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The aim of this study is to compare the growth speed of different cellpopulations measured by their Malthus parameter. We focus on both theage-structured and size-structured equations. A first population (of reference)is composed of cells all aging or growing at the same rate $\bar v$. A secondpopulation (with variability) is composed of cells each aging or growing at arate $v$ drawn according to a non-degenerated distribution $\rho$ with mean$\bar v$. In a first part, analytical answers -- based on the study of aneigenproblem -- are provided for the age-structured model. In a second part,numerical answers -- based on stochastic simulations -- are derived for thesize-structured model. It appears numerically that the population withvariability proliferates more slowly than the population of reference (forexperimentally plausible division rates). The decrease in the Malthus parameterwe measure, around 2% for distributions $\rho$ with realistic coefficients ofvariations around 15-20\%, is determinant since it controls the {\itexponential} growth of the whole population.

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