Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-30T22:48:52.231Z Has data issue: false hasContentIssue false
  • English
  • Français

On the survival of a gene in a subdivided population

Published online by Cambridge University Press:  14 July 2016

Edward Pollak
Edward Pollak*
Affiliation:
Columbia University, New York
Get access Rights & Permissions [Opens in a new window]

Extract

A classical type of problem in population genetics is that of calculating the probability that a line descended from a particular gene will become extinct. In one problem of this sort, dealt with by Fisher (1922) and Haldane (1927), it is assumed that the population being studied is very large and that initially the number of genes of a particular type, say type A, is small. These authors obtained the solution by the use of the theory of branching processes.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 1 , June 1966 , pp. 142 - 155
Copyright
Copyright © Sheffield: Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Fisher, R. A. (1922) On the dominance ratio. Proc. Roy. Soc. Edinburgh 42, 321–341.Google Scholar
[2] Fisher, R. A. (1930) The distribution of gene ratios for rare mutations. Proc. Roy. Soc. Edinburgh 50, 204–219.Google Scholar
[3] Gantmacher, F. R. (1959) Applications of the Theory of Matrices. Translated and revised by Brenner, J. L. with the assistance of Bushaw, D. W. and Evanusa, S. Interscience Publishers, Inc., New York.Google Scholar
[4] Haldane, J. B. S. (1927) A mathematical theory of natural and artificial selection. Part V : Selection and mutation. Proc. Cambridge Philos. Soc. 23, 838–844.Google Scholar
[5] Harris, T. E. (1951) Some mathematical models for branching processes. Proc. Second Berkeley Symposium on Math. Statistics and Probability, 305–328.Google Scholar
[6] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin, Göttingen, Heidelberg.Google Scholar
[7] Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains. D. Van Nostrand Company, Inc., Princeton, New Jersey.Google Scholar
[8] Kimura, M. (1957) Some problems of stochastic processes in genetics. Ann. Math. Statist. 28, 882–901.Google Scholar
[9] Malecot, G. (1952) Les processus stochastiques et la méthode des fonctions génératrices ou caractéristiques. Publ. Inst. Stat. Univ. Paris, 1, (fasc. 3).Google Scholar
[10] Moran, P. A. P. (1960) The survival of a mutant gene under selection. II Austral. J. Math. 1, 485–491.Google Scholar
[11] Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar
[12] Sevastyanov, B. A. (1948) On the theory of branching random processes (in Russian). Doklady Acad. Nauk SS SR, (n.s.) 59, 1407–1410.Google Scholar
[13] Sevastyanov, B. A. (1951) Theory of branching stochastic processes (in Russian). Uspehi Mat. Nauk. (n. s.) 6, 47–99.Google Scholar
[14] Wright, S. (1931) Evolution in Mendelian populations. Genetics 16, 97–159.Google Scholar