In the previous section all the parameters (growth, mortality, etc.) have been assumed to be constant, except for the explicit changes in the fishing mortality or the age at first capture. In fact changes in all are possible, and some, e.g. the annual recruitment, can vary very widely. These changes may be the result, directly or indirectly, of changes in the abundance of stock (and hence possibly influenced by fishing), or be independent of the stock, and the result of changes in the environment - amount of food, etc. The latter can be divided, according to the effect produced, into two types of change. First there are those that alter the shape of the yield curves, so that the results of, for example, an increase of mesh size may be quantitatively different, and secondly those that only affect the height of the yield curve, and which therefore for many purposes can be neglected.
The best example of the second is the big variation that can occur, independent of changes in adult spawning stock, in the strength of successive year-classes of many fish, e.g. in haddock, herring, etc. Calculations omitting data on year-class change may suggest that an increase of mean size from the present (say 100 mm to 110 mm) may increase the steady yield by say 5 percent. From this it need not be true that, if the mesh were increased, the yield in some particular future year would be exactly 5 percent greater than the present, because the year-classes then being fished may be of different strength. What is true (if the calculations are correct) is that the yield would be 5 percent above what it would have been if the old, 100-mm, mesh had been in use. For many practical questions (e.g. is a change from 100 to 110 mm advisable?) the differences due to change in recruitment are not of significance. For this reason, and because, as may be seen in the previous sections, that is the form in which the expression for the yield is often obtained, many assessments are stated in the form of yield per recruit. An exception is when the amount of fishing depends critically on the strength of the year-classes in the fishery, there being little or no fishing when year-classes are weak. A good example is the haddock fishery on Saint Pierre bank, where there was a big fishery on the outstanding 1949 year-class between 1953 and 1957, with little before or since.
Growth changes can have an effect on the shape of the yield curve, particularly that relating yield to size at first capture. In a heavily fished stock the maximum yield may be obtained with a size at first capture, lc, not far below the maximum size, L¥ , but if there is a change in growth with a new and smaller L¥ , not many fish may survive to lc and the yield with that value of lc may be small.
While some changes in the environment may mean that the shape of the yield curves in the future will be different from those under the present conditions, density-dependent effects can mean that the real yield curve is different from that calculated on the assumption of constant parameters. If the stock increases, e.g. following a reduction in fishing, the likely effects are that natural mortality will increase, and the growth decrease, but that the recruitment will increase. These effects act in opposite directions, the first two reducing the yield at high stock levels (i.e. at low fishing intensities, or with a large mesh size), but the last increasing the yield under these conditions of fishing. In a heavily fished stock, where reduced fishing or increased mesh size would be expected to increase the yield, density-dependent mortality and growth have a damping effect, tending to make the yield curve flat, but the recruitment effect will exaggerate the changes. Density-dependent recruitment is therefore rather the more critical effect.
If a relation can be established between any particular parameter and stock abundance, then it is possible to incorporate this into the simple yield equation. Usually it is not possible to produce an explicit mathematical expression for the stock or yield when a parameter changes with stock density, but estimates of stock and yield may be obtained for any given conditions of fishing effort, etc. by successive approximations. For instance, if natural mortality is proportional to stock abundance, then to calculate the yield and stock at say twice the present fishing, we can take a first estimate of a halved stock, and therefore halved M; using this value of M in the equations will give a better estimate of stock, hence of M, which in turn can be used to provide better estimates.
In fact it is often impossible to determine the density effects on the various parameters, especially of natural mortality, and it is probably best to take certain likely relations and see how these affect the shape of the yield curve (see Beverton and Holt, 1957, section 18).
In studying the effect on recruitment two quantities may be related to stock size - the recruitment, i.e. the absolute number of young fish produced from a given stock, and the survival, i.e. the numbers of young per million eggs. If, as is sometimes assumed, recruitment is constant, at least over the range of probable stock sizes, use of both relations may therefore show whether a nonsignificant (in the statistical sense) relation between stock and recruitment is caused by a real and significant (in the biological and practical sense) change in recruitment with stock size which is obscured by variation in the data, or whether the average recruitment is really constant. The second alternative should be detectable by a relation between survival and recruitment.
1. The spawning stock of North sea plaice may be estimated as the catch by weight per 100 hours' fishing by United Kingdom trawlers, and the recruitment as the catch in numbers per hours of four-year-old fish four years later. Available data for the past years are given below (from Beverton, 1962).
|
Year
|
Stock |
Recruitment
|
Year
|
Stock |
Recruitment
|
|
cwt |
cwt |
||||
|
1926 |
16 |
18 |
1945 |
150 |
33 |
|
1927 |
15 |
28 |
1946 |
76 |
32 |
|
1928 |
16 |
61 |
1947 |
54 |
45 |
|
1929 |
16 |
36 |
1948 |
44 |
22 |
|
1930 |
17 |
27 |
1949 |
35 |
20 |
|
1931 |
16 |
18 |
1950 |
33 |
23 |
|
1932 |
16 |
28 |
1951 |
31 |
9 |
|
|
|
|
1952 |
32 |
22 |
|
1943 |
120 |
18 |
|
|
|
|
1944 |
140 |
16 |
|
|
|
Assuming that the number of eggs produced is proportional to stock size, calculate an index of survival from eggs to recruitment. What is the relation (a) between stock and recruitment; (b) between stock and survival?
