Identifying the density-dependent structure underlying ecological time series

A central problem in ecology is explaining the causes of population fluctuations, and an important step in the solution is determining the structure of the negative feedback (density dependent) process regulating population dynamics. The conventional way to determine the dimension or order of density dependence in a time series is to calculate the partial autorcorrelation function (PACF). We maintain, however, that PACF is not designed with biological populations in mind and has the wrong null model for detecting the structure of density dependence. We suggest an alternative diagnostic, the partial rate correlation function (PRCF), which is specifically designed for biological populations and has an appropriate null model for detecting their density dependent structures. Tests with simulated data show PRCF to be superior to PACF in detecting the underlying density dependent structure of two simple mathematical models.