Diffusion approximation for an age-class-structured population under viability and fertility selection with application to fixation probability of an advantageous mutant.

In this paper, we ascertain the validity of a diffusion approximation for the frequencies of different types under recurrent mutation and frequency-dependent viability and fertility selection in a haploid population with a fixed age-class structure in the limit of a large population size. The approximation is used to study, and explain in terms of selection coefficients, reproductive values and population-structure coefficients, the differences in the effects of viability versus fertility selection on the fixation probability of an advantageous mutant.

First-order effect of frequency-dependent selection on fixation probability in an age-structured population with application to a public goods game.

In this paper, we deduce the first-order effect of frequency-dependent viability and fertility selection on the probability of fixation of a mutant in a large finite haploid population with a fixed age structure by applying a direct small perturbation method to the neutral two-timescale genealogical process. This effect is expressed in terms of fixation-fitness coefficients times ancestry coefficients that are related to the effective population size. In the case of constant selection, the fixation-fitness coefficients are functions of the coefficients of viability and fertility selection weighted by reproductive values and population-structure coefficients for the different age classes.

Frequency-dependent growth in class-structured populations: continuous dynamics in the limit of weak selection.

In this paper we consider class-structured populations in discrete time in the limit of weak selection and with the inverse of the intensity of selection as unit of time. The aim is to establish a continuous model that approximates the discrete model. More precisely, we study frequency-dependent growth in an infinite haploid population structured into a finite number of classes such that individuals in each class contribute to a given subset of classes from one time step to the next.