region of Woods Hole, Massaduisetts (Allee l^'U*). 

 In seeking correlations l)et\veen catastrophes and 

 w eatlier or other environmental conditions, one needs 

 to determine tlie period in its life cycle during which 

 the species is most vulnerable, and the weather con- 

 ditions coincident with that period that exert great- 

 est effect. 



CYCLES 



Populations are cyclic or oscillatory when 

 they vary in a more or less uniform maniuT between 

 high and low levels of density. 



Typos 



Although cycles of different duration have been 

 postulated for many species at different times, the 

 best established cycles are those of periodicities of 

 3-4 vears and 9-10 vears (Speirs 1939, Elton 1942, 

 Dvmond 1947, G.R. Williams 1954, Siivonen 1957). 

 The best known 3-4- year cycles are demonstrated 

 in the following species : 



Birds Maiiniials 



Snowy owl European lemming 



Willow ptarmigan Siberian lemming 



(northern Europe) Brown lemming 



Capercaillie Collared lemming 



Blackgame European meadow vole 



Hazel grouse Arctic fo.\ 



Other species that may also vary in a 3-4 year 

 cycle are rough-legged hawk, northern shrike. North 

 American meadow vole, short-tailed meadow vole 

 (England, Scotland), red fox (far North), marten 

 (far North), and sockeye salmon (Pacific coast of 

 North America). Species well recognized as showing 

 the 9-10 year cycle are : 



Birds Mammals 



Ruffed grouse Snowshoe rabbit 



Sharp-tailed grouse Muskrat 



Willow ptarmigan Canada lyn.x 

 (North America) 



In addition, a number of other species may have 

 a 9-10 year cycle : rock ptarmigan, goshawk, great 

 horned owl, red fox (South), marten (South), 

 fisher, mink, and Atlantic salmon. 



Fluctuations in populations, commonly of 5-6 

 years (Mackenzie 1952), occur in the British Isles in 

 red grouse, rock ptarmigan, black game, and caper- 

 caillie, but there is question as to whether they are 

 regular and definite enough to be truly cyclical. 



.\mong invertebrates, insect pests of coniferous for- 

 ests in Ciermany fluctuate in periods variously from 

 6 through 18 years (iMdmann 1931); grasshoi)pers 

 in Manitoba, 7 through 16 years (Criddle 1932) ; 

 chinch hugs in Illinois, from aljout 3 through 16 years 

 (Shelford and Flint 1943). Subjective estimates of 

 damage by the starfish Astcrias jorbcsi on mollusk 

 fisheries between New York and Cape Cod suggest 

 a periodicity of 14 years for this marine species 

 (Burkenroad 1946). 



It is possible to demonstrate mathematically that 

 an a])parent cycle or a series of irregular fluctuations 

 may actually be compounded of several distinct pe- 

 riodicities, each of different duration (Wing 1953). 

 Cycles can thus be postulated in the population fluc- 

 tuations of many species, in the migration of birds, 

 and in human economics (Wing 1935, Huntington 

 1945; see also J. Cycle Res. 1952 on, and other 

 publications of the Foundation for the Study of 

 Cycles), but the biological significance of these hid- 

 den periodicities remains to be demonstrated. 



According to an extensive analysis made by 

 .Siivonen (1948) of data extending back through one 

 hundred years, the short-term cycle averages 3^ 

 years, with two 3-year and one 4-year cycle coming 

 each decade. He believes that the 9-10 year cycle 

 (average 10 years) results from each third short 

 cycle having a greater amplitude than the other two, 

 and that the long-term cycle is therefore only a modi- 

 fication of the more basic short-term cycle. Although 

 there is doubt about the fundamental nature of this 

 relation, it is true that the 3-4 year cycle is better 

 expressed in the far North and the 9-10 year cycle 

 in more southerly latitudes. The 3-4 year cycle may 

 change to a 9-10 year cycle, correlated with latitude, 

 even in the same species (red fox, marten). South 

 of latitudes 45°-50°N in North America and about 

 60° N in Europe, variations in population size appear 

 progressively less extreme and cyclic, more irregular 

 or random in character. Thus the numbers of four 

 species of gallinaceous birds during peak years di- 

 vided by their counterpart numbers during low years 

 changes from 3.8 in I,apland, to 2.4 in northern Fin- 

 land, to 2.0 in central Finland, to 1.7 in southern 

 Finland (Siivonen 1954). Cycles may be distinct 

 and definite in the far North because only a few 

 species are involved and the environment is rela- 

 tively monotonous and severe ; in more southerly lati- 

 tudes, population fluctuation becomes more irregular 

 and uncertain because of the interaction of many 

 species and a more moderate environment. 



To designate fluctuations as cyclic implies con- 

 siderable regularity for them. In mathematical usage, 



Irruptions, catastrophes, and cycles 237 



