This paper analyzes source-sink systems with asymmetric dispersal between two patches. Complete analysis on the models demonstrates a mechanism by which the dispersal asymmetry can lead to either an increased total size of the species population in two patches, a decreased total size with persistence in the patches, or even extinction in both patches. For a large growth rate of the species in the source and a fixed dispersal intensity, (i) if the asymmetry is small, the population would persist in both patches and reach a density higher than that without dispersal, in which the population approaches its maximal density at an appropriate asymmetry; (ii) if the asymmetry is intermediate, the population persists in both patches but reaches a density less than that without dispersal; (iii) if the asymmetry is large, the population goes to extinction in both patches; (iv) asymmetric dispersal is more favorable than symmetric dispersal under certain conditions. For a fixed asymmetry, similar phenomena occur when the dispersal intensity varies, while a thorough analysis is given for the low growth rate of the species in the source. Implications for populations in heterogeneous landscapes are discussed, and numerical simulations confirm and extend our results.

中文翻译：

---

具有源汇总数的两修补系统中的扩散不对称性。

本文分析了两个补丁之间具有非对称分散的源汇系统。对模型的完整分析表明，分散不对称可导致两个斑块中物种种群的总大小增加，在斑块中存在持久性的总大小减小或两个斑块都灭绝的机制。对于源中物种的大生长速率和固定的分散强度，（i）如果不对称性较小，则种群将在两个斑块中均保持存在，并达到比没有分散时更高的密度，在该密度下种群接近其最大值适当不对称的密度；（ii）如果不对称性处于中等水平，则种群在两个斑块中均会持续存在，但密度要小于没有分散的密度；（iii）如果不对称性很大，这两个地区的人口都灭绝了；（iv）在某些条件下，不对称分散比对称分散更有利。对于固定的不对称性，当分散强度变化时会发生类似现象，同时对源中物种的低增长率进行了全面分析。讨论了对异质景观中种群的影响，数值模拟证实并扩展了我们的结果。