The Wright-Fisher model with temporally varying selection and population size
This paper is concerned with the Wright-Fisher model in genetics, for which the population size \(M_ n\) of generation n is allowed to be random, and the selective advantage \(\sigma_ n\) of one of the alleles may also vary with the generation. The authors study the question of whether ultimate genetic polymorphism is possible in the population. In the general case, subject to certain conditions on \(M_ n\) and \(\sigma_ n\), only partial results are obtained. When, however, \(M_ n\) and \(\sigma_ n\) are not density dependent, it is possible to derive complete results. One such, for example, is that fixation occurs with probability 1 if and only if \(\sum^{\infty}_{0}(M_ n^{-1}+\sigma_ n)=\infty\) a.s. The paper ends with the discussion of bounds for the fixation probability in the case where \(\sigma_ n=\sigma\) is a constant.
scientific article; zbMATH DE number 3904389
scientific article