The weight of a stock of fish tends to increase as the fish grow and young fish join the stock. The effects of fishing and natural mortality operate against this tendency to natural increase. E.S. Russell (1942) combined these factors in a simple equation:
51 = weight of stock at the beginning of a year,
52 = weight of stock at the end of that year,
A = annual increment by recruitment of young fish to the stock, G = annual increment due to growth of all fish in the stock, C = total weight of fish removed during the year by fishing, M = weight of fish lost during the year by death from all the other causes, i.e. the natural mortality.
The amount by which the stock weight would increase if no fishing took place, A + G - M, can be termed the natural yield. In the special case where the total stock remains unchanged, C + M must equal A + G. In these conditions the fishery is said to be 'stabilized', and fishing removes an 'equilibrium catch', i.e. a weight of fish that exactly corresponds with the natural yield of the stock. In theory, equilibrium conditions might be established for any level of stock weight, but the natural yield will vary for different weights and compositions of stock.
Underfishing and overfishing are extremes both of which result in low natural yields. Between the two there must be some intermediate intensity of fishing which would provide, in equilibrium conditions, the maximum possible sustained natural yield, i.e. an optimum yield. Such a fishing intensity could be termed the biological optimum fishing rate.
There are also economic factors to be considered. Highest profits do not necessarily result from the heaviest landings. If a market is glutted, prices collapse. A biological optimum fishing rate, giving the heaviest possible sustained landings, may not be the same as an economic optimum fishing rate, i.e. one giving the greatest financial returns. If a fishing policy is to be acceptable to the industry, it must aim to ensure the maximum output consistent with a fair return to all those engaged in fishing.
At the present time, control of natural factors influencing the yield of commercial sea fisheries cannot be envisaged, and it is therefore only in the regulation of fishing activity that there is a practical possibility of achieving optimum yields. But the relationships between fishing, stock, yields and profitability are by no means simple. The same weight of fish can be taken in innumerable ways; as a small number of large fish, a large number of small ones, or any combination of different sizes. Every variation in the composition of the catch will have a different effect upon the composition of the stock and its natural yield. To achieve anything approaching optimum yields it would therefore be necessary to control not simply the gross weight of fish landed, but also the numbers of each size of fish.
There are broadly two ways of studying the dynamics of fish stocks relative to fishing activities, both of which are used as bases for the formulation of fishery regulations. They are generally termed respectively the surplus production approach and the analytical or yield-per-recruit approach.
The surplus production approach visualizes the stock as a single unit, adopting the simple concept of fisheries already outlined. The effect of fishing is regarded as cropping the natural increase of the stock, thereby reducing the stock to a level below the limit set by the environment and promoting the production on which the fishery depends. Equilibrium yields are considered to be determined mainly by the size of the stock which can be controlled by varying the fishing intensity. The data required are fairly simple, mainly the statistics of fish catches and fishing effort. This information indicates general trends of the fishery from year to year with different intensities of fishing, and enables predictions to be made of the effects of changing the fishing effort.
The alternative analytical, yield-per-recruit method attempts a more fundamental elucidation of all factors producing changes in the size and yield of fish stocks. Instead of regarding the population as a single unit it is analysed in terms of all the individual fish constituting a number of separately recruited units, the annual year-classes of the stock. The objective is to estimate the contribution to the yield of the fishery at various fishing intensities from each year-class, or from one year-class throughout its lifespan in the stock. This requires much more detailed data over a wider range of fish biology than for surplus production studies, especially with respect to the relationships of stock size and composition to growth, mortality and recruitment.
The analytical approach offers possibilities of greater precision of prediction. It separates the effects of changes in the total amount of fishing from those of changes in the selectivity of fishing gear, such as are obtained from alterations in mesh size of nets or hook size on lines. The size or age at which fish first become liable to capture must profoundly influence the stock size, recruitment rate and potential yield of a fish population. With sufficient information it is possible mathematically to compute maximum sustainable yields (MSY) for every combination of fishing effort (boat hours) and mesh size. This leads to the concept of eumetric fishing, which may be defined as the optimum combination of effort and mesh giving the maximum sustainable yield.
Theoretical relationships of controlled fishing to fish populations and to fishing industries are discussed in greater depth in references listed at the end of this chapter (Cushing, 1968; Jones, 1974).
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