Impact of demography on extinction/fixation events View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-02

AUTHORS

Camille Coron, Sylvie Méléard, Denis Villemonais

ABSTRACT

In this article we consider diffusion processes modeling the dynamics of multiple allelic proportions (with fixed and varying population size). We are interested in the way alleles extinctions and fixations occur. We first prove that for the Wright-Fisher diffusion process with selection, alleles get extinct successively (and not simultaneously), until the fixation of one last allele. Then we introduce a very general model with selection, competition and Mendelian reproduction, derived from the rescaling of a discrete individual-based dynamics. This multi-dimensional diffusion process describes the dynamics of the population size as well as the proportion of each type in the population. We prove first that alleles extinctions occur successively and second that depending on population size dynamics near extinction, fixation can occur either before extinction almost surely, or not. The proofs of these different results rely on stochastic time changes, integrability of one-dimensional diffusion processes paths and multi-dimensional Girsanov's tranform. More... »

PAGES

549-577

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00285-018-1283-1

DOI

http://dx.doi.org/10.1007/s00285-018-1283-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106341566

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/30145611


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