Long-time behavior and darwinian optimality for an asymmetric size-structured branching process
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.
Cite
@article{arxiv.2007.08797,
title = {Long-time behavior and darwinian optimality for an asymmetric size-structured branching process},
author = {Bertrand Cloez and Benoîte de Saporta and Tristan Roget},
journal= {arXiv preprint arXiv:2007.08797},
year = {2020}
}