COMPARATIVE POPULATION STUDIES IN FISHERY BIOLOGY 55 



An entire family of growth curves can thus be represented in terms of the 

 three parameters, K, m, and W^ (or L^) and the scale factor b. For values of 

 m ranging from 0-5 to 3 or more (m is 0*67 in the simple von Bertalanffy, 

 unity in the Gompertz, and 2 in the autocatalytic equations) the growth 

 curves are very similar over much of their range, and comparison of the 

 values of i«C — which again express relative rate of approach to the asymptote 

 — is possible if m is kept constant for any particular set of comparisons. 



In the following discussion it is proposed therefore to retain the simple 

 von Bertalanffy equation, with the knowledge that any conclusions we may 

 reach would hardly be altered if one of the other equations in this general 

 family had been apphed to the growth data. We may then write an equation 

 for the steady-state annual catch offish, by weight (Y) as: 



3 l]„p-nK{tc-tQ) ^ 



Y = FRW^e-^^^c-tr) 2 zl!i [i _ ^-(z+nK)(tL-tc)^ 



n = ^ + "^ 



where 



Un= +1, —3, +3, —I for n = o, i, 2, 3 respectively. 



tj. = age at which fish are recruited. 



tc = age at which fish are liable to be retained by the fishing gear 

 in use. 



ti^ = age after which fish do not appear in the catch, either because 

 very few reach higher ages, or because they move from the 

 fishing area, or because they have reached a size at which they 

 are no longer taken or retained by the fishing gear. 



R = annual number of recruits. 



F, M and Z are instantaneous coefficients of fishing, natural and total 

 mortality (Z-=F+M). 



In using this equation account is taken of changes in the amount of fishing 

 by varying F (and hence Z) and of changes in the selectivity of fishing by 

 varying tc and sometimes (l- Holt (195 8/j) has shown that the greatest steady 

 catch is theoretically obtained by catching all fish when they reach a size 



though an infinitely high fishing intensity might be needed to do this in 

 practice. 



The catch under these conditions is given by 



M' y/ 3 



Ir ' AdTHTs/ W+ 3, 



>■"•■ = -"fe-B?^r(; 



