COMPARATIVE POPULATION STUDIES IN FISHERY BIOLOGY 67 



SUMMARY 



The annual catch of fish from a stock is given by the integral, over the 

 fishable life-span, of the product of an instantaneous fishing mortality 

 coefficient, a function giving the number of fish remaining at a certain time 

 from an initial number of recruits in terms of coefficients of mortahty, and 

 a function defining the body weight of fish at each age. 



If the ages of fish in a sample can be determined, then the coefficients of 

 mortality may be estimated from the age compositions of catches, and the 

 growth parameters from the curve offish size at age. The growth parameters 

 can also be estimated from, for example, data of marking experiments, 

 without knowledge of absolute age. The process of marking affects, however, 

 the growth rate offish, but it seems to affect L^ rather than K. This would 

 be expected if marking primarily interfered with the feeding of the fish. 



The simple equation for yield can be put in a form in which the mortality 

 coefficients appear only as numerators of fractions in which the denominator 

 is a growth parameter. Tables of the incomplete Beta-function can be used 

 to evaluate yield. The equation can be expressed to give yield in terms of 

 the growth parameter and of the relative lengths of fish at first liabihty to 

 capture and at the end of the fished life-span. 



Comparative studies indicate that the growth parameter K increases with 

 increase in water temperature, but that the natural mortahty may vary in 

 the same direction. Intraspecific (sexual) and interspecific relations between 

 these parameters seem generally to be of a similar kind. Not only is their 

 ratio relatively invariable, but it may have a characteristic Umited range of 

 values for groups of fishes up to the Order level. The ratio may be esti- 

 mated from size compositions of catches if the asymptotic length can be 

 determined. Statements in hterature to the effect that sexual maturity occurs 

 at a size about two-thirds of the fmal length (= one-third of asymptotic 

 weight) suggested comparative study of the relations between maturity size 

 and age and growth rate, because determination of the mean or median size 

 of maturity does not require age-determination. This study revealed that the 

 ratio of size at maturity to asymptotic size does indeed vary over a restricted 

 range, but it is correlated with K. The implications of this relation are 

 considered with regard to the use of maturity studies in stock assessment. 



REFERENCES 



Alm, G. (1959). Connection between maturity, size and age in fishes. Experiments carried out at 

 Kalarne Fishery Research Station. Rep. Inst. Freshw. Res. Drottning., 40, 6-145. 



Arora, H. L. (195 i). An investigation of the CaUfornia sand dab, Citharichthys sordidus (Girard). 

 Calif. Fish Game, 37 (i), 3-42, 



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