A surprising Poisson process arising from a species competition model

Richard Durrett and Vlada Limic

Stochastic Processes and their Applications, 2002, vol. 102, issue 2, 301-309

Abstract: Motivated by the work of Tilman (Ecology 75 (1994) 2) and May and Nowak (J. Theoret. Biol. 170 (1994) 95) we consider a process in which points are inserted randomly into the unit interval and a new point kills each point to its left independently and with probability a. Intuitively this dynamic will create a negative dependence between the number of points in adjacent intervals. However, we show that the ensemble of points converges to a Poisson process with intensity 1/(a(1-x)), and the number of points at time t grows like (log t)/a.

Keywords: Poisson; process; Species; competition; Stationary; measure (search for similar items in EconPapers)
Date: 2002
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