Survival probabilities for some multitype branching processes in genetics
Tóm tắt
Consider a positively regular, slightly supercritical branching process withK types. An approximation to the probability of survival of a line descended from a single individual of typei has recently been derived by Hoppe. IfK is large, however, this approximation may not be easy to compute. A further approximation that is easily computable is given. The result is used to estimate probabilities of survival of an allele A that is originally present in one male or one female in a large, random mating, age-structured population. Both autosomal and sex-linked loci are considered. Another application of the approximation is also discussed.
Tài liệu tham khảo
Eshel, L: On the survival probability of a slightly advantageous mutant gene with a general distribution of progeny size — a branching process model. J. Math. Biol.12, 355–362 (1981)
Eshel, I.: On the survival probability of a slightly advantageous mutant gene in a multitype population: a multidimensional branching process model. J. Math. Biol.19, 201–209 (1984)
Ewens, W. J.: Some applications of multi-type branching processes in population genetics. J. R. Stat. Soc. Ser. B30, 164–175 (1968)
Franklin, J. N.: Matrix Theory. Englewood Cliffs, NJ: Prentice-Hall 1968
Goodman, L. A.: The probabilities of extinction for birth and death processes that are age-dependent or phase-dependent. Biometrika54, 579–596 (1967)
Harris, T. E.: The Theory of Branching Processes. Berlin Heidelberg New York: Springer 1963
Hill, W. G.: Effective size of populations with overlapping generations. Theor. Popul. Biol.3, 278–289 (1972)
Hill, W. G.: A note on effective population size with overlapping generations. Genetics92, 317–322 (1979)
Hoppe, F. M.: The survival probability of a mutant in a multidimensional population. J. Math. Biol.30, 567–575 (1992)
Pollak, E.: Some effects of two types of migration on the survival of a gene. Biometrics28, 385–400 (1972)
Pollak, E.: Effective population numbers and mean times to extinction in dioccious populations with overlapping generations. Math. Biosci.52, 1–25 (1980)
Pollak, E.: On the theory of partially inbreeding finite populations. II. Partial sib mating. Genetics120, 303–311 (1988)
Pollak, E.: The effective population size of an age-structured population with a sex-linked locus. Math. Biosci.101, 121–130 (1990)