Fisheries Risk Assewwefit Sourcesoof. Uncertaznty j
A Case S t u d y of
Georges Bank Haddock
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he development of strategies for the exploita?ion of renewable resources requires an assess-
I below a specified threshold level. The determination of an acceptable risk level sets the basis for further complex decisions, such as allocation among resource user groups. The risk associated with adopting any harvesting policy results primarily from (1) errors in estimates of population size and demographic parameters, 121 random variation in production rates and processes, particularly recruitment (the number of progeny surviving to a specified age or life stage), and ( 3 ) lack of complete information on biological interactions among populations. The first source of uncertainty reflects the inherent difficulties in assessing the size of populations distributed throughout broad areas and in determining their biological characteristics. The second reflects the characteristically large variation in survival rates during the early life history stages of most marine populations. This variability obscures the form of the relationship between the adult population and the number of recruits (those progeny that survive to the age or size of vulnerability to the fishery], and renders precise short-term prediction impossible. The third source of uncertainty reflects the complexity or high-dimensionality of multispecies systems (11. Although progress has been made in addressing each of these concerns, uncertainty will always remain a significant part of
Michael J. Fogarty Andrew A. Rosenberg iVationo1 Oceanic and Atmospheric Administration National Marine Fisheries Service Woods Hole, M A 02543 Michael P. Sissenwine Nation01 Oceonic and Atmospheric Administration National Marine Fisheries Service Silver Spring, MD 2091 0 decisions about the management of living resources ( 2 ) . Here we describe some issues relevant to quantifying the risk to a marine resource under a specified fishery management strategy. We emphasize the importance of defining an appropriate null model and of devising risk-averse management strategies to minimize the probability of stock depletion or "undesirable" alterations to the structure of the system. The generally low power of statistical tests when applied to highly variable fishery systems requires careful specification of the null model ( 3 ) . We illustrate these concepts using the Georges Bank haddock resource, a heavily exploited fishery in the northeastern United States off Cape Cod, as a case study. The Georges Bank region historically has supported one of the most important fisheries in the United States ( 4 ) . Large-scale expansion of the fishery with the arrival of distant water fleets operating on Georges Bank in the early 1960s resulted in profound changes in abundance and relative species composition of the system. Catches initially increased markedly as exploitation rates increased on traditionally harvested species and new fisheries developed on underutilized species. The harvest peaked in 1973 with a removal of nearly 1 million metric tons from the system. Catches sub-
0013-936X/92/0926~440$03.00/0@ 1992 American Chemical Society
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sequently declined precipitously with the virtual collapse of several dominant demersal and pelagic fish populations, including haddock (5). Full implementation of extended jurisdiction (the 200-mile limit) in 1977 curtailed the activities of the distant water fleet, but the expansion of the domestic fleet resulted in renewed heavy exploitation throughout the last decade (6). In this review, we will concentrate on assessing the risk to the haddock resource caused by exploitation.
Risk in exploited populations We are primarily interested in determining the so-called quasiextinction probability that a popul a t i o n w i l l b e d e p l e t e d by harvesting to an arbitrarily small size (7,8). Beddington et al. (9)describe the related concept of a “notional threshold”-the population size below which the probability of poor recruitment increases appreciably. Possible additional criteria for defining the depletion or quasiextinction level in an exploited system include the minimum population size capable of supporting a viable fishery or a minimum ratio of realized yield to the long-term potential harvest from a resource. The primary determinant of the long-term dynamics of any population is the relationship between the adult population and recruitment. For a stable population, the recruits must, on average, replace the parental stock. Consider a simple conceptual life-history model comprising the adult stock (spawning biomass) and the number of recruits. For a closed population (i.e., one where immigration and emigration are negligible), we take the null stockrecruitment model to be a straight line through the origin (a densityindependent stock-recruitment relationship) with slope proportional to the survival rate during the pre-recruit stage (dashed line in Figure la). In contrast, compensatory changes in survival rates during the pre-recruit phase or in reproductive output by the adult stock result in a nonlinear relationship between spawning stock size and recruitment (curved line in Figure la). A compensatory process is one that results in an inverse relationship between the population growth rate and some measure of population size. Notice that the rate of increase of recruitment is substantially higher at low spawning stock size for the com442 Environ. Sci. Technol.. Vol. 26, No. 3.1992
pensatory model than for the null model in this example. Failure to reject the null hypothesis of no compensation will, in general, result in a conservative assessment of production capacity of the stock and its ability to withstand exploitation (20, 2 2 ) . The burden of proof is therefore met by demonstrating that the population can with-
stand higher exploitation rates than those determined under the null model. Under this approach, tests with low statistical power will therefore generally lead to a risk-averse rather than to a risk-prone decision. Closure of the life-cycle model is obtained by specifying the relationship between recruitment and the adult population (is., those that
survived from recruitment to maturation and production of progeny). In the following discussion we will assume that this relationship is linear, although this constraint is easily removed. As mortality on the recruited population increases, the slope of this line decreases monotonically [Figure Ib). Superposition of the stock-recruitment and the recruitment-stock relationships illustrates the predicted equilibrium points for this deterministic model (represented by the intersection points between the stock-recruitment and recruitment-stock relationships in Figure IC).For the compensatory model, as fishing mortality (defined as the ratio of catch to mean number in the population during the time period) increases, stable equilibrium points are expected until the stock-recruitment and the recruitment-stock curves no longer intersect. At this point, a stock collapse is predicted. Notice that the slope of the stockrecruitment curve at the origin defines the critical exploitation level for the population. A population characterized by a steep slope at the origin can withstand higher harvesting rates than one with a lower rate of increase at the origin. For the density-independent stock-recruitment model, only a neutral equilibrium is possible [indicated by a complete superposition of the recruitment-stock and the stockrecruitment lines). This is a highly precarious situation in which the birth rates and death rates must exactly balance to maintain the equilibrium. The principal sonrces of uncertainty and risk in recruitment dynamics involve difficulties in assessing whether the population is, in fact, regulated by compensatory processes [i.e., whether stable equilibria exist) and in determining the slope of the stock-recruitment curve at the origin. To address the first of these concerns, Sissenwine and Shepherd (IO)assumed a density-independent recruitment model and advocated its use unless clear evidence of compensation is available (see also 1 1 ) . Regarding the slope of the stock-recruitment curve at the origin, Sissenwine and Shepherd suggested using a nonparametric estimate of the slope of the null model [defined by the median bisector of the data in the stockrecruitment plane). The slope of the null stock-recruitment model is expressed in units of recruits-perspawning biomass (WSSB). To
complete the life-cycle model, we can further determine the lifetime production of spawning biomass per recruit (SSB/R) for different fishing mortality rates using standard, age-structured models (described in IO). The fishing mortality rate resulting in replacement of the spawning stock by the recruits [F,,) for a specified harvesting pattern corresponds to the level where the inverse of the SSBIR estimate exactly equals the slope of the null stockrecruitment relationship. This will occur when one of the recruitmentstock lines corresponding to a particular fishing mortality rate and age-specific harvesting pattern is exactly superimposed over the stock-recruitment line (see Figure IC).If fishing mortality rates exceed this value, a population collapse is predicted under this deterministic model. Note that errors in the reported catch or the estimated population size result in errors in the fishing mortality rate and introduce an additional source of uncertainty and risk in the calculations. Random variation in recruitment and other components of production must be explicitly treated to cast the problem in the context of a formal risk analysis. We will focus on recruitment variability alone. A probability distribution of recruitment levels for a given level of spawning stock size is a more realistic representation than a point estimate (12).Recruitment distributions are typically asymmetrical
and positively skewed (12. 13). Hennemuth et al. (I 3) note that the lognormal distribution provides a useful empirical characterization of recruitment distributions for many marine fish populations. Stochastic simulations employing information on probability distributions of recruitment, specification of the functional form of the stockrecruitment relationship, and the demographic parameters described above can be used directly to specify the probability that population biomass will be reduced to an arbitrary notional threshold or quasiextinction level under different harvesting regimes. In general, we can poriray the risk to the population as the cumulative probability of the population falling below different threshold population levels under alternative management regimes. The shape of these risk curves is typically sigmoidal; its exact form is determined primarily by the probability distribution of recruitment levels and other stochastic parameters. Case study
The Georges Bank haddock population fluctuated about relatively stable levels during the period 1930-60 [Figure 2). Following the arrival of the distant water fleets on Georges Bank in 1961 and the redirection of effort on the large 1963 haddock year class, fishing mortality rates increased markedly on this population with a subsequent sharp
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reduction in abundance (Figure 2. The empirical relationship be tween spawning stock size and recruitment for haddock is extremely variable, with little indication of the form of the underlying stockrecruitment relationship (Figure 3). It is clear that any deterministic recruitment model can explain only a small fraction of the variance in recruitment as a function of spawning stock size for this population. This variation is a result of the many biotic and abiotic environmental variables that can potentially affect recruitment (22).Relatively small changes in demographic parameters during the early life stages can result in dramatic fluctuations in recruitment. In recognition of this variability, Shepherd ( 1 4 ) advocated using a qualitative estimation method for fitting stock-recruitment models. We adopted this approach for the haddock series (see curved line in Figure 3) and compared these results to the null model (dashed line in Figure 3). See Shepherd ( 1 4 ) for details of the estimation method and Sissenwine et al. (15) for an earlier application to haddock. Superimposed on the figure are straight lines with slopes equal to the inverse of spawning stock biomass per recruit at three fishing mortality rates. We assumed a constant natural mortality rate over all age classes of 0.2 and a constant age-specific harvesting regime based on historical patterns in this analysis. For purposes of illustration, we used the entire stock and recruitment time series; we later consider a partitioning of the data that may reflect changes in ecological conditions with important consequences for setting harvesting levels. An instantaneous fishing mortality rate of approximately F = 0.5 (corresponding to an annual removal rate due to fishing of 36% of the harvestable population) will result in stock replacement under the null recruitment model (Figure 3). Fishing mortality rates in excess of this level will ultimately lead to a population collapse under this densityindependent model. For the compensatory recruitment model, instantaneous fishing mortality rates in excess of F = 0.9 (corresponding to annual removals > 55% of the harvestable population) are predicted to result in a stock collapse. Note that the slope of the compensatory stock-recruitment curve at the origin was determined arbitrarily using the qualitative method of Shepherd ( 1 4 ) and that a 444 Envimn. Sci. Technol., Vol. 26. No. 3,1992
more conservative estimate could be adopted that would result in a lower critical fishing mortality rate. The results for the null and compensatory p o p u l a t i o n models bound the estimates of harvest rates beyond which the risk of population collapse is high. We conclude that instantaneous fishing mortality rates between 0.5 and 0.9 (annual removals of 3655% of the harvestable population) represent the range of harvesting levels where the risk of population decline or collapse is high. Uncertainty in the form of the structural model (density-independent vs. compensatory) therefore translates into uncertainty in the estimate of the critical harvesting level. Difficulties in obtaining a reliable estimate of the slope of the recruitment curve at low population sizes further compound this uncertainty. Clearly, adoption of the null model results in a more conservative harvesting strategy. This conservatism, may, however, be purchased at the expense of foregone yield to the fishery. We emphasize that the above considerations are based on the risk of population decline or collapse alone and do not consider optimum harvesting policies in either an economic or a biological sense. Examination of historical levels of fishing mortality indicates that
relatively stable haddock catches were sustained during the period 1931-1964 at fishing mortality rates of F = 0 . 3 4 . 6 (closed circles in Figure 4). The population declined rapidly when fishing mortality rates increased abruptly to F = 0.8 under heavy exploitation by the distant water fleet. The population was displaced from an apparent equilibrium and has not fully recovered. These results suggest that the bounds provided by the null and compensatory models do adequately circumscribe the critical region for defining permissible harvest rates for the Georges Bank haddock population. We further note that the results under the null model, although conservative, were perhaps not unduly so and that the F, level of F = 0.5 under the null model is close to the biological optimum based on earlier analyses for a compensatory model of haddock dynamics (15.16).This is also evident in the equilibrium yield curve for the compensatory model sketched in Figure 4 (curved line). Notice that the equilibrium yield is maximized at a fishing mortality rate of approximately F = 0.5. During the period of relative stability in the fishery (solid circles), the observed and predicted behavior of the equilibrium model are in reasonable agreement. The increased fishing mortality on had-
dock by the distant water fleet with the appearance of the 1963 cohort, however, resulted in a marked perturbation from the predicted equilibrium behavior (open circles, Figure 4). The population has not recovered to historical levels following this transitory disturbance. The apparent shift in production levels in the haddock population following this perturbation may indicate a further source of uncertainty and risk in determining harvesting strategies. The large-scale harvesting activities of the distant water fleets induced dramatic changes in the structure of the Georges Bank ecosystem (5,6, 17). In particular, the biomass of several commercially important species declined sharply while that of a number of piscivores increased markedly (6,171. These predators notably i n c l u d e s m a l l s h a r k s (spiny dogfish): several species of skates: and Atlantic mackerel, a voracious predator of the early life stages of many fish species. The effect of this increased predator biomass may be to depress further the production of their prey. Uncertainty in the structure of the food web and in multispecies interactions in general therefore further complicates the evaluation of the probable effects of alternative harvesting strategies. The haddock stock and recruitment series can be partitioned int two distinct segments. The earlier segment (closed circles, Figure 3) encompasses the period of relative stability at high production levels as well as the transitional (nonequilibrial) dynamics of the stock. The latter period (open circles, Figure 3) represents the low recruitment and production period. It is clear that a qualitatively different stock-recruitment relationship may obtain for the latter period, and, if so, the population can withstand muchreduced levels of fishing intensity without danger of collapse relative to the earlier period. The overall pattern is consistent with our expectation of the recruitment dynamics under increased predation pressure. However, there are alternative hypotheses for the changes in production, including changes in environmental conditions, that must be systematically examined. Regardless of the underlying mechanisms it appears that haddock populatioi recruitment is sharply reduced relative to earlier levels of production and that management advice must be adjusted accordingly.
Risk analysis Given an estimate of the probability distribution of recruitment during a period of relative stability in spawning stock size, the risk associated with a harvesting strategy can be calculated using simulation techniques. Such an analysis estimates the probability (risk) of the spawning stock dropping below a given level for one year during the time period simulated. In some situations the goal may be to estimate the probability of the stock dropping below a given level and remaining below that level indefinitely (i.e., quasi-extinction): this can be addressed by determining the number of age classes in the spawning stock and in the pre-recruit period and hence the probability of having a succession of poor years of recruitment that would reduce the stock as a whole to a low level (181. For the Georges Bank haddock example, Rosenberg and Brault ( 1 9 ) calculated the probability of the spawning stock being below different levels for various harvesting scenarios (Figure 5). Their simulations were based on the observed distribution of haddock recruitment for the period 1965-1987, when the stock had been reduced to a relatively low level, and therefore re-
flect the additional concerns about changes in system structure raised above. In terms of advice on a particular management strategy, the analysis expresses the risk to stock size of each of the chosen harvest levels. Note that the assumption here is that a notional threshold level of spawning stock can he determined as a target for improving the chances of good recruitment. At low stock sizes, good recruitment is assumed to he less likely.
Conc’usions Assessments of the status of living marine resources must take into account the uncertainty inherent in the estimates of population abundance, errors in estimates of harvest rates, and structural uncertainty in the form of intra- and inter-specific interactions. These uncertainties must be interpreted in a probabilistic framework to evaluate the risk under particular management strategies (20). In this paper we have dealt only with the conservation risks. Managers must also evaluate economic and administrative risks (e.g., credibility and enforceability of regulations). Defining an acceptable level of risk circumscribes the biological “bottom line” as the basis for making informed decisions on the resource management and allocation issues.
a Model developed by coupling the compensatory slock recruilmenl curve lmm FI we 3 wlih an age-Slructured yield and spewnlng~blomass-per-recruit analysis using the melhJo1 Shepherd j 73. Close Circles represent empitical estimates 01 yield 01 haddmk dunng relative wpulation Slabillty Open circles creased exploitation by dlstani water tieels
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Michael I. Fogarty is an opemtions research anolyst for the National Marine Fisheries Service, Northeast Fisheries Center, Woods Hole, MA. He is also on odjunct professor of oceonogmphy at the Universityof Rhode Island, where he teaches fish populotion dynomics. He received o Ph.D. in biologicol sciences from the Universityof Rhode Island. His research interests include the recruitment dynomics of exploited marine populations ond the interoction between harvesting and fish community structure.
We have illustrated some approaches to coping with uncertainty and risk in the Georges Bank haddock population. Additional formal analyses of the haddock population in the context of risk and decision theory have been undertaken recently (22-22).We note that haddock is not necessarily representative of all the species of concern in this system. In particular, it is characterized by high levels of recruitment variability relative to many other species. Cod exhibit a more symmetrical recruitment distribution with lower variance and appear to be more resilient to exploitation (23). Barnthouse et al. (23)further emphasize the importance of understanding the implications of differences in life history characteristics in defining the probable response to exploitation and contaminants in fish populations. We have advocated use of a density-independent recruitment function as the null model. Note that the null hypothesis is often specified (at least implicitly) as no relationship between spawning stock and recruitment (a straight line with zero slope and positive y-intercept; see also 24). This is equivalent to specifying a strongly compensatory system with exogenous inputs (Le., the population cannot be overexploited). This specification is clearly not 446 Environ. Sci. Technol.. Vol. 26, No. 3,1992
appropriate as a null model for any closed population, and its use in this context would result in high risk to the population under intensive exploitation. Fishery management reference points based on yield-per-recruit considerations alone clearly fall in this category. The effects of measurement error on estimates of population size can create important estimation problems in stock-recruitmerit (25,26).The erObscure t h e form Of t h e relationship and often lead to development of an incorrect null model (no relationship between spawning stock and recruitment). Further, the errors-in-variables problem leads to biased parameter estimates that directly iffect management reference points (25). The assumption of stationarity (i.e., population parameters are time-invariant) is implicit in virtually all population models. However, directional changes in the biotic and abiotic environment are clearly important in many natural systems (27).Because production levels of Georges Bank haddock appear to have been affected by a change in biotic environmental conditions, the assumption of stationarity cannot be supported. We suggest that this change in production is related to changes in community structure,
Andrew A. Rosenberg is a research spe-
cialist in population dynamics for the Office of the Senior Scientist, National Marine Fisheries Service. He received o Ph.D. in biology from Dalhousie University, His research include methods of stock assessment, resource monogement, andpopulation ecology.
Michael P. Sissenwine is the senior sci-
entist the US.Notional Marine Fisheries Service. He oversees research conducted in 29 loborotories that provide dota for marine management decisions. His reseorch focuses on population dynomics, fisheries ecology, and oceonogmPhY.
which indicates a need for further research on interspecific interactions in this system and their implications for overall system productivity. Variability in population estimates because of natural fluctuations and measurement error also contributes to uncertainty in resource status that is often used to justify delaying or eliminating management actions until all doubt is removed. Clear parallels are seen in other fields of environmental assessment and management ( 3 ) .This syndrome leads inevitably to riskprone management strategies. Peterman ( 3 ) noted that shifting the burden of proof from scientists and managers to those using or impacting the resource is essential for the effective ma.nagement of natural systems.
References (1) Rothschild, B. J, Dynamics of Marine
Fish Populations; Harvard University Press: Cambridge, MA, 1986. (2) Sissenwine, M. P. Mar. Res. Econ. 1984, 2 , 1-30. (3) Peterman, R. M. Can. J. Fish. Aquat. Sci. 1990, 47, 2-15. (4) Fogarty, M. J.; Sissenwine, M. P.; Grosslein. M. D. In Georges B a n k ;
Backus, R., Ed.; MIT Press: Cambridge, MA, 1987; pp. 494-507. (5) Grosslein, M. D., Langton, R. W.; Sissenwine, M. P. R a p p . P. V. R e u n . Cons. Int. Explor. Mer. 1980, 177, 3 74-404. (6) Sissenwine, M. P.; Cohen, E. B. In Food Chains, Y i e l d s , Models a n d Management of Large Marine Ecosystems; Sherman, K.; Gold, S., Eds.; American Association for the Advancement of Science: Washington, DC, in press. (7) Ginzburg, L. R. et al. Risk Analysis 1982,2, 171-181. (8) Ginzburg, L. R. et al. In Statistics in the Environmental Sciences; Gertz, S . M.; London, M. D., Eds.; ASTM STP 845; 1984, pp. 31-45. (9) Beddington, J. R. et al. Fish. Res. 2990,8,351-65. (10) Sissenwine, M. P.; Shepherd; J. G. Can. J. Fish. Aquat. Sci. 1987, 44, 913-18. (11) Ginzburg, L. R.; Ferson, S.; Akcakaya, H. R. Cons. Biol. 1990, 4, 63-70. (12) Fogarty, M. 7.; Sissenwine, M. P.; Cohen, E. B. Trends Ecol. Evol. 1991, 6, 241-46. (13) H e n n e m u t h , R. C.; Palmer, J. E.; Brown, B. E. J. Northwest Atl. Fish. Sci. 1980, 1 , 101-11. (14) Shepherd, J. G. J. Cons. Int. ExpJor. Mer. 1982, 40, 67-75. (15) Sissenwine, M. P.; Overholtz, W. 7.; Clark; S. H. In “Proceedings of the Workshop on Biological Interactions among Marine Mammals and Commercial Fisheries in the Southeastern
Bering Sea”; Melteff, B.; Rosenberg, D. H., Eds.; Alaska Sea Grant Rep. 841,1984, pp, 119-37. (16) Overholtz, W. J.; Sissenwine, M. P.; Clark, S. H. Con. 1.Fish. Aquat. Sci 1986, 43, 748-53. (17) Fogarty, M. J. et al. “Trends in Aggregate Fish Biomass and Production on Georges Bank”; 1989, North Atlantic Fisheries Organization Scientific Council Studies Document 89/78. (18) Bravington, M. V. et al. In The Surface Water Acidification Programme; Cambridge University Press: Cambridge, U.K., 1990; pp. 467-76. (19) Rosenberg, A. A,; Brault, S. North Atlantic Fisheries Organization Scientific Council Studies 1991, 26, 171-81. (201 Sissenwine, M. P.; Fogarty, M. J , ; Overholtz, W. J. In Fish Population D y n a m i c s ; Gulland, J. A., Ed.; J. Wiley: New York, 1988. (21) Brown, B. E.; Patil, G. P. North Am. J. Fish. Mgt. 1986, 6, 183-91. (22) Rothschild, B. J.; Heimbuch, D. G. F A 0 Fish. Rept. 1983, 291, 1141-59. (23) Barnthouse, L. W.; Suter, G. W. 11; Rosen, A. E. Environ. Toxicol. Chem. 1990, 9, 297-311. (24) Shepherd, J. H.; Cushing, D. H. Phil. Trans. Royal. SOC. London Ser. B. 1991,330,151-64. (25) Ludwig, D.; Walters; C. J. Can. J. Fish. Aquat. Sci. 1981, 38, 711-20. (26) Walters, C. J.; Ludwig, D. Can. J. Fish. Aquat. Sci. 1981, 38, 704-10. (27) Walters, C. J. Can J. Fish. Aquat. Sci. 1987, 44 (SUppl. 2):156-65.
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