Journal of Mathematical Biology

, Volume 79, Issue 6–7, pp 2069–2110 | Cite as

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

  • Cíntia Dalila Soares
  • Sabin LessardEmail author


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.


Age-class-structured population Leslie matrix Frequency-dependent selection Diffusion approximation Fixation probability Two timescales Reproductive value Population-structure coefficient 

Mathematics Subject Classification

Primary 92D25 Secondary 60J70 



This research was supported in part by NSERC of Canada, Grant No. 8833, and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 0968-13-7. We are also grateful to two anonymous referees for helpful comments to improve the manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada

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