论文标题
汉密尔顿 - 雅各比的分散发展方法
A Hamilton-Jacobi Approach to Evolution of Dispersal
论文作者
论文摘要
分散的演变是进化生物学中的一个经典问题，并且已经以广泛的数学模型进行了研究。 perthame and Souganidis [Math [Math]提出了一种选择人口的选择模型，其中人口由空间和表型性状构成，其性状直接作用于分散（扩散）速率。模型。纳特。现象。 11（2016），154-166]研究随机分散对进化稳定策略的演变。对于极少数突变极限，结果表明，平衡种群集中在与最小的分散率相关的单个特征上。在本文中，我们考虑了相应的进化方程，并在罕见的突变极限中表征了时间依赖性溶液的渐近行为，在对基础的哈密顿功能的轻度凸度假设下。
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait, with the trait acting directly on the dispersal (diffusion) rate, was formulated by Perthame and Souganidis [Math. Model. Nat. Phenom. 11 (2016), 154-166] to study the evolution of random dispersal towards the evolutionarily stable strategy. For the rare mutation limit, it was shown that the equilibrium population concentrates on a single trait associated to the smallest dispersal rate. In this paper, we consider the corresponding evolution equation and characterize the asymptotic behaviors of the time-dependent solutions in the rare mutation limit, under mild convexity assumptions on the underlying Hamiltonian function.
