The multi-type Galton-Watson process in a genetical context

J. H. Pollard

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In 1966 Ewens noted that the probability of fixation of a favourable new mutant linked to another gene is practically independent of the population size for a large random-mating population, and that what normally determines the fate of a new mutant gene is the behaviour of its frequency while it is rare. Because the relative frequency of the new mutant is small initially, he was able to obtain a linear recurrence relation over time for the expected relative frequencies of the two gametes which contain the mutant. This is a very interesting result, and immediately suggests a two-type Galton-Watson process as a suitable discrete-time stochastic model. In the present paper, some techniques associated with the multi-type Galton-Watson process and developed in the field of population mathematics are used to study the frequency of occurrence of a rare mutant gene. The use of these techniques in practice is demonstrated by the solution of a numerical example.
LanguageEnglish
Pages147-158
Number of pages12
JournalBiometrics
Volume24
Issue number1
DOIs
Publication statusPublished - Mar 1968
Externally publishedYes

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Galton-Watson Process
Multitype
Mutant
Genes
mutants
Gene
Mathematics
Stochastic models
Population Density
Germ Cells
Population
Linear Recurrence Relation
random mating
genes
Discrete-time Model
Fixation
Recurrence
Population Size
Stochastic Model
Immediately

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Pollard, J. H. / The multi-type Galton-Watson process in a genetical context. In: Biometrics. 1968 ; Vol. 24, No. 1. pp. 147-158.
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The multi-type Galton-Watson process in a genetical context. / Pollard, J. H.

In: Biometrics, Vol. 24, No. 1, 03.1968, p. 147-158.

Research output: Contribution to journalArticleResearchpeer-review

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