Optimal Sex Ratios in Structured Populations

Abstract

In this paper, we develop a general method to determine evolutionary equilibrium sex ratios and to check evolutionary stability, continuous stability and invadability in exact genetic models with or without dominance. This method is then applied to three kinds of models for structured populations: the "rst one concerns Hamilton's LMC model, except that only a fraction of female o!spring mate with male o!spring born in the same colonies, while a fraction 1! mate with male o!spring chosen at random within the whole population; in the second model, it is assumed that partial dispersal of inseminated females occurs after mating; in the third model, partial dispersal of male and female o!spring occurs before mating.In the "rst model, the e!ect of population regulation is studied while, in the other models, two kinds of dispersal are considered: proportional and uniform.

Fitness and evolutionary stability in game theoretic models of finite populations

“…A strategy is NIS when selection favours it to replace other strategies. If equations (2.2) and (3.2) hold, Courteau & Lessard (2000) show that…”

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

“…The second term (P i − M i ) is weighted by the fraction of female carriers (1 − M i ). Thus, the dynamics of parameter M i (9) is determined by the action of female carriers of strategy P i as well as partners of male carriers of this strategy in a tug of war mechanism, which means that the activity of female carriers (the second term) attracts M i to the value encoded by the gene P i and the action of partners of male carriers (the first term) attracts M i to the value of the females' average strategyP pr . In [4], it was shown that for P i ∈ (0, 1] a unique attracting nullcline exists within the interval P pr , P i .…”

“…Figure 1 shows the trajectories of the gene frequency dynamics (8) and the respective trajectories of the carrier sex ratio dynamics (9). The dynamics of gene frequencies is determined by the underlying dynamics of the carriers' sex ratios and the secondary sex ratio, according to the rules (10).…”

“…This leads to the distinction between two classes of modelling approaches, phenotypic and genetic, related to the sex ratio [36]. The genetic models can be analysed and interpreted in the spirit of the ESS approach, i.e., they can be used in the analysis of the fate of the rare mutant in the resident population (see, for example, [9] for the sex ratio case, and in general [14,22,23]). However, these approaches do not use core game theoretic notions, such as explicitly derived strategic payoff functions.…”

A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms

“…As far as we are aware, the first authors to derive local invadability properties directly from the characteristic polynomial of the linearised invasion dynamics were Taylor and Bulmer (1980). Their calculations were taken further by Courteau and Lessard (2000). As these techniques are extremely useful in applications we summarise here their extension to higher dimensional trait spaces.…”