Predicting Extinction Times from Environmental Stochasticity and Carrying Capacity

Abstract

Managers of small populations often need to estimate the expected time to extinction Te of their charges. Useful models for extinction times must be ecologically realistic and depend on measurable parameters. Many populations become extinct due to environmental stochasticity, even when the carrying capacity K is stable and the expected growth rate is positive. A model is proposed that gives Te by diffusion analysis of the log population size nt (= loge Nt). The model population grows according to the equation Nt+1 = RtNt, with K as a ceiling. Application of the model requires estimation of the parameters k = logK, rd = the expected change in n, vr = Variance(log R), and ϱ the autocorrelation of the rt. These are readily calculable from annual census data (rd is trickiest to estimate). General formulas for Te are derived. As a special case, when environmental fluctuations overwhelm expected growth (that is rd- 0), Te = 2no(k ‐ no/2)/vr. If the rt are autocorrelated, then the effective variance is vre- vr (1 + ϱ)/(1 ‐ ϱ). The theory is applied to populations of checkerspot butterfly, grizzly bear, wolf, and mountain lion. Copyright 1994, Wiley Blackwell. All rights reserved