Restrepo et al : Monte Carlo simulation applied to Xiphias gladius and Gadus morhua 747 



for the fishery as a function of the management mea- 

 sures imposed. The simulation approach we present can 

 be used with assessment models other than ADAPT. 

 For example, one could use Monte Carlo simulation to 

 quantify the effects of uncertainty in input data, as- 

 sumptions, and model formulation on the outputs from 

 the CAGEAN (Deriso et al. 1985) or stock synthesis 

 (Methot 1990) methods. We believe that this simula- 

 tion framework is not only a versatile and intuitive 

 method to estimate uncertainty, risks, and costs, but 

 in many cases it may also be the only practical way to 

 incorporate some types of input uncertainty which are 

 not estimated statistically. Because the estimated 

 uncertainties in the model outputs are conditional on 

 what is known and what is assumed about the inputs, 

 failure to acknowledge possible sources of uncertain- 

 ty in a realistic manner may lead to overly optimistic 

 views of the uncertainties in the model outputs. The 

 Monte Carlo approach forces one to examine the nature 

 and magnitudes of the uncertainties in the inputs and 

 in the model formulation, and it allows one to study 

 how uncertainties are propagated through the assess- 

 ment and into the projections ultimately used for 

 management recommendations. 



It appears feasible to quantify risks and costs for a 

 wide variety of management options when the assess- 

 ments are accomplished by any of a variety of analytical 

 models. It remains to determine what risks (and costs) 

 should be quantified, how much risk is acceptable, and 

 for how long. For example, we do not know how to 

 quantify the risk of stock collapse due to recruitment 

 failure, but we might wish to quantify the risk of the 

 spawning biomass falling below 20% of the virgin level 

 in three years out of five. If we assume that this 

 represents a dangerous situation (see Beddington and 

 Cooke 1983, Brown 1990, and Goodyear 1990, for 

 thoughtful discussions), then the risk should be kept 

 low. On the other hand, if we consider the risk of ex- 

 ceeding the economically-optimal fishing mortality 

 (however defined), then we might like the risk to be 

 close to 50%, i.e., as likely to be above the optimum 

 as below it. (Of course, we should consider the relative 

 costs of over- and undershooting the target mortality). 

 If F is not close to the economic optimum fishing mor- 

 tality, then one must also devise a way to determine 

 what is the best trajectory to take for arriving at the 

 long-term goal. It is beyond the scope of this paper to 

 address what are appropriate goals, biological refer- 

 ence points, and trajectories. 



Finally, for any stock assessment, the results of a 

 Monte Carlo simulation study are necessarily condi- 

 tional on what is assumed about the sources of uncer- 

 tainty, including the model chosen for the assessment. 

 Since decisions about some of the sources of uncertain- 

 ty are subjective, the results are personal views of 



uncertainty, risk, cost, etc. If three scientists assess 

 a given stock, they can generate three separate sets 

 of simulation outputs. The combination of their simula- 

 tions provides a picture of their collective uncertainty 

 about the assessment results. Alternatively, they can 

 agree that a minimal estimate of the uncertainty is 

 provided by the one set of results that are the least 

 uncertain. 



A more detailed study of the relative sensitivities of 

 the assessment outputs and risk curves to the choice 

 of input distributions can be carried out via sensitivity 

 analysis (Miller 1974). In this Monte Carlo framework, 

 sensitivity analysis would consist of introducing plann- 

 ed perturbations to the input-uncertainty distributions 

 and then measuring the overall effect on the model's 

 outputs. This should aid in the identification of key in- 

 puts so that more effort could be placed on improving 

 their estimates. This is more difficult than it may seem. 

 A given input that is perturbed during the sensitivity 

 analysis (say, catch at age) will cause different degrees 

 of change in the various output distributions: stock 

 sizes, fishing mortalities, Fqi, projected catches, etc. 

 Furthermore, this impact may change over time. For 

 instance, assumptions about recruitment become very 

 dominant as the projections are made further ahead 

 in time. Nonetheless, sensitivity analysis can be very 

 useful in identifying trade-offs between the benefits of 

 precision and the cost of obtaining that precision. 



Acknowledgments 



Partial support for this study was provided through the 

 Cooperative Institute for Marine and Atmospheric 

 Studies by National Oceanic and Atmospheric Admin- 

 istration (NOAA) Cooperative Agreement NA90-RAH- 

 0075 and by the Canadian Government's Atlantic 

 Fisheries Adjustment Program (Northern Cod Science 

 Program). We thank Nicholas Payton for programm- 

 ing assistance and Peter Shelton, Al Pinhorn, Donald 

 Parsons, and two anonymous reviewers for helpful 

 comments. 



Citations 



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1983 The potential yield of fish stocks. FAO Fish. Tech. Pap. 

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 Bergh, M.O., and D.S. Butterworth 



1987 Towards rational harvesting of the South African anchovy 

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