Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Further results on the survival of a gene represented in a founder population

Abstract

This paper is concerned with gene survival in a population which may increase without density dependence according to a generalization of the Moran model for haploid individuals. A selective advantage to one allele and the possibility of differential reproductive rates are allowed. Simple conditions are given for ultimate homozygosity to be certain and for the possibility of ultimate polymorphism. The results complement and extend those of Heyde (1981, 1982).

This is a preview of subscription content, log in to check access.

References

  1. Hall, P., Heyde, C. C.: Martingale limit theory and its application. New York: Academic Press 1980

  2. Heyde, C. C.: On the survival of a gene represented in a founder population. J. Math. Biology 12, 91–99 (1981)

  3. Heyde, C. C.: The effect of differential reproductive rates on the survival of a gene represented in a founder population. In: Essays in statistical science. (Gani, J., Hannan, E. J., eds.). J. Applied Prob. 19A (1982)

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Daley, D.J., Hall, P. & Heyde, C.C. Further results on the survival of a gene represented in a founder population. J. Math. Biology 14, 355–363 (1982). https://doi.org/10.1007/BF00275398

Download citation

Key words

  • Gene survival
  • Founder population
  • Selective advantage
  • Differential reproductive rates
  • Ultimate homozygosity
  • Polymorphism
  • Martingale methods