IDENTIFYING DELAYED DENSITY-DEPENDENCE IN TIME-SERIES DATA

I investigated the ability of statistical tests to detect delayed dens ity dependence in series of abundances per generation. I generated tim e series containing delayed density dependence using two simple popula tion models (a host-parasitoid model and a version of the Ricker equat ion) and analysed these using the tests for delayed density dependence of Turchin (1990), the lag 2 partial autocorrelation coefficient (PAC F) and a novel modification of Pollard et al's (1987) test. All tests of delayed density dependence are of low statistical power, and so any delayed density dependence that is present may frequently be overlook ed, particularly with short (<25 generation) time series. The modifica tion of Pollard et al's test was the best test for detecting delayed d ensity dependence. The modification of Pollard et al's test has simila r statistical power to Turchin's test. However, the latter test falsel y detects delayed density dependence from approximately 9% of density independent random-walk series (of 20 generations), whereas only 5% of cases of false detection would be expected by chance alone. The modif ied version of Pollard et al's test did not identify delayed density d ependence too often and it has similar power to Turchin's test. The pr esence of delayed density dependence frequently caused tests to detect non-delayed density dependence, despite only delayed density dependen ce being present. This was always true of Varley and Gradwell's test. frequently true of Bulmer's test, but not true of Pollard et al's test with series of 15-25 generations. The difference between tests is pre sumably due to variations in statistical power. Studies where large nu mbers of time series are analysed for density dependence may show non- delayed density dependence more frequently than it is present and show the presence of delayed density dependence less frequently than it is present.