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

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

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Authors and Affiliations

  1. MISTEA, Univ Montpellier, INRAE, Institut Agro, Montpellier, France

    Bertrand Cloez

  2. IMAG, Univ Montpellier, CNRS, Montpellier, France

    Benoîte de Saporta & Tristan Roget

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  1. Bertrand Cloez
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  2. Benoîte de Saporta
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  3. Tristan Roget
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Correspondence to Benoîte de Saporta.

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This work was partially supported by the Chaire Modélisation Mathématique et Biodiversité of Veolia Environment - École Polytechnique - Museum National d’Histoire Naturelle - FX, and the ANR projects MESA (ANR-18-CE40-006) and NOLO (ANR-20-CE40-0015), funded by the French Ministry of Research.

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Cloez, B., de Saporta, B. & Roget, T. Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process. J. Math. Biol. 83, 69 (2021). https://doi.org/10.1007/s00285-021-01695-y

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  • DOI: https://doi.org/10.1007/s00285-021-01695-y

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