a cycle is a recurring variation of regular timing or 

 phasing and of constant amplitude. Fluctuations are 

 considered periodic if the phase is constant but the 

 amplitude varies. What ecologists call cycles are 

 really oscillations because both phase and amplitude 

 are inconstant. Justification for calling the fluctua- 

 tions cyclic, rather than random, lies in the demon- 

 stration that the variability that is evident, especially 

 in phase, is less than is to be expected by chance and 

 that reasonably accurate predictions can be made of 

 the course of future variations in population size 

 (Davis 1957, MacLulich 1937). However, there has 

 been considerable controversy concerning the true 

 significance of cycles (Cole 1954, Hickey 1954). 



The short-term cycle is commonly 3, 4, or 5 years 

 long, although it may be as short as 2 years, or as 

 long as 6 years (Elton 1942). The snowshoe rabbit 

 cycle varies between 8 and 1 1 years ; the lynx cycle, 

 between 8 and 12 years (MacLulich 1937). The 

 coefficient of variation, standard deviation divided by 

 the mean, for different species having the short cycle 

 varies from 30 to 50 per cent, and is of the same 

 order of magnitude for the longer cycle (Cole 1951). 

 It is of interest that by drawing numbered cards 

 from a well shuffled deck or rolling dice (Palmgren 

 1949, Hutchinson and Deevey 1949) or plotting ran- 

 dom numbers (Cole 1951) short and long cycles may 

 be obtained of about the same relative lengths and vari- 

 ation coefficients as animal population cycles. 



In comparing the frequency of peaks in popula- 

 tions and in random numbers it has been a common 

 practice to designate any number as a peak which is 

 higher than both the preceding and following num- 

 bers, regardless of the amount of difiference between 

 them. This, however, is not justified with natural 

 populations of animals, since minor variations may 

 be due to sampling errors or to secondary factors 

 modifying a major trend. According to criteria used 

 in this text, a peak would not be considered real un- 

 less the size of the population at that time is at least 

 two or three times its size during the preceding and 

 following depression. When only such conspicuous 

 peaks are considered, oscillations in random numbers 

 are lengthened and some of their correspondence to 

 natural cycles is lost (Cole 1954). Extreme fluctua- 

 tions between peaks and lows in population cycles 

 are ordinarily of much greater amplitude than occur 

 in mathematical models (Pitelka 1957). Of course, 

 the criteria by which a particular peak is to be evalu- 

 ated depend on the accuracy to which the population 

 size was measured. These peaks should be deter- 

 mined in as objective a manner as possible. Before 

 oscillations in the size of natural populations are 

 considered cyclic, they should first be tested statis- 

 tically for randomness. Only after that is done is it 

 profitable to look for periodic or automatic mech- 

 anisms that may be involved. 



The reality of cycles may be further tested by 

 the amount of synchrony that they exhibit. If it is 

 shown that peaks and troughs in the oscillations of 

 different species in a local area are not correlated in 

 time, and oscillations of populations in different re- 

 gions occur independently of each other, one should 

 take warning that a variety of factors may be involved 

 that fluctuate in their action at different times, in 

 different places, and on different species, in essen- 

 tially a random manner. If such synchrony is deter- 

 mined, then some master factor or set of factors must 

 be affecting all populations alike, although it is still 

 necessary to determine whether the action of the 

 master factor on the population is cyclic in its timing 

 and effect, or whether it is being exerted in an 

 irregular manner. We need to examine the extent 

 to which population oscillations are synchronized. 



Synchrony 



With the 9-10 year cycle, local areas may show 

 peak populations that are out of phase with other 

 local areas by one, two, or three years. But when 

 large regions are considered, the peak is manifested 

 over three or four years in the course of which most 

 local areas reach maximum populations while the 

 following trough in the regional cycle may spread 

 over five or six years when very few, if any, local 

 areas have large populations (Butler 1953). A sim- 

 ilar relation probably holds between local and regional 

 fluctuations with the 3-4 year cycle. Synchrony is 

 sometimes evident in local populations that are iso- 

 lated by a hundred or more miles from other popula- 

 tions of the species (Brooks 1955). 



Some variation in cyclic tempo occurs in different 

 parts of the world, although generally they are close 

 to being in phase. Local areas out of phase with the 

 main cycle commonly come back into phase by the 

 time the next peak is reached. The main cycle of 

 grouse and ptarmigan over most of Canada and in 

 northern United States has shown peaks in 1896, 

 1905, 1914, 1923, 1932-33, 1941-42, and 1950-51. 

 In the maritime provinces of Canada — Newfound- 

 land, New Brunswick, Nova Scotia, and Prince Ed- 

 ward Island — the cycle is advanced 3 years ahead of 

 the main cycle ; in Alaska, the cycle lags by 3 years. 

 In Britain, the grouse and ptarmigan cycle has a 

 mean length of 5-6 years, but in Finland and Scan- 

 dinavia it is only 3^ years, although some of the 

 same species are involved. In North America the 

 grouse cycle is nearly synchronous with the cycle of 

 the snowshoe rabbit, while in Scandinavia it coin- 

 cides with the cycle of lemmings (G.R. Williams 

 1954). 



The lemming cycle in Canada is similar to that 

 in Norway (Elton 1927). Recent peaks in the 3-A 

 year cycle for small rodents in Finland, Norway, and 



238 Ecological processes and dynamics 



