Icelandic Cod Stock

Basic bioeconomic models which incorporate uncertainty are reviewed to show and compare the principal methods used and results reported in the literature. Beginning with a simple linear control model of stock uncertainty, we proceed to discuss more complex models which explicitly recognize risk preferences, firm and industry behavior, and market price effects. The effects of uncertainty on the results of bioeconomic analysis are rarely unambiguous, and in some instances differ little from corresponding deterministic results. This review is presented to enhance readers' appreciation of the papers to follow in this and the next issue of the journal.

The purpose of this paper is to discuss rules for deciding Total Allowable Catch (TAC) for Icelandic cod. For this purpose, a bioeconomic model describing harvesting and processing of cod, capelin, and shrimp in the Icelandic marine ecosystem is constructed and estimated. The model is used to analyze the probable effects of harvesting strategies on biomass, catch, and economic benefits from the exploitation of these species. Simulations are used to investigate probability profiles of biological and economic variables, taking into account inaccuracies in assessments and uncertainties in predictions. Optimal harvesting strategies are also investigated using a deterministic version of the model and taking into account problems of unemployment, overcapacity, and aversion to fluctuations in consumption. The analysis shows that it is beneficial to reduce fishing from the cod stock in order to allow the stock to recover to its optimum size. This increase in the cod stock will result in big decreases in the catch of capelin and shrimp.

The Icelandic cod stock is analysed with respect to the probable effects of different harvesting strategies on yield, spawning stock biomass, and economic benefits. Simulations are used to investigate the probability of stock recovery and collapse. Potential yield and economic benefits/costs are also investigated, using stochastic and deterministic models. In stochastic simulations, attention is paid to the apparent stock-recruitment relationship, the highly variable weight-at-age and maturity-at-age in Icelandic waters along with the inevitable inaccuracies in current and future assessments. Regardless of method, substantial reduction in catches from recent (1993) levels is seen to be necessary in order to rebuild the stock. In the deterministic model, profit maximization mandates closure of the fishery until the stock is rehabilitated. Using the stochastic model, it is predicted that recent catch levels lead to eventual extinction of the stock with high probability. A management procedure is formulated and its application to the model is shown to lead to stabilization of the stock around an economically and biologically acceptable level.

The single cohort model shows that we delay the harvest of a cohort beyond the age at which the cohort's growth rate equals the discount rate when harvesting costs are proportional to the harvest rate (Clark 1990). With more than one cohort, one needs to determine if cohorts of various age classes should be harvested at the same time and rate or selectively at different times and harvest rates. This paper establishes that knife-edge selectivity can be optimal in some cases, but is dominated by selective harvesting when either harvesting is costless, gear congestion costs are relatively large, or it is feasible and desirable to harvest older cohorts at a larger harvest rate than younger cohorts. It is furthermore shown that in most cases it is optimal to harvest fish at an earlier age than the single cohort model predicts, but it might even be optimal to harvest fish that grow faster than the discount rate. In some cases, it may be optimal to utilize two gears to harvest two cohorts, even if gears have different operating costs.

The purpose of this paper is to discuss rules for deciding Total Allowable Catch (TAC) for Icelandic cod. For this purpose, a bioeconomic model describing harvesting and processing of cod, capelin, and shrimp in the Icelandic marine ecosystem is constructed and estimated. The model is used to analyze the probable effects of harvesting strategies on biomass, catch, and economic benefits from the exploitation of these species. Simulations are used to investigate probability profiles of biological and economic variables, taking into account inaccuracies in assessments and uncertainties in predictions. Optimal harvesting strategies are also investigated using a deterministic version of the model and taking into account problems of unemployment, overcapacity, and aversion to fluctuations in consumption. The analysis shows that it is beneficial to reduce fishing from the cod stock in order to allow the stock to recover to its optimum size. This increase in the cod stock will result in big decreases in the catch of capelin and shrimp.

The use of multistock/multispecies models of marine stocks in relation to stock size estimation has been on the rise. The marine ecosystems that these models attempt to describe are, however, complex and it is computationally impossible to emulate all species interactions. Therefore, reasonable approximations need to be made regarding the ecosystem in order to obtain results that are of interest. Stock size estimations can be sensitive to these approximations. An ecosystem simulator is presented and used to verify multispecies models such as Gadget. In particular a two stock two area model is simulated and used as input to Gadget using different special assumptions . Various methods for estimating uncertainty are compared, including the use of the Hessian matrix, a bootstrap approach and Monte – Carlo simulation.

Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance estimates. Regardless of the method used to obtain point estimates, a method is needed for variance estimation. A bootstrap technique is introduced for the evaluation of uncertainty in such models, taking into account inherent spatial and temporal correlations in the data sets thus avoiding many model-specification issues, which are commonly transferred as assumptions from a likelihood estimation procedure into Hessian-based variance estimation procedures. The technique is demonstrated on a real data set and used to look for estimation bias and the effects of different aggregation levels in population dynamics models.

The Icelandic cod stock is analysed with respect to the probable effects of different harvesting strategies on yield, spawning stock biomass, and economic benefits. Simulations are used to investigate the probability of stock recovery and collapse. Potential yield and economic benefits/costs are also investigated, using stochastic and deterministic models. In stochastic simulations, attention is paid to the apparent stock-recruitment relationship, the highly variable weight-at-age and maturity-at-age in Icelandic waters along with the inevitable inaccuracies in current and future assessments. Regardless of method, substantial reduction in catches from recent (1993) levels is seen to be necessary in order to rebuild the stock. In the deterministic model, profit maximization mandates closure of the fishery until the stock is rehabilitated. Using the stochastic model, it is predicted that recent catch levels lead to eventual extinction of the stock with high probability. A management procedure is formulated and its application to the model is shown to lead to stabilization of the stock around an economically and biologically acceptable level.

Environmental conditions in Icelandic waters are reviewed. The period from 1920 to 1964 was particularly warm in Icelandic waters and following this a sharp downward trend in temperature and salinity in both surface and intermediate layers was observed in all of the years from 1965 to 1971. From 1972 to 1996 cold and mild years have alternated and ice conditions generally improved from the preceding cold period. The cod catches have twice reached more than half a million tonne (early 1930s and mid-1950s). Both peaks were associated with immigration of strong year classes from Greenland. Other important demersal species are haddock, saithe, Greenland halibut and red®sh. Only two pelagic species have been of importance in the Icelandic ®sheries, i.e. herring and capelin. Catches of these species have¯uctuated widely but in most recent years their yield has been in the range of one to one and half a million tonne. The ®shery for northern shrimp has increased dramatically during the previous two decades. The management of marine resources in Iceland has varied over the years as have the methods for assessing the stocks. Recently, the emphasis has changed from simple stock assessments to the evaluation of harvesting strategies, which is seen as a part of a larger process, the comprehensive assessment. Important ingredients of such comprehensive assessments include risk analyses and multispecies considerations.

The northernmost Atlantic marine ecosystems (or Boreal systems) tend to have a cod stock as a major predator and shrimp and capelin among the prey species. Variations have been observed in the abundance of all cod stocks and variations have been measured in some of the shrimp and capelin stocks. Some models of these systems and some stomach content analyses have indicated that these interactions should be quite important. When these interactions are important enough and measurement errors are sufficiently small, the interactions between stocks should show up in aggregate abundance and growth indices. This paper illustrates several such effects in the Boreal system off Iceland.

Despite an increase in northern shrimp (Pandalus borealis) female biomass in the past years, the recruitment of the offshore population north and northeast of Iceland has remained very low. In this study, the influence of abiotic and biotic factors was studied in relation to shrimp recruitment. Two factors, cod (Gadus morhua) abundance and summer sea surface temperature (SST), were found to have a negative effect on offshore shrimp recruitment, explaining 71 % of the observed variation. Both cod abundance and temperature on the offshore shrimp grounds have increased in the past years, while recruitment has decreased and been at historically low levels since 2005. No significant relationship was found between recruitment and spawning biomass, indicating that recruitment variability is mainly driven by other factors. Cod abundance and summer SST are likely to affect different life stages of shrimp, as SST influences shrimp during its planktonic phase while cod abundance influences the demersal stage.

Despite an increase in northern shrimp (Pandalus borealis) female biomass in the past years, the recruitment of the offshore population north and northeast of Iceland has remained very low. In this study, the influence of abiotic and biotic factors was studied in relation to shrimp recruitment. Two factors, cod (Gadus morhua) abundance and summer sea surface temperature (SST), were found to have a negative effect on offshore shrimp recruitment, explaining 71 % of the observed variation. Both cod abundance and temperature on the offshore shrimp grounds have increased in the past years, while recruitment has decreased and been at historically low levels since 2005. No significant relationship was found between recruitment and spawning biomass, indicating that recruitment variability is mainly driven by other factors. Cod abundance and summer SST are likely to affect different life stages of shrimp, as SST influences shrimp during its planktonic phase while cod abundance influences the demersal stage.

The multispecies fisheries management looks at a bigger picture in addressing the long-term consequences of present decisions. This implies an ecosystem management that includes a number of species and their physical, biological and economic interactions. These interactions make the growth of resources stochastic and increase complexity in understanding stock dynamics and optimal catch for such a stochastic and multiple stocks´ system. To address the issue of identifying optimal catch of stochastically growing multi stocks, we have formulated and applied a time-continuous stochastic model. The model contributes to multispecies bioeconomic management of marine ecosystems. An application of model in a predator-prey relationship in Barent Sea revealed that the optimal catch for stochastically growing stocks in a multispecies interaction model is different from the deterministic model.

We explore a fishery targeting the mature part of a stock, while bycatching the immature part. Both targeted catch and bycatch may have positive market values. Cost of effort is supposed to be a function of the selection properties of the fishing gears. Mature fish is assumed to cannibalise on the immature part of the stock. A bioeconomic model of the problem is set up and it is shown that the model possesses a unique nontrivial stable equilibrium and moreover that both cannibalism and catch act as stabilising factors. Necessary conditions for a bioeconomic optimum are also provided. The model is applied on the Northeast Arctic cod stock where time series of stock biomasses, catches and fishing mortality rates covering the period 1946-2000 have been used to estimate the model parameter values. The economic parameters have been estimated on the basis of previous open access to the fishery, assuming bioeconomic equilibrium. It is shown that bioeconomic optimum could not be obtained at any discount rate, without reducing the rate of fishing mortality, first of all on the mature part of the cod population.

Twelve species of cetaceans are regarded as regular inhabitants in Icelandic and adjacent waters. Based on available estimates of the total food consumption of the cetaceans in the area, this paper explores potential interactions between three baleen whale species off Iceland and the relevant fish resources that constitute a part of their diet prey. The three species of whales are fin whale (Balaenoptera physalus), the largest cetacean consumer in this area, feeding mainly on krill (Meganyctiphanes norvegica) but also preying on some fish species like capelin (Mallotus villosus); minke whale (Balaenoptera acutorostrata), taking krill as well as a variety of fish, including capelin and gadoids (e.g. cod, Gadus morhua); and humpback whale (Megaptera novaeangliae) assumed to be feeding mainly on capelin.

The single cohort model shows that we delay the harvest of a cohort beyond the age at which the cohort's growth rate equals the discount rate when harvesting costs are proportional to the harvest rate . With more than one cohort, one needs to determine if cohorts of various age classes should be harvested at the same time and rate or selectively at different times and harvest rates. This paper establishes that knife-edge selectivity can be optimal in some cases, but is dominated by selective harvesting when either harvesting is costless, gear congestion costs are relatively large, or it is feasible and desirable to harvest older cohorts at a larger harvest rate than younger cohorts. It is furthermore shown that in most cases it is optimal to harvest fish at an earlier age than the single cohort model predicts, but it might even be optimal to harvest fish that grow faster than the discount rate. In some cases, it may be optimal to utilize two gears to harvest two cohorts, even if gears have different operating costs.

Basic bioeconomic models which incorporate uncertainty are reviewed to show and compare the principal methods used and results reported in the literature. Beginning with a simple linear control model of stock uncertainty, we proceed to discuss more complex models which explicitly recognize risk preferences, firm and industry behavior, and market price effects. The effects of uncertainty on the results of bioeconomic analysis are rarely unambiguous, and in some instances differ little from corresponding deterministic results. This review is presented to enhance readers' appreciation of the papers to follow in this and the next issue of the journal.