Ill] A POPULATION OF FLIES 155 



we draw the corresponding Gaussian curve; and the close "fit" 

 between the observed population-curve and the calculated Gaussian 

 curve is sufficiently shewn by Mr Per Ottestad's figure (Fig. 31). 

 This is a very remarkable thing. We began to think of the curve 

 of error as a function with which time had nothing to do, but here 

 we have the same curve (or to all intents and purposes the same) 

 with time for one of its coordinates. We might (I think) add one 

 more to the names of the curve of error, and call it the curve 

 of optimum ; it represents on either hand the natural passage from 

 best to worst, from Ukehest to least likely. 



A few flies (Drosophila) in a bottle illustrate the rise and fall of 

 a population more complex than yeast, as Raymond Pearl has 

 shewn* The colony dwindles to extinction if food be v/ithheld; 

 if it be sufficient, the numbers rise in a smooth S-shaped curve; 

 if it be plentiful and of the best, they end by fluctuating about an 

 unstable maximum. "The population waves up and down about 

 an average size," as Raymond Pearl says, as Herbert Spencer had 

 foreseen t, and as Vito Volterra's differential equations explain. 

 The growth-rate slackens long before the hunger hne is reached; 

 crowding affects the birth-rate as well as the death-rate, and a 

 bottleful of flies produces fewer and fewer offspring per pair the 

 more flies we put into the bottle {. It is true also of mankind, as 

 Dr WiUiam Farr was the first to shew, that overcrowding diminishes 

 the birth-rate and shortens the "expectation of Hfe§ ." It happened 

 so in the United States, pari passu with the growth of immigration, 

 incipient congestion acting (or so it seemed) as an obstacle, or a 

 deterrent, to the large families of former days. Nevertheless, children 

 still pullulate in the slums. The struggle for existence is no simple 

 affair, and things happen which no mathematics can foretell. 



* Raymond Pearl and S. L. Parker, in Proc. Nat. Acad. Sci. vni, pp. 212-219, 

 1922; Pearl, Journ. Exper. Zool. Lxm, pp. 57-84, 1932. 



t "Wherever antagonistic forces are in^ action, there tends to be alternate 

 predominance." 



X In certain insects an optimum density has been observed; a certain amount 

 of crowding accelerates, and a greater amount retards, the rate of reproduction. 

 Cf. D. Stewart Maclagan, Effect of population-density on rate of reproduction, 

 Proc. R, S. (B), CXI, p. 437, 1932; W. Goetsch, Ueber wachstumhemmende Factoren, 

 Zool. Jakrb. (Allg. Zool.), xlv, pp. 799-840, 1928. 



§ Dr W. Farr, Fifth Report of the Registrar-General, 1843, p. 406 (2nd ed.). 



