V GROWTH IN TIME OF THE TOTAL ORGANISM 203 



turnover rates are much less standardizable and hence estimates obtained show 

 a greater variation than those of respirometry and calorimetry, owing to factors 

 such as diet preceding the experiment, nutritive status, etc. There are also 

 theoretical difficulties involved in the determination of turnover rates (Reiner, 

 1953). The scarce data available on size dependence of N-excretion (Brody, 1945; 

 Table 14b) show hardly more than that the intraspecific allometry exponent 

 for N-excretion is somewhere not far from unity. Further experimentation on 

 size dependence of catabolic processes, particularly with isotope labeling, is 

 urgently needed. 



It is advisable, therefore, to examine to what extent deviations of n from i 

 influence the shape of growth curves. 



The necessary condition for limited growth and for the difference between 

 curves of length and weight growth is : 



2/3 = m < n (5.42) 



There cannot be 



m = n = 2/3 



for in this case, equation (5.16) would become: 



2/3 2/3 " ''/3 



dt 



w^'^ = C + c't I , , 



I = l^ -\- ct ) 



That is, the curve for length growth would be a straight line which is certainly 

 not true for postembryonic growth. 



Hence, there must he n > 2/3, and the consequences of deviations of ?i from 

 I have to be investigated. It can be seen that such differences do not substantially 

 alter the shape of the curves. In the First Growth Type, the curve for length 

 growth retains its characteristic shape (no inflexion) in any case if m = 2/3; 

 for under this condition, / always disappears in the first term of the second 

 derivative of the equation for growth in linear dimensions. Hence the monotonic 

 leveling of the curve of length growth, and the difference of this and the sigmoid 

 curve of weight growth are not altered if 2/3 < n < i. The question remains 

 to what extent such deviations alter the point of inflexion in the weight curve. 

 This is determined by equating to zero the second derivative. Expressed in terms 

 of the final value, the weight at the inflexion of the growth curve is: 



i-Q""" <=-) 



For m = 2/3, n = I, the inflexion is at Wj = 8l2'jw* = o.296!X'*. If, e.g., 

 m = 2/3, n = 3/4, we obtain w,- = (8/9)'^ = o.243!X'*. Therefore, variations of « 

 between 2/3 and i, that is, deviations of catabolism from weight proportionality 

 do not substantially alter the shape of the curves. 



Literature p. 253 



