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Conditions for fixation of an allele in the density-dependent wright–Fisher models

Published online by Cambridge University Press:  14 July 2016

Fima C. Klebaner
Fima C. Klebaner*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
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Abstract

A density-dependent Wright–Fisher model is a model where the population size changes randomly depending on the genetic composition process. If population sizes Mn vary without density dependence then the condition ΣMn–1 = ∞ is necessary and sufficient for fixation. It is shown that the above condition is no longer necessary for fixation in the density dependent models. Another necessary condition for fixation is given. Some known results on series of functions of sums of i.i.d. random variables are generalized to weighted sums.

Keywords

DENSITY DEPENDENCEWEIGHTED SUMS OF RANDOM VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 247 - 256
Copyright
Copyright © Applied Probability Trust 1988 

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