Hostname: page-component-7dd5485656-wxk4p Total loading time: 0 Render date: 2025-10-31T00:37:19.721Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffusion models of temporally varying selection in population genetics

Published online by Cambridge University Press:  01 July 2016

Shoichiro Seno  and
Tokuzo Shiga
Shoichiro Seno*
Affiliation:
Tokyo Institute of Technology
Tokuzo Shiga*
Affiliation:
Tokyo Institute of Technology
*
∗ Postal address: Department of Applied Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152, Japan.
∗ Postal address: Department of Applied Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a diploid model of random selection. Assuming that the selective fitness is of the SAS–CFF type introduced by Gillespie, we obtain a diffusion approximation. We also discuss the existence of stationary distributions and recurrent properties.

Keywords

DIPLOID MODELRANDOM SELECTIONSAS–CFF MODELDIFFUSION APPROXIMATIONSTATIONARY DISTRIBUTIONRECURRENT PROPERTIES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 260 - 280
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Brown, L. D. (1971) Admissible estimators, recurrent diffusions and insoluble boundary value problems. Ann. Math. Statist. 42, 855–903.CrossRefGoogle Scholar
[2] Gillespie, J. H. (1978) A general model to account for enzyme variation in natural populations. V. The SAS-CFF model. Theoret. Popn Biol. 14, 1–45.CrossRefGoogle ScholarPubMed
[3] Ibragimov, L. A. and Linnik, Yu. V. (1971) Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, Groningen, The Netherlands.Google Scholar
[4] Ichihara, K. (1978) Some global properties of symmetric diffusion processes. Publ. Res. Inst. Math. Sci. Kyoto Univ. 14, 441–486.CrossRefGoogle Scholar
[5] Ikeda, N. and Watanabe, S. (1981) Stochastic Differential Equations and Diffusion Processes. North-Holland/Kodansha.Google Scholar
[6] Kesten, H. and Ogura, Y. (1981) Recurrence properties of Lotka-Volterra models with random fluctuation. J. Math. Soc. Japan 32, 335–366.Google Scholar
[7] Kesten, H. and Papanicolau, G. C. (1979) A limit theorem for turbulent diffusion. Commun. Math. Phys. 65, 97–128.CrossRefGoogle Scholar
[8] Kushner, H. J. and Hai-Huang, (1981) On the weak convergence of a sequence of general stochastic difference equations. Siam J. Appl. Math. 40, 528–541.CrossRefGoogle Scholar
[9] Shiga, T. (1981) Diffusion processes in population genetics. J. Math. Kyoto Univ. 21, 133–151.Google Scholar
[10] Turelli, M. (1981) Temporally varying selection on multiple alleles; A diffusion analysis. J. Math. Biol 13, 115–129.CrossRefGoogle Scholar
[11] Watanabe, H. (1984) Diffusion approximations of some stochastic difference equation II. Hiroshima J. Math. CrossRefGoogle Scholar