Razib Khan One-stop-shopping for all of my content

September 8, 2010

Sexual selection: lowered expectations edition

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.

sexratio1

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.

sexratio3

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.

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

May 18, 2010

An umbrella against the mutational showers

Filed under: Biology,Genetics,Good Genes,Selection,Sex — Razib Khan @ 2:41 am

Mutations are as you know a double-edged sword. On the one hand mutations are the stuff of evolution; neutral changes on the molecular or phenotypic level are the result of from mutations, as are changes which enhance fitness and so are driven to fixation by positive selection. On the other hand mutations also tend to cause problems. In fact, mutations which are deleterious far outnumber those which are positive. It is much easier to break complex systems which are near a fitness optimum than it is to improve upon them through random chance. In fact a Fisherian geometric analogy of the affect of genes on fitness implies that once a genetic configuration nears an optimum mutations of larger effect have a tendency to decrease fitness. Sometimes environments and selection pressures change radically, and large effect mutations may become needful. But despite their short term necessity these mutations still cause major problems because they disrupt many phenotypes due to pleiotropy.

But much of the playing out of evolutionary dynamics is not so dramatic. Instead of very costly mutations for good or ill, most mutations may be of only minimal negative effect, especially if they are masked because of recessive expression patterns. That is, only when two copies of the mutation are present does all hell break loose. And yet even mutations which exhibit recessive expression tend to generate some drag on the fitness of heterozygotes. And if you sum small values together you can obtain a larger value. This gentle rain of small negative effect mutations can be balanced by natural selection, which weeds does not smile upon less fit individuals who have a higher mutational load. Presumably those with “good genes,” fewer deleterious mutations, will have more offspring than those with “bad genes.” Because mutations accrue from one generation to the next, and, there is sampling variance of deleterious alleles, a certain set of offspring will always be gifted with fewer deleterious mutations than their siblings. This is a genetics of chance. And so the mutation-selection balance is maintained over time, the latter rising to the fore if the former comes to greater prominence.

The above has been a set of logic inferences from premises. Evolution is about the logic of life’s process, but as a natural science its beauty is that it is testable through empirical means. A short report in Science explores mutational load and fitness, and connects it with the ever popular topic of sexual selection, Additive Genetic Breeding Values Correlate with the Load of Partially Deleterious Mutations:

The mutation-selection–balance model predicts most additive genetic variation to arise from numerous mildly deleterious mutations of small effect. Correspondingly, “good genes” models of sexual selection and recent models for the evolution of sex are built on the assumption that mutational loads and breeding values for fitness-related traits are correlated. In support of this concept, inbreeding depression was negatively genetically correlated with breeding values for traits under natural and sexual selection in the weevil Callosobruchus maculatus. The correlations were stronger in males and strongest for condition. These results confirm the role of existing, partially recessive mutations in maintaining additive genetic variation in outbred populations, reveal the nature of good genes under sexual selection, and show how sexual selection can offset the cost of sex.

mutAdditive genetic variance just refers to the variation of genes which affect the phenotype by independent and usually small effects which sum together to produce the range of variation of the trait. Imagine for example that the range of variation in height within the population was 10 inches, and that there were 10 genes which varied, and that each gene exhibited co-dominance. One could construct a model where every gene pair could add 0, 0.5 or 1 inch to the height independently, so that the maximum height could be constructed by adding 10 inches to the baseline and 1 inch per locus, and the minimum height by adding no inches to the baseline when each locus is homozygous for null alleles.

Mutations can be conceived of in the same manner, with each mutation being a new variant which changes trait value. Even if most of the impact of a mutation is masked there is a small effect in the heterozygote state, and this may serve as a fitness drag. The range in mutational load can then naturally be analogized to additive genetic variance, in this case the trait under consideration ultimately being fitness, mediated through life history and morphological phenotypes.

In this report they focused primarily on the weevil’s ability to obtain resources and transform those resources into size, which correlates with greater sexual access for males and fecundity for females (ergo, greater fitness). They bred various outbred and inbred lineages across families of these weevils, because these sorts of crosses gauge the impact of masked deleterious alleles, which will manifest in homozygote state more often between related pairs who share mutations than unrelated ones. They found a correlation of -0.24 between inbreeding and breeding value; in other words the more inbred the pair the fewer offspring. The impact of these recessively expressed alleles is mitigated in heterozygous individuals, but because of the non-trivial impact the number of these alleles within an individual will determine its fitness all things equal.

328_892_F1Interestingly when background variables were controlled males tended to show the greatest fitness drag due to inbreeding depression. This would comport with models of sexual selection where males justify their expense (because they can not bear offspring) within the population by serving as the perishable dumping grounds of bad genes. In particular in a polygynous population a few healthy males with good genes could give rise to most of the next generation, and so providing the balance of selection to the background mutational rate.

Of course mating patterns vary between taxa. The more reproductive skew there is, in particular for males, the more recourse selection has every generation to dump deleterious alleles via selection. In contrast monogamous populations will have less power to expunge mutations in this fashion because there is more genetic equality across males, the bad will reproduce along with the good, more or less. Therefore a breeding experiment of weevils may have more limited insight than these authors may wish to admit. Geoffrey Miller’s The Mating Mind attempted to take the insights of sexual selection and develop a model of human evolutionary history, but it does not seem that this theory has swept all before it. Only time will tell, but until then more breeding experiments can’t help but clarify where theory goes wrong or right.

Citation: Tomkins, J., Penrose, M., Greeff, J., & LeBas, N. (2010). Additive Genetic Breeding Values Correlate with the Load of Partially Deleterious Mutations Science, 328 (5980), 892-894 DOI: 10.1126/science.1188013

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