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－被捕食者系统，其中捕食者在两个斑块之间移动。一个斑块是一个来源，捕食者和被捕食者可以持久存在，而另一个斑块是一个掠食者无法生存的汇。我们的目的是证明分散是否对捕食者处于平衡状态的总丰度有利。使用动力学系统理论，我们证明了分散捕食者可以持续存在的条件。我们的分析表明，在中间分散速度下，捕食者的平衡丰度可以高于没有分散时的捕食者平衡丰度，而过大或小的分散速度都可能导致捕食者的灭绝。此外，我们找到了总丰度的一个明确表达式，该表达式清楚地表明了分散速率和不对称性对捕食者丰度的作用。