Jiang Hongyan, Lam King-Yeung, Lou Yuan
Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, China.
Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA.
Bull Math Biol. 2020 Oct 6;82(10):131. doi: 10.1007/s11538-020-00803-1.
We study the dynamics of two competing species in three-patch models and illustrate how the topology of directed river network modules may affect the evolution of dispersal. Each model assumes that patch 1 is at the upstream end, patch 3 is at the downstream end, but patch 2 could be upstream, or middle stream, or downstream, depending on the specific topology of the modules. We posit that individuals are subject to both unbiased dispersal between patches and passive drift from one patch to another, depending upon the connectivity of patches. When the drift rate is small, we show that for all models, the mutant species can invade when rare if and only if it is the slower disperser. However, when the drift rate is large, most models predict that the faster disperser wins, while some predict that there exists one evolutionarily singular strategy. The intermediate range of drift is much more complex: most models predict the existence of one singular strategy, but it may or may not be evolutionarily stable, again depending upon the topology of modules, while one model even predicts that for some intermediate drift rate, singular strategy does not exist and the faster disperser wins the competition.
我们研究了三斑块模型中两个竞争物种的动态，并说明了有向河网模块的拓扑结构如何影响扩散的演化。每个模型假设斑块1在上游端，斑块3在下游端，但斑块2可能在上游、中游或下游，这取决于模块的具体拓扑结构。我们假定，个体在斑块之间既会进行无偏扩散，也会因斑块的连通性而从一个斑块被动漂移到另一个斑块。当漂移率较小时，我们表明，对于所有模型，突变物种在稀少时能够入侵的充要条件是它是扩散较慢的物种。然而，当漂移率较大时，大多数模型预测扩散较快的物种会获胜，而一些模型预测存在一种进化奇异策略。漂移的中间范围要复杂得多：大多数模型预测存在一种奇异策略，但它可能是进化稳定的，也可能不是，这同样取决于模块的拓扑结构，而有一个模型甚至预测，对于某些中间漂移率，奇异策略不存在，扩散较快的物种赢得竞争。
