterozygote de®ciency at the WKB population. Although multiple paternity was detected in all populations, there was considerable variation among them in the estimated rates (Table 3). Estimates from methods 1 and 3, which ought to correspond the most for any single population because of their similar premises, ranged over an order of magnitude; method 2 yielded only a ®ve-fold range. The probabilities of not detecting multiple siring by using direct observation of three or more paternal alleles varied over a two-fold range. There was no qualitative relationship of multiple paternity rate estimated by any method with the number of broods observed in a population. The three methods were most consistent for LHP even though the small brood sizes might have created a signi®cant progeny sampling problem. Nonetheless, all three estimates are below 0.10, and the standard error for Standard length (14.91) (17.51) (19.71) (19.91) (27.72) CV(%) CD n mean CV(%) 77 28 42 56 42 0.72 0.21 0.54 0.59 0.66 36 33 19 29 ± 30.11 23.42 42.53 40.63 ± 17 14 26 16 ± method 3 is not large. All of the extant evidence indicates that multiple paternity rates here were very low. The three methods were reasonably consistent for LOS. In this population, methods 1 and 3 provided comparable estimates and indicated a multiple-paternity rate of about 0.35; method 2 provided a slight underestimate. Method 2 uses the progeny information least and is more likely to be awry when compared to the others. Although there was less numerical consistency among methods for LOF, methods 1 and 3 estimated very high rates of multiple paternity. The estimate from method 1 was 12-fold larger than the comparable estimate for LHP, and the method 3 estimate was 9-fold larger. As was the case for LOS, method 2, which uses the least Table 2 Allelic frequencies of the three loci examined. Data from all adult females (gravid and nongravid) and males are pooled; n indicates sample size. Allelic designations are ordered by rate of migration Locus Population MDS LHP WKB LOS LOF Pgm-3 (n) 1 2 3 144 0.208 0.750 0.042 150 0.213 0.773 0.013 49 0.204 0.745 0.051 94 0.101 0.835 0.064 28 0.196 0.804 0.000 Gpi-2 (n) 1 2 3 4 144 0.083 0.781 0.118 0.017 154 0.097 0.789 0.110 0.003 49 0.102 0.673 0.163 0.061 101 0.035 0.817 0.129 0.020 29 0.017 0.759 0.207 0.017 Icd-2 (n) 1 2 3 4 5 135 0.093 0.670 0.148 0.074 0.015 151 0.083 0.530 0.235 0.126 0.026 50 0.160 0.580 0.170 0.090 0.000 96 0.063 0.521 0.266 0.141 0.010 29 0.259 0.448 0.207 0.034 0.052 301 Table 3 Concurrent multiple-paternity estimates obtained from three techniques; n indicates the number of females examined, 3PA is the number of females identi®ed as multiply mated by the presence of 3 paternal alleles, G is the number of females indicated as multiply mated by G-test, and total refers to the estimated number of multiply mated females by 3PA and G-test. Rate method 1 is the multiple paternity rate estimated by method 1. Pnd indicates the cumulative probability of two males' siring a brood and contributing less than 3 unique alleles, and rate method 2 is the resulting estimate of multiple paternity rate. Rate method 3 indicates the results from the Williams-Evart technique and their associated standard errors Population n 3PA G Total (3PA+G) Rate method 1 Pnd Rate method 2 Rate method 3 MDS LHP WKB LOS LOF 22 42 16 28 18 5 2 3 4 4 4 0 3 6 7 9 2 6 10 11 0.41 0.05 0.37 0.36 0.61 0.40 0.29 0.19 0.34 0.23 0.38 0.07 0.23 0.22 0.29 0.62 0.09 0.17 0.33 0.85 progeny information, provided a much lower estimate than the others. The magnitude of the discrepancy suggests a strong departure from the conditions assumed by method 2; it is reasonable to conclude the rate of multiple paternity was very high in LOF. The three methods agree broadly for MDS in diagnosing a rate of multiple paternity that was intermediate between the low rate of LHP and the high rate of LOF. Methods 1 and 2 yielded essentially the same answer. The higher estimate from method 3 probably re¯ects the increase indicated by accounting for progeny sampling because, like LHP, MDS had relatively low brood sizes. The MDS sample had the largest standard error, which was also a likely re¯ection of a progeny sampling problem. The most dicult statistical results to reconcile are those in WKB. The direction of the discrepancy between methods 1 and 3 is puzzling. In principle, method 3 should provide an estimate comparable to or greater than that provided by method 1; in this case, method 3 estimated a rate of multiple paternity that was about half that detected by method 1. It is very possible that the maximum likelihood method is poorly behaved here. Method 3 works by pooling the less common alleles into a single class and thereby recreating a two-allele situation (the most common single allele and the pooled alternatives). The more polymorphic the locus, the less accurately the method performs. WKB is the most polymorphic population at Pgm-3 and Gpi-2, and this may be the source of the discrepancy. Method 1 indicates a rate of multiple paternity comparable to that of LOS. Logistic regression analysis indicated no relationship between the probability that an individual female was multiply mated and her body or brood size in three of the ®ve samples (Figs. 1, 2). The change in the log likelihood estimate for the full model and one with only a constant was not signi®cant for the data from WKB, LOS, and LHP (Fig. 1; WKB: 2 ˆ 0:971; P ˆ 0:39; LOS: 2 ˆ 2:64; P ˆ 0:11; LHP: 2 ˆ 0:494; P ˆ 0:51). There was evidence that female characteristics were related to multiple siring of broods in the spring sample from the Live Oak population (LOS). The LOS populations displayed a signi®cant relationship between the ‹ ‹ ‹ ‹ ‹ 0.33 0.27 0.22 0.21 0.25 probability of multiple paternity and female size and brood size (Fig. 2; full model, LOS: 2 ˆ 10:17; P ˆ 0:002). However, there was an interaction between female size and fecundity in the probability of multiple paternity (Fig. 3). The source of this interaction is illustrated in plots of the predicted probability of multiple paternity from the full model versus female length and brood size (Fig. 2). The two largest and most fecund females in this sample (marked A and B) were scored as singly mated (Fig. 2, top); the model predicted a low probability of multiple mating for them (Fig. 2, middle and bottom). However the largest females scored as multiply mated (marked 3 and 4) had lower fecundity than a third multiply mated female that was smaller (marked 1). The full model yielded a moderate predicted probability of multiple paternity for female 1 and high probabilities for females 3 and 4. Female 2 had the highest probability of multiple paternity; she had the second highest fecundity of the multiply mated females (Fig. 2, bottom panel) but was not especially large (Fig. 2, middle panel). The interaction e€ect of the full model thus indicates that either large body size or brood size separately yields high probability of multiple paternity, whereas females that are both large and fecund have much lower probabilities. This result is undoubtedly caused by a high leverage e€ect of females A and B on the regression and is probably not a real phenomenon. We found evidence of a relationship of multiple paternity and female characteristics in the MDS population (Fig. 1, full model: 2 ˆ 2:96; P ˆ 0:09). Neither female size, brood size, nor their interaction was signi®cant individually in the MDS data, probably because of their weak individual e€ects and small sample sizes. The full model was made signi®cant by the combined e€ects of female size and brood size, strengthened by their colinearity. This is the same pattern seen in the results from LOS, where all three model terms are highly signi®cant when removed singly from a saturated model but are less signi®cant when compared to a model with only a constant (Fig. 3). Given the similarities in data structure between LOS and MDS, we conclude that the e€ects are real in the MDS population but were not statistically signi®cant because of low statistical power. 302 Fig. 1 Brood size relative to female standard length for females examined for multiple paternity from four of the ®ve study populations.Filled circles indicate females identi®ed as multiply mated by direct or indirect methods; open circles indicate females not shown to be multiply mated Discussion Our ®ndings are consistent with our earlier study in indicating that the characteristics of females can in¯uence the probability of multiple paternity, but they also suggest seasonal and geographic variation in the mating system. When we consider the estimates, sample sizes, and standard errors, we conclude that there was genuine variability among these populations in the rate of concurrent multiple paternity. The most reasonable conclusion is that the rate was genuinely very low at LHP, genuinely very high at LOF, and intermediate elsewhere. This study, along with our earlier work, provides indirect evidence that male sail®n mollies in natural populations can identify more fertile females and make them a focus of their mating e€orts. Two lines of evidence support the primacy of sizespeci®c fertility over that of female body size as the best predictor of the probability of multiple paternity. First, in the LOS data, brood size yields a greater reduction in log likelihood when removed from a reduced model than does standard length. The same pattern was noted in 1985 (Travis et al. 1990; Trexler and Travis 1993). Second, the rank order of relative variation in fertility (Table 1, CV) in spring is comparable to that of multiple paternity rate (LHP < WKB £ LOS < MDS). Malemale competition for the most fertile females may be greatest in those populations where the range of sizespeci®c fertility is greatest. Male mollies can clearly distinguish receptive from nonreceptive females (Farr and Travis 1986; Sumner et al. 1994) so it is reasonable to postulate that their diagnostic abilities may be even more re®ned. We failed to identify any consistent pattern of multiple paternity with respect to the size distribution of males. The two populations with the lowest frequency of multiple paternity included the ones with the smallest and largest average size of male ®sh (LHP and WKB). There might be a crude pattern with respect to male courtship behavior; Ptacek and Travis (1996) showed that the sizespeci®c rate of male courtship behavior varied among these populations in the order MDS > LO > WKB (LHP was not studied), and this rank order is reminiscent of that of spring multiple paternity at least insofar as MDS exceeds the others. It is striking that this is also the rank order for these three populations in the variance in size-speci®c fertility; perhaps male courtship rates match the variance in size-speci®c fertility (being higher where there is more variance and more potential ®tness variance at stake), and the di€erent social interactions that result determine rates of multiple paternity. Although it is tempting to speculate about this trivariate relationship, the data are too tenuous at this time to consider this more than a working hypothesis. We observed a marked di€erence in the probability of multiple paternity between our spring and fall LO data, but it is unclear whether this di€erence has a biological signi®cance. One possibility is that multiple paternity in the fall is higher as a result of accumulated sperm stored 303 Fig. 3 A ¯ow chart of the results of analysis of probability of multiple mating relative to female length and brood size for females from Live Oak in spring. Numbers in the boxes indicate the log likelihood of each model, and the numbers on the arrows indicate the change in log likelihood as each term is excluded from analysis. The change in log likelihood multiplied by )2 is a chi-square statistic with 1 df Fig. 2 Analysis of e€ects of brood size relative to standard length on the probability of multiple paternity for females from the spring sample from Live Oak Island. The top panel illustrates brood size relative to standard length, the middle panel is the predicted probability from logistic regression relative female standard length, and the bottom panel is the predicted probability relative to brood size. Filled circles indicate females identi®ed as multiply mated by direct or indirect methods; open circles indicate females not shown to be multiply mated. Numbers and letters identify particular females discussed in the text over the summer reproductive season (but see below regarding sperm longevity). We observed a signi®cant association between female body size and size-speci®c fertility and the probability of carrying a multiply sired brood in this population from collections made in the springs of both 1985 and 1990. In contrast, we observed no such associations in the fall 1990 sample, and there is little indication in the data that a larger sample size would reveal an association comparable in strength to that found in the spring samples. This result supports the argument that the seasonal di€erence is real and meaningful; the argument would be stronger with another autumn sample. Large females may have higher rates of multiple mating because they are older and have accumulated more sperm over their reproductive lifetime. Within a population, the relatively large females tend to be older females (female size is an increasing but decelerating function of female age: Snelson 1982; J. Travis, unpublished work), while among population di€erences in female size may re¯ect environmental in¯uence on growth in addition to age structure (Trexler et al. 1990). Although poeciliid sperm can retain viability within folds of the ovary for several brood cycles, two observations weaken the likelihood of this hypothesis as the sole explanation for the patterns in our data. First, there is a marked decline in the viability of stored sperm by a female's third brood with such sperm (Lodi 1981; K. Silvestre, M. Ptacek, and J. Travis, unpublished work); female mollies produce a third brood at a body size within the range of the larger females in this study, so this decline is relevant within the size range of females observed here. Second, newer sperm may displace older sperm (Winge 1937). This hypothesis cannot, of course, be rejected and a de®nitive answer awaits further study. The major source of sampling error in estimating the rate of multiple paternity in this study arises from parental sampling. The error rate from progeny sampling depends on brood sizes, o€spring sample sizes, and allele frequencies. Our sample sizes are constant for WKB, LOS, and LOF because all broods exceeded size 25. Thus, our observation of increased multiple paternity in larger females at LOS, and not at WKB, which had the same directly observed rate (method 1), is not a sampling artifact. For species with large broods, we recommend samples in excess of 20 such that males siring a minimum of 5% of the o€spring are likely to be represented in the progeny sample screened (i.e., to minimize progeny sampling error). Variation among populations in brood size produces an unavoidable bias from parental sampling for making comparisons. In our study, most 304 broods from LHP were substantially smaller than the 25 embryos screened for the other populations. Progeny sampling was not a problem because we sampled entire broods of o€spring, but parental sampling error was increased compared to populations with large broods. Small brood sizes decrease the power to detect multiple males with some genotypic combinations, e.g., a heterozygote and a homozygote sharing one of the heterozygote's alleles. This results in larger uncertainty for multiple paternity estimates made from small, compared to large, samples. Williams and Evarts (1989) discuss this in more detail and evaluate cases with variation in sample size and allele frequencies. Our methods 1 and 2 do not account for this source of bias in estimating multiple paternity rate, while method 3 does (as does the method of Akins et al. 1984). Although it is tempting to consider DNA ®ngerprinting methods for increasing our power to detect multiple paternity, their statistical power in this context is not clearly greater than that of allozymes. The dilemma with DNA ®ngerprinting in a study of a natural population like this one is that there are no putative sires against which to test the o€spring. The detection of multiple paternity therefore translates into one of two statistical problems, either the detection of half-sib pairs among broodmates or the rejection of an average level of relatedness consonant with all individuals being full sibs. The higher the rate of band-sharing among unrelated individuals, the more formidable these problems become (Lynch 1988). We found that a CAC5 probe applied to these sail®n molly populations yielded a band-sharing rate among randomly chosen males of 0.25; large standard errors in the estimation of relatedness can be expected with this rate of band-sharing. With several moderately polymorphic allozyme loci available and the ability to apply Mendelian expectations in their interpretation, we found the allozymes to have more power than this single ®ngerprint probe. To be sure, the addition of more ®ngerprint probes could tip the balance in their favor, but resolution of additional inexpensive allozyme systems might be an equally productive e€ort. It would be useful to examine whether females derive bene®ts from carrying multiply sired young or whether the distribution of concurrent multiple paternity is strictly a function of male-male interactions around agnostic females. Three classes of bene®ts have been postulated to accrue to females from carrying multiply sired broods. First, when males provide nutritional material with spermatophores, females receive a net energy gain from being multiply inseminated (Pardo et al. 1995). This is not the case for mollies; there is no known energy transfer with spermatophores, and experimental studies have revealed no fertility gains through multiple mating (J. Travis, unpublished work). Second, carrying multiply sired broods can represent a form of genetic bet-hedging when o€spring may be released into a variable environment (Westneat et al. 1990; Keller and Reeve 1994). There is no reason to discard this hypothesis in mollies. Third, through multiple insemination, females might ensure that their o€spring are sired by males with preferred phenotypes, perhaps by engaging in matings that circumvent male-male competition (MoÈller and Birkhead 1994) or through passive acceptance of the outcome of sperm competition (presuming a genetic covariance between competitive ability of sperm and preferred male phenotype; Madsen et al. 1992; Murie 1995). It is unclear how this hypothesis could apply to mollies; female predilections and the outcome of male-male interactions favor the same bodysize phenotype, larger males, and there would seem little additional constructive role for multiple insemination in this context (Farr and Travis 1986; Travis 1994; M. Ptacek and J. Travis, unpublished work). Our ®ndings have considerable implications for other research into mating systems in natural populations. The primary one is that seasonal and geographic variation in mating system are likely to be more commonplace than presently appreciated. The secondary one is the suggestion that mating systems could be structured around variance in female fertility as much as in male behavior or genotype; although not new, this suggestion deserves more attention than it presently receives. Acknowledgements We gratefully acknowledge Chris Williams for generously sharing his programs and knowledge for estimating concurrent multiple paternity rate. Also, Tom Laughlin and Bruce Turner provided instruction and laboratory space of DNA ®ngerprint analyses. This research was funded by National Science Foundation grants BSR 88-18001 and DEB 92-20849 to J. Travis and a faculty development grant to J. Trexler from the University of Mississippi. 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Behav Ecol Sociobiol 37:179±188 Communicated by J.D. Reynolds