Weak population regulation in ecological time series.

How strongly natural populations are regulated has a long history of debate in ecology. Here, we discuss concepts of population regulation appropriate for stochastic population dynamics. We then analyse two large collections of data sets with autoregressive-moving average (ARMA) models, using model selection techniques to find best-fitting models. We estimated two metrics of population regulation: the characteristic return rate of populations to stationarity and the variability of the stationary distribution (the long-term distribution of population abundance). Empirically, longer time series were more likely to show weakly regulated population dynamics. For data sets of length > or = 20, more than 35% had characteristic return times > 6 years, and more than 29% had stationary distributions whose coefficients of variation were more than two times greater than would be the case if they were maximally regulated. These results suggest that many natural populations are weakly regulated.