School of Mathematics, Sun Yat-sen University, Guangzhou 510275, PR China.
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, PR China.
Theor Popul Biol. 2020 Oct;135:1-8. doi: 10.1016/j.tpb.2020.06.002. Epub 2020 Jul 10.
This paper considers predator-prey systems in which the predator moves between two patches. One patch is a source, where the predator and prey can persist, while the other is a sink where the predator cannot survive. Our aim is to show whether or not the dispersal is beneficial to the predator's total abundance at equilibrium. Using dynamical systems theory, we demonstrate conditions under which a dispersing predator can persist. Our analysis shows that the predator equilibrium abundance at intermediate dispersal rates can be higher than that without dispersal, while extremely large or small dispersal rates could result in predator's extinction. Moreover, we find an explicit expression for the total abundance, which clearly shows the role of dispersal rates and asymmetry on the predator's abundance. Numerical simulations confirm and extend our results.
本文考虑了捕食者-猎物系统，其中捕食者在两个斑块之间移动。一个斑块是源，捕食者和猎物可以在那里生存，而另一个是汇，捕食者无法在那里生存。我们的目的是展示扩散是否有利于捕食者在平衡时的总丰度。使用动力系统理论，我们证明了扩散捕食者能够持续存在的条件。我们的分析表明，在中等扩散率下，捕食者的平衡丰度可能高于没有扩散的情况，而非常大或小的扩散率可能导致捕食者灭绝。此外，我们还找到了总丰度的显式表达式，清楚地显示了扩散率和不对称性对捕食者丰度的作用。数值模拟证实并扩展了我们的结果。
