310 



POPULATIONS 



fact that the population grew so fast at this 

 temperature that the investigators did not 

 consider it advisable to take more censuses. 



Natural Populations 



The illustrations that can be mustered to 

 illustrate the logistic curve appUed to nat- 

 ural populations are few indeed. This is 

 most probably due to the lack of adequate 

 data rather than to any fundamental defi- 

 ciency in the curve itself. Four cases are 

 here presented as examples. These are taken 

 from Bitancourt (1941) for populations of 

 the Brazilian ant, Atta sexdens rubropilosa; 

 Bodenheimer (1937) for bees; Davidson 

 (1944) for thrips; and Davidson (1938, 



latter apparently furnishes an excellent in- 

 dex of increase in size. Figure 101 brings 

 out this point clearly. The total colony, or 

 as Bitancourt calls it, the "super-organismo' 

 (see pp. 426-435), increases slowly for 

 about a year, rapidly during the second 

 year, after which growth slows down 

 as the asymptote is approached. The 

 author points out that, when the total col- 

 ony attains its maximimi size of 1000 

 craters, "sexual maturity," as revealed by 

 the nuptial flight, ensues. This occurs dur- 

 ing the twenty-seventh month at a time 

 when the population is approximately 

 50,000 times larger than it was when the 

 first crater opened. 



Fig. 102. The logistic growth of two bee colonies in the same apiary. (From Bodenheimer.) 



1938a) for the growth of populations of 

 sheep in South AustraHa and Tasmania. The 

 logistics, with the exception of that for 

 thrips, are reproduced as Figures 101, 102, 

 103, and 104, respectively. 



Bitancourt's analysis is excellent for three 

 reasons: (1) It deals with a social popula- 

 tion for which sound population data are 

 hard come by; (2) it utilizes a novel or- 

 dinate to express growth; and (3) the fit 

 between points and function is first rate. 

 Using the data of Autuori (1941), Bitan- 

 court plots the age of three colonies of Atta 

 over a twenty-eight months' period against 

 the average monthly total of openings of 

 craters as they appear over the nest. The 



Another application of the logistic curve 

 to social insect populations (Bodenheimer, 

 1937) concerns the growth of ItaUan and 

 Cyprian bee colonies raised in the same 

 apiary. The curves are reproduced as Figure 

 102, in which it can be seen that the logis- 

 tic describes the period of positive growth 

 with considerable fidehty. Those points that 

 cluster near the asymptote depart some- 

 what from the fitted function, but the de- 

 viation does not appear to be excessive. In 

 the same study Bodenheimer also presents 

 logistic curves for populations of the ter- 

 mite, Neotermes ( = Kalotermes) tectonae, 

 the ant, Lasius alienus, and the wasps, 

 Vespa maculata, V. diaholica, and V. vul- 



