Male skew; dude likes ladies

PLoS Genetis has a neat paper up which clarifies something which we kind of already knew, Sex-Biased Evolutionary Forces Shape Genomic Patterns of Human Diversity:

Like many primate species, the mating system of humans is considered to be moderately polygynous (i.e., males exhibit a higher variance in reproductive success than females). As a consequence, males are expected to have a lower effective population size (Ne) than females, and the proportion of neutral genetic variation on the X chromosome (relative to the autosomes) should be higher than expected under the assumption of strict neutrality and an equal breeding sex ratio. We test for the effects of polygyny by measuring levels of neutral polymorphism at 40 independent loci on the X chromosome and autosomes in six human populations. To correct for mutation rate heterogeneity among loci, we divide our diversity estimates within human populations by divergence with orangutan at each locus. Consistent with expectations under a model of polygyny, we find elevated levels of X-linked versus autosomal diversity. While it is possible that multiple demographic processes may contribute to the observed patterns of genomic diversity (i.e., background selection, changes in population size, and sex-specific migration), we conclude that an historical excess of breeding females over the number of breeding males can by itself explain most of the observed increase in effective population size of the X chromosome.

Autosomal refers to the genome which excludes the Y and X chromosome (and mtDNA of course). Assuming equal numbers of males and females in any given generation you expected a ratio of diversity of 0.75 between the X and the autosomes; remember that the number of copies of X circulating within the population are reduced by 25% because males carry only one copy, while women carry two.

But is the 1:1 ratio realistic? There is where effective population size comes in. In any given generation at time t only a proportion of individuals will reproduce to the next one, t + 1 (let's pretend discrete generations here). This varies by species to species, but the effective population size is always smaller than the census population size. Some of this is due to selection; those with fitness enhancing traits replicate and those without do not. But some of this is just pure stochastic process, ergo, the focus on neutral loci in this paper. Using the assumption of neutrality you expect diversity in the genome to vary due to the endogenous parameter s as well as exogenous historically contingent events. If you note a population is very genetically homogeneous, but discover that they have a legend of recent migration and rapid population expansion from a few pairs, it is rather explicable as a function of contingent demographic history. On the other hand, you expect that a population where the effective population has been very small even if it is fixed will be buffeted greatly by stochastic processes in comparison to one with a very large effective population size (though attend to the details here).*

So what if we deviate from a 1:1 ratio in terms of who contributes genetically to the next generation? Effective population while varying sex ratios can be modeled like so:

4 × { (number of males) × (number of females) } / { number of males + number of females }

As an example, imagine a population of 100 where there are 10 breeding males and 90 breeding females. Ignore between individual variance and so on, which would reduce the effective population further, just using the formalism above gives an effective population of 36.

What's going on here? Males contribute about half the genome content to their offspring. So 10 males contribute ~ 50% of the genome, and 90 females ~50%. This obviously reduces the chances of replication of genetic information from females to the next generation vis-a-vis males, while a few males have a outsized "voice" in the genome content of the future. Iterate and you see the implication.

In our own species when we talk about something like "polygamy" we often think of a cultural institution. In the context of evolutionary genetics, don't. What you're curious about is the distribution of reproductive output for males vs. those of females. In general among mammals one assumes that males will exhibit more skew than females, with some males getting more than "their fair share" to a greater extent than females (note that reproduction is often assumed to be a poisson process, when in biologically realistic contexts this likely underestimates reproductive variance). The apotheosis of this trend can be found among elephant seals, while among our close genetic relations one can see the outcome of this evolutionary trajectory among the gorilla.

The authors conclude from the genetic data that there likely was a long term pattern of a larger female breeding population than a male one. Because of the structure of sex ratios at birth the excess is concluded to be a genetic artifact; some males simply do not breed their fair share, and some do breed more than their fair share. It is important to remember that cultural polygamy may differ from genetic polygamy. After all, a society may be officially monogamous, but women who have children with men who are not their spouses may contribute to greater male reproductive skew than would be expected in a pure monogamous mating situation (taking into account normal reproductive variance of course). Additionally, in societies with formalized forms of polygamy there may be less variance than one would expect. For example. in some Australian Aboriginal tribes old men who married many young women often looked the "other way" when their young wives entered into affairs with younger men. Here many of the notional children of the husband with his multiple wives might be the children of the other men in the band. Reproductive variance would be lower than one would expect.

But genetics isn't the only thing that can be brought to exploring this question. I note above that this paper simply clarifies, or adds more ammunition, to something we should already expect. The reason is size differences in sexual dimorphism. In species which are highly polygynous like gorillas and elephant seals male-male competition drives a radical increase in the size of males in relation to females. In contrast, in purely monogamous species there is less male-male competition and so less need for greater size. This heuristic should guide our expectations, as Nature is One. Among the apes one notes that the monogamous gibbons (at least in terms of reproductive skew if not in terms of optimal fidelity) exhibit little between sex difference in size. Gorillas exhibit a great deal. Our own species manifests a modest size difference between the sexes. Ergo, we shouldn't be surprised to see a modest difference in reproductive skew between the sexes leaving an imprint on our genes.

Related: All of the above obviously has a relation to the Trivers-Willard hypothesis.

* I'm making this simpler than it really is, but good enough for the purposes of this post.

Related: Also over at Anthropology.net.