COMPARATIVE POPULATION STUDIES IN FISHERY BIOLOGY 6i 



Several partial compilations of the ratio of mean or median length at 

 maturity to the asymptotic length (IJLJ) have recently been published 

 (Beverton & Holt, 1959 and also Holt, 1959^ and b). From these it is clear 

 that the variation is considerable — from about o- 3 to more than o- 9. Allow- 

 ing for the fact that some of this variation is referrable to errors in estimating 

 Loc, and that some more can be ascribed to lack of precision in both defmitions 

 and measurement of maturity size, it seems nevertheless that only the order 

 of magnitude of L^c could be estimated from this ratio. This could, however, 

 be better than nothing. 



Some of the variability of the ratio lj,JL^ can be ascribed to differences in 

 growth rate, up to the onset of maturity. This growth rate is defmed by 

 both K and L^, but plotting IJL^ values from the compilation cited above 

 against corresponding values of L^o shows no indication of a relation. On the 

 other hand there appears to be some correlation between IJL:^ and K, such 

 that fish which grow rather rapidly towards their asymptotic size (high K 

 values) mature at a size which is larger relative to that asymptote than that 

 offish which approach the asymptotic size relatively more gradually (low K 

 values). This is true in spite of an apparent inverse relation between K and 

 Loo (see later), and is illustrated in Fig. i in which the transformation 

 — logg (i — LI La,) is plotted against K. (See Tables I and IL) This trans- 

 formation was chosen because it can, like K, take values from o to oc, it is 

 theoretically equal to [K {tm — ^0)]' ^^^ gi^^^, when plotted against K, 

 no obvious departure from linearity. 



The relation of maturity to size or age offish has been considered by very 

 many authors. Most recently Aim (i959) has reviewed the hterature, 



Table I. Frequency distribution of— log j i — y^' ) [from data of Beverton & 



Holt (1959)] 



,/L3c= 0-64). 



