Extended haplodiploidy hypothesis

Abstract

Evolution of altruistic behavior was a hurdle for the logic of Darwinian evolution. Soon after Hamilton formalized the concept of inclusive fitness, which explains how altruism can evolve, he suggested that the high sororal relatedness brought by haplodiploidy could be why Hymenopterans have a high prevalence in eusocial species, and why helpers in Hymenoptera are always female. Later it was noted that in order to capitalize on the high sororal relatedness, helpers would need to direct help toward sisters, and this would bias the population sex ratio. Under a 1:3 males:females sex ratio, the inclusive fitness valuation a female places on her sister, brother, and an own offspring are equal-apparently removing the benefit of helping over independent reproduction. Based on this argumentation, haplodiploidy hypothesis has been considered a red herring. However, here we show that when population sex ratio, cost of altruism, and population growth rate are considered together, haplodiploidy does promote female helping even with female-biased sex ratio, due the lowered cost of altruism in such populations. Our analysis highlights the need to re-evaluate the role of haplodiploidy in the evolution of helping, and the importance of fully exploring the model assumptions when comparing interactions of population sex ratios and social behaviors.

Keywords: Haplodiploidy hypothesis; inclusive fitness; kin selection; reproductive altruism.

Figure 1

The population sex ratio, population growth rate, and the cost of altruism (c‐term in the Hamilton's rule, i.e., the number of offspring a juvenile expects to produce) are all interconnected, so that changing one and keeping the other two constant is impossible in a homogenous population (see eqs. (3), (4), (5)). (A) In previous analyses of the haplodiploidy hypothesis, the cost of altruism was assumed to remain constant when population sex ratio changes from 1:1 to 1:3 males:females. However, our analysis shows that a shift in population sex ratio induces a shift in population growth rate, which is not sustainable on evolutionary time scales. (B) A biologically more plausible assumption is an approximately constant population growth rate, and especially an approximately constant population size. In this case, a shift in population sex ratio induces a shift in the cost of altruism (as has been pointed out for example by Gardner and Ross 2013 and Davies et al. 2016). This shift in the cost of altruism brings about the lowered benefit threshold of helping for haplodiploid females also in female‐biased population sex ratios.

Figure 2

The benefit thresholds of helping for (A) haplodiploid female, inequality 8; (B) diplodiploid female, inequality 9; (C) male under either haplodiploidy diplodiploidy, inequality 10, as a function of population sex ratio (z). In each panel, red line presents helping sisters, blue line presents helping brothers, and dashed line presents helping administered according to the population sex ratio ($z_{\mathrm{h}}=0$,$z_{\mathrm{h}}=1$, and $z_{\mathrm{h}}=z$, respectively). Helpers have a selection pressure to bias their helping toward the sex with the lower benefit threshold until the population sex ratio shifts so that the benefit thresholds are equal. Haplodiploid female helpers will thus, if able, shift the population sex ratio to $z=0.25$. At this equilibrium point, the benefit threshold for any type of helping is 4/3. Diplodiploid female helpers and male helpers would be selected to keep the population sex ratio at $z=0.5$, and the benefit threshold for helping is two.