Long-time behavior and darwinian optimality for an asymmetric size-structured branching process

Bertrand Cloez; Benoîte de Saporta; Tristan Roget

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arXiv · 2007.08797

Long-time behavior and darwinian optimality for an asymmetric size-structured branching process

Bertrand Cloez·Benoîte de Saporta·Tristan Roget

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Abstract

We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at division. We show that the process exhibits a Malthusian behavior; that is that the global population size grows exponentially fast and that the trait distribution of individuals converges to some stable distribution. The proof is based on a generalization of Lyapunov function techniques for non-conservative semi-groups. We then investigate the fluctuations of the growth rate with respect to the parameters guiding asymmetry. In particular, we exhibit that, under some special assumptions, asymmetric division is optimal in a Darwinian sense.

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BibTeX RIS

Bertrand Cloez, Benoîte de Saporta, Tristan Roget. 2020-07-17. Long-time behavior and darwinian optimality for an asymmetric size-structured branching process. https://arxiv.org/abs/2007.08797

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