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On the persistence of random genetic drift

Published online by Cambridge University Press:  14 July 2016

Peter L. Antonelli  and
Kenneth Morgan
Peter L. Antonelli
Affiliation:
University of Alberta
Kenneth Morgan
Affiliation:
University of Alberta
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Abstract

It is demonstrated that standard Brownian motion in the tangent plane at the centroid of frequency space does not well approximate the discrete Wright—Fisher process for more than 2N generations where N is the effective population size. This result is obtained using Wright's concept of negligible mutation rate for the study of systematic evolutionary effects together with Ludwig's notion of the persistence of a dynamical system. This work may be viewed as a mathematical elaboration of a portion of Wright's shifting balance theory of evolution.

Keywords

WFK PROCESSRANDOM GENETIC DRIFTSTOCHASTIC PERTURBATIONPERSISTENCECHRISTOFFEL VELOCITY FIELDGEOMETRIC DIFFUSIONSTATIONARY DENSITYPERCOLATION OF GENESWRIGHTS SHIFTING BALANCE THEORYHUMAN EVOLUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 179 - 183
Copyright
Copyright © Applied Probability Trust 1978 

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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, 238–249.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, 250–259.CrossRefGoogle Scholar
[3] 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.Google Scholar
[4] Crow, J. F. and Kimura, M. (1970) An Introduction to Population Genetics Theory. Harper and Row, New York.Google Scholar
[5] Edwards, A. W. F. and Cavalli-Sforza, L. L. (1972) Affinity as revealed by differences in gene frequencies. In The Assessment of Population Affinities in Man, ed. Weiner, J. and Huizinga, J. Clarendon Press, Oxford.Google Scholar
[6] Eisenhart, L. P. (1926) Riemannian Geometry. Princeton University Press, Princeton, N.J.Google Scholar
[7] Ludwig, D. (1975) Persistence of dynamical systems under random perturbations. SIAM Rev. 17, 605–640.CrossRefGoogle Scholar
[8] Ventsel', A. D. and Freidlin, M. I. (1970) On small random perturbations of dynamical systems. Russian Mathematical Surveys 25, 1–55.Google Scholar
[9] Wright, S. (1964) Stochastic processes in evolution. In Stochastic Models in Medicine and Biology, ed. Gurland, J. University of Wisconsin Press, Madison.Google Scholar