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Duality and fixation in Ξ-Wright-Fisher processes with frequency-dependent selection
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González Casanova, Adrián and Spanò, Dario (2018) Duality and fixation in Ξ-Wright-Fisher processes with frequency-dependent selection. Annals of Applied Probability, 28 (1). pp. 250-284. doi:10.1214/17-AAP1305
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Official URL: http://doi.org/10.1214/17-AAP1305
Abstract
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals first choose a (random) number of \emph{potential} parents from the previous generation and then, from the selected pool, they inherit the type of the fittest parent. The probability distribution function of the number of potential parents per individual thus parametrises entirely the selection mechanism. Using sampling- and moment-duality, weak convergence is then proved both for the allele frequency process of the selectively weak type and for the population's ancestral process. The scaling limits are, respectively, a two-types $\Xi$-Fleming-Viot jump-diffusion process with frequency-dependent selection, and a branching-coalescing process with general branching and simultaneous multiple collisions. Duality also leads to a characterisation of the probability of extinction of the selectively weak allele, in terms of the ancestral process' ergodic properties.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics Faculty of Science > Statistics |
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| Library of Congress Subject Headings (LCSH): | Branching processes, Stochastic processes, Markov processes, Diffusion processes | ||||||
| Journal or Publication Title: | Annals of Applied Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1050-5164 | ||||||
| Official Date: | 3 March 2018 | ||||||
| Dates: |
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| Date of first compliant deposit: | 19 March 2018 | ||||||
| Volume: | 28 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 250-284 | ||||||
| DOI: | 10.1214/17-AAP1305 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
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