论文标题
长期行为和达尔文式的最优性，用于非对称尺寸结构的分支过程
Long-time behavior and darwinian optimality for an asymmetric size-structured branching process
论文作者
论文摘要
我们研究了不对称尺寸结构化测量的生长裂片分支过程的长期行为，该过程对分裂的生理和形态不对称性进行了模拟的细胞群体的动力学。我们表明该过程表现出马尔萨斯的行为。那就是全球人口规模的增长速度快速增长，并且个人的性状分布会融合到某种稳定的分布。该证明基于对非保守半组的Lyapunov功能技术的概括。然后，我们研究了有关引导不对称的参数的增长率的波动。特别是，我们表明，在一些特殊的假设下，在达尔文的意义上，不对称分裂是最佳的。
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.
