Density Dependence in Time Series Observations of Natural Populations: Estimation and Testing

We report on a new statistical test for detecting density dependence in univariate time series observations of population abundances. The test is a likelihood ratio test based on a discrete time stochastic logistic model. The null hypothesis is that the population is undergoing stochastic exponential growth, stochastic exponential decline, or random 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 how some previous tests in the literature for density dependence suffer from either excessive Type I or excessive Type II error. The new test appears robust against sampling or measurement error in the observations. In fact, under certain types of error the power of the new test is actually increased. Example analyses of elk (Cervus elaphus) and grizzly bear (Ursus arctos horribilis) data sets are provided. The model implies that density—dependent populations do not have a point equilibrium, but rather reach a stochastic equilibrium (stationary distribution of population abundance). The model and associated statistical methods have potentially important applications in conservation biology.