水平性状转移下的祖先谱系：超越平稳性的脊柱分解与时间反转

中文摘要 AI 辅助

我们研究了一个具有性状依赖的繁殖、死亡、竞争、变异和有害转移的随机个体基础种群模型。非线性出现在竞争项和转移形式中，且转移形式是不对称的。在大种群极限下，该过程收敛到一个确定性的测度值方程。后者帮助我们揭示现存个体的过去历史。我们在相互作用中用确定性大种群近似替换原始随机过程，得到一个非齐次测度值分支过程，并对其使用脊柱分解，推广了一种仅存在于平稳情形的方法。通过反转时间，我们识别了典型祖先谱系的分布。该方法涵盖多种设定，需要精细的函数分析。与文献中早期依赖随机演算或平稳假设下有利跳跃结构的方法相比，我们的方法提供了更直接且更一般的视角。

英文摘要

We investigate a stochastic individual-based population model with trait-dependent reproduction, death, competition, variation, and deleterious transfer. Nonlinearities appear in the competition term and the transfer form, which moreover is asymmetric. In the large-population limit, the process converges to a deterministic measure-valued equation. The latter helps us to uncover the past history of living individuals. We replace in the interactions the original stochastic process with the deterministic large population approximation obtaining a nonhomogeneous measure-valued branching process, for which we use a spinal decomposition, generalizing a method that existed only for the stationary case. Reversing time, we identify the law of typical ancestral lineages. This approach encompasses a variety of settings and requires delicate functional analysis. In contrast to earlier approaches in the literature, which relied either on stochastic calculus or on favourable jump structures under stationarity assumptions, our method provides a more direct and more general point of view.

发表机构

• Ecole Polytechnique Paris, Centre de Mathématiques Appliquées（巴黎综合理工学院，应用数学中心）

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