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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Antonelli, Peter L. Chapin, Jared and Voorhees, B. H. 1980. The geometry of random genetic drift VI. A random selection diffusion model. Advances in Applied Probability, Vol. 12, Issue. 01, p. 50.
    Tier, Charles 1979. A tri-allelic diffusion model with selection, migration, and mutation. Mathematical Biosciences, Vol. 44, Issue. 1-2, p. 41.
    Tier, Charles and Keller, Joseph B. 1978. A Tri-Allelic Diffusion Model with Selection. SIAM Journal on Applied Mathematics, Vol. 35, Issue. 3, p. 521.
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An asymptotic formula for the transition density of random genetic drift

  • Peter L. Antonelli (a1)
Abstract

Stochastic models in population genetics which lead to diffusion equations are considered. A geometric formula for the asymptotic expansions of the fundamental solutions of these equations is presented. Specifically, the random genetic drift process of one-locus theory and the Ohta–Kimura model of two-locus di-allelic systems with linkage are studied. Agreement with the work of Keller and Voronka for the two-allele one-locus case is obtained. For the general n-allele problem, the formulas obtained here are apparently new.

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COPYRIGHT: © Applied Probability Trust 1978 
References
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[1] Antonelli, P. L. and Strobeck, C. (1977) The geometry of random drift, I. Stochastic distance and diffusion. Adv. Appl. Prob. 9, 238–249.
[2] Antonelli, P. L., Morgan, K. and Lathrop, G. M. (1977) The geometry of random drift, III. Recombination and diffusion. Adv. Appl. Prob. 9, 260–267.
[3] Friedman, A. (1975) Stochastic Differential Equations and Applications, Vol. I. Academic Press, New York.
[4] Helgason, S. (1961) Differential Geometry and Symmetric Spaces. Academic Press, New York.
[5] Keller, J. B. and Voronka, R. (1975) Asymptotic analysis of stochastic models in population genetics. Math. Biosci. 25, 331–362.
[6] Molchanov, S. A. (1975) Diffusion processes and Riemannian geometry. Russian Math. Survey 30, 1–75.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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