Density dependence, population persistence, and largely futile arguments.

Wolda and Dennis (1993) suggest that no valid conclusions about population regulation can be drawn on the basis of statistical tests of density dependence in time series data of population abundance. They give some examples in which a 'population' persists even if it is not regulated by a density-dependent process: a sequence of independent, identically distributed random variables, the numbers of the migrant moth Autographa gamma in Britain, annual rainfall data. We suggest that such time series data may show persistence because of a static constraint, which compels the numbers to remain within finite, positive limits, or to fit some prescribed distribution. But this mechanism can explain persistence in a biological population only when the 'population' represents a sample from a regulated population (the case of A. gamma). We also comment on some suggestions made by Wolda and Dennis (1993) concerning the general value of statistical tests of density dependence, frequency of delayed versus non-delayed density dependence in natural populations, relative performance of different kinds of insect traps in sampling local populations, and the wider issue of how ecologists are likely to make progress in the study of population dynamics.