论文标题
在异质环境中适应。 I：持久性与灭绝
Adaptation in a heterogeneous environment. I: Persistence versus extinction
论文作者
论文摘要
了解农业生态系统中植物的多样性如何影响农业生态学关键问题中病原体的适应。我们分析了PDE系统，描述了两个表型结构化种群适应的动力学，在两个斑点环境中突变，选择和迁移的影响下，每个斑块都与不同的表型最佳相关联。我们考虑依赖于N-维表型特征的两种类型的生长函数：局部和线性或非本地非线性。在这两种情况下，我们都会根据主要特征值的迹象获得解决方案（持久性或灭绝）的大时间行为（持久性或灭绝）的表征。我们表明，两个环境之间的迁移降低了持久性的机会，在某些情况下，“致命的迁移阈值”在上面是不可能的。与随机个体基于单个的模拟的比较表明，PDE方法准确地捕获了此阈值。我们的结果说明了品种混合物对疾病预防和控制的重要性。
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under the effects of mutation, selection and migration in a two-patches environment, each patch being associated with a different phenotypic optimum. We consider two types of growth functions that depend on the n--dimensional phenotypic trait: either local and linear or nonlocal nonlinear. In both cases, we obtain existence and uniqueness results as well as a characterization of the large-time behaviour of the solution (persistence or extinction) based on the sign of a principal eigenvalue. We show that migration between the two environments decreases the chances of persistence, with in some cases a 'lethal migration threshold' above which persistence is not possible. Comparison with stochastic individual-based simulations shows that the PDE approach accurately captures this threshold. Our results illustrate the importance of cultivar mixtures for disease prevention and control.
