Frank Karin, Wissel Christian
UFZ-Centre for Environmental Research Leipzig-Halle, Department of Ecological Modelling, P.O. Box 500136, D-04301 Leipzig, Germany.
Am Nat. 2002 May;159(5):530-52. doi: 10.1086/338991.
We present a formula for the mean lifetime of metapopulations in heterogeneous landscapes. This formula provides new insights into the effect of the spatial structure of habitat networks on metapopulation survival, with consequences for modeling, landscape evaluation, and metapopulation management. In the whole study, the spatially realistic metapopulation model of Frank and Wissel is taken as a basis. First, as a key result on the way toward the desired formula, it is shown that a simple nonspatial (Levins-type) model is able to reproduce the behavior of the complex spatial model considered regarding the mean lifetime, provided its parameters appropriately summarize all the relevant details of spatial heterogeneity. Second, the formula presented reveals how data from species and landscape have to be combined to estimate the survival chance of a metapopulation without having to run any simulation or to solve numerically any model equation. Third, by taking the formula as a basis, landscape measures are derived that allow dissimilar habitat networks to be evaluated, compared, and ranked in terms of their effect on metapopulation survival. Fourth, a combination of analytical, nonlinear regression as well as aggregation techniques was used to deduce the formula presented. The potential of these techniques for simplifying (meta)population models that are complex due to spatial heterogeneity is discussed.
我们提出了一个关于异质景观中集合种群平均寿命的公式。该公式为栖息地网络的空间结构对集合种群生存的影响提供了新的见解，对建模、景观评估和集合种群管理具有重要意义。在整个研究中，以Frank和Wissel的空间现实集合种群模型为基础。首先，作为推导所需公式过程中的一个关键结果，研究表明，一个简单的非空间（Levins型）模型能够再现所考虑的复杂空间模型在平均寿命方面的行为，前提是其参数适当地总结了空间异质性的所有相关细节。其次，所提出的公式揭示了如何将物种和景观的数据结合起来，以估计集合种群的生存机会，而无需进行任何模拟或数值求解任何模型方程。第三，以该公式为基础，推导出了景观度量，从而能够根据不同栖息地网络对集合种群生存的影响进行评估、比较和排序。第四，综合运用了分析、非线性回归以及聚合技术来推导所提出的公式。讨论了这些技术在简化因空间异质性而复杂的（元）种群模型方面的潜力。
