DENSITY-DEPENDENCE IN TIME-SERIES OBSERVATIONS OF NATURAL-POPULATIONS- ESTIMATION AND TESTING

We report on a new statistical test for detecting density dependence i n univariate time series observations of population abundances. The te st is a likelihood ratio test-based on a discrete time stochastic logi stic model. The null hypothesis is that the population is undergoing s tochastic exponential growth, stochastic exponential decline, or rando m walk. The distribution of the test statistic under both the null and alternate hypotheses is obtained through parametric bootstrapping. We document the power of the test with extensive simulations and show ho w some previous tests in the literature for density dependence suffer from either excessive Type I or excessive Type Il error. The new test appears robust against sampling or measurement error in the observatio ns. In fact, under certain types of error the power of the new lest is actually increased. Example analyses of elk (Cervus elaphus) and griz zly bear (Ursus arctos horribilis) data sets are provided. The model i mplies that density-dependent populations do not have a point equilibr ium, but rather reach a stochastic equilibrium (stationary distributio n of population abundance). The model and associated statistical metho ds have potentially important applications in conservation biology.