lotka: discontinuous evolution 71 



Probability of elimination 



of individual 



depends on 



Passive resistance Probability of meeting any 



stated strain 



Relative frequency of the Arrangement of 



several fluctuations of individuals in 



the system space 



May be independent of the May be correlated 3 with 



fluctuations in condition fluctuations in condi- 



of system tion of system 



Let us now briefly consider how this correlation between the 

 conditions of the system from point to point and the disposition 

 of the individuals in space is established. It will be useful to 

 illustrate by means of a simile the phenomena here involved. 



The individual in its struggle for existence may be likened to 

 a fencer A, whose opponent B represents the external world. 

 We will think of B as being immortal, a condition which might 

 be realized for example by immediately replacing him by a 

 substitute as soon as he received a serious injury. Then, how- 

 ever excellent A's fencing might be, short of absolute perfection, 

 sooner or later he must succumb to the attack of his assailant. 

 Now we may roughly represent the course of the combat as 

 follows : B makes the attack. Let x' y' z' be the coordinates of 

 the point of his sword. For the sake of simplicity we will suppose 

 that these coordinates define B's position at every moment 

 sufficiently for our purposes. A's task is to parry each of B's 

 thrusts. In other words, if x y z are the coordinates of A's 

 swordpoint, A's problem is to make x y z such functions of 

 x' y' z', that the latter coordinates at no instant fall within the 

 geometrical boundaries of his vital organs. 



3 Such correlation is probably possible only in a system having a fund of 

 free energy. The phenomenon is closely related to "relay action," in which 

 "action and reaction" are not equal. 



