Mass extinctions: an alternative to the Allee effect

Details Mass extinctions: an alternative to the Allee effect Mass extinctions: an alternative to the Allee effect

2005-03-24

arxiv.org/abs/math/0503525v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 984-991

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000819 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000819

We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \phi until the maximum of N individuals has been reached at the site. Once the flock reaches N individuals, then, and only then, it starts giving birth on each of the 2d neighboring sites at rate \lambda(N). Finally, disaster strikes at rate 1, that is, the whole flock disappears. Our model shows that, at least in theory, there is a critical maximum flock size above which a species is certain to disappear and below which it may survive.

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