Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada.
Université Côte d'Azur, Inria BIOCORE Team, INRA, Sophia Antipolis, France.
Bull Math Biol. 2019 Jun;81(6):1916-1942. doi: 10.1007/s11538-019-00593-1. Epub 2019 Mar 7.
We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with implicit movement, there exists a threshold number of source patches such that the population potentially becomes extinct below the threshold and established above the threshold. In the case where the matrix describing the movement of populations between spatial locations is irreducible, the result is global; further, assuming a complete mobility graph with equal movement rates, we use the principle of equitable partitions to obtain an explicit expression for the threshold. Brief numerical considerations follow.
我们考虑一个具有个体在斑块间明确迁移的简单化汇-源种群模型，其中每个斑块要么是源斑块要么是汇。我们证明，类似于具有隐式迁移的斑块占有型汇-源种群，存在一个源斑块的阈值数量，使得种群潜在的在阈值以下灭绝，而在阈值以上建立。在描述种群在空间位置间迁移的矩阵不可约的情况下，结果是全局的；进一步，假设具有相同迁移率的完全迁移图，我们使用公平分区原理来获得阈值的显式表达式。随后进行简要的数值考虑。
