BOX 1.

Choices in how to model sexual and parental antagonism on sex chromosomes

When modeling evolutionary conflict, evolutionary geneticists choose between traditions that emphasize either the agendas of conflicting parties or the genetic details of the biological system. Because there has been no third tradition that allows us to train a clear lens on all of the selective angles while simultaneously preserving a focus on the particulars of the genetics, we advocate a form of pluralism, where conflict is modeled in both ways to harness the unique strengths of each.

As an illustration, consider Haig (2006) and Patten and Haig (2009). In the former, Haig neatly reasons that matrigenic interests are preferentially served by X chromosomes when there is parentally antagonistic selection. That is, when alleles confer benefits on matrilineal inclusive fitness and harm on patrilineal inclusive fitness or vice versa. Haig arrives at this prediction in a manner similar to how others have predicted a female bias on the X when it comes to sexually antagonistic selection. He reasoned that because the X chromosome will be maternally derived twice as often as paternally derived, genes on the X will be selected more strongly when in the maternally-derived class and so the X chromosome should evolve effects that benefit matrilineal inclusive fitness at the expense of patrilineal inclusive fitness, where all relatednesses are computed in reference to the maternally or paternally derived allele at a locus (Haig 2006).

Left uncertain by this approach, however, is whether a population will actually evolve to meet this prediction. Might it get hung up on an internal polymorphism instead? And does it matter how strong the selective differences among alleles are? From Haig’s (2006) model, it is clear what X chromosomes “want” to do, but whether genetic particulars will get in the way and prevent them from getting what they want is best tested by population genetic models.

Patten and Haig (2009) produce such a test with their population genetic model of parental antagonism on the X chromosome. To avoid the unwieldiness that comes with trying to capture social complexities in a population genetic model, they adopt a seemingly odd assumption about the fitness of reciprocal heterozygotes. Specifically, they “captured” parental antagonism by setting reciprocal heterozygotes as the most and least fit female genotypes, respectively (see also Patten et al. 2013).

This theoretical contrivance ensures that one allele fares better when maternally derived, and vice versa for the other when paternally derived. Because this is not an inclusive fitness scheme, it misrepresents the true causal structure of Haig’s (2006) system, but it nonetheless captures the direction of the forces at play and allows predictions about which sorts of alleles—matrilineal-benefitting or patrilineal-benefitting—have an easier time of invading a population when rare.

In this case, the two approaches arrive at the same prediction. Modeled either way, the X chromosome has a matrilineally-biased agenda, and alleles that benefit matrilines should therefore come to be over-represented on the X chromosome. Yet, the benefits of pluralism are there to see. From the more agential models, one can clearly identify where selection is operating—who benefits, who suffers the costs—and see intuitively how selection can spur evolutionary change. And from the population genetic models, one comes to trust that details of the genetics do not get in the way of achieving the predicted result from the agential models.

As a second illustration, we turn to sexual antagonism on the X chromosome where again the two approaches have been profitably combined (see Rice 1984; Patten and Haig 2009; Fry 2010; Frank and Crespi 2011; Mullon et al. 2012; Patten 2019; Frank and Patten 2020)—sometimes even in the same paper (e.g. Hitchcock and Gardner 2020; Klein et al. 2021). The question here is how sexually antagonistic selection will shape genes residing on X chromosomes. Should we expect these genes to be biased in favor of producing male-beneficial or female-beneficial effects? Or unbiased? The early intuition was that owing to the X chromosome spending 2/3 of its time in female bodies, it should achieve a female bias. This intuition has roots in the theory of reproductive value (Frank and Crespi 2011). But with a population genetic approach Patten (2019) showed the possibility that the X chromosome should actually be male-biased in its effects, despite the extra time it spends in females. To arrive at this, he took the standard approach of specifying genotypes and their corresponding fitnesses and then he solved for the conditions that allowed for invasion of novel mutant alleles.

Specifically, he compared two models (Table 1). These differ in which sex receives the benefit of the mutant allele, X1, but were taken to be otherwise comparable, provided dominance, h1, was equal to 1–h2, this latter assumption made to equalize the dominance of the beneficial allele in the ensuing comparison. Patten (2019) then showed that the first model, in which males gain the benefit of the mutant allele, yielded invasion conditions that were easier to satisfy than the second. Further, when polymorphic equilibria were achieved, Model 1 had higher allele frequencies for X1 than Model 2.

When two approaches to the same problem reach different results, there is cause for concern. Here, the resolution of the disagreement is found in the details of the genetics, which are the focus of population genetic models. The two models from Table 1 can only be taken as comparable if we assume that dosage compensation is complete. Note that in Model 1 a single X1 allele confers a benefit of + S on males, but in Model 2 it requires a double dose of X1 alleles to achieve the same. If we were to do away with that equivalence and instead assume that males, with their lone copy of X1, were, in terms of fitness, equivalent to female heterozygotes, who also have just the one copy of X1, then the results from the population genetic analysis would be quite different. As Frank and Patten (2020) showed, it could even yield a female bias.

The benefits of pluralism are again on display. The agential way of reasoning helps to identify what Hitchcock and Gardner (2020) refer to as the “agenda” of the X chromosome. It is correct to infer that the X chromosome wants to push phenotypes closer to the female optimum. But whether the X chromosome achieves this comes down to its “power” to do so, which power depends on the details of the genetics. From the population genetic approach, we can see clearly how different assumptions about dosage compensation shape the power dynamics between the sexes and how they influence the prediction of any bias on the X chromosome.