Extinction rates of established spatial populations

Details Extinction rates of established spatial populations Extinction rates of established spatial populations

2010-08-28

arxiv.org/abs/1008.4854v4

Physics

Condensed Matter

Statistical Mechanics

26 pages including 3 appendices, 16 figures

Scientific paper

This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations between neighboring sites. In extinction scenario I the zero population size is a repelling fixed point of the on-site deterministic dynamics. In extinction scenario II the zero population size is an attracting fixed point, corresponding to what is known in ecology as Allee effect. Assuming a large population size, we develop WKB (Wentzel-Kramers-Brillouin) approximation to the master equation. The resulting Hamilton's equations encode the most probable path of the population toward extinction and the mean time to extinction. In the fast-migration limit these equations coincide, up to a canonical transformation, with those obtained, in a different way, by Elgart and Kamenev (2004). We classify possible regimes of population extinction with and without an Allee effect and for different types of refuge and solve several examples analytically and numerically. For a very strong Allee effect the extinction problem can be mapped into the over-damped limit of theory of homogeneous nucleation due to Langer (1969). In this regime, and for very long systems, we predict an optimal refuge size that maximizes the mean time to extinction.

Affiliated with

Also associated with

No associations

Rating

Extinction rates of established spatial populations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Extinction rates of established spatial populations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extinction rates of established spatial populations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-529627