Estimated population size-selectivity curve for the ocean quahog off Iceland in a commercial clam dredge, with approximate 95% confidence intervals shown. 

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... conditions were ideal, and the position of the dredge relative to core samples was relatively certain. The main disadvantage was that no direct information on capture efficiency in deep water (or under difficult sampling conditions) was obtained. The applicability of estimates of capture efficiency to the US fishery is uncertain, and Icelandic estimates should not be used for the US fishery. Estimates of size selectivity from our study are likely robust, in contrast, and applicable to commercial dredges in US water of the same design and similar bar width. NEFSC (2007a, b) considered size selectivity in estimating capture efficiency by excluding the data for relatively small animals. Our study shows that methods that simultaneously estimate both parameters are feasible and probably better, because it is not necessary to discard data. Our approach involves a reason- able number of parameters to estimate (four parameters for ocean quahogs in this study), because capture efficiency replaces the split parameter [ p in Equation (4)] used in the original SELECT model (Millar, 1992). In comparison, the spatial model of Rago et al . (2006) has three or four estimated parameters, but does not estimate size selectivity or include random effects. Using the SELECT model, we were able to estimate correlations among estimates of capture-efficiency and size-selectivity parameters ( Table 3). Of course, our SELECT model and experimental methods would be more difficult to apply for ocean quahogs off the United States, in relatively deep water. The approach used in our study is among the best methods used to estimate capture efficiency for bivalves (Mason et al ., 1979). Another method for estimating dredge efficiency involves comparing the number of shellfish left unharvested in the dredge track with the number of animals captured in the dredge (Caddy, 1968; Medcof and Caddy, 1971; Mason et al ., 1979). Using this method, Medcof and Caddy (1971) estimated E to be 76% for hydraulic dredges taking ocean quahogs. We parameterized the SELECT model in terms of capture efficiency E and additional data ( A , f , and a ), and estimated E rather than p . It may be generally useful to parameterize the SELECT model in this manner because capture efficiency is easy to inter- pret, has a long history in fisheries (Paloheimo and Dickie, 1963), and has a particular importance in assessment of non- mobile benthic invertebrates such as ocean quahogs. Similar approaches have been used elsewhere. For example, the SAS NLMIXED program given (Appendix A.2 of Millar et al ., 2004), which accommodates sampling fractions, and random effects on a and on catchability, could have been used in our analysis with modification and redefinition of terms. The software we used incorporated random effects in capture efficiency and all selectivity parameters, but the only random effects that proved useful were those on a . We used K in Equation (1) to scale the SELECT model to a maximum value of 1.0 at 107.5 mm SL. This technique makes selectivity estimates directly useful in size-structured stock assessment models, where maximum selectivity is 1 by definition. Selectivity is scaled to a maximum of 1 in stock assessment models so that fishing mortality ( F ) and selectivity estimates are unique and not confounded in the product Fs L (Deriso et al ., 1985). Without rescaling, efficiency estimates would be for a hypothetical ocean quahog of infinite size, rather than a realisti- cally large animal. Non-linear models (such as growth curves; Schnute, 1981) can be easier to fit, and estimates may have better statistical characteristics when parameters measure proper- ties in the range of the data. Mixed-effect models, in particular, can be difficult to fit because the number of parameters increases with marginal likelihoods being computed. If L MAX is relatively large, as in our study, the scaling factor K probably has little effect on the estimated selectivity curves beyond potential benefits in character- izing fishing mortality and reducing statistical correlations between estimates of size selectivity and capture efficiency. Estimates of capture efficiency are important in managing fisheries off the United States and Iceland. Ocean quahogs are relatively unproductive and probably sensitive to overharvest that might result from inaccurate estimates of harvest efficiency. Results of our study indicate that capture efficiency is high ( E 1⁄4 0.92) for ocean quahogs in commercial dredges off Iceland. The estimate from our work off Iceland was significantly higher than the distribution of estimates from commercial depletion studies in US waters. There was substantial variability in size selectivity among tows. The estimated population selectivity curve was relatively steep, with L 50 1⁄4 50.5 mm and SR 1⁄4 17.6 mm. Confidence intervals indicate that the estimated population selectivity curve is suffi- ciently precise for use in stock assessment work (Table 4, Figure 3), but statistical precision does not guarantee applicability to a particular situation. Selectivity estimates from our experiments off Iceland are probably applicable to similar commercial dredges of the same design and with similar bar width in the US fishery. Those who use the selectivity or efficiency parameters from our analysis should confirm, however, that the fishing gear involved is similar to our experimental gear. We thank Erlendur Bogason who conducted underwater sampling, Tryggvi Sveinsson, skipper of “Einar ́ Nesi” (EA-49), the crew of the commercial ocean quahog vessel Foss ́ (TF-ZT 2404), Fred Serchuk (Northeast Fisheries Science Center, Woods Hole, MA, USA), anonymous reviewers, and John Walter (Southeast Fisheries Science Center, Miami, FL, USA), who provided useful technical and editorial advice. Anon. 2005. States of marine stocks in Icelandic waters, 2005 / 2006. Prospects for the Quota Year 2005 / 2006. Hafrannso ́ knastofnunin Fj ̈lrit, 121. 182 pp. (in Icelandic, with English abstract). Beukers-Stewart, B. D., Jenkins, S. R., and Brand, A. R. 2001. The efficiency and selectivity of spring-toothed scallop dredges: a comparison of direct and indirect methods of assessment. Journal of Shellfish Research, 20: 121–126. Caddy, J. F. 1968. Underwater observations on scallop ( Placopecten magellanicus ) behaviour and dredge efficiency. Journal of the Fisheries Research Board of Canada, 25: 2123–2141. Cargnelli, L. M., Griesbach, S. J., Packer, D. B., and Weissberger, E. 1999. Essential fish habitat source document: ocean quahog, Arctica islandica , life history and habitat characteristics. NOAA Technical Memorandum, NMFS-NE-148. Deriso, R. B., Quinn, T. J., and Neal, P. R. 1985. Catch-age analysis with auxiliary information. Canadian Journal of Fisheries and Aquatic Sciences, 42: 815–824. Eir ́ksson, H. 1988. Um stofnstærð og veiðim ̈guleika ́ ku ́ fskel ́ Breiðafirði, Faxaflo ́ a og við SA-land. Ægir, 2: 58 –68 (in Icelandic). Fifas, S. 1991. Analyse et mod ́lisation des param `tres d’exploitation du stock du coquilles Saint-Jacques ( Pecten maximus , L) en baie de Saint-Brieuc (Manche Quest, France). PhD thesis, Universite de Bretagne Occidentale, Brest. Fifas, S., and Berthou, P. 1999. An efficiency model of a scallop ( Pecten maximus , L.) experimental dredge: sensitivity study. ICES Journal of Marine Science, 56: 489 –499. Fryer, R. J. 1991. A model of between-haul variation in selectivity. ICES Journal of Marine Science, 48: 281 –290. Hilborn, R., and Walters, C. J. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York. Jones, D. S. 1983. Reading the record of the molluscan shell. American Scientist, 71: 384–391. Kilada, R. W., Campana, S. E., and Roddick, D. 2007. Validated age, growth, and mortality estimates of the ocean quahog ( Arctica islandica ) in the western Atlantic. ICES Journal of Marine Science, 64: 31 –38. Lewis, C. V. W., Weinberg, J. R., and Davis, C. S. 2001. Population structure and recruitment of the bivalve Arctica islandica (Linnaeus, 1767) on Georges Bank from 1980 –1999. Journal of Shellfish Research, 20: 1135–1144. Littell, R. C., Milliken, G. A., Stroup, M. W., Woldfinger, R. D., and Schabenberger, O. 2006. SAS for Mixed Models, 2nd edn. SAS Institute, Cary, NC. Mason, J., Chapman, C. J., and Kinnear, J. A. M. 1979. Population abundance and dredge efficiency studies on the scallop, Pecten maximus (L.). Rapports et Proc `s-Verbaux des R ́unions du Conseil International pour l’Exploration de la Mer, 175: 91 – 96. Medcof, J. C., and Caddy, J. F. 1971. Underwater observations on per- formance of clam dredges of three types. ICES Document CM 1971 / B: 10. Merrill, A. S., and Ropes, J. W. 1969. The general distribution of the surf clam and ocean quahog. Proceedings of the National Shellfish Association, 59: 40 –45. Millar, R. B. 1992. Estimating the size-selectivity of fishing gear by conditioning on the total catch. Journal of the American Statistical Association, 87: 962–968. Millar, R. B., Broadhurst, M. K., and Macbeth, W. G. 2004. Modelling between-haul variability in the size selectivity of trawls. Fisheries Research, 67: 171–181. Millar, R. B., and Fryer, R. J. 1999. Estimating size-selection curves of towed gears, traps, nets and hooks. Reviews in Fish Biology and Fisheries, 9: 89– 116. Murawski, S. A., and Serchuk, F. M. 1989a. Mechanized shellfish har- vesting and its management: the offshore clam fishery of the eastern United States. In Marine Invertebrate Fisheries: their Assessment and Management, pp. 479– 506. Ed. by J. F. Caddy. John Wiley, New York. Murawski, S. A., and Serchuk, F. M. 1989b. Environmental effects of offshore dredge fisheries for bivalves. ICES Document CM 1989 / K: 27. NEFSC. 2000. Ocean quahog. In Report of the 31st Northeast Regional Stock Assessment Workshop (31st SAW): Stock Assessment Review Committee (SARC) Consensus Summary of Assessments. Northeast ...

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... set of all possible fixed-effects models with either one (for all tows) or nine (one for each tow) sets of a , b , D , and h parameters were fitted, and the AIC and BIC statistics were compared. The set included models with asymmetrical selectivity curves (1 or 9 D parameters), and symmetrical selectivity curves with D 1⁄4 0. The simplest model had a single set of a , B , and E parameters, and D 1⁄4 0 (three estimated parameters). The most complicated or “full” model successfully fitted had nine a , b , and h parameters, and a single asymmetry parameter D (28 estimated parameters). Intermediate models had all possible combinations of one and nine a , b , and h parameters (e.g. one b , and nine a and h parameters). Fixed-effects models with multiple asymmetry parameters did not converge. Based on goodness-of-fit statistics (AIC 1⁄4 554.7, BIC 1⁄4 590.6), the best fixed-effects model was symmetrical ( D 1⁄4 0), with different a parameters for each tow, and single b and capture-efficiency parameters ( E 1⁄4 0.92, s.e. 0.076), for a total of 11 estimated parameters. For comparison, selectivity estimates from the full fixed-effects model with 28 estimated parameters were AIC 1⁄4 569.5 and BIC 1⁄4 687.2, and the capture efficiencies were 0.65, 0.74, 0.79, 0.90, 1.00, 0.61, 0.61, 0.68, and 0.79 (order the same as in Table 1), with an average value of E 1⁄4 0.74 (s.e. 1⁄4 0.13). The preferred mixed-effects model was symmetrical ( D 0), with random effects on a ( s 2 v 1⁄4 0.53, s.e. 1⁄4 0.30) only (Table 2). Estimated capture efficiency was E 1⁄4 0.92 (s.e. 1⁄4 0.076) for ocean quahogs of 107.5 mm SL, L 50 1⁄4 70 mm (s.e. 1⁄4 2.7) mm, and SR 1⁄4 18 (s.e. 1⁄4 1.1) mm. There were substantial correlations with absolute value . 0.5 among estimates of the capture- efficiency parameter ( h ) and size-selectivity ( a , B ) parameters (Table 3). However, the correlation between final estimates of size selectivity and capture efficiency were minimized because maximum selectivity was rescaled to 1 in Equation (1). Diagnostic plots showed a generally good model fit, although there was a cluster of positive residuals for ocean quahogs 60 þ mm SL in the fit to data from Tow 1 in Experiment 2. For the preferred model, AIC 1⁄4 568.5 and BIC 1⁄4 569.3, compared with AIC 1⁄4 554.7 and BIC 1⁄4 590.6 for the best fixed-effects model. Therefore, the best fixed-effects model was better based on AIC, whereas the preferred mixed-effects model was better based on BIC. The mixed-effects modelling approach was preferred overall because it provided an estimate of the mean underlying population size-selectivity curve and a formal estimate of the variability in size selectivity among tows (Table 4, Figure 2). We did not use AIC and BIC models to choose between the fixed- and mixed-effects modelling approaches. Our strategy was to choose the best among all possible fixed-effects models based on AIC, then to identify a preferred mixed-effects model that was nearly equivalent in structure (Pinheiro and Bates, 2000). The best fixed-effects and preferred mixed-effects models gave identical estimates of average capture efficiency ( E 1⁄4 0.92), although the standard error was much smaller for the preferred mixed-effects model (0.076; Table 2) than for the best fixed-effects model (0.13). As expected based on other studies, the commercial hydraulic clam dredge used in this study was highly selective towards large ocean quahogs. In dredge catches, 18% of all ocean quahogs were , 60 mm SL (Figure 1). In comparison, 68% of ocean quahogs were , 60 mm SL in diver samples. Length composition data for ocean quahogs from commercial dredges in US studies are similar, with animals , 60 mm SL rarely caught (NEFSC, 2007a). The potential effects of assuming that the mean weight of ocean quahogs in dredge samples during Experiment 1 was 112 g (Table 1) are relatively small. The mean weight is used to compute the sampling fraction f 1⁄4 Nw / C in Equation (4), where N is the number of ocean quahogs sampled from the dredge catch, w 1⁄4 0.112 kg the mean weight, and C the total dredge catch in kilogrammes. The sampling fraction influences capture efficiency but not estimates of size selectivity. Substituting Nw / C for the sampling fraction f in Equation (4) and solving for capture efficiency gives E 1⁄4 paC / ANw (1 2 p ) 1⁄4 K / w , where K is a constant calculated with the data from Experiment 1. This means that a 1% underestimate of mean weight would result in a 1% overestimate of capture efficiency in Experiment 1, and vice versa. Effects on the best estimate of capture efficiency from all three experiments would be smaller. There was substantial variability among tows in the a selectivity parameter ( s 2 v 1⁄4 0.540; Table 2) not apparent to Thorarinsdo ́ ttir and Jacobson (2005). The variance in a caused substantial variability in L among tows (Figure 2). Based on our preferred mixed-effects model (Figure 3), L 50 70 mm and SR 18 (Table 2). In comparison, Thorarinsdo ́ ttir and Jacobson (2005) estimated L 50 1⁄4 72 mm and SR 1⁄4 21 mm by combining all data- sets and using a simple fixed-effects SELECT approach. The estimates ( E 1⁄4 0.92, s.e. 1⁄4 0.076) from our preferred model indicate that capture efficiency was close to 1.0 for ocean quahogs taken by the commercial dredge in our experiments. The 95% confidence interval for h 1⁄4 2 2.45 (s.e. 1⁄4 1.03) from the NLMIXED program is ( 2 4.83, 2 0.0671). Ignoring non-linear effects, an approximate 95% confidence interval for E 1⁄4 1 / (1 þ e h ) is (0.517, 0.992). Capture-efficiency estimates from depletion studies in US waters for Atlantic surfclam (at depths of 21– 41 m; NEFSC, 2007b) and ocean quahogs (35–65 m; NEFSC, 2007a) indicate that capture efficiency is , 1 for commercial clam dredges. Large ocean quahogs displaced by the dredge or observed in the dredge track would be the strongest direct evidence that capture efficiency is , 1. No ocean quahogs . 65 mm SL were found in core samples in the dredge tracks in Experiment 3. However, the number of samples (six cores) was relatively small, and the probability of detecting a large quahog after fishing with a highly efficient ( E 1⁄4 0.92) commercial clam dredge may be low. In contrast, Murawski and Serchuk (1989b) reported ocean quahogs remaining in and displaced laterally up to 5 m away from the dredge track. It seems likely that there is displacement in shallower waters off Iceland too. The preferred mixed-effects estimate for capture efficiency ( E 1⁄4 0.92, s.e. 1⁄4 0.076) was substantially higher than the mean commercial capture-efficiency estimates for ocean quahog off the United States, i.e. E 1⁄4 0.66 (s.e. 1⁄4 0.065) from the spatial model of Rago et al . (2006) and 17 commercial depletion experiments in US waters (see Table A12 of NEFSC, 2007a). However, the 95% confidence interval for capture efficiency in our experiments (0.517, 0.992) contains the mean E 1⁄4 0.66 and lies within the range of individual estimates ( E 1⁄4 0.15–1.0) for ocean quahogs in US waters, demonstrating that statistical difference cannot be shown. Differences in SL do not explain the difference between capture-efficiency estimates from our study and from depletion experiments in US waters. As described above, NEFSC’s (2007a) estimate of E 1⁄4 0.60 (Table A12 of NEFSC, 2007a) is for ocean quahogs ! 90 mm SL that were assumed to have size selectivity ! 0.85. Animals included with shell heights near the cut-off have selectivity near 0.85 and cause negative bias in NEFSC’s (2007a) estimates of capture efficiency. Using the product of capture efficiency (Table 2) and size selectivity (Table 4) to adjust for shell height differences, the capture efficiency for ocean quahogs ! 90 mm SL off Iceland is ! 0.75, still higher than the correspond- ing estimate for US waters. We were not able to evaluate fully the hypothesis that season, habitat, and substratum type explained the differences in capture- efficiency estimates for the United States and Iceland. It is possible, for example, that ocean quahogs in depletion experiments were relatively deep in sediments and hard to sample because of season effects. However, US depletion experiments were conducted from April to September at depths of 35–65 m, where catch rates are normally high (Table A11 of NEFSC, 2007a). Rocks and habitat structure may reduce capture efficiency, but US depletion experiment sites were in sandy habitats where ocean quahogs were abundant, catch rates relatively high, commercial dredges operate efficiently, and where rocks would not be expected to interfere with the depletion ...