A genealogical approach to variable-population-size models in population genetics
- 1 June 1986
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 23 (2) , 283-296
- https://doi.org/10.2307/3214173
Abstract
A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.Keywords
This publication has 16 references indexed in Scilit:
- The Wright-Fisher model with temporally varying selection and population sizeJournal of Mathematical Biology, 1985
- An alternative approach to asymptotic results on genetic composition when the population size is varyingJournal of Mathematical Biology, 1983
- The genetic balance between varying population size and selective neutralityJournal of Mathematical Biology, 1983
- 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
- 5716The American Mathematical Monthly, 1971
- Rates of Approach to Homozygosity for Finite Stochastic Models with Variable Population SizeThe American Naturalist, 1968
- A mathematical study of the founder principle of evolutionary geneticsJournal of Applied Probability, 1966
- Random processes in geneticsMathematical Proceedings of the Cambridge Philosophical Society, 1958