COMPARATIVE POPULATION STUDIES IN FISHERY BIOLOGY 59 



Just as the rate of descent of the right-hand hmb of an age distribution 

 provides estimates of total mortahty coefficient, so the right-hand hmb of the 

 size distribution, corrected as described above for gear selectivity, can 

 provide estimates of the ratio of growth rate to mortahty. 



In the simplest case we may regard size as roughly linearly related to age ; 

 this is true, for example, of the weight of fish in the region of the curve of 

 growth in weight near its inflexion. In this case plotting logarithms of 

 relative frequencies against weight gives a straight line, the slope of which is 

 equal to —Z\x where x is weight increment per unit time. If two size 

 distributions are available relating to two periods in the history of the fishery 

 between which there was a known difference in fishing intensity it is possible 

 to calculate two values, Z^\x and Z^\x and from these, if it is assumed that 

 M and x are constant, values ofFjx, Fjx and Mjx. A yield equation which 

 incorporates a growth function in which size increases linearly with age is 

 readily shown to contain the mortality and growth parameters only in these 

 ratios, and thus it may be solved by the use of data for size distribution 

 alone. This is essentially the method used by GuUand (1956) to assess a 

 Merluccius merluccitis fishery. 



Unfortunately it is not satisfactory to assume a linear growth function in 

 the absence of any clues as to the range of sizes offish represented in catches 

 in relation to the whole growth curve. A better assumption is that growth 

 can be represented by a three-parameter equation of the von Bertalanify 

 form. One of these parameters (^q) is essentially a scale adjustment. Beverton 

 & Holt (1956) showed that in this case 



where / is the mean length of all fish greater than some arbitrary length /', 

 provided that the decrease in frequency at size for fish bigger than /' can be 

 ascribed to mortality (or emigration). It is convenient to choose /'= /^. Thus 

 the problem of assessment in the absence of knowledge of age composition 

 is, in favourable circumstances, reduced to the estimation of L^ so that 

 measures of average size may be used as before to estimate ZJK, Z^jK and 

 hence F^jk FJK and MjK. In the rest of this paper I shall explore briefly 

 some possible methods of doing this. 



MARKING EXPERIMENTS 



A general method of estimating L^ and K which may be applied to size 

 increments observed between marking and recapture, has recently been 

 described by Gulland & Holt (1959). The procedure is to plot length incre- 

 ments per unit time x against the average of the initial length and the length 



