This art icle was downloaded by: [ Pedro Wolf ] On: 24 Oct ober 2011, At : 22: 56 Publisher: Rout ledge I nform a Lt d Regist ered in England and Wales Regist ered Num ber: 1072954 Regist ered office: Mort im er House, 37- 41 Mort im er St reet , London W1T 3JH, UK Biodemography and Social Biology Publicat ion det ails, including inst ruct ions f or aut hors and subscript ion inf ormat ion: ht t p: / / www. t andf online. com/ loi/ hsbi20 Fecundity, Offspring Longevity, and Assortative Mating: Parametric Tradeoffs in Sexual and Life History Strategy Pedro S. A. Wolf a & Aurelio José Figueredo b a Depart ment of Psychology, Universit y of Cape Town, Cape Town, Sout h Af rica b Depart ment of Psychology, The Universit y of Arizona, Tucson, Arizona Available online: 24 Oct 2011 To cite this article: Pedro S. A. Wolf & Aurelio José Figueredo (2011): Fecundit y, Of f spring Longevit y, and Assort at ive Mat ing: Paramet ric Tradeof f s in Sexual and Lif e Hist ory St rat egy, Biodemography and Social Biology, 57: 2, 171-183 To link to this article: ht t p: / / dx. doi. org/ 10. 1080/ 19485565. 2011. 614569 PLEASE SCROLL DOWN FOR ARTI CLE Full t erm s and condit ions of use: ht t p: / / www.t andfonline.com / page/ t erm s- and- condit ions This art icle m ay be used for research, t eaching, and privat e st udy purposes. Any subst ant ial or syst em at ic reproduct ion, redist ribut ion, reselling, loan, sub- licensing, syst em at ic supply, or dist ribut ion in any form t o anyone is expressly forbidden. The publisher does not give any warrant y express or im plied or m ake any represent at ion t hat t he cont ent s will be com plet e or accurat e or up t o dat e. The accuracy of any inst ruct ions, form ulae, and drug doses should be independent ly verified wit h prim ary sources. The publisher shall not be liable for any loss, act ions, claim s, proceedings, dem and, or cost s or dam ages what soever or howsoever caused arising direct ly or indirect ly in connect ion wit h or arising out of t he use of t his m at erial. Biodemography and Social Biology, 57:171–183, 2011 Copyright © Society for the Study of Social Biology ISSN: 1948-5565 print / 1948-5573 online DOI: 10.1080/19485565.2011.614569 Fecundity, Offspring Longevity, and Assortative Mating: Parametric Tradeoffs in Sexual and Life History Strategy PEDRO S. A. WOLF 1 AND AURELIO JOSÉ FIGUEREDO2 1 Downloaded by [Pedro Wolf] at 22:56 24 October 2011 2 Department of Psychology, University of Cape Town, Cape Town, South Africa Department of Psychology, The University of Arizona, Tucson, Arizona Genetic diversification of offspring represents a bet-hedging strategy that evolved as an adaptation to unpredictable environments. The benefits of sexual reproduction come with severe costs. For example, each offspring only carries half of each parent’s genetic makeup through direct descent. The lower the reproductive rate, the more substantial the cost when considering the proportion of genes represented in subsequent generations. Positive assortative mating represents a conservative bet-hedging strategy that offsets some of these costs and preserves coadapted genomes in stable and predictable environments, whereas negative assortative mating serves the inverse function of genetic diversification in unstable and unpredictable environments. Genetic diversification of offspring represents a bet-hedging strategy that evolved as an adaptation to unpredictable environmental contingencies and when environmental cues that might otherwise selectively trigger developmentally plastic changes are of limited reliability or validity (Figueredo, Hammond, and McKiernan 2006; West-Eberhard 2003). Although sexual recombination is a common means of genetic diversification, the evolution of sexual reproduction has been called one of the great mysteries of evolutionary biology (Hamilton, Axelrod, and Tenese 1990). For example, many evolutionary theorists believe that sexual recombination might have evolved primarily as a result of an interspecific arms race between the immunodefenses of multicellular organisms and the parasitic strategies of single cell organisms (Hamilton etal. 1990; Maynard-Smith 1978). The benefits accrued by multicellular species through sexual reproduction, however, come with severe costs. An obvious cost that troubled biologists for decades is that every offspring only carries half of each parent’s genetic makeup through direct descent, and there are differential costs incurred by the sexes. Given differential parental effort, the more investing sex bears a disproportional cost of sexual reproduction, producing selective pressure against sexual reproduction. To offset some of these costs, many species have evolved a facultative sexuality, wherein sexual recombination of genetic material is engaged in only when it would be beneficial and avoided when it would be detrimental. In some facultatively sexual species, for example, sexual reproduction appears under conditions of environmental fluctuations and disappears under conditions of environmental stability, switching back and Address correspondence to Pedro S. A. Wolf, Department of Psychology, University of Cape Town, Rondebosch 7701, Cape Town, South Africa. E-mail: pedro.wolf@uct.ac.za 171 Downloaded by [Pedro Wolf] at 22:56 24 October 2011 172 P. S. A. Wolf and A. J. Figueredo forth as needed from sexual to asexual reproduction. Species with such triggers have been documented and include the Cladoceran, Moina macrocopa (D’Abramo 1980), and the Rotiferan, Bronchionus plicatilis (Snell 1986). Some Oligochaete earthworm populations in the vicinity of the Chernobyl Power Plant disaster (Tsytsugina and Polikarpov 2003) have been found to switch to sexual reproduction as a function of the severity of cytogenetic damage, presumably to help remove deleterious mutations (Kondrashov 1988; Smith 1978). For obligately sexually species that cannot switch between sexual and asexual reproduction in response to such environmental changes, we propose that the degree of sexual recombination can be adaptively modulated to achieve similar results in response to the same selective pressures. This can be achieved by a flexible degree of conditional assortative mating for genetic similarity, selected to be responsive to cues to environmental harshness and unpredictability. Assortative mating has been implicated as an evolutionary force in sympatric speciation (Dieckmann and Doebeli 1999; Johnson, Hoppensteadt, Smith, and Bush 1996; Kondrashov and Shpak 1998). In this view, assortative mating acts as the evolutionary force through nonrandom mating patterns rather than geographic isolation or natural selection. Speciation through assortative mating has been observed in various species thought to be in the process of speciating to include mole rats, Spalax ehrenbergi (Beiles, Heth, and Nevo 1983) cicadas (Simon et al. 2000), and the European corn borer Ostrinia nubilalis (Malausa et al. 2005). Despite all the work that has been conducted on the long-term evolutionary effects of assortative mating, little attention has been focused on the ultimate causes of assortative mating. Thiessen and Gregg (1980) document the extent of assortative mating in both human and nonhuman species. They also propose that in humans, positive assortative mating among nonrelatives is an adaptation that maximizes fitness by increasing relatedness among kin. The assortative mating while avoiding consanguineous mating is a tactic that both limits inbreeding depression and increases fitness. They argue that this increased relatedness facilitates communication, altruism, and inclusive fitness. In addition, this mating strategy maximizes gene representation in subsequent generation without an increase in mating effort. We extend this theoretical position by relating it to life history theory by presenting a mathematical model. We further propose that conditions favoring faster life history (LH) strategies also put a selective premium on higher rates of genetic recombination. Unstable, unpredictable environments that are uncontrollable by genetically influenced developmental processes, with predominantly extrinsic sources of mortality select against slow LH strategies (Charnov 1993; Ellis, Figueredo, Brumbach, and Schlomer 2009; Roff 1992, 2002; Stearns 1992). In contrast, stable, predictable environments that are controllable by genetically influenced (and hence evolvable) developmental processes with predominantly intrinsic sources of mortality select against fast LH strategies. Thus, short-term stochastic variations in environmental conditions that result in widely varying levels of juvenile and adult mortality simultaneously favor the evolution of both (1) diversified bet-hedging and (2) faster LH strategies (Ellis, Figueredo, Brumbach, and Schlomer 2010; Murphy 1968; Roff 2002). If a sufficiently large number of offspring is produced, as is characteristic of faster LH strategists, the diversification of offspring genotypes (genetic bet-hedging) increases the likelihood that at least some proportion of them will survive under harsh and unpredictable conditions. In contrast, stable, predictable, and controllable environments put a selective premium on lower rates of genetic recombination to preserve the integrity of locally well-adapted, and perhaps co-adapted genomes. Thus, Downloaded by [Pedro Wolf] at 22:56 24 October 2011 Assortative Mating and Life History Strategy 173 it follows that conditions favoring the evolution of slower LH strategies simultaneously favor the positive assortative mating of genetically similar individuals. Therefore, we predict that natural selection should have favored the evolution of higher assortative mating coefficients on heritable traits for slower LH strategists than for faster LH strategists. We support the logic of this argument by presenting a series of mathematical expressions that tie selective pressures that we postulate should drive mate preferences for phenotypic similarity with the evolution of a slow LH strategy. The underlying logic being that there is a genetic component underlying phenotypic similarity and that positive assortative mating on traits should be favored when other selective pressures favor a slow LH strategy. In short, a positive assortative mating strategy should coevolve with slow LH to offset some of the costs associated with sexual reproduction while maintaining many of its benefits. We propose that in species that do not mate at random, there are underlying evolved mating systems that take into account and behave in ways that both increase genetic diversity for loci that code for immunocompetency while at the same time exhibit positive assortative mating on phenotypic traits when it comes to loci that do not. In addition, we argue that as the LH of the individual slows, the cost of sexual reproduction increases and, therefore, the optimal degree of positive assortative mating on traits not involved with the immune system should also increase. Though no new empirical tests will be presented in the present theoretical article, we discuss the results of a previously published article designed to test this model. This model generates several novel predictions that go beyond those presented by Thiessen and Gregg. The proposed link between the degree of positive assortative mating and that of slow LH strategy, as coevolved adaptations, is an entirely original prediction of our own. Mathematical Model The total gene-copying success (g) achieved by an organism in any single bout of reproduction is the product of three terms that determine the survival probability of the organism’s genome: the number of offspring produced (no ), the expected longevity of those offspring (lo ), and the coefficient of genetic relationship between the parent and its offspring (rpo ): Expression 1. g = (no )(lo )(rpo ) The function g can be interpreted as the gene-copying success of the entire genome over a specified period of time but also gives us the number of copies of any given gene surviving to any given point in time at which offspring survivorship is assessed. This is because the coefficient of genetic relationship (rpo ) is equal to the probability of any given offspring carrying that particular gene. The probability of that particular gene surviving (rpo ) is then multiplied by the number of offspring being produced (no ) and the probability of those offspring surviving to a certain point in time (lo ). This represents the instantaneous replication of a genome achieved by any single bout of reproduction. For semelparous species, which achieve all their reproduction in a single bout, this represents the total lifelong gene-copying success of a single parental individual. Conversely, for iteroparous species, which achieve their reproduction iteratively in repeated bouts over their lifespan, the total lifelong gene-copying success of an individual organism is this same term integrated over all successive bouts of reproduction over the individual’s lifespan, Downloaded by [Pedro Wolf] at 22:56 24 October 2011 174 P. S. A. Wolf and A. J. Figueredo discounted by the age-specific survivorship of the parental organism, representing the probability of that individual surviving from any single bout of reproduction to the next. In the context of the present model, we will assume the operation of that well-known relationship but not unnecessarily complicate our mathematical expressions by including that ever-present weighting by parental survivorship. We will, however, consider it briefly further below where allocation of any given amount of parental effort might affect parental survivorship in ways that might influence total lifetime gene-copying success. LH theory divides the total reproductive effort of an organism into mating effort and parental effort. Mating effort is defined as that portion of the bioenergetic and material resources within the total reproductive effort that is invested in obtaining and retaining mates in sexually reproducing organisms. The parental effort is that portion of the reproductive effort invested in producing and enhancing the survivorship of offspring. According to classical LH theory (MacArthur and Wilson 1967), r-selected and K-selected life histories are based upon allocating different proportions of the total reproductive effort among these different categories. For example, fast LH (r-selected) strategists should allocate more bioenergetic and material resources into producing a higher total number of offspring but should allocate less into producing offspring with high individual survivorship. Conversely, slow LH (K-selected) strategists should allocate more resources into producing offspring with relatively high individual survivorship but producing a lesser number of these. According to Expression 1, it is possible (ceteris paribus) to obtain the same gene-copying success results with differentially allocating resources into no and lo , which is the product of these two terms, holding rpo constant for present purposes. Thus, the total parental effort expended by any organism (Etotal ) is the sum of that portion of the parental effort put into creating any given number of offspring (En ) and that portion of the parental effort invested in increasing the longevity of that particular number of offspring (El ). Expression 2. Etotal = En + El The actual number of offspring produced will be some function of the fecundity effort, En . We may model this by creating a “fecundity coefficient” (fo ) that serves as a conversion factor from parental effort (in bioenergetic terms) to the number of offspring (no ) that can be produced by that investment: Expression 3. no = fo En This fecundity coefficient is determined by the reproductive biology of the species. We may model the conversion of parental effort energy into the longevity of offspring by means of a similar “offspring survivorship coefficient” (so ) applied to the offspring longevity effort, El : Expression 4. lo = so El Assortative Mating and Life History Strategy 175 Although in the brief discussion previously we implied that the same gene-copying success result could be obtained by differentially reallocating total parental effort into En and El , the optimal allocation of parental effort may be biased by differing values of the fecundity (fo ) and survivorship (so ) coefficients, which represent the different “returns on investment” of bioenergetic resources from allocating them to the different components of fitness. These coefficients are partially determined by the ecology in which a given organism finds itself, permitting the formulation of optimal life history models under ecological constraints. Possible discrepancies, where they exist, between the fecundity (fo ) and survivorship (so ) coefficients will determine the optimal allocation of resources. Where they are similar in magnitude, a range of possible alternative strategies may exist. By substitution, we may thus construct the following Expression: Expression 5. Downloaded by [Pedro Wolf] at 22:56 24 October 2011 g = (fo En )(so El )(rpo ) In Expression 5, the total gene-copying success of an organism is the product of three terms that determine the survival probability of the organism’s genome. The three terms represent the number of offspring produced by the amount of fecundity effort expended (fo En ), the survival probability of those offspring produced by the offspring longevity effort expended (so El ), and the coefficient of genetic relationship between the parent and its offspring (rpo ). Sexual Reproduction and Interactions among Variables Because offspring produced by diploid sexual reproduction only contain half of an individual’s genome, the chances of sharing any particular gene between a parent and a single offspring is 50%. However, this estimate assumes exogamy, or the mating of individuals who are not genetically related. It follows that the probability of transmission to the next generation for a single gene is a function of the total number of offspring produced (no ), as represented by Expression 1. Expression 6. no g = 1 − rpo Where rpo is the coefficient of relatedness between parent and offspring, and g is the genecopying success, or degree of certainty (expressed as a proportion) of the representation of any given gene in the following generation. Under the presumption of exogamy, where rpo is equal to .5, this reduces to Expression 2. Expression 7. g = 1 − .5npoo Plotted in Figure 1, the curve representing Expression 7 shows that each additional offspring increases the probability of representation for any given gene; however, there is never absolute certainty. Under conditions of positive assortative mating, where mates share more genes than expected when mating at random or an exogamy (where the parents are not genetically 176 P. S. A. Wolf and A. J. Figueredo 0.9 0.8 0.7 0.6 Proportion of Unique Genetic Contribution When assortative mating= 0.0 0.1 0.2 0.3 0.5 Downloaded by [Pedro Wolf] at 22:56 24 October 2011 1.0 Genetic Contribution by Number of Offspring 2 4 6 Number of Offspring 8 10 Figure 1. Visual representation of the probability of gene representation for differing degrees of positive assortative mating, (rpp = 0, .1, .2, and .3) and number of offspring produced (no = 1:10) for the following degrees of assortative mating: rpp = 0 (long and short dashes); rpp = .1 (solid line); rpp = .2 (dash and dotted line); rpp = .3 (dashed line). The x-axis represents the number of offspring produced, and the y-axis represents the certainty in the next generation. The four values for rpp were chosen for illustrative purposes. These positive assortative mating coefficients represent the proportion of genes shared that vary within a population; a population that has a history of assortative mating and complex familial relationships making any number of coefficients possible. For example, a .1 assortative mating coefficient would be the equivalent of a consanguineous mating somewhere between a first cousin and a first cousin once removed whose ancestors had an assortative mating coefficient of zero. related), it follows that the number of offspring required to meet this same criterion will be lower. This is because the coefficient of relatedness between parent and offspring (rpo ) will be higher as a function of the coefficient of relatedness between the two diploid parents (rpp ), as given by Expression 8. Expression 8. rpo = .5 + rpp /2 We arrive at Expression 9 by substituting rpo in Expression 6 with (.5 + rpp /2), allowing the total number of offspring required to achieve a transmission probability of g under conditions of endogamy to be calculated. Expression 9. n  g = 1 − .5 + rpp 2 o For example, if the coefficient of relatedness among parents is .10, the four offspring will yield a genetic transmission probability of 95.90% rather than the 93.75% obtained 177 by calculating Expression 2. This means that positive assortative mating permits a smaller number of offspring to transmit an equivalent portion of one’s entire genome into the subsequent generation. Figure 1 illustrates this principle where the dashed line represents an assortative mating coefficient of .10. A logical implication of this model is that a potential parent organism possessing a slow life history would be able to use a positive assortative mating strategy to achieve high fidelity of genetic transmission with a smaller number of offspring. We, therefore, predict an increased bias toward positive assortative mating as LH strategies slow and an increase in negative assortative mating as LHs speed up. Although these increases in probabilities may seem small, they add up over time. Figure 2 plots the probabilities of any particular gene’s presence in generations 1 through 10, if all the subsequent offspring maintain the same reproductive rates when mating is random. Notice that the reproductive tactic of having only one offspring almost ensures the extinction of the gene, four offspring only confers a little more than 50% probability of representation at generation 10, and not until an eight offspring tactic is employed does any particular gene’s probability of survival at generation 10 exceed 99%. Assortative Mating and m All else being equal, due to the risk of genetic drift, the change in gene frequency of an allele due to random sampling, there is a minimum point (m) on this curve delineating the Number of offspring per generation 1 2 3 4 5 6 7 8 9 10 –0.5 0.0 0.5 1.0 Genetic Representation Over Generations: Assuming Exogamy Probability of Individual Gene’s Representation In Generations Downloaded by [Pedro Wolf] at 22:56 24 October 2011 Assortative Mating and Life History Strategy 0 2 4 6 8 Number of Generations 10 Figure 2. Mating systems that reliably produce no = 1:10 offspring per generation, for 10 generations, where 1 offspring per generation is represented by the solid and circle lines, and the dashed line at the top of the graph represents 10 offspring per generation. The x-axis represents the number of generations, and the y-axis represents the certainty. 178 P. S. A. Wolf and A. J. Figueredo point where having fewer offspring than the value represented by this point is equivalent to reduced genetic replication due to the risk of deletion from subsequent generations due to genetic drift alone. In this framework, having a number of offspring (no ) higher than this minimum is equivalent to having positive gene-copying success. Given random mating, eight offspring may very well be where m lies as it confers a 99% chance of being represented at generation 10. To estimate m for 99% certainty of genetic replication, .99 can be substituted for g into Expression 9 to obtain m for various assortative mating strategies and then solving for no . Expression 10. Reproducing any more than this minimum number (m) adds gene-copying success in that more copies of the parental organism’s genes are represented in the subsequent generation; however, any increase in the certainty of being represented in the subsequent generation becomes vanishingly small. The value for m is not fixed. As assortative mating increases the certainty of a gene’s being passed on to the following generation, the theoretical minimum m will thus decrease. This decrease in m makes it possible for carriers of slow LH genes to produce fewer offspring without increasing the risk of omission from the gene pool due to genetic drift alone. Figure 3 emphasizes this point. Under random mating, it takes four offspring to have about a 50% certainty of being represented at generation 10, whereas under a positive 4 and 5 exogomous offspring vs. 3 and 4 under .2 assortative mating Probability of Individual Gene’s Representation In Generation 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Downloaded by [Pedro Wolf] at 22:56 24 October 2011 no > m assuming exogamy 4 Exogamy 5 Exogamy 0 2 assuming .20 assortative mating 3 4 4 6 Number of Generations 8 10 Figure 3. Mating system comparison. The lines represent the following: 1. 2. 3. 4. Solid line with circles represents a mating system with rpp = 0 and a reproductive rate of 4. Solid line without circles represent mating systems with rpp = .2 and a reproductive rate of 3. Dashed line with circles represents a mating system with rpp = 0 and a reproductive rate of 5. Dashed line without circles represent mating systems with rpp = .2 and a reproductive rate of 4. Assortative Mating and Life History Strategy 179 assortative mating strategy (at .2 assortative mating), it takes around three offspring to have the same relative outcome. If we extend this example by one offspring for each strategy, an endogamous (.2 assortative mating) strategist having four offspring produces a 77% certainty whereas five offspring under exogamy produces a lower certainty at 73%. Assortative mating thus enables slow LH strategies to evolve despite the failure of the parent to completely replicate its entire genome, which is essentially equivalent to the threat of genetic drift at the population level. Downloaded by [Pedro Wolf] at 22:56 24 October 2011 Assortative Mating and Homozygosity Although assortative mating may evolve to manipulate m when a slow LH strategy is employed, there is a point where the coefficient of relatedness actually decreases fitness due to the increase in homozygosity for deleterious mutations; however, this point is also not fixed. What has been traditionally been called a fitness indicator may actually serve the purpose of manipulating the point where any increase in assortative mating actually decreases g. If a trait is in fact a true signal of how few deleterious mutations potential partners carry, the signal may serve as an evolved indicator for how much assortative mating continues to increase g. If an individual carries fewer deleterious mutations when compared to the average mutation load within a population, it will be safer to assortatively mate with that particular partner beyond the point where the coefficient of relatedness would predict a decrease in fitness. Therefore, the same conditions favoring high assortative mating should also favor the evolution of preferences for mating with individuals displaying high fitness. For example, take four individuals all carrying the same genotype with the exception of two genes. Each of the phenotypes creates a reproductive rate of three offspring. Where these four individuals differ is hypothetical genes A and B. Gene A controls assortative mating where A codes for positive assortative mating at .20 and a codes for no assortative mating. Gene B controls mate choice in response to fitness indicators where B increases probability of mating with individuals with few deleterious mutations and b does not influence mate choice in terms of fitness indicators. The mating preference genes exhibit the following phenotypic behaviors: 1. 2. 3. 4. (ab) no assortative mating; no preference for genetic quality, (aB) no assortative mating, preference for genetic quality, (Ab) assortative mating, no preference for genetic quality, (AB) assortative mating, preference for genetic quality. These genetic combinations should produce the following results in terms of genetic replication. The first and second genotypes have a 26% chance of being represented at generation 10, whereas the third and fourth genotypes have a 51% chance of being represented in population 10 due to genetic drift alone. Mating at random with respect to the presence of deleterious mutations would decrease g by decreasing offspring longevity (lo ). If this happens at a rate comparable to the increase in g produced by assortative mating, the following should occur: (1) Genotype ab should be out-competed by all other genotypes; (2) genotypes aB and Ab should be equal as the benefits of one mate selection strategy will cancel out the beneficial effects of the other strategy; and (3) genotype AB should outcompete all other genotypes in this system as the beneficial effects of both mate selection tactics will be present. Over time, there should be an increase in the proportion of the AB genotype in the population and result in a correlation between genotype A and B. In reality, these two traits do not evolve in isolation because the number and longevity of offspring are not constant across different LH strategies. A more complex version of 180 P. S. A. Wolf and A. J. Figueredo this model, involving three traits rather than two, would show that assortative mating and preference for genetic quality would not only become genetically correlated to each other through natural selection but that both would become genetically correlated to a slow LH strategy. Downloaded by [Pedro Wolf] at 22:56 24 October 2011 Premature Death and m The risk of premature death of a parent organism’s offspring before those offspring complete their sexual reproductive lives originates from many causes other than deleterious mutations. These premature deaths change the value for n in Expression 10. Any premature death negates the effect of each offspring’s contribution to the certainty of genetic representation in subsequent generations. Previous treatments of LH theory (Roff 1992, 2002; Stearns 1992) assume that the premature death rate that is attributable to unpredictable or extrinsic causes (de ) is fundamentally different than the death rate attributable to predictable or intrinsic causes (di ) when it comes to the evolution of reproductive behavior within a species. The unpredictable nature of extrinsic mortality makes it impossible for adaptations to evolve that solve the adaptive problems posed by these risks of mortality, whereas the predictable nature of intrinsic causes makes it possible and even likely that adaptations that solve those adaptive problems may evolve. One could expand Expression 10 by taking into account the effects of de and di allowing us to solve for the minimum number of offspring needed to maintain a gene that produces positive gene-copying success in spite of these death rates. To keep up with these death rates, the organism would have to increase reproduction in relation to these death rates, possess adaptations that increase offspring survival rates above the population norm or a combination of the two. The amount needed to keep up with these death rates through increased reproduction alone and maintain a positive gene-copying success is expressed in Expression 11. Expression 11. no ≥ m + de m + di m Since di allows for the possibility of evolving adaptations, which decrease the likelihood of premature death, Expression 11 is incomplete. Implied in Expression 12, and in the definition of intrinsic mortality, is the prediction that the longevity effort expended upon offspring (so El ) will decrease their intrinsic mortality. Because a total lack of offspring longevity effort will produce 100% intrinsic mortality, we get the following Expression: Expression 12. di = 1 − so El According to Hamilton’s rule, the optimal degree of offspring longevity effort will be a function of the coefficient of genetic relatedness between parent and offspring (rpo ). In Expression 13, the inclusive fitness of expending offspring longevity effort (El ) is weighted by the offspring survivorship coefficient (so ) and then discounted by the coefficient of genetic relationship (rpo ). In Hamilton’s terms, the benefit to the offspring is, therefore, assessed by (so El ), which is their increased survival probability. Similarly, Expression 14 gives us the cost of the parental effort by weighting the offspring longevity effort (El ) Assortative Mating and Life History Strategy 181 expended by the parental survivorship coefficient (sp ), which is the additional probability of survival of the parent that would have been obtained by not expending the given amount of longevity effort upon the offspring, but instead investing it in parental somatic effort. This therefore gives us the following Expression: Expression 13 (rpo )(so El ) > sp El Because (El ) is found on both sides the inequality, we can divide it out and get the following Expression: Expression 14 Downloaded by [Pedro Wolf] at 22:56 24 October 2011 (rpo )(so ) > sp Similarly, dividing both sides by (so ), we get the following Expression: Expression 15 (rpo ) > sp /so Now, as in Expression 9, we may substitute (rpo ) with (.5 + rpp /2) and obtain the following Expression: Expression 16 (.5 + rpp /2) > sp /so Finally, Expression 17 can be algebraically rearranged to obtain the following solution: Expression 17 (rpp /2) > (sp /so ) − .5 Expression 18. (rpp ) > 2(sp /so ) − 1 This gives us the minimal degree of assortative mating (rpp ) as a simple algebraic function of the ratio of the parental to the offspring survivorship coefficients (sp /so ). This is the only place where an explicit consideration of parental survivorship affects our model. As indicated earlier, the instantaneous, “age-specific” fecundity of an individual iteroparous parent has to be integrated over time (representing repeated bouts of reproduction) but discounted by its probability of surviving into any given point in the future (“age-specific” survivorship) where it might engage in a subsequent bout of reproduction. The optimal allocation of resources between so El and sp El in Expression 13 is, therefore, moderated not only by rpo but by the effects of parental survivorship on future reproduction. The qualitative theoretical prediction that higher degrees of positive assortative mating would increase the optimal degree of parental investment in offspring had been previously made by Rushton (1989, 2009), reasoning that the coefficient of relationship between the parents and the offspring would be increased. 182 P. S. A. Wolf and A. J. Figueredo Downloaded by [Pedro Wolf] at 22:56 24 October 2011 Discussion Sexual reproduction has both substantial benefits and substantial costs. Genotypes that optimize the balance of these costs and benefits will, in the long run, outcompete genotypes that do not. This optimization occurs within the context of environmental regularities in mortality rates due to both intrinsic and extrinsic causes. These environmental regularities, therefore, constrain the optimal solutions to the sexual recombination of genetic material. As the minimum number of offspring (no ) needed to ensure a given certainty of genomic replication (g), or gene-copying success, is not fixed and is partially dictated by the environmental conditions described by intrinsic (di ) and extrinsic (de ) mortality, this theory predicts that there should be a range of LH strategies within a species that may be considered equally adaptive if the species occupies a broad enough range of ecological niches. In addition, intrinsic mortality (di ) is also, by definition, not fixed by the ecology. It is subject to change based on the genetic makeup of the individual, which is in turn based on the history of reproductive and selective events that shaped that particular individual’s genome. As the environment and relevant reproductive events may be constantly changing, any particular individual’s certainty (g) that its genes are going to be adequately represented in future generation can be optimized, as represented mathematically in our final Expression (18). In conclusion, we have presented a mathematical model that ties the selective pressures for positive assortative mating with those for slow LH. As far as we are aware, this is an entirely novel prediction and has survived at least one empirical test (Figueredo and Wolf 2009) using cross-cultural data on assortative mating in humans. This secondary analysis was performed on preliminary data from a large cross-cultural study on assortative pairing in which independently sampled pairs of opposite-sex romantic partners and of same-sex friends rated themselves and each other on LH strategy and on mate value. Data were collected in local bars, clubs, coffee houses, and other public places from three different cultures: Tucson, Arizona; Hermosillo, Sonora; and San José, Costa Rica. It was confirmed that slow LH individuals assortatively pair with both sexual and social partners more strongly than fast LH individuals and that this relation was statistically equivalent in all three cultures sampled. One of the main predictions of our model is that species with faster LH should practice less positive assortative mating, whereas species with slow LH should practice more positive assortative mating. This theory could be further tested in the future using the comparative method, as by examining the animal behavior literature and systematically comparing the LH strategies of various species and the degree of assortative mating that they practice. For example, the enhanced genetic relatedness between parent and offspring under positive assortative mating should selectively favor higher degrees of parental investment, reinforcing slow LH. Another testable prediction is that sympatric speciation due to assortative mating rather than geographic isolation is more likely when the parent species practices a slower LH due to the mutual reproductive isolation among genotypes produced by positive assortative mating. We should, therefore, observe higher rates of sympatric speciation among species with a slower LH. References Beiles A., G. Heth, and E. Nevo. 1983. Origin and evolution of assortative mating in actively speciating mole rats. Theoretical Pop Biol 26:265–270. Charnov, E. L. 1993. 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