THE GROWTH FORM OF POPULATIONS 



309 



a permissible conclusion for our present 

 purposes. Granting this and knowing that 

 the population is indeed growing in a sig- 

 moid fashion, it follows that any disa- 

 greement between observed and theoret- 

 ical points results from errors of sampling; 

 from technical defects in censusing or 

 in husbandry that arise during the popula- 

 tions' growth; from unknown environmental 

 factors; or from some biological character- 

 istic peculiar to the species in question. 



production is relatively simple; (2) the cen- 

 sus is based on large numbers (the ordinate 

 is founded, not on counts of yeast cells, but 

 rather on the weights of aHquots ("bio- 

 mass") drawn at random from the popula- 

 tion and centrifuged); and (3) the hus- 

 bandry is essentially simple and control- 

 lable. 



The logistics for Drosophila (Fig. 97) 

 and Paramecium (Fig. 94) are also clear 

 graphic descriptions of the growth of these 



NDJFMAMJJASONDj FMAMJJASONDj f 

 1938 1939 1940 '941 



AGE IN MONTHS 

 Fig. 101. The logistic growth of the population of workers (an estimate) within a nest of the 

 ant, Atta sexdens rubropilosa. The ordinate plots the number of crater openings, which are 

 roughly proportional to the number of ants. The circles are observed counts of craters; the 

 curve is the fitted function. ( From Bitancourt. ) 



These possibilities cannot be differentiated 

 with any precision for the five examples 

 presented. The examples, however, can be 

 reviewed in their Ught, and certain infer- 

 ences can be drawn. 



The best fit between curve and observed 

 points is that of yeast (Fig. 98). Here the 

 points fall so closely along the line that all 

 possible sources of variabihty discussed can 

 be excluded except that owing to a negligi- 

 ble amount of random sampling. In short, 

 the logistic curve describes the growth with 

 excellent fidelity. This is probably true for 

 three reasons: (1) The method of yeast re- 



two experimental populations. While there 

 is greater scatter of the observed points 

 than for the yeast, the degree of agreement 

 is still satisfactory. 



Certain of the Triboliiim (Fig. 99) and 

 Moina (Fig. 100) curves are less reUable 

 representations of the observed data. The 

 16 gm. Tribolium and the 24.8° Moina 

 curves are better descriptions than are the 

 64 gm. and the 19.8° C. curves. The 33.6° 

 curve for Moina appears to have too few 

 points to allow an adequate judgment, al- 

 though this is obviously explained by the 



