Dependence and interaction in branching processes
Paper in proceeding, 2013

Independence of reproducing individuals can be viewed as the very defining property of branching processes. It is crucial for the most famous results of the theory, the determination of the extinction probability and the dichotomy between extinction and exponential increase. In general processes, stabilisation of the age-distribution under growth follows, and indeed of the over-all population composition, and so do the many fine results of the area, like conditional stabilisation of the size of non-extinct subcritical processes. The last two decades have witnessed repeated attempts at treating branching processes with various kinds of dependence between individuals, ranging from local dependence between close relatives only to population size dependence. Of particular interest are very recent findings on processes that change from being supercritical to subcriticality at some threshold size, the carrying capacity of the habitat. We overview the development with an emphasis on these recent results.

Dependence

Age-structure

General branching processes

Carrying capacity

Author

Peter Jagers

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Fima C. Klebaner

Monash University

Springer Proceedings in Mathematics and Statistics

21941009 (ISSN) 21941017 (eISSN)

Vol. 33 325-333
9783642335488 (ISBN)

Subject Categories

Probability Theory and Statistics

DOI

10.1007/978-3-642-33549-5_19

ISBN

9783642335488

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1/3/2024 9