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.
title = "The multi-type Galton-Watson process in a genetical context",
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.",
In: Biometrics, Vol. 24, No. 1, 03.1968, p. 147-158.
Research output: Contribution to journal › Article
TY - JOUR
T1 - The multi-type Galton-Watson process in a genetical context
AU - Pollard, J. H.
PY - 1968/3
Y1 - 1968/3
N2 - 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.
AB - 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.
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