NUMBERS : DYNAMICS 65 



the actual density is unknown. Trap-census work 

 on mammals has given good results, e.g. with voles 

 (Middleton, 1930 and 1931), while trapping has also 

 been used for insects, e.g. blowflies that attack sheep. 

 The flies per-boy-per-yard method employed in tsetse 

 fly research is another example of an effective means 

 of estimating relative abundance (cf. Nash, 1933 

 a and 6) . It is of value, not only in comparing changes 

 in numbers from time to time, but densities in 

 different habitats. 



Fluctuations in numbers sometimes show both 

 long and short components. For instance, the 

 irruptions of Pallas's sand-grouse from the Gobi 

 Desert into Europe (which are believed to be caused 

 by periodic over-population) began apparently in 

 1863. They were repeated at intervals of about 

 twenty-two years (major invasions), with smaller 

 ones centring round the intermediate years. There 

 is a suggestion that some factor started the periodic 

 fluctuations after the middle of last century, after 

 which they tended to fall into eleven- or twenty-two- 

 year cycles (Elton, 1924 ; Thomson, 1926)."^ The 

 latest invasion was in 1909, and another is to be 

 expected about the present time — unless the longer 

 cyclical factor has ceased to operate and the invasions 

 have ceased. Similar short-term fluctuations which 

 arose and then died down again have been recorded 

 for the cockchafer (Melolontha) in Denmark (NussUn 

 and Rhumbler, 1922), the grey squirrel in North 

 America (Seton, 1920) and the springbuck in South 

 Africa (CronwTight-Schreiner, 1925). Storrow (1932) 

 has shown how a short-term fluctuation under the 

 influence of a long-term trend of climate may gradually 

 change its periodicity owing to a shifting of the 

 optimum conditions for mult ipHcat ion of the animal 

 affected. We know that climate displays numerous 

 pulsations, some regular or fairly regular, as with the 

 two- to three-year pleionic cycle of tropical tempera- 

 ture studied by Arktowski (1916), or the thirty-five- 



