Abstract
| Language | English |
|---|---|
| Pages | 147-158 |
| Number of pages | 12 |
| Journal | Biometrics |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 1968 |
| Externally published | Yes |
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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 journal › Article › Research › peer-review
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.
UR - http://www.scopus.com/inward/record.url?scp=0014266161&partnerID=8YFLogxK
U2 - 10.2307/2528466
DO - 10.2307/2528466
M3 - Article
VL - 24
SP - 147
EP - 158
JO - Biometrics
T2 - Biometrics
JF - Biometrics
SN - 0006-341X
IS - 1
ER -