适应不同的环境。第一章：持久与灭绝
Adaptation in a heterogeneous environment. I: Persistence versus extinction
摘要：
了解农业生态系统中植物的多样性如何影响病原体的适应是农业生态学的一个关键问题。我们分析PDE系统描述的动态适应两个表型结构的人口，突变，选择和迁移的影响下，在两个补丁的环境，每个补丁与不同的表型最佳。我们考虑两种类型的增长函数，依赖于n维表型性状：无论是本地和线性或非本地非线性。在这两种情况下，我们得到的存在性和唯一性的结果，以及大的时间行为的解决方案（持久性或灭绝）的基础上的主要特征值的符号的表征。我们发现，这两个环境之间的迁移减少了持久性的机会，在某些情况下，一个“致命的迁移阈值”以上的持久性是不可能的。与基于随机个体的模拟比较表明，PDE方法准确地捕捉到了这个阈值。我们的研究结果说明了品种混合物对疾病预防和控制的重要性。
英文摘要：
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.
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