328 George A. Sacher 



expectations (14) considerably greater than mammals (15) of equal body size 

 and metabolic rate. Some primates (16) outlive carnivores or herbivores of 

 equivalent body size by a considerable margin. This is obvious in the case of 

 man compared with lower animals. In a study on grasshoppers, in which 

 growth rate and Hfe expectation were investigated as functions of temperature 

 (17), the Arrhenius coefficient for growth rate was /^ = 18,400 cal and that for 

 mean death rate was jj, = 6300 cal. Though both are temperature-dependent, 

 the difference in /j, values suggests that survival is not directly dependent on 

 metabolic rate. 



An association between the level of metabolic activity and the rate of 

 accumulation of irreversible molecular change is certainly to be expected on 

 physico-chemical grounds. The presence of poisons in the environment, and 

 the ever-present possibility of incorrect reactions, imply the existence of a 

 non-zero error rate per molecular event. 



Finally we consider the influence of macroscopic fluctuations in physiologic 

 state on the rate of accumulation of irreversible molecular changes. The 

 calculation of the error rate due to fluctuation for a particular biochemical 

 reaction would require a more detailed specification of the fluctuation process 

 than is envisaged in the previous development, which dealt with a comparatively 

 small number of important physiologic functions. This fluctuation in state of 

 the organism as a whole would certainly play a part, but it would be necessary 

 to consider in addition the independent fluctuations of small regions. These 

 would usually have little immediate influence on the state of the whole organism, 

 but they would be significant for the probabilities of irreversible change within 

 the regions. The consideration of the problem of local fluctuations cannot be 

 undertaken here. 



It is presumed that the physiological steady state condition is one in which, 

 through the action of natural selection, the ratio of incorrect to correct reactions 

 is a minimum. This minimum rate is the metabolic error rate e^i, defined 

 above. Deviations from the steady state in any direction bring about conditions 

 in which the probability of incorrect reactions increases. This component of 

 the error rate is called the fluctuation error rate, e^. The fluctuation error rate 

 would then in general be a monotone increasing function of the displacement, 

 and the simplest assumption is that this function is a quadratic. 

 In one dimension this is 



Ej, = /77.\-2 (40) 



where x is the displacement from the steady state . Then, for the one-dimensional 

 model process discussed above, with stationary distribution of displacements 

 given by equation (12), the mean error incidence per unit time is 



r)0-< 



■ x^e 2rT2^.v (41) 



(2770- 



We find 



Ep = ma^ (42) 



This is not a solution of the problem, for the evaluation of m cannot yet be 

 carried out. However, the essential point for the present discussion is that 

 the fluctuation error rate is an increasing function of m and of the dispersion 

 of displacements, g. 



