The Dynamics of Sex Ratio Evolution: The Impact of Males as Passive Gene Carriers on Multilevel Selection

Abstract

In game theoretic models, it is possible that not all individuals are active players exhibiting strategies; some of them are passive carriers of the strategy genes. A nontrivial illustration of this problem is the sex ratio evolution. The classical sex ratio models can be divided into two classes. The first class contains the static strategic models related to the Dusing–Fisher–Shaw–Mohler fitness measure, based on the reproductive value of the offspring of the focal female. The second class contains the population genetic models focused on the dynamics of allele frequencies. The approaches are not fully compatible because the strategic models disregard the role of the male individuals as the passive carriers of the strategy genes. In the previous two papers in this cycle, a new synthetic model combining the strategic analysis with more rigorous genetics and considering male carriers was presented. The new model shows that sex ratio self-regulation is a complex multistage process that can be regarded as an example of multilevel selection. One of the elements of this process is the dynamic equilibrium between passive male and active female gene carriers associated with convergence of the dynamics to the manifold termed the male subpopulation equilibrium (MSE). This paper attempts to explain this phenomenon and analyse its properties. We show that sex ratio self-regulation is the by-product of the convergence of the stable sex ratios in the monomorphic subpopulations of particular gene carriers to the MSE manifold. We present a method of derivation of static fitness measures from the dynamic model based on the double-level selection process. This will lead to a new fitness measure free from the bias of the classical approach. We also show that the classical Dusing–Fisher–Shaw–Mohler fitness measure is a biased approximation of the new approach and that an alternative simple approximation of the new approach is possible.