lotka: discontinuous evolution 69 



ticular form of energy and mode of redistribution of the same. 

 Each system has a definite set of such limiting strains, which 

 represent characteristic properties, and which we may speak of 

 collectively as the " passive resistance" of the system to im- 

 pressed modifications. 



If we turn our thoughts back now to the consideration of the 

 individual organism whose history we were following up, we 

 observe that in general, among the fluctuating influences to 

 which it is subjected, there will sooner or later arise conditions 

 in which a "limiting strain" is exceeded — the individual suffers 

 a discontinuous change, which may be of such character as to 

 kill it, i. e., eliminate it from the aggregate. 



Under the conditions of the problem as it presents itself to 

 us in nature we can not in general foretell when a particular 

 individual will meet with the fatal variation. We may know, 

 however, in a statistical way, what fraction p(a) out of some 

 large number of individuals, picked out at random and counted 

 at the moment of their birth, will reach age a, or, what amounts 

 to the same thing, what proportion /x(a) of individuals at age a 

 are eliminated per unit of time. Our problem is to analyse 

 /*(a) in its relation to the properties of the organism. 



An analysis of the factors which determine ,u(a) leads us first 

 of all to a division of these into two classes. For the probability 

 that a given individual shall be eliminated from its continuum, 

 in a small interval of time dt say, depends on two kinds of con- 

 ditions: Firstly on the "passive resistance" of the individual, 

 as defined above, and as measured by the set of values of the 

 several P c ; secondly on the probability that the individual shall 

 be exposed to any stated strain during the interval dt. This 

 latter probability itself in turn depends on two factors; firstly 

 on the relative frequency of the several fluctuations in the con- 

 ditions of the system; and secondly on the probability that a 

 given fluctuation occur in such relation to time and space that 

 the individual under consideration is affected thereby. Finally, 

 this last probability depends on the distribution and disposition 

 (arrangement) of the individuals in space. And in this respect 

 there are two cases to be distinguished. On the one hand the 



