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# Mass Extinctions: An Alternative to the Allee Effect

Rinaldo B. Schinazi
The Annals of Applied Probability
Vol. 15, No. 1B (Feb., 2005), pp. 984-991
Stable URL: http://www.jstor.org/stable/30038342
Page Count: 8
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## Abstract

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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