@article {Cornell:2004:1369-1473:87,
title = "Ultimate Extinction of the Promiscuous Bisexual GaltonWatson Metapopulation",
journal = "Australian & New Zealand Journal of Statistics",
parent_itemid = "infobike://bpl/anzs",
publishercode ="bp",
year = "2004",
volume = "46",
number = "1",
publication date ="2004-03-01T00:00:00",
pages = "87-98",
itemtype = "ARTICLE",
issn = "1369-1473",
eissn = "1467-842X",
url = "https://www.ingentaconnect.com/content/bpl/anzs/2004/00000046/00000001/art00012",
doi = "doi:10.1111/j.1467-842X.2004.00315.x",
author = "Cornell, Stephen J. and Isham, Valerie S.",
abstract = "Summary A variant of a sexual GallonWatson process is considered. At each generation the population is partitioned among nhosts (population patches) and individual members mate at random only with others within the same host. This is appropriate for many macroparasite systems, and at low parasite loads it gives rise to a depressed rate of reproduction relative to an asexual system, due to the possibility that females are unmated. It is shown that stochasticity mitigates against this effect, so that for small initial populations the probability of ultimate extinction (the complement of an epidemic) displays a tradeoff as a function of n between the strength of fluctuations which overcome this mating probability, and the probability of the subpopulation in one host being rescued by that in another. Complementary approximations are developed for the extinction probability: an asymptotically exact approximation at large n, and for small n a short-time probability that is exact in the limit where the mean number of offspring per parent is large.",
}