Abstract
There have been many attemps to explain the apparent regularity of fluctuations in size of natural populations. It is commonly considered that 2 basic periodicities exist, a 3-4 year cycle and one at roughly 10 years, and some workers have postulated a common causation of the two cycle lengths. In 1949 Palmgren suggested that the "cycles" might be merely rarfcom fluctuations. If this suggestion is tenable the various hypotheses invoking more complicated explanations should be tentatively rejected as unnecessary. Tippett''s random sampling numbers are found to exhibit "cycles" with a mean interval of 3 between peaks and with a tendency for higher peaks to occur at intervals of 3 "cycles." When graphed they resemble graphs of population data. The coeff. of variation of "cycle" lengths in random numbers is 37.3+ %, which is identical with the values obtained from some tree-ring data and comparable to the values for some animal populations. Various hypotheses postulating entirely random fluctuations in the environment may lead one to predict population oscillations apparently indistinguishable from observed cycles on the basis of established facts. Two of the simplest possible cases are derived theoretically, (1) where population size is a random variable, and (2) where the favorability of the environment for population growth is assumed to fluctuate randomly about its avg. value from year to year. The theoretical distrs. of cycle lengths are worked out and compared with empirical data. The 2d hypothesis predicts a basic "cycle" of 4-years and a coeff. of variation of 50%. It is concluded that complicated explanations of population cycles are premature. Many independent environmental variables affect population size and in the aggregate they may lead to essentially random fluctuations. Random oscillations are more "regular" than has generally been appreciated.