Mü nster-Swendsen, M. and Berryman, A. 2005. Detecting the causes of population cycles by analysis of R-functions: the spruce needle-miner, Epinotia tedella , and its parasitoids in Danish spruce plantations. Á/ Oikos 108: 495 Á/502.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. ).Mikael Mü nster-Swendsen and I were working on this paper at the time of his untimely death in 2003. The purpose of the paper was to show how my approach to population analysis (Berryman 1990(Berryman , 1999(Berryman , 2001 could be used to detect the causes of population cycles in his data on the spruce needle-miner, Epinotia tedella (Cl.) (Mü nster-Swendsen 1979, 1982, 1985. I should point out here that, at the time we first met, Mikael was not too impressed with my approach, being a proponent of the life table Á/key factor approach (Varley et al. 1975). In time, however, he was to change his mind, and the reason for that is one of the lessons of this paper. I, on the other hand, was very impressed with his data. For 19 years he measured, with considerable precision (Mü nster-Swendsen 1985), the density of spruce needle-miners and their primary insect parasitoids emerging annually from the litter of a Danish spruce plantation. He then constructed detailed life tables, including all suspected mortality factors, for 9 of those years. Finally, he repeated the sampling for various shorter periods of time at 10 additional locations. Others may have longer time series, more detailed life tables, or more spatial replication, but none to my knowledge have more of all three. Mikael recently reviewed his analysis in chapter 2 of a book that I edited (Mü nster-Swendsen 2002), so there is no need for me to repeat it here. Suffice to say that the needle-miner population was found to exhibit spatially synchronous 6 Á/7 year cycles of abundance, and that the key factor affecting the population change was reduced fecundity. He also briefly mentions how my approach led to a different conclusion, that insect parasitoids were mainly responsible for the cyclic dynamics, and that the discovery of pseudoparasitism reconciled this conflict. However, he did not cover details of our analysis, referring instead to the present paper, which was