Comment arising from a paper by Wolda and Dennis: using and interpreting the results of tests for density dependence

We argue that tests for density dependence are useful in analyses of population dynamics and suggest guide lines for their use and interpretation of results which avoid many of the problems discussed by Wolda and Dennis (1993). Processes other than density dependence per se can cause statistical tests to indicate the presence of density dependence (Wolda and Dennis 1993 and unpublished simulations). Tests for density dependence cannot reveal the mechanism of regulation, but they do indicate the nature of long-term population dynamics. Tests for density dependence give misleading results if sampling is not at generation intervals; however, this problem is avoided if we only use tests on data collected in each generation (Holyoak 1993a). Similarly, species should be semelparous. Non-delayed density dependence should not be considered without looking for delayed density dependence, since the presence of delayed density dependence can lead to over-detection of non-delayed density dependence (Woiwod and Hanski 1992; Holyoak 1993b). The partial autocorrelation function and knowledge of life-history are more useful than tests for density dependence for indicating whether any density dependence is delayed or not (Royama 1992; Holyoak 1993b). Estimation error with a constant upper size limit causes tests for density dependence to overestimate the frequency of delayed density dependence; however we do not know whether estimation error is bounded in real populations. Work in progress suggests that 20-40 generations (depending on the nature of population dynamics) gives a moderate level of accuracy with tests for density dependence, and >40 generations are necessary for tests to be accurate in their assessment of the strength of density dependence. We conclude that tests are useful indicators of whether density dependence, or other feedback mechanisms are likely to be acting.