The Limiting Behaviour of Hanski's Incidence Function Metapopulation Model

McVinish, Ross; Pollett, P. K.

doi:10.1239/jap/1402578626

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…Proof. 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: (622)mentioning

confidence: 61%

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A metapopulation model with Markovian landscape dynamics

McVinish,

Pollett,

Chan

2014

Preprint

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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.

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“…Proof. 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: (622)mentioning

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%

A metapopulation model with Markovian landscape dynamics

McVinish,

Pollett,

Chan

2014

Preprint

Self Cite

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“…Together with (31), this implies (28). We shall now prove (29). By iterating equation ( 27), for any k ≥ 0 and 0 ≤ t < δ,…”

Section: Appendix A: Independent Site Approximationmentioning

confidence: 80%

Fast approximate simulation of finite long-range spin systems

McVinish¹,

Hodgkinson²

2019

Preprint

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Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy some form of scaling behaviour. In a similar spirit to tau leaping, we propose a new method for approximate simulation of spin systems which approximates the evolution of spin at each site between sampling epochs as an independent two-state Markov chain. When combined with fast summation methods, our method offers considerable improvement in speed over the standard Doob-Gillespie algorithm. We provide a detailed analysis of the error incurred for both the number of sites incorrectly labelled and for linear functions of the state.

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