Conditions for fixation of an allele in the density-dependent wright–Fisher models
- 1 June 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (2) , 247-256
- https://doi.org/10.2307/3214433
Abstract
A density-dependent Wright–Fisher model is a model where the population size changes randomly depending on the genetic composition process. If population sizesMnvary 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
This publication has 7 references indexed in Scilit:
- The Wright-Fisher model with temporally varying selection and population sizeJournal of Mathematical Biology, 1985
- A note on some results of SchuhJournal of Applied Probability, 1984
- An alternative approach to asymptotic results on genetic composition when the population size is varyingJournal of Mathematical Biology, 1983
- Sums of i.i.d. random variables and an application to the explosion criterion for markov branching processesJournal of Applied Probability, 1982
- The effect of selection on genetic balance when the population size is varyingTheoretical Population Biology, 1977
- The genetic balance between random sampling and random population sizeJournal of Mathematical Biology, 1975
- A NOTE ON THE BALANCE BETWEEN RANDOM SAMPLING AND POPULATION SIZE (ON THE 30TH ANNIVERSARY OF G. MALÉCOT'S PAPER)Genetics, 1974