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The geometry of random drift III. Recombination and diffusion

Published online by Cambridge University Press:  01 July 2016

Peter L. Antonelli ,
Kenneth Morgan  and
G. Mark Lathrop
Peter L. Antonelli
Affiliation:
University of Alberta
Kenneth Morgan
Affiliation:
University of Alberta
G. Mark Lathrop
Affiliation:
University of Alberta
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Abstract

A new diffusion model for random genetic drift of a two-locus di-allelic system is proposed. The Christoffel velocity field and the intrinsic geometry of the diffusion is computed for the equilibrium surface. It is seen to be radically non-spherical and to depend explicitly on the recombination fraction. The model has not been shown to be a limit of discrete Markov chains. For large values of the recombination, the present model is radically different from that of Ohta and Kimura, which is an approximation to the discrete process of random mating in the limit as the value of the recombination fraction goes to zero.

Keywords

LINKAGETWO-LOCUS DI-ALLELIC SYSTEMRECOMBINATION DIFFUSIONRIEMANNIAN GEOMETRYSAMPLING PROCESSLINKAGE DISEQUILIBRIUMCURVATUREGENE FREQUENCY SPACESTRATONOVICH STOCHASTIC CALCULUSAVERAGE FLUCTUATING FORCEMAXIMUM LIKELIHOOD CURVES
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 2 , June 1977 , pp. 260 - 267
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Antonelli, P. L. and Strobeck, C. (1977) The geometry of random drift. I. Stochastic distance and diffusion. Adv. Appl. Prob. 9.Google Scholar
[2] Antonelli, P. L., Chapin, J., Lathrop, G. M. and Morgan, K. (1977) The geometry of random drift. II. The symmetry of random genetic drift. Adv. Appl. Prob. 9.Google Scholar
[3] Ohta, T. and Kimura, M. (1969) Linkage disequilibrium due to random genetic drift. Genetical Res. 13, 47–55.Google Scholar
[4] Stratonovich, R. L. (1966) A new representation for stochastic integrals and equations. SIAM J. Control 4, 362–371.Google Scholar
[5] Stratonovich, R. L. (1963) Topics in the Theory of Random Noise, Vol. 1. Gordon and Breach, New York.Google Scholar