There Is Nothing New under the Sunspots

Abstract

Life on earth is totally dependent on solar energy. Consequently, it is a straightforward assumption that any regularity in solar activity should be observed in at least some biotic production processes as well. Indeed, the number of sunspots, reflecting solar activity, is known to fluctuate with regular intervals, period length averaging 10-11 yr (Waldmeier 1961). Although it is controversial whether this regular fluctuation in solar activity causes any weather variable to fluctuate in phase with sunspot numbers (Molnar 1981) it is tempting to think so. Presumably this was the reasoning behind Charles Elton's classic paper (1924) in which he states that periodic fluctuations in the numbers of certain animals must be due to climatic factors. Elton (1924) suggested that the causal link between the fluctuation in sunspot numbers and animal populations are recurring favorable climatic conditions for vegetation due to solar activity. It is interesting that although Elton, as well as several others, has abandoned the above reasoning later on (MacLulich 1937, Elton and Nicholson 1942, Moran 1949, 1953a, b, Royama 1992), the idea of sunspot regulated population dynamics has survived over decades, as recently evidenced by Sinclair et al. (1993). They suggest that there is a solar cycle-climate-hare population link. As snowshoe hare, Lepus americanus, is the main prey of lynx, Lynx canadensis (e.g., Parker et al. 1983, Koehler 1990), it is a reasonable assumption that changes in the hare population numbers should affect the lynx fluctuation as well. Here, our aim is to explore the MacKenzie River series of lynx fur returns 1821-1934 (Elton and Nicholson 1942) and Wolfer sunspot series for the corresponding period (Waldmeier 1961) with the aid of time series analysis. We shall use an autoregressive (AR; Box and Jenkins 1970) time series model as an adequate enough characterization of the process: