The Limiting Behaviour of Hanski's Incidence Function Metapopulation Model

McVinish, Ross; Pollett, P. K.

doi:10.1017/s0021900200011256

Cited by 1 publication

(3 citation statements)

References 22 publications

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“…The proof follows closely the arguments of the proof of Lemma 6.1 and the proof of Theorem 3.1 [41]. By assumption µ n,0 d → µ 0 for some non-random measure µ 0 .…”

Section: Theorem 62 Suppose That Assumptions (A) -(F) Hold and Thatmentioning

confidence: 61%

“…In order to address this question, we study the limiting behaviour of the metapopulation when the number of patches is large. Using an analysis similar to our earlier work [38,39,41], we show large metapopulations display a deterministic limit and asymptotic independence of local populations. All proofs are given in the Appendix.…”

Section: Introductionmentioning

confidence: 57%

“…If there exists a sub-transition kernel P * such that 40) for all A, B ∈ Σ, then P * is called a dual of P with respect to π. If 41) for all A, B ∈ Σ, then P is said to be reversible with respect to π.…”

Section: Appendix B -Dual Process Constructionmentioning

confidence: 99%

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A metapopulation model with Markovian landscape dynamics

McVinish

Pollett

Chan

2016

Theoretical Population Biology

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ABSTRACT. We study a variant of Hanski's incidence function model that allows habitat patch characteristics to vary over time following a Markov process. The widely studied case where patches are classified as either suitable or unsuitable is included as a special case. For large metapopulations, we determine a recursion for the probability that a given habitat patch is occupied. This recursion enables us to clarify the role of landscape dynamics in the survival of a metapopulation. In particular, we show that landscape dynamics affects the persistence and equilibrium level of the metapopulation primarily through its effect on the distribution of a local population's life span. IntroductionA metapopulation is a collection of local populations of a single focal species occupying spatially distinct habitat patches. Much of the research on metapopulations has focussed on identifying and quantifying extinction risks, with mathematical modelling playing an important role. Levins [33] proposed the first model of a metapopulation, which, despite its many simplifying assumptions, provided a number of important insights [21]. The importance of spatial features such as landscape heterogeneity and patch connectivity to metapopulation persistence was demonstrated in subsequent research [22,50,45,24] and by connections to interacting particle systems [34,17,18]. Of particular relevance to the current work is the Incidence Function Model (IFM) [22], which relates the colonisation and local extinction probabilities to landscape characteristics. This model has been used which breeds only in burned trees [53]. In these examples, the landscape dynamics are driven by secondary succession, and this is often the case regardless of whether the focal species is part of a seral community or the climax community.Some authors [9,63,28] have attempted to deal with landscape dynamics by incorporating the time elapsed since the patch was created through the local extinction probability. A more widely used and studied approach incorporates landscape dynamics by allowing each patch to alternate between being suitable or unsuitable for supporting a local population. In its simplest form all patches are treated equally [31,55,65,54]. A more general form used by DeWoody et al. [14] and Xu et al. [66] incorporates differences between patches in area and extinction rates. These studies demonstrate an important relationship between the time scale of metapopulation dynamics and landscape dynamics.When the habitat life span is too short, the metapopulation is unable to become established [31,14]. Furthermore, ignoring landscape dynamics leads to inaccurate persistence criteria. In general, the persistence criteria is optimistic [55,66], though not necessarily for species which are able to react to habitat destruction [54].The main problem we see with the suitable/unsuitable classification is that it is too coarse. Treating patches as being unsuitable may be reasonable following a destructive event, but this approach is unable to handle typical en...

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“…The proof follows closely the arguments of the proof of Lemma 6.1 and the proof of Theorem 3.1 [41]. By assumption µ n,0 d → µ 0 for some non-random measure µ 0 .…”

Section: Theorem 62 Suppose That Assumptions (A) -(F) Hold and Thatmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 57%