Abstract
This paper presents a comparatively simple approximation formula for the mean life time of a metapopulation in a habitat network where habitat patch arrangement may be irregular and patch sizes differ. It is based on previous work on the development of an analytical approximation formula by Frank and Wissel [K. Frank, C. Wissel, A formula for the mean lifetime of metapopulations in heterogeneous landscapes, Am. Nat. 159 (2002) 530] and extends it by abstracting from individual patch locations. The mean metapopulation lifetime is expressed as a function of four macroscopic network properties: the ratio of dispersal range and network size, the ratio of range of environmental correlation and network size, and the total number and (geometric mean) size of the patches. The analysis takes into account that (ceteris paribus) patches close to the boundary of the habitat network contribute less to metapopulation survival than patches close to the centre of the network. Ignoring this fact can lead to a substantial overestimation of the mean metapopulation lifetime. Due to its numerical simplicity, the formula can be used as a conservation objective function even in complex network design problems where the number of patches to be allocated is very large. Numerical tests of the formula show that it performs very well within a wide range of network structures.
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