GROWTH 553 



The Struggle for Existence 



The mathematical analysis of the question of survival by Volterra, 

 Lotka, Haldane, and others has established certain principles. Gause 

 (1934, 1935) has contributed to both the experimental and the theoreti- 

 cal advancement of the subject. The mathematical analyses are compli- 

 cated, even though in the state of first approximations, and the interested 

 reader should consult the original articles. Cf. Lotka (1925, 1934), 

 Kostitzin (1934), Gause (1934, 1935). Chapman (1931) gives a 

 translation of part of Volterra's work. Protozoan populations have been 

 used to test the hypothesis, and some of the experiments of Gause are 

 here summarized to illustrate the beginning of a quantitative attack on 

 the problems of struggle for existence and survival of the fittest. 



Separate and mixed populations of Paramecium caudatum and Sty- 

 lonychia mytilus were grown on an oatmeal infusion inoculated with 

 B. subtilh. Neither species grew as well in mixed populations, but the 

 influence of Stylonychia on Paramecium is about forty times as great 

 as the effect of the latter on the former. With more food, provided by 

 mixed, wild bacteria, Paramecium grew to about the same level in mixed 

 populations as it did in pure population. Stylonychia grew only to about 

 half the number when competing in the same environment with Para- 

 mecium as it would have alone, and its population soon declined, while 

 that of the Paramecium maintained itself despite the competition. 



Paramecium caudatum and P. aurelia may be grown together, and 

 will compete for the same food. It is necessary to make comparisons 

 in terms of volume of protoplasm, as discussed in the previous section. 

 In mixed populations the growth curves for the two populations are 

 quite similar for the first eight days, after which the P. aurelia popula- 

 tion continues to grow, while that of the P. caudatum declines, reaching 

 the point of extinction in about sixteen days. P. caudatum has an ad- 

 vantage in a greater coefficient of geometrical increase, but requires 1.64 

 times as much food as P. aurelia. Consequently, the greater rate of growth 

 is a liability in competition. P. aurelia is less affected by excretion prod- 

 ucts, as it can live twice as long in the presence of a strong concentration 

 of waste excretion products as P. caudatum. With the amount of food 

 available and the medium used, only the P. aurelia could survive the 

 competition of the mixed population. Glaucoma scintillans, growing in 

 competition with P. aurelia, will survive when the latter perishes. 



