An ergodic theorem for evolution in a random environment
- 1 March 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 12 (04) , 661-672
- https://doi.org/10.1017/s0021900200048622
Abstract
Let w 1, w 12 and w 2 be the fitnesses of genotypes A 1 A 1, A 1 A 2 and A 2 A 2 in an infinite diploid population, and let pn be the A 1, gene frequency in the nth generation. If fitness varies independently from generation to generation, then pn is a Markov process with a continuum of states. If E[In(wi /w 12)] < 0 for i = 1, 2, then there is a unique stationary probability, and the distribution of pn converges to it as n → ∞.Keywords
This publication has 3 references indexed in Scilit:
- Random temporal variation in selection intensities: Case of large population sizeTheoretical Population Biology, 1974
- Polymorphism in random environmentsTheoretical Population Biology, 1973
- Criteria for the recurrence or transience of stochastic process. IJournal of Mathematical Analysis and Applications, 1960