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We introduce a spatial stochastic process on the lattice Z^d to model massextinctions. 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 theflock reaches N individuals, then, and only then, it starts giving birth oneach of the 2d neighboring sites at rate \lambda(N). Finally, disaster strikesat rate 1, that is, the whole flock disappears. Our model shows that, at leastin theory, there is a critical maximum flock size above which a species iscertain to disappear and below which it may survive.

Mass extinctions: an alternative to the Allee effect