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New approaches of source-sink metapopulations decoupling the roles of demography and dispersal

By Vincent Bansaye and Amaury Lambert

Abstract

Source-sink systems are metapopulations of habitat patches with different, and possibly temporally varying, habitat qualities, which are commonly used in ecology to study the fate of spatially extended natural populations. We propose new techniques that allow to disentangle the respective contributions of demography and dispersal to the dynamics and fate of a single species in a source-sink metapopulation. Our approach is valid for a general class of stochastic, individual-based, stepping-stone models, with density-independent demography and dispersal, provided the metapopulation is finite or else enjoys some transitivity property. We provide 1) a simple criterion of persistence, by studying the motion of a single random disperser until it returns to its initial position; 2) a joint characterization of the long-term growth rate and of the asymptotic occupancy frequencies of the ancestral lineage of a random survivor, by using large deviations theory. Both techniques yield formulae decoupling demography and dispersal, and can be adapted to the case of periodic or random environments, where habitat qualities are autocorrelated in space and possibly in time. In this last case, we display examples of coupled time-averaged sinks allowing survival, as was previously known in the absence of demographic stochasticity for fully mixing \cite{JY98} and even partially mixing \cite{ERS12, Sch10} metapopulations

Topics: Source-sink system, dispersal, transitive graph, random walk, persistence criterion, growth rate, ergodic theorem, asymptotic frequency, pedigree, large deviations, periodic environment, stochastic environment, autocorrelated environment, 60J70, 60J80, 60J85, 92D15, 92D25, 92D40, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], [ SDV.BID.EVO ] Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE]
Publisher: HAL CCSD
Year: 2011
OAI identifier: oai:HAL:hal-00639011v2
Provided by: Hal-Diderot

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