We present a single-species metapopulation model structured by population size that is discrete in time. The novel formulation of our model allows for explicit incorporation of both the local, in space, dynamics and new details of the dispersal process. To study the impact of between-patch dynamics in the model, we construct various functions to describe density-dependent dispersal, recolonization, and between-patch stochasticity. Due to the complexity of the model, numerical simulations are used to obtain the distribution of the metapopulation. Moreover, we can use our model to predict the proportion of patches occupied, expected patch density, and variance in patch density. Our results provide insight into the influence that each of these processes play in the distribution of the metapopulation. In particular, our findings emphasize the benefit of explicitly modelling these processes. We consider two density-dependent dispersal strategies based upon individuals wanting to form average-sized patches and illustrate the differences in the metapopulation distributions. For recolonization of empty suitable patches, we look at two simplistic redistribution strategies modeled as either a continuous uniform or Laplace distribution. The between-patch stochasticity is modelled using redistribution kernels where we consider both thin-tailed and fat-tailed kernels. We find that the form of density-dependent dispersal has a major influence on the distribution of the metapopulation while recolonization is a key process for metapopulation persistence. In addition, fatter tails for the between-patch stochasticity can decrease the proportion of occupied patches and increase the expected patch density and variance in patch density.

我们提出了一种按种群数量在时间上离散的结构的单物种混合种群模型。我们模型的新颖表达方式允许将局部，空间，动力学和分散过程的新细节都明确纳入。为了研究补丁间动力学在模型中的影响，我们构建了各种函数来描述依赖于密度的扩散，重新殖民化以及补丁间随机性。由于模型的复杂性，使用数值模拟来获得后代的分布。而且，我们可以使用我们的模型来预测斑块占据的比例，期望的斑块密度以及斑块密度的变化。我们的结果提供了对这些过程中的每一个在种群分布中的影响的见解。尤其是，我们的发现强调了对这些过程进行显式建模的好处。我们考虑了两种基于密度的分散策略，这些策略基于想要形成平均大小斑块的个体，并说明了不同种群分布的差异。为了对空的合适补丁进行重新殖民化，我们研究了两种简化的重新分配策略，它们被建模为连续均匀分布或拉普拉斯分布。使用重新分配内核对补丁之间的随机性进行建模，其中我们同时考虑了细尾和胖尾内核。我们发现，密度依赖性分散的形式对后代的分布有重要影响，而重新定殖是后代持久性的关键过程。此外，