Sampling-Variance Effects on Detecting Density Dependence from Temporal Trends in Natural Populations

Monte Carlo simulations were conducted to evaluate robustness of four tests to detect density dependence, from series of population abundances, to the addition of sampling variance. Population abundances were generated from random walk, stochastic exponential growth, and density-dependent population models. Population abundance estimates were generated with sampling variances distributed as lognormal and constant coefficients of variation (cv) from 0.00 to 1.00. In general, when data were generated under a random walk, Type I error rates increased rapidly for Bulmer's R, Pollard et al.'s, and Dennis and Taper's tests with increasing magnitude of sampling variance for n > 5 yr and all values of process variation. Bulmer's R* test maintained a constant 5% Type I error rate for n > 5 yr and all magnitudes of sampling variance in the population abundance estimates. When abundances were generated from two stochastic exponential growth models (R = 0.05 and R = 0.10), Type I errors again increased with increasing sampling variance; magnitude of Type I error rates were higher for the slower growing population. Therefore, sampling error inflated Type I error rates, invalidating the tests, for all except Bulmer's R* test. Comparable simulations for abundance estimates generated from a density-dependent growth rate model were conducted to estimate power of the tests. Type II error rates were influenced by the relationship of initial population size to carrying capacity (K), length of time series, as well as sampling error. Given the inflated Type I error rates for all but Bulmer's R*, power was overestimated for the remaining tests, resulting in density dependence being detected more often than it existed. Population abundances of natural populations are almost exclusively estimated rather than censused, assuring sampling error. Therefore, because these tests have been shown to be either invalid when only sampling variance occurs in the population abundances (Bulmer's R, Pollard et al.'s, and Dennis and Taper's tests) or lack power (Bulmer's R* test), little justification exists for use of such tests to support or refute the hypothesis of density dependence.