Year around closed areas or refuges as management mechanisms for controlling fishing mortality are explored using a two-component, spatial model with movement between areas. The model assesses the fate of a cohort when only a portion of it is vulnerable to fishing. The yield per recruit and spawning stock biomass per recruit are compared for equivalent amounts of fishing effort with and without a refuge.The results indicate that the institution of a closed area can lead to substantial increases in spawning stock biomass realized from a cohort and, as such, could be a viable shortterm management option to reduce overall fishing mortality on an overexploited stock. Yield per recruit with a refuge is a complex function of the size of the refuge, fishing mortality rates and movement rates. The results suggest that the proportional loss in yield per recruit will be less than the initial proportion of the cohort contained within the refuge. In some instances, the yield per recruit with a refuge can exceed the yield per recruit without one, but the net increases are usually small. The size of the refuge needed to achieve a specified gain in spawning biomass depends upon the mobility of the fish. Higher movement rates require a larger refuge to achieve the same increase, but any loss in yield per recruit will be less even though the refuge is larger.The assumptions underlying the model are discussed, and the importance of information on movement rates for assessing the possible effect of closed areas is stressed.KEY WORDS: Closed areas, fishery management, refuge, spawning stock biomass per recruit, yield per recruit.

School of Fisheries WH-I 0, University of Washington, Sea ttk, WA 98 1 95, USA Polacheck, T., 8. Hilborn, and A.E. Punt. 1 993. Fitting surplus production models: comparing methods and measuring uncertainty. Can. J. Fish. Aquat. Sci. 50: 2597-2607.Three approaches are commonly used to Fit surplus production models to observed data: effort-averaging methods; process-error estimators; and observation-error estimators. We compare these approaches using real and simulated data sets, and conclude that they yield substantially different interpretations of productivity. Effort-averaging methods assume the stock is in equilibrium relative to the recent effort; this assumption is rarely satisfied and usually leads to overestimation of potential yield and optimum effort. Effort-averaging methods will almost always produce what appears to be "reasonable" estimates of maximum sustainable yield and optimum effort, and the r2 statistic used to evaluate the goodness of fit can provide an unrealistic illusion of confidence about the parameter estimates obtained. Process-error estimators produce much less reliable estimates than observation-error estimators. The observation-error estimator provides the lowest estimates of maximum sustainable yield and optimum effort and is the least biased and the most precise (shown in Monte-Carlo trials). We suggest that observation-error estimators be used when fitting surplus production models, that effort-averaging methods be abandoned, and that process-error estimators should only be applied id simulation studies and practical experience suggest that they will be superior to observation-error estimators.On emploie commun6ment trois methodes pour ajuster les moddes de production exc6dentaire aux r6sultats observes; il y a les methodes de la moyenne d'effort, les estimateurs des erreurs de traitement ainsi que les estimateurs des erreurs d'observation. Nous comparons ces trois demarches au moyen d'ensembles de donn6es reelles et simul6es, et nous parvenons A la conclusion que ces m6thodes conduisent A des interpretations largement diff6rentes de la productivite. Les methodes fond6es sur les moyennes d'effort suppssent que le stock est en kquilibre relativement 2 Ifeffort recent; c'est rarement le cas, mais cela conduit ordinairemerit A une surestimation du rendement potentiel et de I'effort optimal. Ces mkthodes produiront presque toujours ce qui semble Gtre des estimations (( raisonnables D du rendement soutenable maximal et de I'effort optimal, et la valeur statistique r2 qui sert h 6vaiuer la validit6 de i'ajustemeeat peut donner I'illusion nori fondee de confiance dans les estimations des paramkres qui sont obtencres. bes estimateurs d'erreurs de traitement donnent des estimations beaucoup moins fiables que les estimateurs des erreurs d'observation. Ces derniers conduisent aux estimations les plus faibles de rendement soutenable maximal et d'efiort optimal; ce sont aussi les estimateurs les plus pr6cis et qui cornportent le moins d'erreur systkmatique (selon la mkthode Monte-Carlo). Nous ...

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Summary1. Several albatross species, including the wandering albatross Diomedea exulans , have shown marked declines in abundance throughout their range. These seabirds are frequently taken as by-catch in longline fisheries and this mortality has been implicated in the population declines. 2. We developed a deterministic, density-dependent, age-structured model for assessing the effects of longlining on wandering albatross populations. We used demographic data from field studies at South Georgia and the Crozet Islands, data on albatross abundance from 1960 to 1995, and reported effort data from the tuna longline fisheries south of 30 ° S, to model estimated by-catch levels and other population parameters in the model. 3. The model used two alternative assumptions about patterns of at-sea distribution of wandering albatross (uniform between 30 ° S-60 ° S; proportional to the distribution of longline fishing effort between these latitudes). 4. Our model was able to predict reasonably closely the observed data from the Crozet Islands wandering albatross population, but the fit to the South Georgia population was substantially poorer. This probably reflects: (i) greater overlap in the Indian Ocean than in the Atlantic Ocean between the main areas of tuna longline fishing and the foraging ranges of wandering albatrosses from the Crozet Islands and South Georgia, respectively; and (ii) greater impact of poorly documented longline fisheries, especially the tuna fisheries in the south Atlantic and the Patagonian toothfish Dissostichus eleginoides fishery, within the foraging range of wandering albatrosses from South Georgia. 5. The model results suggest that the marked decline in both populations, and subsequent recovery of the Crozet Islands population (but not the continued decline of the South Georgia population), can be explained by the tuna longline by-catch. They further indicate that populations may be able to sustain some level of incidental take. However, the likely under-reporting of fishing effort (especially in non-tuna longline fisheries) and the delicate balance between a sustainable and unsustainable level of by-catch for these long-lived populations suggest great caution in any application of such findings.