Volume 122, Number 1, April 2018
|Number of page(s)||7|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||21 May 2018|
Reduction of a metapopulation genetic model to an effective one-island model(a)
1 Frankfurt Institute for Advanced Studies - 60438 Frankfurt am Main, Germany
2 Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester Manchester M13 9PL, UK
Received: 18 February 2018
Accepted: 9 May 2018
We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. We analyse this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.
PACS: 87.10.Mn – Stochastic modeling / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ey – Stochastic processes
© EPLA, 2018
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