Survival probabilities for some multitype branching processes in genetics

✍ Scribed by Edward Pollak

• Book ID: 104652336
• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 590 KB
• Volume: 30
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00175608

✦ Synopsis

Consider a positively regular, slightly supercritical branching process with K types. An approximation to the probability of survival of a line descended from a single individual of type i has recently been derived by Hoppe. If K 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 .4 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.