386 



Fishery Bulletin 92(2). 1994 



approximation. DiCiccio and Tibshirani (1987) dem- 

 onstrate an example in which "the BC and BC Q meth- 

 ods seem to pull the percentile interval in the wrong 

 direction and hence the coverage gets worse." (The 

 BC Q method, due to Efron [1987], incorporates a sec- 

 ond-order correction to the BC method.) In that ex- 

 ample, bias correction for the point estimate would also 

 have made it worse. The example presented by DiCiccio 

 and Tibshirani (1987) (estimating the variance of a cor- 

 relation coefficient, true value 0.9, from a data set of 

 15 observations) seems rather extreme, but it does serve 

 to emphasize that model results, including estimated 

 bias corrections, must not be accepted blindly. 



Confidence intervals estimated by bootstrap meth- 

 ods entail fewer assumptions than those made by 

 parametric methods, but most likely are still opti- 

 mistic. In a study of an econometrics equation (in- 

 cluding a lagged term) that was fit by generalized 

 least squares with an estimated covariance matrix, 

 Freedman and Peters ( 1984) found the bootstrap es- 

 timates of standard error far superior to those made 

 with asymptotic assumptions. The bootstrap esti- 

 mates were 20% to 30% too low, but estimates from 

 asymptotic formulas were too low by factors of al- 

 most three. One reason for underestimation by the 

 bootstrap was that, due to the effect of fitting, the 

 residuals used for resampling were smaller than the 

 true values of the disturbance term (Freedman and 

 Peters, 1984). A suggested correction is given by 

 Stine, 1990, p. 338. 



There are other reasons why estimated confidence 

 intervals for fisheries models are likely to be opti- 

 mistic. The time frame encompassed by the data used 

 to fit fisheries models is usually short and does not 

 encompass the full range of environmental variation 

 that can add unexplained variation to observed data. 

 As the time series becomes longer, the random ef- 

 fects of environmental variation tend to become more 

 extreme, making earlier confidence intervals appear 

 overly optimistic (Steele and Henderson, 1984). An- 

 other cause of optimistic confidence intervals is the 

 use of preliminary models (e.g. ANOVA) to construct 

 abundance indices; such models tend to filter the 

 indices and thus reduce apparent variance. There 

 may also be systematic errors in the data (from, e.g. 

 gradual changes in q or gradual or sudden changes 

 in the proportion of the catch reported); these can 

 bias the results, but the confidence intervals include 

 only the effects of variability, not bias from model 

 misspecification. Schenker ( 1985) stated that "boot- 

 strap confidence intervals should be used with cau- 

 tion in complex problems." It is probably appropri- 

 ate to consider estimated confidence intervals from 

 fisheries population models to be, in general, mini- 

 mum estimates. 



Is there life after death? 



The concept of maximum sustainable yield was given 

 its epitaph about 15 years ago in a critical review by 

 Larkin (1977). Notwithstanding the title of his pa- 

 per, Larkin's main target was not the concept of MSY 

 itself, but what he called the "religion" of applying 

 MSY dogmatically to every stock. Undoubtedly, one 

 must recognize that MSY is not an immutable quan- 

 tity, and that model results should not be used dog- 

 matically. However, compensation in population dy- 

 namics does give rise to some form of maximum sus- 

 tainable yield. Whether MSY is estimable from the 

 data available for a given stock, and whether it is a 

 useful concept given the stock's dynamics, are rea- 

 sonable questions that, even if answered in the nega- 

 tive, do not invalidate the concept of MSY. 



In a response to Larkin's (1977) paper, Barber 

 (1988) pointed out that MSY, far from being dead, 

 was still in widespread use. Barber cited the utility 

 of MSY as a formal management objective; its sim- 

 plicity and ability to be understood by the fishing 

 industry, administrators, and managers; and the 

 grounding of the MSY concept in basic ecological 

 theory. He concluded by repeating Holt's ( 1981) sug- 

 gestion that MSY be considered part of a multi-fac- 

 eted management scheme. 



Shortly following Larkin's ( 1977 ) paper, Sissenwine 

 ( 1978) discussed several shortcomings of MSY as the 

 basis for optimum yield (OY), the "legally mandated 

 immediate objective of marine fisheries management 

 in the coastal waters of the United States beyond 

 the territorial sea of the individual states." In this 

 section, I address those items not discussed earlier. 

 Sissenwine pointed out that it is difficult to estimate 

 q, and that q may vary with population size. This 

 difficulty might be overcome, to some degree, by the 

 methods described earlier for estimating changes in 

 q. More importantly, this problem is not unique to 

 production models. The common use of CPUE series 

 to tune age-structured models also requires strong 

 assumptions about q. Indeed, because an age-struc- 

 tured model generally provides little information 

 about a cohort before it has been substantially fished, 

 its estimate of population biomass in a year close to 

 the present may be more influenced by random varia- 

 tions in q than would a similar estimate from a pro- 

 duction model. 



Sissenwine (1978) made a number of criticisms of 

 production models fit by equilibrium assumption. The 

 methods described here do not use the equilibrium 

 assumption and are not subject to those problems. 

 Once the assumption is dropped, one is much less 

 likely to get a good, but spurious, fit, when modeling 

 a population whose dynamics are not approximated 



