标题： 随机矩阵元种群模型与快速迁移：将生存重新缩放至快速尺度 显示英文标题

标题： Stochastic matrix metapopulation models with fast migration: re-scaling survival to the fast scale

摘要： 在本工作中，我们研究了受环境随机性影响的结构化集合种群的离散时间模型的分析。 先前关于这些模型的研究利用了这样一个事实，即斑块之间的迁移相对于种群中的种群动态（成熟、存活、繁殖）可以被认为是快速的。 假设在模型的每个时间步中，有许多快速的迁移步骤，随后是一个缓慢的种群动态事件。 这一假设使得可以应用近似约简技术，从而简化了模型的分析。 然而，在某些情况下，这一假设是有疑问的，因为特别是个体可以在时间步的任何时刻死亡。 我们提出了新的非等价模型，在这些模型中，我们对存活率进行重新缩放，以考虑其对快速尺度的影响。 我们提出了更一般的近似约简技术的表述，使其也适用于所提出的新型模型。 我们证明了这类随机模型的主要渐近元素，即随机增长率（SGR）和缩放对数方差（SLV），可以在原始系统和约简系统之间建立联系，从而使后者的分析能够确定第一种系统的种群命运。 然后我们进一步考虑了一些案例，其中我们展示了约简技术，并说明了两种建模方式之间的差异。 在某些情况下，使用一种方法表示指数增长，而另一种方法则导致灭绝。 显示英文摘要

摘要： In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered fast with respect to demography (maturation, survival, reproduction) in the population. It was assumed that, within each time step of the model, there are many fast migration steps followed by one slow demographic event. This assumption allowed one to apply approximate reduction techniques that eased the model analysis. It is however a questionable issue in some cases since, in particular, individuals can die at any moment of the time step. We propose new non-equivalent models in which we re-scale survival to consider its effect on the fast scale. We propose a more general formulation of the approximate reduction techniques so that they also apply to the proposed new models. We prove that the main asymptotic elements in this kind of stochastic models, the Stochastic Growth Rate (SGR) and the Scaled Logarithmic Variance (SLV), can be related between the original and the reduced systems, so that the analysis of the latter allows us to ascertain the population fate in the first. Then we go on to considering some cases where we illustrate the reduction technique and show the differences between both modelling options. In some cases using one option represents exponential growth, whereas the other yields extinction.