A Statistical Analysis of the 10-Year Cycle in Canada

Despite the great interest of the 10-year wildlife cycle and the abundance of data, little effort has been made to analyse it by statistical methods; this is particularly surprising in view of the doubts about the reality of cycles expressed by Cole (1951, 1954). The best statistical treatment is that of Moran (1953), who considered the trapping records of the lynx* in the Mackenzie River district of north-west Canada over the period 1821-1934; the data were obtained from records of the Hudson's Bay Company by Elton & Nicholson (1942). Fig. 1 shows the logarithm of the number trapped in each year. The reasons for using a logarithmic transformation are discussed by Moran (1949, 1953) and Williamson (1972). It will be seen from Fig. 1 that there is an oscillation of considerable regularity with a period of about 10 years, but that the amplitude of the oscillations is rather irregular. The effect of the logarithmic transformation is to make the oscillations more symmetrical than in the arithmetic plot which is usually presented. Similar features are seen in data for other periods and other species. In view of the regularity of the oscillations, the most obvious model to fit to the data is a sine function with a superimposed error term:

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