52 S. J. HOLT 



may be represented by a sigmoid curve, which might be either the logistic 

 or a derivative of it, or any empirical curve. Schaefer (1959) has shown, how, 

 with such assumptions and with a set of observations covering a suitable 

 range of stock sizes, it may be possible to determine the parameters of such 

 curves from measures of catch, indices of stock size (as by catch per unit 

 effort) and a measure of the coefficient of assumed proportionality between 

 fishing effort and the ratio of catch to stock size, such as might be obtained 

 from tagging experiments. 



The third line of approach is by constructing mathematical models of 

 particular fish stocks, in which rates of reproduction, individual growth, and 

 death are represented by functions based primarily on an analysis of the size 

 and age structure of the population, and containing a series of parameters for 

 all of which there exist methods of estimation. An advantage of this method 

 is that it offers the possibihty of predicting the effects on catches of changes 

 not only in the amount of fishing, but also in the kind of fishing, and par- 

 ticularly in the selectivity of fishing operations in terms of the sizes and ages 

 offish accepted or rejected by the fishery. In practice predictions are required 

 of the effects on catches of changes in size selection resulting from changes 

 in the characteristics of the fishing gear (such as mesh or hook sizes), and in 

 the pattern of operations (such as concentration of fishing at grounds on 

 which the fish gathered there tend to be smaller or larger than the average 

 size in the population). Predictions may also be needed of the effects of 

 changes in the seasonal and spatial distribution of fishing operations. 



Such predictions are facilitated by the use of analytical models, and a 

 requirement for the employment of all such models has been the availability 

 of data for the age composition of the stock. This presents difficulties in 

 many areas, especially — but not by any means only — in tropical waters, 

 where the ages of fish cannot reliably be determined from rings on hard 

 structures such as scales, otoliths, opercular bones, fm-rays or vertebral 

 centra. Other methods of inferring age-composition, for example from 

 polymodal length frequency curves or from the seasonal progression of 

 modal sizes, are also not universally applicable; the former can, even in the 

 most favourable circumstances, be used to distinguish only the few youngest 

 age-groups in the population, and the latter method may not be successful 

 when spawning or recruitment to the stock is spread over a very long season. 

 Even when age can be determined, it is usually a procedure so demanding 

 of the time of scientists and technicians that there is a general interest in 

 finding means of avoiding it, or at least reducing it as much as possible. 

 This general problem and the contribution to its solution that might come 

 from comparative population studies will be considered here. It should be 

 said, however, that there appears to be plenty of scope for practical com- 



