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A note on a singular diffusion equation in population genetics

Published online by Cambridge University Press:  14 July 2016

Knut Aase*
Affiliation:
University of Bergen, Norway

Abstract

This note points out an error made in an earlier paper treating a diffusion equation for the probability distribution of gene frequencies under selection. The main interest lies in the orthogonality properties of certain eigenfunctions and the determination of the corresponding Fourier coefficients. Two particular cases of selection parameter values are considered. Approximate formulas are given for the two smallest eigenvalues for arbitrary values of the selection parameters.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1976 

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References

Eastham, M. S. P. (1970) Theory of Ordinary Differential Equations. Van Nostrand Reinhold, London.Google Scholar
Jensen, L. (1974) Solving a singular diffusion equation occurring in population genetics. J. Appl. Prob. 11, 115.CrossRefGoogle Scholar
Kimura, M. (1955) Stochastic processes and distribution of gene frequencies under natural selection. Cold Spring Harbor Symposium on Quantitative Biology 20, 3353.Google Scholar
Miller, G. F. (1962) The evaluation of eigenvalues of a differential equation arising in a problem in genetics. Proc. Camb. Phil. Soc. 58, 588593.CrossRefGoogle Scholar
Morse, P. M. and Feshbach, H. (1953) Methods of Theoretical Physics, Part I. McGraw Hill, New York.Google Scholar
Stratton, J. A., Morse, P. M., Chu, L. J. and Hutner, R. A. (1941) Elliptic Cylinder and Spheroidal Wave Functions. Wiley, New York.Google Scholar