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

##### Soares, Cíntia.Dalila.; Lessard, S.

#### Journal of Mathematical Biology 79(6-7): 2069-2110

#### 2019

**ISSN/ISBN: 0303-6812**

PMID: 31468115

DOI: 10.1007/s00285-019-01420-w

Accession: 069291791

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.