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- W4298423001 abstract "This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in each patch at a rate proportional to the number of pairs of individuals in the patch (sexual reproduction) rather than simply the number of individuals as in the basic contact process. Offspring produced at a given patch either stay in their parents' patch or are sent to a nearby patch with some fixed probabilities. As the patch size tends to infinity, we identify a mean-field limit consisting of an infinite set of coupled differential equations. For the mean-field equations, we find explicit conditions for survival and extinction that we call expansion and retreat. Using duality techniques to compare the stochastic model to its mean-field limit, we find that expansion and retreat are also precisely the conditions needed to ensure survival and extinction of the stochastic model when the patch size is large. In addition, we study the dependence of survival on the dispersal range. We find that, with probability close to one and for a certain set of parameters, the metapopulation survives in the presence of nearest neighbor interactions while it dies out in the presence of long range interactions, suggesting that the best strategy for the population to spread in space is to use intermediate dispersal ranges." @default.
- W4298423001 created "2022-10-02" @default.
- W4298423001 creator A5087856948 @default.
- W4298423001 date "2015-04-06" @default.
- W4298423001 modified "2023-10-14" @default.
- W4298423001 title "Survival and extinction results for a patch model with sexual reproduction" @default.
- W4298423001 doi "https://doi.org/10.48550/arxiv.1504.01409" @default.
- W4298423001 hasPublicationYear "2015" @default.
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