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Fishery Bulletin 90(1). 1992 



For Dungeness crab, there is little evidence of stock- 

 dependence. In fact, it is not clear whether a local stock, 

 such as that in Grays Harbor, is self-reproducing or 

 depends on larval drift from other areas. For this rea- 

 son, we chose to use only short-term loss predictions. 



The choice of slope for the regression of crab entrain- 

 ment on trawl catch will strongly influence model 

 results. We gave long consideration to the choice of 

 regression models. Problems arise because there are 

 few data points and large measurement errors asso- 

 ciated with both variables. Costs of sampling (which 

 involved simultaneous operations of a specially modi- 

 fied hopper dredge and a chartered trawler) prohibited 

 any increase in data quantity or precision. Initially, we 

 chose to use least-squares regression (LSR) with its 

 underlying assumptions of normal errors with equal 

 variances. There are two forms of LSR in common use: 

 predictive LSR which assumes that all error is in mea- 

 surement of the Y (dependent) variate, and functional 

 LSR which incorporates errors in both X and Y vari- 

 ates. In the overall context of DIM, the entrainment 

 regression serves the role of a calibration curve predic- 

 ting entrainment from a set of observed trawl catches. 

 For this reason, we used a predictive regression con- 

 ditional on the observed trawl catches. (This implies 

 that the result is not generalizable to any other method 

 of crab density estimation, but such generalization is 

 not needed here.) Two outliers were dropped from the 

 LSR analysis; both points were from the same station 

 in different years, and both were influenced by one or 

 two extremely high trawl catches. Because we were 

 not entirely satisfied with the assumptions of the LSR 

 analysis, the data was reanalyzed using a nonpara- 

 metric regression technique which is robust to non- 

 normality, inequality of variances, and errors in mea- 

 surement of the X variate. Because this analysis agreed 

 with the final LSR model (Eq. 8), we accepted that 

 model as the most reasonable. 



Another limitation was our inability to reliably dis- 

 tinguish age-classes beyond 1 -i- and obtain mortality 

 estimates for older age-groups. Because of this, we 

 stopped our calculations at age 2 -i- , but there is a 

 strong desire to relate the results to fishery stocks with 

 recruitment at 3-5 years of age. It is possible to per- 

 form some rough calculations of actual impact to 

 fisheries, if we are willing to make some assumptions. 

 Using Scenario 2 (limited confined disposal) as an ex- 

 ample, estimated age 2 -i- equivalent losses ranged from 

 166 to 587 thousand crab (Fig. 8). The fishery harvests 

 males only, so with a 50% sex ratio these numbers 

 become 83-298 thousand age 2+ male crab lost. To 

 relate these to the fishery, we need to know survival 

 from age 2 -i- to recruitment. We have rough estimates 

 of mortality from age 2 -i- to 3 h- and from age 3 -i- to 

 4 -H (Table 6) calculated from the trawl survey data set. 



These estimates are confounded with the decline in 

 gear efficiency with crab size, and so are probably 

 underestimates of true survival. They also depend on 

 tenuous assumptions about size-at-age. Accepting these 

 estimates and assuming the bulk of the fishery recruits 

 at age 3 -i- , our estimates of age 2 -i- loss correspond to 

 losses to the fishery of 37-134 thousand age 3-i- male 

 crab. As exploitation rates are quite high (~70-90%; 

 Methot and Botsford 1982), these numbers can be 

 related directly to annual catch. The ten-year average 

 catch for the Washington coast has been about 3000 

 metric tons, which corresponds to 3.3 million crab 

 (average individual weight of 0.9kg). So, losses for this 

 hypothetical scenario would be on the order of 1-4% 

 of the average annual catch by the Washington coast 

 fishery. 



The model was limited by several other factors, par- 

 ticularly problems of data quality and parameter esti- 

 mates. Primary among these was lack of data on beam 

 trawl efficiency and size selectivity (Gunderson and 

 Ellis 1986). We have implicitly assumed that the trawl 

 sampling was 100% efficient for all sizes of crab, which 

 is certainly not the case. The gear was designed for cap- 

 turing juvenile crab, and we believe it to be relatively 

 efficient for juvenile sizes, but crab approaching legal 

 size are able to avoid or escape the small net. For 

 estimating absolute numbers entrained, this is not a 

 problem because the entrainment function is essentially 

 a calibration of entrainment against trawl catch, re- 

 gardless of trawl efficiency. However, to the extent 

 that gear efficiency is below 100%, we underestimate 

 total populations within the estuary. Calculations of en- 

 trainment as a proportion of the local population are 

 thus biased upward. Trawl efficiency also affects 

 natural mortality rate estimates, to which equivalent 

 adult loss calculations are extremely sensitive. 



Overall, DIM has proved useful even with its limita- 

 tions. In project planning, the model allowed schedul- 

 ing gear and work seasons to reduce impacts on the 

 crab population, and provided some quantitative predic- 

 tions of loss on which to base mitigation programs. DIM 

 is now being used in conjunction with crab survey data 

 gathered during construction to estimate actual crab 

 losses and to fully define levels and type of mitigation. 

 Beyond these intended uses, the model served to focus 

 concerns about crab impacts, which tended to be some- 

 what ill-defined, onto specific questions of data qual- 

 ity and reliability of predictions, providing all sides a 

 common basis for argument. 



Ackno\A/ledgments 



This work was done under a combination of support 

 from the Seattle District, U.S. Army Corps of Engi- 



