![]() We thank Chris Tofts, Margaret Mackinnon and two anonymous reviewers for helpful comments. Material on bisexual Galton–Watson processes can be found in Daley 22. Griffiths 16 covers the multitype process applied to the spatial spread of an epidemic. ![]() For the less mathematical reader, we recommend the book by Resnick 26, which contains many helpful examples. Athreya and Ney 23 and Karlin and Taylor 25 contain derivations of all of the basic theory, and both have excellent introductions to the multitype process. Harris 24 is the standard reference on the Galton– Watson process. However, under some of the transmission strategies used by Where to learn more Often, the effect of sexual reproduction is not very important if there is an equal sex ratio and if females are always able to mate, growth of a population can be treated as a normal Galton–Watson process. In describing sexually reproducing organisms, this assumption is obviously untrue. In the Galton–Watson process, the particles of interest produce offspring independently, without the need to interact with other particles. Suppose there is more than one type of offspring, for example: a host population might contain both susceptible individuals and carriers a parasitized cell undergoing mitotic division might produce daughter cells containing various numbers of parasites these parasites might enter resting spore stages or there might be different forms of the parasite that are resistant to Sexual reproduction, age dependence and immigration Perhaps the most important refinement of the Galton–Watson process for parasitology is the multitype branching process. Given, for instance, one initial ancestor, what was the chance that the family name would survive through successive generations? Obviously, survival of the surname in the first generation Multitype branching processes ![]() The problem involved the rate of disappearance of surnames in the British peerage, a subject of some controversy at the time. The study of branching processes originated with a mathematical puzzle posed by Sir Francis Galton, the noted cousin of Charles Darwin, in the Educational Times of 1 April 1873. Section snippets Definition and historical background
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