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Sexual Selection

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41czavSUnNL._SY344_BO1,204,203,200_ Beauty matters a lot in our world. The entertainment and fashion industries are based on beauty. Obviously some aspect of beauty is socially constructed and contextual. Beauty standards can change. There was a time when many aspects of European physical appearance, from light hair and eyes, down to the lack of an epicanthic fold, were excluded from idealized canons in East Asia. Obviously that is not the case today, and one can give a very plausible explanation through recourse to recent history as to why those norms shifted. Similarly, there is even a possibility that something as central to evolutionary psychology as preference for a particular waist-to-hip ratio may vary as a function of material conditions. I is clear from the social historical scholarship that the ideal characteristics of a female mate are strongly conditioned on the resources of the male; lower status males put greater emphasis on the direct economic benefits which their partner may bring because they are more on the margin of survival. For much of history lower status males meant most males. That is, peasants.

And yet cross-culturally there does seem to be a certain set of preferences which one might argue are “cultural universals.” People from “small-scale” societies are still able to consistently rank photographs of people from WEIRD societies in facial attractiveness which correlation with results from participants in developed nations. This indicates that there is a strong innate basis. An element of taste deep in our bones, even if we may inflect it on the margins, or increase or decrease its weight in our calculations of what makes an optimal mate. There may be societies where Lena Dunham’s “thick” physique may be preferred to Bar Refaeli‘s svelte profile, but I am skeptical that there would be societies where the former’s facial features would strike individuals as preferable to those of the latter (one might have to correct for Refaeli’s species-atypical hair and eye color, but European norms are pretty widespread outside of small-scale societies now, so that shouldn’t be a major issue). So the question then becomes: is this adaptive?

Evolutionary psychologists have a panoply of ready explanations. They are often grounded in correlations, and then adaptationist logic. For example, women with lower waist to hip ratios (0.7 being the target) have more estrogen, and are more likely to be nubile, and so are more fertile, all things equal. Since being more fertile is going to be a target of selection, a lower waist to hip ratio is going to be a target of selection, because implicitly there is a genetic correlation between estrogen and waist to hip ratio. The problem is that genetic correlations have to be proved, not assumed. Correlations are not necessarily transitive. Just because A has a positive correlation with B and B has a positive correlation with C, does not entail (necessarily) that A has a positive correlation with C.

With that in mind, a new paper looks at facial attractiveness, averageness of facial features, and heritability of both these traits. They use a twin design, with an N of ~1,800. And, they relate it to a comprehensible causal mechanism: mutational load resulting in increased developmentally instability. Basically, the more mutations you have, the more likely you have to exhibit facial asymmetry, and therefore facial averageness is a good proxy for genetic quality. It is well known that average faces tend to be rated better looking than non-average faces. This is part of an argument that Geoffrey Miller put forth in The Mating Mind, a very fertile work. There is an elegance to it. Unfortunately follow up work over the past ten years is suggesting that this simple model is either wrong, or, everything is a whole lot more complicated.

First, the paper, Facial averageness and genetic quality: Testing heritability, genetic correlation with attractiveness, and the paternal age effect. The abstract gives away the game:

Popular theory suggests that facial averageness is preferred in a partner for genetic benefits to offspring. However, whether facial averageness is associated with genetic quality is yet to be established. Here, we computed an objective measure of facial averageness for a large sample (N = 1,823) of identical and nonidentical twins and their siblings to test two predictions from the theory that facial averageness reflects genetic quality. First, we use biometrical modelling to estimate the heritability of facial averageness, which is necessary if it reflects genetic quality. We also test for a genetic association between facial averageness and facial attractiveness. Second, we assess whether paternal age at conception (a proxy of mutation load) is associated with facial averageness and facial attractiveness. Our findings are mixed with respect to our hypotheses. While we found that facial averageness does have a genetic component, and a significant phenotypic correlation exists between facial averageness and attractiveness, we did not find a genetic correlation between facial averageness and attractiveness (therefore, we cannot say that the genes that affect facial averageness also affect facial attractiveness) and paternal age at conception was not negatively associated with facial averageness. These findings support some of the previously untested assumptions of the ‘genetic benefits’ account of facial averageness, but cast doubt on others.

I’m going to reproduce some of the results from Table 4 below.

Averageness Attractiveness
Heritability Non-heritable Heritability Non-heritable Genetic correl Env correl
Female 0.21 0.79 0.6 0.38 0.11 0.21
Male 0.22 0.78 0.62 0.39 0.11 0.08
Overall 0.21 0.79 0.6 0.4 0.11 0.16

What you see is very modest heritability for averageness, and a decent one for attractiveness. But, there’s no statistically significant evidence that the genetic correlation is there (the confidence intervals are huge around 0.11, from 0 to 0.35). Though they state the environmental correlation passes statistical muster (so common environmental variables might be producing attractiveness and facial averageness). Please note that a heritability of 0.6 does no mean a correlation of 0.6. The heritability of height is 0.8 to 0.9, but correlation of the trait across siblings is ~0.5. Heritability is the proportion of variation of the trait explained by variation in genes, in the population.

If you just look at heritabilities, averageness seems to have been under stronger selection than attractiveness all things equal. Usually strong directional selection removes the heritable variation on a trait. The high heritability gives us a clue that there are a lot of ugly people around still, and some of that is just the way they are born. In contrast, there are fewer people with lop-sided faces. These are subjects from a Western society, so I bet the results are going to be different in a high pathogen load environment (my expectation is that heritability will decrease, but perhaps it will actually increase because as genetic factors which allow for one to be robust to disease will become more important in explaining variation in the trait).

Finally, in the near future there will be high coverage genomic sequences from many people. If you hit the same marker more than 30 times you can conclude with decent confidence if it’s a de novo mutation unique to the individual. You can actually check how well mutational load tracks with averageness and attractiveness (each human has <100 de novo mutations, so there’s a lot of inter-sibling variance presumably). At this point I’m moderately skeptical of a lot of the selectionist models, whereas five years ago I’d have thought there would be something there, and it would be easy to discover. And it may be that beauty, like many aspects of culture, is not about adaptation and function in any direct sense, but simply a cognitive side effect. Like what Steve Pinker has stated about music. I don’t really believe that, but we can’t dismiss that position out of hand anymore.

• Category: Science • Tags: Beauty, Sexual Selection 
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Citation: Figure adapted from Lumley, Alyson J., et al. “Sexual selection protects against extinction.” Nature (2015).

9780198503361_200 Sex is a big deal. William Hamilton spent a significant part of his career on the topic, and the second volume of his collected papers, The Narrow Roads of Gene Land, is focused on this issue. Whenever I talk about sex in an evolutionary biological context one thing that always pops up is why males? In other words, why do so many complex organisms have a whole sex which does not bear offspring? Parthenogenetic lineages of organisms where females can reproduce asexually have double the per generation reproductive output as sexual lineages. And yet over evolutionary history it seems clear that in lineages where sexual and asexual species coexist, the latter are always novel derived lineages. In other words, asexual lineages have a high extinction rate. Sex, and more specifically males, must be good for something. What then?

One hypothesis is that males are good for purging genetic load via sexual selection. On a genetic level all individuals carry deleterious mutations, which they pass on to their offspring. But, because of sample variance in transmission, there will be a distribution of outcomes in any given set of offspring. By chance some individuals will exhibit a higher load of deleterious alleles, while others will carry fewer alleles. If this load is correlated to traits which are visible to the opposite sex, then excess load every generation can be purged through reproductive skew. In other words, one might envisage a situation of sexual selection-mutation balance, where de novo mutations introduced every generation are balanced against deleterious alleles purged from the population through selection of more fit males.

330px-Tribolium_castaneumAll good in theory. But is this empirically true? A new paper in Nature suggests it is. At least for the red flour beetle. The paper is titled Sexual selection protects against extinction. Recall that asexual lineages seem to be more likely to go extinct when one examines them with comparative phylogenetic methods (i.e., with in a clade asexual lineages are invariably young in evolutionary time scales, implying that they do not last long).

41SSqWzJIGL._SY344_BO1,204,203,200_ The adapted figure above shows the experimental results which support the proposition that sexual selection purge deleterious alleles. These experiments ran for ~10 years, and consisted of varying primary treatments which differed in terms of intensity of sexual selection in red flour beetles. In panel A you see a comparison between a male and female skewed sex ratios (9:1), red and blue lines respectively. In a male skewed ratio the males are competing for the attention of a few females, and in a female skewed ratio the situation is the reverse. To test for the fitness of the lineages the researchers took the outcomes of long term breeding in these scenarios (fixing the effective population sizes to be comparable) and then forced them to engage in sibling matings. This would “expose” deleterious recessive alleles because of the nature of inbreeding. As is evident above in the female skewed (blue) lineages there is a much quicker extinction rate as inbreeding begins to expose deleterious alleles in the recessive phenotype. In the second set of experiments the authors compared polyandrous (5 males to 1 female) and monogamous lineages. Again, you see that the polyandrous lineages are much more robust to inbreeding, suggesting that sexual selection driving reproductive skew correlated with mutational load is resulting in a lower population wide genetic load.

41czavSUnNL._SY344_BO1,204,203,200_ There are many arguments for why sex persists (though many of them do not seem to directly address the cost of males, since sexuality does not necessarily entail two different sexes where one does not bear offspring or produce eggs). I don’t think that sexual selection needs to be the explanation as such. Additionally, I think there is the problem that extremely skewed sex ratios as is the case above does not seem biologically plausible in many organisms. In big and slow breeding organisms, such as humans, extreme sex ratios are not typically common. It seems unlikely that sex is maintained purely through purging of deleterious alleles via a “good genes” model of sexual selection. But then to truly test this hypothesis it strikes me that some sequencing methodologies could be brought to bear. For example, do individuals with lower load have a higher realized reproductive fitness? This is entirely testable.

Citation: Lumley, Alyson J., et al. “Sexual selection protects against extinction.” Nature (2015).

• Category: Science • Tags: Sex, Sexual Selection 
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Citation: Sexual selection drives evolution and rapid turnover of male gene expression

cover150x250 Charles Darwin’s sequel to was The Origin of Species is often known popularly as The Descent of Man. But of course the full title was The Descent of Man , and Selection in Relation to Sex. Darwin was then an early expositor of sexual selection theory, though R. A. Fisher also made his contribution. My own interest in the topic has been partly motivated by the fact that I perceive many people seem use sexual selection as a deus ex machina to explain variation or change where no plausible mechanism can otherwise be provided (recall that this has come up with EDAR). Over a decade ago Geoffrey Miller wrote a book, The Mating Mind, which attempted to take Charles Darwin’s original ideas to heart. I’m not sure how much of the original arguments Miller would stand by today, but it was an entertaining read. My own first encounter with the idea of sexual selection was in the work of Jared Diamond in the early 1990s. In particular, in The Third Chimpanzee he offered that racial variation in human types might be due to sexual selection for aesthetic characters, as opposed to ecological adaptation (see also Peter Frost’s model of the origin of European complexion). But all this conjecture of human variation often strikes me as a touch too speculative. Ultimately what does the theory and the patterns on the tree of life say? More substantively, as a genomicist I’m curious as to the sequence wide signals which one might see presuming a species is subject to sexual selection. Ergo, two weeks ago I blogged The Once and Future Genomics of Sexual Selection.

mating-mind-193x300 So naturally I was very interested when this came into my PNAS feed: Sexual selection drives evolution and rapid turnover of male gene expression. Basically the authors looked at differential gene expression and sequence level evolution across a lineage of birds to see if there were patterns correlated with presumed intensity of sexual selection. The figure above illustrates several such trends. Species which were subject to stronger sexual selection on males showed a higher proportion of male-biased genes. I’m not usually very interested in work on transcriptomes, but it strikes me that this is going to be a really big deal in the near future if sexual selection is common and it operates primarily through modifying patterns of gene expression. With only six species the p-values above aren’t the greatest. Perhaps the results won’t stick, but, they open a window toward examining evolutionary processes in a comparative manner which allows us to gauge just how pervasive sexual selection is as a force in driving phenotypic variation.

I’ll finish with this conclusion from the authors:

Taken together, our results indicate that the focus of sexual selection shifts rapidly across lineages. Our results also suggest that sexual selection acts primarily on expression, which may be more labile and less functionally constrained than coding sequence and therefore more likely to be influenced by short-term mating system dynamics among related species. The lability of gene expression evolution is illustrated in recent experimental evolution approaches that found an association between sex-biased gene expression and variations in sex-specific selection (11, 13). Gene expression lability is also clearly illustrated by the rapid turnover of sex-biased genes in our phylogeny (Fig. 2), which has also been observed in other animal clades (6, 46). Furthermore, rank order correlations show that gene expression divergence increases with evolutionary time across the Galloanserae (Fig. 3), again illustrating the lability of gene expression.

Citation: Sexual selection drives evolution and rapid turnover of male gene expression.

• Category: Science • Tags: Genomics, Sexual Selection, Transcriptome 
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250px-Paonroue Evolutionary biology predates genetics. This is well known. One of the major problems with Charles Darwin’s original theory is that its lack of a plausible mechanism of inheritance meant that it was difficult for him to conceive of how heritable variation could be maintained over the generations. A “blending” model, where the offspring are a synthesis of the trait values of the parent, is intuitively appealing, but also implies that all the variation is going to be “mixed away” very quickly. In contrast, a Mendelian genetic framework, where traits are encoded by discrete and particulate units of inheritance, “genes,” illustrates simply how variation can be maintained despite mixing between lineages in sexual organisms. In short, each generation is simply a reconfiguration of the discrete elements of variation of the previous generation (see: Mendel’s laws).

255217 Eventually R. A. Fisher fused what had been rival traditions, the Darwinian/biometrical and Mendelian genetical, into a single framework in his The Correlation between Relatives on the Supposition of Mendelian Inheritance. This was further extended in The Genetical Theory of Natural Selection, and elaborated in more detail by the broader coterie of population geneticists in the early to middle decades of the 20th century, culminating in the Neo-Darwinian Synthesis.

The fusion of genetics with evolutionary biology allowed for a deeper investigation of the dynamics of evolutionary process. This is because of the fact that genes are concrete and definable units of evolutionary bookkeeping (the reason that economics is the most prominent of the social sciences also is grounded in the existence of transparent currencies which mediate exchanges). Though there are models of evolutionary processes which do not rely explicitly on genes, when possible genetic models are optimal. The broader population genetic worldview conceives of evolution as change in allele frequencies over time, and as such made evolution measurable in a very concrete sense via genetic analysis. The emergence of molecular methodologies in the 1960s, and genomics in the 2000s, has resulted in progressively more power to understand how evolutionary change affects the distribution of genetic variation amongst organisms. With genome-wide analyses now available researchers can ascertain the power of selection (positive, negative, background, and balancing) within natural populations.

But one area of evolutionary biology that has been relatively untouched by the genomics revolution is that of the study of sexual selection. This is a major gap, because sexual selection is an intuitively appealing idea which often serves as a deus ex machina when you have no other explanation on hand. So it was of great interest to me to see this review paper, The locus of sexual selection: moving sexual selection studies into the post-genomics era, in the Journal of Evolutionary Biology. There are several major issues with genomics and sexual selection which are highlighted in this review. First, it seems that many sexually dimorphic traits which are being driven by sexual selection vary due to differences in gene expression across the sexes, possibly due to modifications on regulatory elements or alternative splicing. Simple sequence level analyses then may not be good at capturing these sorts of dynamics. Second, sexual selection can leave different signatures because in some cases there are antagonistic pressures between the two sexes. Additionally, sexual selection is often frequency dependent, rather than a simple positive sweep toward fixation (as noted in the paper, a simple sweep would result in exhaustion of variation, meaning sexual selection is a very ephemeral phenomenon). Finally, there is extensive discussion of the utilization of GWAS to discover loci associated with mating fitness. Much of this work has already been done in Drosophila.

Which brings me to the point that from reading this review I have a hard time believing that sexual selection is a strong force for humans for most of history. The reason being that our reproductive skew is just not that notable in comparison to the experimental models cited within the paper. But it seems to me that a better understanding of the relationship between sequence level and regulatory variations in humans could get at this question indirectly, since there are still live debates as to the long term nature of human mating patterns. Presumably if sexual selection was copious then there’d be more extant regulatory variation, perhaps maintained by balancing selection.

Citation: Wilkinson, Gerald S., et al. “The locus of sexual selection: moving sexual selection studies into the post‐genomics era.” Journal of Evolutionary Biology (2015).

• Category: Science • Tags: Evolution, Genomics, Sexual Selection 
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Frank analytic clarity?

Sexual selection is a big deal. A few years ago Geoffrey Miller wrote The Mating Mind: How Sexual Choice Shaped the Evolution of Human Nature, which seemed to herald a renaissance of the public awareness of this evolutionary phenomenon, triggered in part by debates over Amotz Zahavi’s Handicap Principle in the 1970s. Of course Charles Darwin discussed the process in the 19th century, and it has always been part of the arsenal of the evolutionary biologist (I first encountered it in Jared Diamond’s The Third Chimpanzee, where he lent some credence to Darwin’s supposition that human racial differences may be a consequence of sexual selection). But this bump in recognition for sexual selection seems to be accompanied by its co-option as a deus ex machina for all sorts of unexplained events. And yet as they say, that which explains everything explains nothing.

To get a better sense of the current scientific literature I consulted A Guide to Sexual Selection Theory in the Annual Review of Ecology, Evolution, and Systematics. The image above is from an actual box in this review! Normally technical boxes illuminate with an air of superior authority (e.g. “it therefore follows from eq. 1…/”), but it seems to me that the admission that a parameter can be represented by the verbal assertion that it’s complicated tells us something about the state of sexual selection theory. In short: its formal basis is baroque because the dynamic itself is not amenable to easy decomposition.

Not just for the peacocks
Credit: George Biard

First, for those who are unfamiliar with the topic, sexual selection theory comes in several flavors. As the term implies sexual selection emerges from differential fitness due to the preferences of individuals for various favored traits. I will admit beforehand that my personal preference is that sexual selection not be so artificially detached from natural selection more broadly, but the nature of the discussion is usually one where such strong distinctions are made. So I won’t make too much of a fuss about that.

Perhaps the most obvious area of difference is that there are forms of sexual selection where there is no strong exogenous fitness implication. By this, I mean that there is no great adaptive value to the trait being favored proportional to its selective value (note: the trait may not necessarily be totally neutral initially, one could imagine non-sexual preferences which triggered subsequent sexual dynamics). This is at the heart of Fisherian runaway process. The basic principle here is that if there is a correlation for a trait which is preferred, and the preference for that trait, then the two will amplify each other’s fitness and rapidly sweep up in frequency within the population. A simple illustration will suffice. Imagine that within a bird population a subset of females prefers longer beaks. There is normal variation within the population for beak length, which implies that the fitness of the shorter and longer beaked individuals is not so different. If a subset of females prefers longer beaks, then males with longer beaks will have higher fitness, because they have reproductive access to all the females, while those with shorter beaks only have access to those females who do not exhibit a preference. In the next generation there will be a correlation between longer beaks (from the fathers) and preference for longer beaks (from the mothers). Because of the correlation there is now also selection for the preference as a byproduct of selection for the longer beaks! This means that selection for longer beaks is greater, and therefore selection for the preference is greater, and so forth.

Credit: Doug Janson.

This dynamic is a byproduct of the structural factors inherent in sexual reproduction. In particular, dimorphism between the sexes, and the importance of selection in mate choice. Fisherian process is rapid, it is arbitrary, and, it is likely subject to oscillations as it is kept in check by other evolutionary forces. In the example above continuous selection for long beaks would obviously have some deleterious consequences as natural selection began to take its told. At that point no matter how “sexy” long beaked sons were, it would all be for naught if they couldn’t even be viable. This sort of sexual selection predicts a constant bubble of diversity of morphology over space and time.

Another sexual selection framework where fitness is a consequence of indirect forces is sensory bias. Again, an example will suffice. Imagine birds which are frugivores. In this situation there will be a natural preference for bright and vibrant colors, because those are the colors of the main food item, fruit. Females may naturally prefer individuals with the same vibrant colors as their primary food item (this may even be selectively beneficial, as it indicates strong preference of high quality food). As in the Fisherian process above obviously this can come at a cost. Bright fruit want to be eaten. Bright animals do not.

Credit: Pavel Riha

This highlights again the fact that over and over sexually selected traits may not be beneficial in the conventionally adaptive sense. They may even be a detriment to fitness! And this is also an observation of the Handicap Principle, though it turns logic on its head at the end of the game. Its counter-intuitive thesis is that costly signals in fact indicate that an organism is extremely fit. The underlying reason is that costly signals are by their nature honest. Massive antlers for example take a great deal of biological energy in production and maintenance, and, they may also make one more vulnerable to predators. Only the most superior individuals could incur such costs! The relationship here to Thorstein Veblen’s idea of “conspicuous consumption” is so obvious that I won’t bother to elaborate on it. Crazy as it may sound, from what I can tell the Handicap Principle has now come to be accepted by many biologists (Richard Dawkins’ for example has done an about face on the theory).

The Handicap Principle is arguably a model of a “good genes” of sexual selection. Unlike Fisherian runaway or sensory bias the preference is rooted in the genuine fitness of the individual as evaluated by external metrics (at least in the indirect sense of genetic health). Theories of beauty in evolutionary psychology are often implicitly predicated on this model, where high symmetry and extreme secondary sexual characteristics suggest few deleterious mutations interfering with the idealized development of the individual. The explanations for why larger size in males and larger breasts and buttocks might signal fitness are also so obvious in comparison to something like Fisherian runaway that many people find direct benefit models also more plausible. That is, not only do these traits signal good genes, but they confer immediate benefits for survival and function.

But plausibility does not lead us toward the truth in all cases. Sexual selection models explicated in verbal terms often tend toward circularity and confusion. A real thought experiment could run like so. You have a population where females prefer attractive males (e.g. they are more vibrant in their plumage). But the fitness of the females (in particular, the suvivorship of their offspring) is also depend upon mate provisioning of supplementary resources. One can easily imagine a scenario where promiscuous attractive males and monogamous less attractive males converge upon the same equilibrium fitness because of heterogeneity in female mate choice. Some females may opt for “cads,” who stray and invest little in their offspring, even though those offspring are of high genetic quality. Other females may opt for “dads,” males who have lower genetic quality, but remain more invested in their smaller number of offspring. These offspring may have higher survivorship because of the added investment. Verbal elaborations of sexual selection seem never to give a “final answer,” because there is always “on the other hand.”

And this is why I wanted to review the available literature. Unfortunately I gained little extra clarity, as the formalism above implies. The authors suggest there are four primary avenues by which sexual selection is explored: population genetics, quantitative genetics, invasion approaches, individual-based simulations. I am not particularly familiar with ‘invasion approaches,’ though in its broad outlines it seems similar to the quantitative genetic method. The population genetic methods are powerful because they start from first principles and explicitly model parameters such as linkage. But there are limits to the analytic tractability of complex phenomena such as sexual selection in population genetic models, for example, multilocus approaches tend to be difficult. The quantitative genetic methods make the standard assumptions of normal distributions for straits, and are gene blind (they look at the phenotype). They seem a nice complement to the population genetic methods, and are often useful in more practical field research. Finally, the simulation approach suffers from the lack of computational power to explore the whole parameter space.

In relation to the simulation approach, last year a phylogeneticist told me that 15 years ago researchers assumed they could never operationalize maximum likelihood models in their lifetimes. Of course today ML based packages are the ‘fast’ strategies in relation to the more heavy duty Bayesian frameworks in phylogenetics. I point this out because I have faith that simulation may be the ultimate way to go for understanding sexual selection over the long run, supplemented by the other methods as scaffolds to reduce the parameter space. We may not be able to explore the whole space of possibilities, but that is the nature of science.

My primary concern for the formal models as outlined in the review is that many of them assumed weak selection. This is a feature of many population genetic models (e.g. see W. D. Hamilton’s original work on inclusive fitness), but from the perspective of evolutionary genomics some of the most fascinating possibilities for sexual selection are subject to strong selection. For example, many researchers appeal to sexual selection to explain the pigmentation complex of European populations, but more and more evidence suggests that these loci have been subject to relatively strong selection. Is this plausible for sexual selection? Do we even know how strong sexual section might operate? Fisherian runaway is an obvious candidate, but this process is so rapid, and so protean, that it seems unlikely.

A major long term problem with sexual selection theories is that they seem to imply oscillatory dynamics when equilibria are more easy to digest (and traditionally many classical models are oriented toward solving for equilibria). This is why models of positive natural selection are so straightforward, they have a beginning and an end. This does not seem to be the case for more realistic sexual selection models. Rather than a specific answer to a given biological question sexual selection theory may be more useful as a way to explain the constant background flux of evolutionary process. At this point I am not convinced that it is robust enough to give us good “rough and ready” rules of thumb which we can apply as a sieve upon the welter of evolutionary genomic results.

But progress is being made, and in concert with fields like game theory and computer science I suspect that the future is going to be bright.

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800px-Pfau_imponierendSexual selection is, for lack of a better term, a sexy concept. Charles Darwin elaborated on the specific phenomenon of sexual selection in The Descent of Man, and Selection in Relation to Sex. In The Third Chimpanzee Jared Diamond endorsed Darwin’s thesis that sexual selection could explain the origin of human races, as each isolated population extended their own particular aesthetic preferences. More recently the evolutionary psychologist Geoffrey Miller put forward an entertaining, if speculative, battery of arguments in The Mating Mind: How Sexual Choice Shaped the Evolution of Human Nature. It’s clearly the stuff of science that can sell.

Sexual selection itself comes in a variety of flavors. Perhaps the most counterintuitive one on first blush is the idea that many traits, such as antlers, are positively costly and exist only to signal robust health which can incur the cost without debility. The idea was outlined by Amotz Zahavi in The Handicap Principle in the 1970s. Initially dismissed by Richard Dawkins in the original edition of The Selfish Gene, Zahavi’s ideas have come into modest mainstream acceptance, and the second edition of Dawkins’ seminal work reflects a revised appraisal. This is really a subset of a “good genes” model of sexual selection, whereby females select from a range of males which would exhibit variance in mutational load. A more capricious and erratic form of sexual selection is “runaway,” which like genetic drift needs no rhyme or reason. Rather, arbitrary initial preferences can become coupled with heritable preference in a positive feedback loop which drives the mean phenotypic value of a population off the previous median, until natural selection enforces a countervailing pressure once the trait starts to become excessively maladaptive (e.g., imagine selection for longer and longer tail feathers until the ability of a bird to fly is inhibited).

ResearchBlogging.orgPaul_Giamatti_2008But notwithstanding the inevitable press which the theory gets, and its centrality to several popular science books, the main action in the area of sexual selection is in the academic literature (contrast this with the aquatic ape hypothesis). Many of the verbal outlines of sexual selection are highly stylized, as economists might say. We are treated to images of stags with massive antlers facing off, elephant seals strutting their stuff, and beautifully plumaged birds gathering for a lek. Set next to this is a body of mathematically oriented models, short on color, long on Greek symbols. But these formal models are valuable. Obviously there is a wide range of variation across species in terms of how sexual selection plays out (if it does so at all within a given species, sexual or asexual). The sexual dimorphism of elephant seals is not the norm against which all species are judged. To explore the variables which produce this pattern of difference one must analyze them in an algebraic fashion, where each can be manipulated in isolation so as to properly characterize its impact. So with that, a paper from The American Naturalist which purports to show how assortative mating could emerge in a sexual selective framework, Make love not war: when should less competitive males choose low-quality but defendable females?:

Male choosiness for mates is an underexplored mechanism of sexual selection. A few theoretical studies suggest that males may exhibit—but only under rare circumstances—a reversed male mate choice (RMMC; i.e., highly competitive males focus on the most fecund females, while the low‐quality males exclusively pair with less fecund mates to avoid being outcompeted by stronger rivals). Here we propose a new model to explore RMMC by relaxing some of the restrictive assumptions of the previous models and by considering an extended range of factors known to alter the strength of sexual selection (males’ investment in reproduction, difference of quality between females, operational sex ratio). Unexpectedly, we found that males exhibited a reversed mate choice under a wide range of circumstances. RMMC mostly occurs when the female encounter rate is high and males devote much of their time to breeding. This condition‐dependent strategy occurs even if there is no risk of injury during the male‐male contest or when the difference in quality between females is small. RMMC should thus be a widespread yet underestimated component of sexual selection and should largely contribute to the assortative pairing patterns observed in numerous taxa.

The title is accessible and charming, but the paper is dense on mathematical formula and computational esoterica. It screams “trust me with my parameters!” But reality is a complex and manifold thing, and it may be that to model it one must go beyond elegant simplicity. As noted in the above abstract sexual selection models are often spare. That’s the beauty of a model, you remove all you can from the reconstruction of reality until you start losing the aspects of reality which you’re trying to understand and predict. I am not totally familiar with the sexual selection literature, so the first table is helpful insofar as it gives a sense of the scope of previous models which this paper is an extension of, and to some extent rejoinder to.


The main parameters to focus on in this study are the quality of the males and females, the competition between males, and the cost of mating. All the parameters checked off for the current study relate to these broad classes; density for example would increase competition, as would shifting the sex ratio. This being a model of the “mating game” rather than all the phenomena which might occur in the life history of individuals in a species, it is constrained in a somewhat peculiar manner. Males have a specific finite lifetime, and can enter into a serial set of relationships. These relationships are of finite length naturally, and, a particular fraction of the lifetime of a given male, though that fraction may vary within the model. Additionally, males have to engage in “pre-copulatory guarding” before gaining a reproductive payoff. Basically, the male can not mate for a period of time after pairing up with a female. During this guarding period the male may have to fend off suitors, so there is a risk that the investment is all for naught. This is the dimension where the quality of both male and female come into play. For example, low quality males are not good defenders, and high quality females will attract a lot of attention. There are also factors such as predation risk while seeking a partner, which one must do if one loses one’s current partner to a superior male, or, one is initially unpaired and is deciding whether to reject to accept the offers of pairing up with a female.

Frankly, the model outlined in the paper is convoluted, and it probably says something that they have to nest a lot of the details into the supplements. Table 2 has all the parameters of interest.


As you can see some of the parameters have a few discrete values. Some of these are obviously continuous variables in reality, but for the purposes of modeling you have to simplify, especially if you’re going to do something computationally intensive. They ran the “game” of interactions over several different variations of the parameters, and noted how males varied in their evolutionarily stable strategy. Below are three figures which illustrate the response topographies of males of high and low quality to females of high and low quality, with number of interactions on the y-axis (the axis projecting “away” from your viewpoint perspective), and “rejection index” on the z-axis (vertical). High quality males are in the top panels, low quality males in the bottom panels, high quality females in the left panels, and finally, low quality females in the right panels. Each figure has a different parameter varied on the x-axis, as per the labels.

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The rejection index is such that below 0 denotes acceptance and above rejection. In the first figure the variable is the time invested in each reproductive event, ranging from 1% to 50% of the male’s lifetime. In this situation high quality males accept high quality females, and reject low quality females, invariably. But low quality males are more accepting of low quality females as the time invested increases, and tend to reject high quality females. Why? High quality females would likely attract attention from high quality males, against whom the low quality males could not compete successfully. In the mating game pairing up with a high quality female would be a low payoff action, as the probability of keeping such a female and reproducing is low. The logic is inverted for low quality females, who would attract less attention from other males. Granted, these females are less fecund, but low fecundity is better than no fecundity from the perspective of the low quality male.

The second figure varies fecundity ratio between the high and low quality females, from 5% to 100%. In the second case there’s no difference in fecundity between the two classes, and that explains panel B, where the high quality males drop sharply into acceptance territory for low quality females as the x-axis verges to 100%. For low quality males the picture is different, as they begin to reject much more quickly once the ratio difference starts to converge. Observe however the effect of the y-axis, number of female interactions assuming one is not guarding a mate. As the number of these interactions increases the rejection threshold keeps dropping as low quality males become less and less inclined to guard high quality males. This has to be because the greater the number of interactions which freelance males have, presumably the greater the number of competitive interactions whereby these males may “steal” a female from a male who is guarding one.

Finally, the last set of figures focuses on “operational sex ratio,” OSR. The OSR ranges from 0.2, female-biased, to 2.4, male-based. When there is a deficit of females high quality males will begin to accept pairings with low quality females, as is clear in panel B of the third figure. This makes rational sense in an environment of “scarcity.” The behavior of low quality males is more peculiar. In a situation of extreme female surplus their behavior converges upon that of high quality males: they reject low quality females, and accept high quality ones. As the sex ratio verges toward 1 the low quality males begin to reject high quality females and accept low quality ones. It seems that balanced mating ratios result in optimal trait matching, at least in terms of genetic quality, in the context of male competition for females (i.e., low quality males may prefer high quality females, but that is not an optimal decision because the likelihood of a payoff is low). But as the sex ratio verges toward a male surplus there are no good options for low quality males; the high quality females will reject them, because there are high quality males galore for them to select from, and the low quality females are now acceptable to high quality males, who will win them in the competition with low quality males.

Much of this is common sense. The mapping between formal quantitative model and verbal description is rather good. We know intuitively that in a context of male surplus it is the low quality males who will be shafted, and that low quality females will become valuable. You can offer up anecdote from engineering universities, or the army, or cite historical examples such as frontier societies with male-biased sex ratios. In modern day Punjab men import wives from poorer regions of eastern South Asia because of a sex-ratio imbalance. But here is where numbers are of the essence, as quantitative models show you how shifting the variates shifts the response. There has been some concern in relation to “bare branches”, men who can not marry in Asia, and its possible impact on societal stability. But one must keep in mind the exact proportion of bare branches within a society when predicting instability due to manic competition for women. Formal models can give us a better guide as to thresholds which should concern us.

Ultimately papers like this need to be validated by experiment and observation. But they’re useful toolkits, sharpeners of thought and conceptualization. It’s hard to test, verify, and refute, if you don’t pose the question and make a prediction in a clear and distinct manner.

Citation: Venner S, Bernstein C, Dray S, & Bel-Venner MC (2010). Make love not war: when should less competitive males choose low-quality but defendable females? The American naturalist, 175 (6), 650-61 PMID: 20415532

Image Credit: BS Thurner Hof, Kristin Dos Santos

Razib Khan
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