Stochastic stock–recruitment ity, which is usually dominated by the effects of

8.2.5 Stochastic stock–recruitment ity, which is usually dominated by the effects of

relationships fishing. If the recruitment is taken as given, it is

not too difficult to assess the effects of varying the All the discussion in this chapter so far has implic- intensity and nature of fishing. Such yield-per- itly assumed that there is some compensatory rela- recruit calculations have been for many years the tionship between recruitment and spawning stock main tool for determining the appropriateness of size, even though this may be comprehensively various amounts and types of fishing, and remain obscured by the high variability of recruitment useful for that purpose today. (Myers, Chapter 6, Volume 1). Even this assump-

However, recruitment to fish stocks is far from tion may, however, be questionable. The possi- constant in practice, but varies on all time-scales, bility that there is no such deterministic com- from years through to centuries. The reasons for pensatory relationship at all has been explored these variations remain to a large extent unknown. by Shepherd and Cushing (1990). The somewhat This severely compromises the usefulness of long- subversive idea is that one might have only vari- term forecasts for fish stocks, which must invari- ability around a constant median level of R/SSB. ably be heavily qualified with ‘other things being On the face of it, this would not supply a regulatory equal’. In particular, in most cases there is no clear mechanism. However, if the frequency distribu- indication of the effects of spawning stock size on tion of the variability is sufficiently skewed, and recruitment, and this is particularly important if the variability increases as the stock size de- because it is intimately connected with the possi- creases, as has often been suggested, then the arith- bility of stock collapse under fishing. Further- metic mean recruitment would be inflated above more, the interactions between species make the the median level at low stock sizes, and would thus absolute size of recruitment important – and may follow a compensatory relationship, of an unusual make the ‘other things’ unequal after all. This form, even though the median does not. The stock issue is discussed further in Section 8.3 below. size, at fixed fishing mortality, is of course just

Given all these problems, it is clear that long- some weighted running arithmetic mean of term forecasting is a difficult area, which must be recruitment, and so responds like the arithmetic approached with considerable caution and mature

Chapter 8

judgement. The attempt is however essential, predictions. This was seen particularly strongly in since it is only in the long-term that the effects of the late 1980s when the northeast Arctic cod failed management are fully expressed, and any attempt to grow as expected (ICES 1990). However, in gene- to manage a fishery without the perspective of the ral the use of multispecies considerations is the long-term effects would be foolhardy. The assess- exception rather than the rule for short-term ment of the long-term effects is also the arena in predictions. which the skill and judgement of the fisheries

In practice the same could also be said for long- scientist is most crucial. The short-term effects of term predictions. However, it is far less certain most fishery management actions are fairly obvi- that ignoring multispecies effects is sensible for ous to all concerned. The long-term effects are medium- to long-term predictions. Predation mor- however much less obvious, more subtle, and tality can make considerable changes to average often counter-intuitive. The assessment, and levels of natural mortality rate on pre-recruit ages explanation of these effects is arguably the most of larger fish such as the North Sea cod depicted in important, and probably the most difficult task Fig. 7.14, and it affects all ages of smaller species. which fisheries scientists are called upon to It is well known that increasing natural mortality undertake.

alters the shape of yield per recruit curves. It will also affect the number of recruits living long enough to form the spawning biomass.

8.3 MULTISPECIES

The equations for multispecies cohort analysis

FORECASTS

and the equivalent equations for multispecies VPA can be reversed and long-term simulations

It was noted in Chapter 7, this volume, that, while produced, to predict how the equilibrium yield in principle changes in predation mortality might will change under various exploitation regimes for

be considered in some short-term predictions, in the fish stocks included. Since fishing mortality practice for the larger species rather little is to be rate might alter, or exploitation patterns may be gained from doing so. The reason is that for these changed on any of the predator or prey stocks, a species predation mortality acts mostly on pre- wide range of scenarios is possible and the compu- recruit ages and their numbers can often be esti- tations are quite complex. A computer model, mated from research surveys at a time after the MSFOR, which makes long-term predictions major part of the predation mortality has occurred. based upon the equations and estimates of In areas with important fisheries for prey species MSVPA, was written by Sparre. It was tested and the need for considering the effect of predation used extensively by the ICES Multispecies Assess- mortality rate on short-term yield is likely to be ment Working Group (see ICES 1986). greater. As an example of this, routine calculations

The wide range of possible scenarios possible of predation losses are made in the case of the with a multispecies prediction on a number of northeast Arctic capelin TAC (ICES 2000).

stocks makes it rather difficult to provide under-

Multispecies effects may, however, affect the standing of how the system may behave. However, growth of predator species and also their reproduc- we may generalize to a certain extent. Yield-per- tive capability. For example, Marshall et al. (1998) recruit curves typically become flatter-topped and showed that condition and fecundity in northeast their maximum moves to higher values of fishing Arctic cod was determined to a large extent by mortality rate as levels of natural mortality in- capelin abundance. Effects on growth are particu- crease on recruited ages. When natural mortality larly likely in areas heavily dependent on one key increases on pre-recruit ages the effect is to reduce prey species such as capelin in the northeast the numbers of recruits entering the fishery. This Arctic, Iceland and Newfoundland. Weight-at-age would generally depress yield-per-recruit curves if is a significant component of catch prediction so the constant recruitment of the model was at a changes in growth are likely to affect short-term younger age than some of those that the predation

185 mortality acted on. In either case yield would seem ences are particularly large between the two runs

Dynamic Pool Models II: Forecasting

likely to be lower when predation mortality is for haddock and herring. This largely resulted from high. This is likely to have occurred in periods apparent changes in predation patterns of saithe when fishing mortality was low. Thus the pre- between the two stomach-sampling data sets. dictions of single-species yield-per-recruit curves

A further concern with such predictions is that are likely to be unsound when fishing mortality (like single-species yield-per-recruit) they do not rate is typically low throughout an ecosystem. necessarily include stock–recruitment considera- We may therefore conclude that predation mortal- tions. However, since multispecies models gener- ity generated from multispecies interactions leads ally predict asymptotic yield curves because of the to flatter-topped yield-per-recruit curves with buffering effect of predation, it is clearly even more maxima at higher levels of fishing mortality.

important that stock–recruitment effects are in- This is illustrated by Fig. 8.10. This shows the cluded in multispecies models. If these are includ- calculated change in yield per average recruit for

ed then it seems likely that yield curves would North Sea fish stocks that would occur if fishing initially increase more slowly with increasing mortality rate was lowered by 10% on all species. fishing mortality than a single-species yield curve The three lines show the changes expected when due to predation mortality effects. However, once predation mortality rates were based upon the recruitment overfishing occurred, the decrease in 1981 stomach-sampling data, the 1991 stomach- yield would be far more rapid than a single-species sampling data and a key run based upon both sets yield-per-recruit curve would predict. of stomach-sampling data. This illustrates that

This pattern is illustrated in Fig. 8.11, which for under a multispecies model decreasing fishing the northeast Arctic cod shows the 7-year running mortality decreases yield for most of these stocks. average of yield plotted on the 7-year running This is in sharp contrast with current long-term average of fishing mortality rate, transformed to single-species predictions for these stocks which the yield/biomass ratio, expressed as the harvest would predict most yields increasing with de- percentage. This is contrasted with a single- creased fishing intensity. The figure also indicates species yield-per-recruit curve for the same stock, that the predictions are affected by the stomach scaled to the same maximum yield. It is apparent data set used in MSVPA and the consequent choice that the slope of actual yield at low fishing mortal- of suitability with which to run MSFOR. Differ- ity, as indicated by the running average curve, is

7-year average

Scaled yield-per-

Yield and scaled Y/R 200

recruit curve

1986–91 After Pope 1979 –10

0 10 20 30 40 50 60 70 80 90 Percentage caught

–15 Cod Whiting Haddock Herring Sprat N. Pout Sandeel

Fig. 8.11 Yield-per-recruit curve for the northeast Arctic cod compared to a 7-year running average of

Fig. 8.10 Yield of North Sea species after a general yield-against-harvest rate, and to an early production reduction of 10% in all fishing mortality. N = Norway.

curve fit due to Pope (1979).

Chapter 8

shallower than the response predicted with a sin- gle-species yield-per-recruit curve. Predation mor- tality (which is mostly caused by cannibalism in this case), and density-dependent growth seem the likely cause of this discrepancy. It is also apparent that the actual yield has dropped away very precipi- tately at higher harvest rates and this is doubtless due to stock–recruitment effects, which might have been exacerbated by reductions in prey avail- ability. The figure also shows a surplus production curve (Pope 1979) fitted to the biomass and harvest rates estimates of VPA. While not exact, this makes more sensible management predictions than the single-species yield-per-recruit curve and it is notable that it did so before the steep decline in yield occurred in the 1980s.

Because of the likely changes in growth and stock-recruitment effects on yield functions, the ICES Multispecies Working Group has usually declined to predict long-term yield which takes the North Sea stocks far from their average situa- tion. They have thus usually just indicated the changes that might result from changing effort by 10% on seven broadly defined fishing fleets. This produces what may be converted to a Jacobian matrix ∂Y(s,f)/∂E(g) of yield Y(s,f) of species (s) by fleet (f) relative to a change of effort E(g) in another fleet (g). This provides information on the local slope of the multispecies yield per average recruit surface. Interestingly this and contemporary yield provides just sufficient information to fit a multi- species production model which can be used to predict yield in the near vicinity and can also be used to predict the position of multispecies analogues to the more usual reference points (ICES 1989).

In conclusion, multispecies effects sometimes affect short-term predictions and can undoubtedly have a strong effect on long-term predictions. However, the increasing detail of multispecies models can mean that while they may improve on single-species models, particularly in the low fish- ing mortality range, their long-term predictions may be very variable. There may be an argument for making long-term predictions using simple production models which implicitly include many

of the compensatory effects that multispecies models and stock–recruitment models attempt to provide. However, the formulation of these sim- pler models is helped by more detailed understand- ing of the biology. Moreover, they are undoubtedly best fitted to the solid estimates of past time-series of mortality and biomass provided by age-based es- timation techniques such as VPA, rather than to the less reliable estimates derived directly from CPUE data.