134 



THE STRUGGLE FOR EXISTENCE 



that "an epidemic" of predators cannot break out if the concentra- 

 tion of the prey has not attained the threshold value a h . Below it 

 predators disappear 5 and leave a pure population of prey, but above 

 it we find usual relaxations. 



Taking into account all these features we can write for Paramecium 

 and Didinium a complicated equation of relaxation representing an 

 adequate expression of what actually exists. We admit that the mor- 

 tality of predators appears not only with Ni = 0, but that a slight 

 mortality generally exists increasing with a diminution of the concen- 



Theoreticz/ curves calcu- 

 lated from the equation fiib) 



^(Didi nilim) pro 0,S~cc -S* 



Fig. 36. The solution of the equation 21b (to the left) and empirical obser- 

 vations on Paramecium and Didinium (to the right). No "residual growth" of 

 the population of predators (in the absence of the prey) is taken into account 

 in the theoretical equation. From Gause and Witt, '35. 



tration of N 2 , and that the intensity of hunting also increases with an 

 insufficiency of prey. 



6 In these experiments were used predators possessing no 'residual growth,' 

 e.g. already diminished in size. See experiments with immigrations where 

 predators usually did not find any prey in the microcosms containing very few 

 Paramecia, and consequently perished. 



