%0 Journal Article %1 pollak1966survival %A Pollak, Edward %D 1966 %I Applied Probability Trust %J Journal of Applied Probability %K local_adaptation parallel_adaptation probability_of_survival selection spatial_structure %N 1 %P 142--155 %T On the Survival of a Gene in a Subdivided Population %U http://www.jstor.org/stable/3212043 %V 3 %X A classical problem in population genetics consists in finding the probability that a line descending from a particular gene $A$ will become extinct. A simple assumption R. A. Fisher, Proc. Roy. Soc. Edinburgh 42 (1922), 321--341; J. B. S. Haldane, Proc. Cambridge Philos. Soc. 23 (1927), 838--844 is that of a large population where, initially, the number of $A$-genes is small. Another assumption R. A. Fisher, Proc. Roy. Soc. Edinburgh 50 (1930), 204--219; S. Wright, Genetics 16 (1931), 97--159 is that of a population with a constant number $N$ of genes where $A$ has a certain selective disadvantage over another gene $A$. The present author considers $K$ subpopulations which inhabit $K$ different ecological niches with possible migration between the niches. First, it is assumed that there is no limit to the size a population can attain and that the $A$-genes reproduce independently of each other. Let $\pi_i\ (i=1,2,\cdots,K)$ be the conditional probability that the line descending from an $A$-gene becomes extinct if the ancestral gene of the line is in niche $i$; the probability that $A$ survives is then expressible in terms of the $\pi_i$. Next, we assume that the population possesses a large but finite number $N_i$ of genes ($A$ or $A$) in niche $i$. If certain assumptions of independence are made, then the probability that $A$ survives is approximated by a function of the above $\pi_i$, provided these are not all equal to unity.

@article{pollak1966survival, abstract = {A classical problem in population genetics consists in finding the probability that a line descending from a particular gene $A$ will become extinct. A simple assumption [R. A. Fisher, Proc. Roy. Soc. Edinburgh 42 (1922), 321--341; J. B. S. Haldane, Proc. Cambridge Philos. Soc. 23 (1927), 838--844] is that of a large population where, initially, the number of $A$-genes is small. Another assumption [R. A. Fisher, Proc. Roy. Soc. Edinburgh 50 (1930), 204--219; S. Wright, Genetics 16 (1931), 97--159] is that of a population with a constant number $N$ of genes where $A$ has a certain selective disadvantage over another gene $\overline A$. The present author considers $K$ subpopulations which inhabit $K$ different ecological niches with possible migration between the niches. First, it is assumed that there is no limit to the size a population can attain and that the $A$-genes reproduce independently of each other. Let $\pi_i\ (i=1,2,\cdots,K)$ be the conditional probability that the line descending from an $A$-gene becomes extinct if the ancestral gene of the line is in niche $i$; the probability that $A$ survives is then expressible in terms of the $\pi_i$. Next, we assume that the population possesses a large but finite number $N_i$ of genes ($A$ or $\overline A$) in niche $i$. If certain assumptions of independence are made, then the probability that $A$ survives is approximated by a function of the above $\pi_i$, provided these are not all equal to unity. }, added-at = {2010-05-16T18:54:29.000+0200}, author = {Pollak, Edward}, biburl = {https://www.bibsonomy.org/bibtex/23c3cf150aea743a3bfe52155d00cbf7b/peter.ralph}, description = {JSTOR: Journal of Applied Probability, Vol. 3, No. 1 (Jun., 1966), pp. 142-155}, interhash = {bfcd5617e13e1892aee93a85c4578edb}, intrahash = {3c3cf150aea743a3bfe52155d00cbf7b}, issn = {00219002}, journal = {Journal of Applied Probability}, keywords = {local_adaptation parallel_adaptation probability_of_survival selection spatial_structure}, number = 1, pages = {142--155}, publisher = {Applied Probability Trust}, timestamp = {2010-05-16T18:54:29.000+0200}, title = {On the Survival of a Gene in a Subdivided Population}, url = {http://www.jstor.org/stable/3212043}, volume = 3, year = 1966 }