一个种群在空间和表型结构上传播速度的定性性质

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-09-30 DOI:10.1016/j.matpur.2025.103804

Nathanaël Boutillon

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引用次数: 0

摘要

我们考虑一个非局部Fisher-KPP方程，该方程模拟了在空间和表型上结构的种群。种群生活在异质周期性环境中：个体的扩散系数、突变系数和适合度可能取决于其空间位置和表型。我们首先证明了人口扩散速度的Freidlin-Gärtner公式。然后，我们研究了不同尺度极限（小周期和大周期，小突变系数和大突变系数）下的传播速度行为。最后，我们展示了由于表型维度而产生的新现象。当表型被视为另一个空间变量时，我们的结果也是有效的，种群不会沿着这个空间变量传播。

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Qualitative properties of the spreading speed of a population structured in space and in phenotype

We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of an individual may depend on its spatial position and on its phenotype.

We first prove a Freidlin-Gärtner formula for the spreading speed of the population. We then study the behaviour of the spreading speed in different scaling limits (small and large period, small and large mutation coefficient). Finally, we exhibit new phenomena arising thanks to the phenotypic dimension.

Our results are also valid when the phenotype is seen as another spatial variable along which the population does not spread.

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来源期刊

Journal de Mathematiques Pures et Appliquees 数学-数学

CiteScore

4.30

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.