Detecting the causes of population cycles by analysis of R-functions:: the spruce needle-miner, Epinotia tedella, and its parasitoids in Danish spruce plantations

Explaining the causes of regular multi annual oscillations (cycles) in animal populations has been a major problem for ecology, partly due to a lack of methodological rigor. In this paper we show how the analysis of R-functions, the functional relationship between the per capita rate of change of a species and components of its environment, can be used to detect the causes of population cycles. Analysis of the R-functions enables one to separate cycles due to negative feedback between species (endogenous causes) from those forced by one-way effects (exogenous causes). We illustrate the approach by reference to the spruce needle-miner inhabiting Danish spruce plantations, and conclude that population cycles in this insect are probably caused by interactions with two species of parasitic hymenoptera.