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Solving a singular diffusion equation occurring in population genetics

Published online by Cambridge University Press:  14 July 2016

Louis Jensen
Louis Jensen*
Affiliation:
Iowa State University, Ames
*
*Now at The University of Michigan, Ann Arbor.
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Abstract

A technique for solving a partial differential equation is presented. The technique is based upon the known solution of a similar equation. The method is used to attempt to solve the equation describing the change in the frequency of an allele in the presence of selection and random drift in a finite population. Two cases can be solved within a reasonable degree of approximation: (a) the viabilities are additive and (b) heterozygotes are symmetrically overdominant to the homozygotes. The solutions in both cases are compared with the exact discrete solutions found by powering the re evant transition matrix.

Keywords

DIFFUSION EQUATIONSCHANGE IN GENE FREQUENCY AND SELECTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 1 - 15
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

Journal Paper No. J-7168 of the Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 1669. Research supported in part by NIH Grant GM-13827.

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