Entropic Contributions to Mortality and Aging 319 



sharply limiting on the low side than on the high. Blood pH must be held to 

 very close tolerances on both sides of normal. 



III. SOME PROPERTIES OF FLUCTUATIONS 



From a consideration of the components of variation within and between 

 individuals under different environmental conditions, it can be inferred that 

 the observed variation can be attributed to (a) random fluctuations in the 

 common environment that have a uniform influence on all animals maintained 

 therein and (b) independent random fluctuations of each animal that must 

 originate either within the animal or in local fluctuations of the environment 

 that are independent for each animal. The magnitude of the fluctuation arising 

 within the animal due to internal random noise is reasonably well known in 

 a few experimental situations of a psychophysical or neurophysiological nature. 

 Except for certain obvious aspects, such as temperature and humidity, the 

 nature and properties of the environmental random variables is for the most 

 part unknown. More significant perhaps than the purely environmental random 

 variables are these that might be classified as organism-environment inter- 

 actions. Such relations as pathogenicity, parasitism, dominance-submission, 

 predator-prey relationships, etc., are in this class, and make contributions 

 to the variability of individual perfonnance that defy estimation. For the 

 present purpose, the fact that intra-individual fluctuations exist is sufficient : 

 the question of their nature can be deferred. 



IV. FLUCTUATION AND THE PROBABILITY OF MORTALITY 



The set of physiologic processes can be written formally as 



^i = ^i k„ ^,;, ^;, /] (/,;■= 1, ..., n) (1) 



where the X^ denote the set of physiologic variables, the a,_,- denote internal 

 parameters, and the A^ external parameters. 



The state of an individual at a given moment is specified by the values at 

 that moment of the n physiologic variables X^. One can conceive of, and in 

 principle construct, a population made up of indistinguishable individuals, 

 in which the value of each internal parameter for every member lies within 

 an arbitrarily small range. In such a population under constant environmental 

 conditions the time-average of any function of the physiologic variables, X,, 

 for one individual is equal to the average over the population of the same 

 function of the A'j at any moment in time. 



If we locate a frequency distribution of physiologic states in the configuration 

 space, the result is as seen in Fig. 1. The contours enclosing percentages of 

 the distribution (such as 50, 90, 99) are drawn approximately in accord with 

 the supposition that the bivariate distribution of states is Gaussian, and the 

 situation is roughly in scale for a 'healthy' population, i.e. there is only a small 

 probability of observing states near the lethal bound. 



Since contact with the lethal bound removes an individual from the popula- 

 tion, the distribution of states must be modified in the neighborhood of the 

 boundary. Furthermore, the frequency distribution of states is not by itself 



