326 



POPULATIONS 



Our final illustration of fluctuations in 

 natural populations of mammals concerns 

 the "coloured fox" in Labrador. This is also 

 discussed by Elton (1942) and is based on 

 fur trade statistics from Moravian Missions 

 and, later, the Hudson's Bay Company. 

 This, a striking case of cyclic regularity, is 

 clearly summarized in Figure 120 and 

 covers fur returns from 1834 to 1932. The 

 curve, as Elton phrases it, "hits the eye at 

 once." For the ninety-two years (1834 to 

 1925) during which the fox trade was 

 under the control of the Missions, the mean 

 length of the cycle was precisely four years 

 and the intervals in years starting in 1835 

 were 4, 3, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 3, 3, 

 4, 5, 6, 4, 4, 5, 3, 4, 4. Elton assembles 

 these figures in a frequency distribution as 

 follows: 



Length of cycle 2 3 4 5 6 7 



Frequency 1 5 13 3 1 



Percentage frequency 4 22 57 13 4 



This shows that the modal frequency is 4 

 and that the distribution is slightly skewed 

 to the left. 



Elton quite properly stresses that these 

 findings are based, not on a total census of 

 the population, but on pelt records, and is 

 properly critical for that reason. Even so he 

 believes, one would judge, that this reflects 

 in truth something real in terms of actual 

 fox-fluctuations. In fact he says, "The man- 

 ner in which the cycle colours even small 

 trapping results and comes at places hun- 

 dreds of miles apart gives it a bold and al- 

 most cosmic quality. There must be some 

 very powerful forces behind it" (p. 272). 



Data on fluctuations in bird populations 

 are not so extensive as those for mammals 

 and fishes. Some observations along this line 

 appear in the book by Stoddard (1932) and 

 in the monograph on the song sparrow by 

 Nice (1937). A helpful treatment is the 

 analysis by Kendeigh (1944) of census 

 methods applied to bird groups, and it ij 

 from this source that we choose one case for 

 review. 



Kendeigh has this observation to record 

 about the possible cyclic character of the 

 bobwhite population: 



"There is still a difference of opinion among 

 students of the bob-white as to whether the 

 species is cyclic in numbers, irmptive, or 

 relatively constant. Perhaps there will be differ- 

 ences between regions (compare with Erring- 



ton, 1941), but for Ohio this curve strongly 

 suggests variations of a rhythmical or cyclical 

 nature with former peaks in 1911 or 1912, 

 1923 or 1924, and about 1935, with low points 

 about 1909 (?), 1915, 1928 or 1929, and 1940. 

 Eliminating the doubtful low year of 1909, 

 these points in the curve come at intervals of 

 12 or 13 years" (p. 82). 



Oscillations 



We have already suggested that popula- 

 tion oscillations are hard to illustrate by 

 actual example because most departures 

 from equilibrium are asymmetrical rather 

 than symmetrical. We shall, however, pre- 

 sent several selected cases that serve the 

 purpose fairly well. 



Cause has interested himself in the pos- 

 sible oscillation in numbers in interspecies 

 populations in which one species is the prey 

 component and the other the predator com- 

 ponent. We return to this problem in more 

 detail in Chapter 22 when discussing Pre- 

 dation. Our concern with it here is that it 

 afiFords perhaps the best illustration of dem- 

 onstrated oscillation. Lotka (1934) and 

 Volterra (1926) concluded on the basis of 

 purely theoretical considerations that a bio- 

 logical system comprised of two species, 

 each dependent upon the other, will exhibit 

 regular, periodic fluctuation in the relative 

 and absolute abundance of each species. 

 This is true even when random fluctuations 

 caused by external environmental factors 

 have been eliminated. Cause investigated 

 this conclusion in the laboratory, using sev- 

 eral species of microorganisms and mites as 

 experimental material. His findings appear 

 in a number of papers, including two 

 monographs (1934a, 1935). To make the 

 point, we reproduce one graph (Fig. 121). 



This particular experiment, the details of 

 which can be omitted, was conducted with 

 mixed populations of the yeast, Sacchar- 

 omtfces exiQinis, and the ciliate, Paramecium 

 aurelia. The figure shows that essentially 

 smooth oscillations of the Lotka- Volterra 

 lype actuallv occur under these controlled 

 experimental conditions. The three cycles 

 shown for each species are regular, depart 

 but slightlv from the observed census 

 points, and are of approximately the same 

 magnitude. 



Studies somewhat similar to those of 

 Cause have been reported by DeBach and 

 Smith (1941) and deal with interactions 

 between populations of an insect host (the 



