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Article Dans Une Revue Journal of Mathematical Biology Année : 2021

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

Résumé

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, symmetric division is sub-optimal in a Darwinian sense.

Dates et versions

hal-02902640 , version 1 (20-07-2020)

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Bertrand Cloez, Benoîte de Saporta, Tristan Roget. Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process. Journal of Mathematical Biology, 2021, 83 (69), pp.6-7. ⟨10.1007/s00285-021-01695-y⟩. ⟨hal-02902640⟩
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