The Dynamics of Sex Ratio Evolution: From the Gene Perspective to Multilevel Selection

The new dynamical game theoretic model of sex ratio evolution emphasizes the role of males as passive carriers of sex ratio genes. This shows inconsistency between population genetic models of sex ratio evolution and classical strategic models. In this work a novel technique of change of coordinates will be applied to the new model. This will reveal new aspects of the modelled phenomenon which cannot be shown or proven in the original formulation. The underlying goal is to describe the dynamics of selection of particular genes in the entire population, instead of in the same sex subpopulation, as in the previous paper and earlier population genetics approaches. This allows for analytical derivation of the unbiased strategic model from the model with rigorous non-simplified genetics. In effect, an alternative system of replicator equations is derived. It contains two subsystems: the first describes changes in gene frequencies (this is an alternative unbiased formalization of the Fisher-Dusing argument), whereas the second describes changes in the sex ratios in subpopulations of carriers of genes for each strategy. An intriguing analytical result of this work is that fitness of a gene depends on the current sex ratio in the subpopulation of its carriers, not on the encoded individual strategy. Thus, the argument of the gene fitness function is not constant but is determined by the trajectory of the sex ratio among carriers of that gene. This aspect of the modelled phenomenon cannot be revealed by the static analysis. Dynamics of the sex ratio among gene carriers is driven by a dynamic "tug of war" between female carriers expressing the encoded strategic trait value and random partners of male carriers expressing the average population strategy (a primary sex ratio). This mechanism can be called "double level selection". Therefore, gene interest perspective leads to multi-level selection.Comment: 3 figure

List of important symbols:

<p>List of important symbols:</p

A comparison of “single level” selection and “double level” selection.

<p>A comparison of “single level” selection and “double level” selection.</p

Trajectories of a population of individuals with strategies for sex ratios of <i>0.2, 0.5</i> and <i>0.8</i> for initial conditions.

<p> Panel <i>a</i>) shows the trajectories of gene frequencies Therefore, increases when and or and and decreases when and or and . This mechanism is clearly shown in the trajectories of strategy <i>0.5</i>. The trajectory switches from a decrease to an increase when trajectory of passes the trajectory of (see panel <i>b</i>). Panel <i>b</i>) shows the respective changes of sex ratios in carrier subpopulations Note that sex ratios in carrier subpopulations rapidly converge to the values determined by the MSE phenomenon, and after that, they follow the changes of the primary sex ratio that slowly converges to <i>0.5</i>. The sex ratio among carriers of male biased strategies change due to the dynamics of the primary sex ratio while among female biased strategies, it converges to the neighbourhood of the value encoded by the gene.</p