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February, 1974 Limit Theorems for Some Stochastic Evolution Models
Harry A. Guess
Ann. Probab. 2(1): 14-31 (February, 1974). DOI: 10.1214/aop/1176996748


Limit theorems are proved for two stochastic models of molecular evolution in finite populations of fixed size. An additive fitness model is shown to be asymptotically neutral in the sense that the relative fitnesses converge in probability to one and the gene frequency distribution converges to the same limiting distribution as when all mutations are selectively neutral. A multiplicative fitness model is studied and weak convergence theorems are proved for the vector whose components are the fitnesses of individuals in the population.


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Harry A. Guess. "Limit Theorems for Some Stochastic Evolution Models." Ann. Probab. 2 (1) 14 - 31, February, 1974.


Published: February, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0276.60029
MathSciNet: MR368817
Digital Object Identifier: 10.1214/aop/1176996748

Primary: 60F05
Secondary: 92A10

Keywords: Brownian motion , Evolution , mutation , natural selection , Stochastic model , weak convergence

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 1 • February, 1974
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