Some Features of Random Population Cycles

Under the intriguing title Why do we sometimes get nonsense-correlations between time-series? Yule (1926) brought to general attention some of the properties which impress us as sheer perversity when we attempt to analyze time-series by ordinary statistical methods. Biologists are among those who frequently find themselves concerned with data on fluctuations in time and it seems unfortunate that even modern statistical methods leave much to be desired for the analysis of such data (see, for example, the last 2 chapters of Kendall (1946) ). Although at least 70 years ago Swinton (1883) postulated a connection between locust outbreaks and sunspot numbers, the appearance of Yule's paper approximately coincided with a great upsurge of interest among zoologists in the possibility that animal populations might undergo periodic fluctuations in size. Literally hundreds of papers have been written on the subject analyzing the phenomenon, proposing explanations, or expostulating its importance. Under this virtual barrage of literature it was natural for biologists generally to discount the many conflicts of opinion among students of the subject and to accept the basic hypothesis that there must be some factor or factors either in the physical environment or within populations or ecosystems possessing a tendency to induce rhythmic population fluctuations. It seemed, therefore, an almost outrageous suggestion when Palmgren (1949) proposed to regard population cycles as random fluctuations. This hypothesis, however, had the merit of being susceptible to testing. The consequences of random fluctuation could be deduced and compared with population data in a much more direct way than was possible for any hypothetical remote connection between, for example, an empirical series of sunspot numbers and the population data. The hypothesis of random population fluctuations has the further advantage of being probably the simplest possible explanation for population cycles and in any logical study of the subject it seems that this possibility should be eliminated first before consideration is