2o6 J. A. GULLAND 



and thus the magnitude of the recruitment will be determined by the size 

 of the stock in that earher year. The observed gross increase in stock in any 

 year is therefore determined in part by the stock in that year, and in part by 

 the stock some years earlier. Unless, therefore, the sizes of the stock in these 

 two years are roughly the same, i.e. the population is in more or less a steady 

 state, the relation between population size and gross increase cannot be 

 simply determined. A somewhat more empirical approach, designed to 

 overcome the difficulties in analysing a rapidly changing fishery, has been 

 used by Gulland (1961). It is assumed that the mortality due to fishing is 

 proportional to the fishing effort, and that the other characteristics of the 

 population (growth, natural mortality, recruitment) are unchanged, even 

 indirectly. This corresponds to the 'constant parameter' model of the 

 analytical type discussed later. Therefore the abundance of an age-group of 

 fish which has been exposed to fishing for, say, five years is determined by 

 the total fishing effort in those five years. The stock at any time will contain 

 fish which have been exposed to fishing for periods ranging from a few days 

 up to perhaps a dozen years, the average duration being, say, four years. 

 The stock, as measured by catch per unit effort, may be plotted against the 

 average effort over the past four years and this will give the steady state 

 relation. By simple multiphcation the corresponding relation between catch 

 and effort can be determined. This has given useful results in fisheries where 

 there have been large changes in the amount of fishing, a condition satisfied 

 by most of the important commercial fisheries of the eastern Atlantic, and 

 requires little detailed information beyond statistics of total effort and catch 

 per unit effort. The method may be illustrated by the plot for the hake off 

 the west coast of Scotland (Fig. i). The average life-span in the fishery has 

 been taken as three years and the index of density as the catch per 100 hours* 

 fishing of English steam trawlers. Such a model has, like the previous one, 

 the inability to distinguish and analyse quahtative changes in the stock or in 

 the catch, due, for example, to changes in the selectivity of the gear, as well 

 as the disadvantages of the constant parameter models discussed later. Some 

 analysis of the effect of gear selectivity changes can be made if they have 

 been in operation long enough to distinguish two separate relations in the 

 plot of catch per unit effort against effort, before and after the change. A 

 further pecuhar disadvantage is that the average life-span in the fishery is not 

 constant, but is determined by the level of fishing, being reduced by intense 

 fishing; however this is not hkely to have any major effect. 



SEPARATION OF GROWTH, RECRUITMENT 



AND MORTALITY 



Another main class of models divides the net change in the population into 



