384 



Fishery Bulletin 92|2). 1994 



Table 2 



Results of two bootstrapped production model analyses loosely based on swordfish, Xiphias gladius, in the North 

 Atlantic Ocean. The base model used only yield and standardized effort data. The tuned model also used a hypo- 

 thetical index of abundance (Table 1). Each conventional parameter estimate is designated 6, the corresponding 

 bias-corrected estimate is designated 6 BC . Nonparametric bias-corrected 80% confidence intervals are derived from 

 the bootstrap; as with most fishery analyses, these are conditional on correct model structure and probably under- 

 estimate true uncertainty (see text). The relative interquartile (IQ) range, a unitless measure of precision, is the 

 50% confidence interval divided by the median bias-corrected estimate. All results are rounded to three significant 

 digits. 



Base model 



Tuned model 



Quantity 

 estimated 



80% 80% Relative 



lower CL upper CL IQ range 



80% 80% Relative 



lower CL upper CL IQ range 



Management benchmarks 



MSY 



MWSY 

 'MSY 

 °MSY 



"W^^MSY 

 *199l'' MSY 



13,800 



0.257 



72.6 



53,800 



0.932 



1.03 



13,700 



0.259 



71.1 



53,100 



0.929 



1.03 



Directly estimated parameters 



r 0.514 0.517 



K 108,000 106,000 



q 0.00354 0.00363 



11,800 

 0.161 



61.7 



37,400 



0.755 



751) 



0.323 

 74,800 



0.00236 



15,100 



0.393 



82.2 



79,700 

 1.17 

 1.32 



0.785 

 159,000 

 0.00541 



11.8% 

 45.3% 

 14.5% 

 40.7%- 

 21.8% 

 28.3%' 



45.3% 

 40.7% 

 43.3% 



13,400 



0.264 



68.7 



50,900 



0.829 



1.18 



0.528 

 102,000 

 0.00384 



13,400 



0.269 



68.3 



50,000 



0.820 



1.18 



0.537 

 100,000 

 0.00393 



11,700 

 0.169 

 0.590 



33,600 

 0.650 

 0.892 



14,900 



0.432 



0.781 



71,900 



1.01 



1.53 



0.337 0.865 



67,200 144,000 



0.00260 0.00612 



11.7% 

 50.9% 

 14.1% 

 39.6% 

 23.6% 

 29.3% 



50.9% 

 39.6% 



45.7%- 



information or assumptions. (For an example, see 

 Conser et al., 1992, and Prager, 1993). This would 

 not be a serious objection if estimates made by mod- 

 els without process error were known to be severely 

 flawed, but to my knowledge the fisheries literature 

 includes no comprehensive comparisons of equiva- 

 lent models with and without process error. 



The work by Ludwig et al. (1988) does shed some 

 light on this question, as their simulations and mod- 

 els included both types of error. The authors found 

 that when observation error was ignored (its vari- 

 ance assumed to be zero) during parameter estima- 

 tion, the resulting estimates were biased and resulted 

 in an average loss in harvest value of at least 20%. 

 In contrast, when the relative variance of the pro- 

 cess error component was assumed to be half of its 

 correct value, a substantially smaller loss in harvest 

 value resulted. Unfortunately, Ludwig et al. (1988) 

 did not present results for estimation under the as- 

 sumption that process error was zero. Further re- 

 search into estimation methods for systems with both 

 process error and observation error would allow fish- 

 ery scientists and managers to better balance com- 

 plexity and accuracy in population models. 



Precision of estimates 



Production models tend to estimate some quantities 

 much more precisely than others. Hilborn and Wal- 



ters ( 1992) discuss this phenomenon at some length; 

 the comments here reflect my own experiences. For 

 most stocks, the main biological reference points 

 (MSY, /" MSY ) are estimated relatively precisely. How- 

 ever, absolute levels of stock biomass B T and fishing 

 mortality rate F x are usually estimated much less 

 precisely. This occurs because very few data sets con- 

 tain sufficient information to estimate q well. (The 

 example illustrates this point well — Table 2.) By di- 

 viding biomass and fishing-mortality estimates by 

 estimates of the corresponding biological reference 

 points, the effects of imprecision in estimating q can 

 be removed. The relative levels thus obtained are 

 useful measures in their own right: the relative level 

 of biomass B T I S MSY describes whether a population 

 is above or below the level at which MSY can be ob- 

 tained, and the relative level of fishing mortality rate 

 F / F M a Y suggests whether an increase or decrease 

 in fishing effort might provide a higher sustainable 

 yield. 



When two or more catchability coefficients are es- 

 timated, ratios of catchability coefficients are typi- 

 cally estimated more precisely than the individual 

 values of q. Thus it is possible to compare two differ- 

 ent gears without being able to estimate very pre- 

 cisely the catchability of either one. If a parameter- 

 ization involving K and r is used in fitting, the esti- 

 mates of these quantities are usually quite impre- 



