Timescales of population rarity and commonness in random environments

Theoretical Population Biology
Regis FerriereIrina Kurkova

Abstract

This is a mathematical study of the interactions between non-linear feedback (density dependence) and uncorrelated random noise in the dynamics of unstructured populations. The stochastic non-linear dynamics are generally complex, even when the deterministic skeleton possesses a stable equilibrium. There are three critical factors of the stochastic non-linear dynamics; whether the intrinsic population growth rate (lambda) is smaller than, equal to, or greater than 1; the pattern of density dependence at very low and very high densities; and whether the noise distribution has exponential moments or not. If lambda < 1, the population process is generally transient with escape towards extinction. When lambda > or = 1, our quantitative analysis of stochastic non-linear dynamics focuses on characterizing the time spent by the population at very low density (rarity), or at high abundance (commonness), or in extreme states (rarity or commonness). When lambda >1 and density dependence is strong at high density, the population process is recurrent: any range of density is reached (almost surely) in finite time. The law of time to escape from extremes has a heavy, polynomial tail that we compute precisely, which contrasts with the thin t...Continue Reading

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Citations

Dec 12, 2007·Ecology Letters·Sébastien Lion, Minus van Baalen

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