How does variability in cells aging and growth rates influence the malthus parameter?

International audienceThe aim of this study is to compare the growth speed of different populations of cells measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same rate $v¯$. A second population (with variability) is composed of cells each aging or growing at a rate v drawn according to a non-degenerated distribution $ρ$ with mean $v¯$. In a first part, analytical answers are provided for the age-structured model. In a second part, numerical answers based on stochastic simulations are derived for the size-structured model. It appears numerically that for experimentally plausible division rates the population with variability proliferates more slowly than the population of reference. The decrease in the Malthus parameter we measure, around 2% for distributions $ρ$ with realistic coefficients of variations around 15-20%, is determinant since it controls the exponential growth of the whole population