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An application of time reversal of Markov processes to a problem of population genetics

Published online by Cambridge University Press:  01 July 2016

Masao Nagasawa  and
Takeo Maruyama
Masao Nagasawa
Affiliation:
Tokyo Institute of Technology
Takeo Maruyama*
Affiliation:
National Institute of Genetics, Mishima
*
∗∗Postal address: National Institute of Genetics, Mishima, Shizuoka, Japan.
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Abstract

A formula is proved for the expected value of sum of a function of gene frequency along a sample path in the past, given the present frequency. The proof and the explanation of the formula is based on the general theory of time reversal of Markov processes. Moreover, a relation between time reversal and conditional processes is discussed, and it is shown that the fictitious drift term appears when one looks back at the history of mutants given the present frequency.

Keywords

POPULATION GENETICSDIFFUSION PROCESSESTIME REVERSAL OF MARKOV PROCESSESCONDITIONAL SOJOURN TIMES OF GENE FREQUENCYCONDITIONAL DIFFUSIONSFICTITIOUS DRIFT
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 3 , September 1979 , pp. 457 - 478
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

∗

Present address: Seminar für Angewandte Mathematik der Universität Zürich, Freiestrasse 36, CH-8032 Zürich, Switzerland.

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