Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches

Population cycles have long fascinated ecologists. Even in the most-studied populations, however, scientists continue to dispute the relative importan ce of various potential causes of the cycles, Over the past three decades, theoretical ecologists have cataloged a large number of mechanisms that are capable of generating cycles in population models. At the same time, stati sticians have developed new techniques both for characterizing time series and for fitting population models to time-series data. Both disciplines are now sufficiently advanced that great gains in understanding can be made by synthesizing these complementary, and heretofore mostly independent, quant itative approaches. In this paper we demonstrate how to apply this synthesi s to the problem of population cycles, using both long-term population time series and the often-rich observational and experimental data on the ecolo gy of the species in question. We quantify hypotheses by writing mathematic al models that embody the interactions and forces that might cause cycles. Some hypotheses can be rejected out of hand, as being unable to generate ev en qualitatively appropriate dynamics, We finish quantifying the remaining hypotheses by estimating parameters, both from independent experiments and from fitting the models to the time-series data using modern statistical te chniques, Finally, we compare simulated time series generated by the models to the observed time series, using a variety of statistical descriptors, w hich we refer to collectively as "probes." The model most similar to the da ta, as measured by these probes, is considered to be the most likely candid ate to represent the mechanism underlying the population cycles. We illustr ate this approach by analyzing one of Nicholson's blowfly populations, in w hich we know the "true" governing mechanism. Our analysis, which uses only a subset of the information available about the population, uncovers the co rrect answer, suggesting that this synthetic approach might be successfully applied to field populations as well.