Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-30T02:58:37.993Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on a singular diffusion equation in population genetics

Published online by Cambridge University Press:  14 July 2016

Knut Aase
Knut Aase*
Affiliation:
University of Bergen, Norway
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

DIFFUSION EQUATIONSGENE FREQUENCY CHANGES
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 1 - 8
Copyright
Copyright © Applied Probability Trust 1976 

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.)

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, 1–15.CrossRefGoogle Scholar
Kimura, M. (1955) Stochastic processes and distribution of gene frequencies under natural selection. Cold Spring Harbor Symposium on Quantitative Biology 20, 33–53.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, 588–593.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