On the Path to Extinction
by Professor Peter Jagers
Abstract: Populations can die in many ways. Arguably the most basic is extinction for intrinsic reasons, by stably insufficient, i.e. subcritical, reproduction. We â€¨consider (moderately) large, subcritical general branching processes, and ask what the time T to extinction is.
It turns out that T has two components, both carrying weight, a deterministic part, proportional to the logarithm of initial population size, and a random part, with an approximate Gumbel distribution.
Then we consider the path to extinction. How large will the population be at time uT, 0
(Joint work with Fima Klebaner and Serik Sagitov, published in the Proc Nat.â€¨ Acad. of US (2007) and J. Appl. Prob. (2007)).
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