The Limiting Behaviour of Hanski's Incidence Function Metapopulation Model

Hanski's incidence function model is one of the most widely used metapopulation models in ecology. It models the presence/absence of a species at spatially distinct habitat patches as a discrete-time Markov chain whose transition probabilities are determined by the physical landscape. In this analysis, the limiting behaviour of the model is studied as the number of patches increases and the size of the patches decreases. Two different limiting cases are identified depending on whether or not the metapopulation is initially near extinction. Basic properties of the limiting models are derived.

The Limiting Behaviour of Hanski's Incidence Function Metapopulation Model

Hanski's incidence function model is one of the most widely used metapopulation models in ecology. It models the presence/absence of a species at spatially distinct habitat patches as a discrete-time Markov chain whose transition probabilities are determined by the physical landscape. In this analysis, the limiting behaviour of the model is studied as the number of patches increases and the size of the patches decreases. Two different limiting cases are identified depending on whether or not the metapopulation is initially near extinction. Basic properties of the limiting models are derived.

Modelling the effect of habitat fragmentation on range expansion in a butterfly

There is an increasing need for conservation programmes to make quantitative predictions of biodiversity responses to changed environments. Such predictions will be particularly important to promote species recovery in fragmented landscapes, and to understand and facilitate distribution responses to climate change. Here, we model expansion rates of a test species (a rare butterfly, Hesperia comma ) in five landscapes over 18 years (generations), using a metapopulation model (the incidence function model). Expansion rates increased with the area, quality and proximity of habitat patches available for colonization, with predicted expansion rates closely matching observed rates in test landscapes. Habitat fragmentation constrained expansion, but in a predictable way, suggesting that it will prove feasible both to understand variation in expansion rates and to develop conservation programmes to increase rates of range expansion in such species.