Comparison Between Effective and Individual Fitness in a Heterogeneous Population
Résumé
Is there an advantage of displaying heterogeneity in a population where the individuals grow and divide by fission? This is a wide-ranging question, for which a universal answer cannot be easily provided. This article thus aims at providing a quantitative answer in the specific context of growth rate heterogeneity by comparing the fitness of homogeneous versus heterogeneous populations. We focus on a size-structured population, where an individual's growth rate is chosen at its birth through heredity and/or random mutations. We use the long-term behaviour to define the Malthus parameter of such a population, and compare it to the ones of averaged homogeneous populations. We obtain analytical formulae in two paradigmatic cases: first, constant rates for growth and division, second, linear growth rates and uniform fragmentation. Surprisingly, these two cases happen to display similar analytical formulae linking effective and individual fitness. They allow us to investigate quantitatively the crossed influence of heredity and heterogeneity, and revisit previous results stating that heterogeneity is beneficial in the case of strong heredity.
Effective fitness v
Mots clés
bacterial growth
mother-daughter inheritance
population dynamics effective fitness growth-fragmentation equation heterogeneity bacterial growth mother-daughter inheritance
population dynamics
Population dynamics 2000 Mathematics Subject Classification 35A05
Population dynamics AMS subject classifications 93B03
effective fitness
growth-fragmentation equation
heterogeneity
bacterial growth
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