TY - JOUR
AU - Keatinge, M.
AB - Expeditious uptake of quad-rig trawling in the economically important Irish fishery for Nephrops norvegicus outpaced technical understanding of this newly introduced gear. The main driver for its introduction is increased catch rates of Nephrops. Higher Nephrops discard rates associated with quad-rig trawling are likely to be problematic under the landing obligation unless size selectivity can be improved. Catch comparison methods are suitable for assessing the performance of fishing gear modifications to reduce discards. Utilizing a quad-rig potentially increases the number of gears that can be included in a catch comparison study to four but current modeling methods are limited to two gears. Our study provides a new general multinomial mixed effects modeling framework that can be applied to two or more gears, elucidates how case-specific and choice-specific covariates may influence catch at length, and facilitates discussion on appropriate gear based management measures. Application of the method to catches from four different cod-end mesh sizes revealed significant effects of carapace length, catch weight and net position, on the numbers of Nephrops retained in each cod-end. Results suggest that management measures which specifically address different catch profiles associated with different numbers of trawling rigs are required to optimize Nephrops size selectivity. Introduction Nephrops norvegicus is a commercially important species distributed throughout the North East Atlantic and Mediterranean Sea. Total landings of 66 500 tonnes in 2010 were predominantly attributed to the United Kingdom (58.1%) followed by Ireland (11.7%) and various other European Union (EU) countries operating in Atlantic and Mediterranean waters (FAO, 2010). More than 95% of EU Nephrops landings are taken by single or multi-rig trawlers which target Nephrops in mixed species fisheries (Ungfors et al., 2013). The high value of Irish Nephrops landings at the first point of sale (estimated at €44.5M in 2014) make it the most commercially important demersal species in Ireland (Cosgrove et al., 2015). The simultaneous use of four trawls, known as quad-rig trawling (Figure 1), is practiced in shrimp trawl fisheries in the United States of America and Australia (e.g. Eayrs, 2012; Broadhurst et al., 2013) and commenced in the Irish Nephrops fishery in October 2012. By the end of 2014, quad-rigs accounted for ∼ 80% of Nephrops landings by the Irish fleet (unpublished data, Marine Institute, Ireland). Figure 1 Open in new tabDownload slide Outline of quad-rig gear including net position in relation to the vessel. Reproduced and edited from Seafish (2010) with permission from Seafish. The main driver for increased uptake of quad-rig trawling is increased catch rates of Nephrops which are likely to result from a wider swept area of seabed compared with single or twin-rig trawling (Montgomerie, 2015). Nephrops catch weights were observed to increase by at least 50% in the North Sea and Celtic Sea in studies comparing quad with twin-rig trawling (Revill et al., 2009; BIM, 2014a). Such increases in efficiency may be beneficial in terms of improving operational performance but could lead to increases in the 15% discard rate of Nephrops below minimum legal or market size in Irish waters (BIM, 2014b; MI, 2014). Bycatch of undersized and non-targeted fish species is also a major issue in Nephrops trawl fisheries (e.g. Catchpole et al., 2005; Catchpole and Revill, 2008; Ungfors et al., 2013; Nikolic et al., 2015). New requirements to restrict discarding of demersal species under Article 15 of EU regulation 1380/2013, the landing obligation, are likely to have negative impacts on the economics of Nephrops fisheries unless species and size-selectivity can be improved. Gear modifications to reduce bycatch are generally assessed using either selectivity (e.g. Millar, 1992; Millar and Walsh, 1992; Millar and Fryer, 1999; McClanahan and Mangi, 2004) or catch comparison experiments (e.g. Sangster and Breen, 1998; Holst and Revill, 2009; Krag et al., 2014; van Marlen et al., 2014). Practical advantages of the catch comparison method include commercial-like performance and handling of the gear. In addition, the ease with which results of catch comparison experiments can be reported and interpreted (Holst and Revill, 2009) is likely to be of particular assistance to the fishing industry in addressing challenges posed by regulation of their catch composition, for example the EU landing obligation. While a limitation of the latter approach is that results can only be used for comparison of the gears included in a given experiment (Frandsen, 2010), utilizing a quad-rig increases the number of gears that can be evaluated in the experiment to four. This facilitates assessment of more concurrent experimental settings and provides substantially more information than twin or single-rig catch comparisons. Development of a Generalized Linear Mixed Model (GLMM) approach to catch comparison provided a statistical comparison of catch at length by two fishing gears, improving the power of catch comparison analyses (Holst and Revill, 2009). Binomial GLMMs are, however, limited to experiments with two response categories. Multinomial logit models generalize binomial logistic regression to multi-category response problems (McCullagh and Nelder, 1989), i.e. those with two or more fishing gears. Here, we develop and test the potential benefits of applying a multinomial modelling approach to a comparison of Nephrops catches in a quad-rig trawl fishery. Our goals are to provide a general statistical framework that incorporates the multivariate response; elucidates how covariates may influence catch at length; and facilitates discussion on appropriate gear-based management measures. Materials and methods Experimental design Data were collected from a catch comparison experiment conducted in the western Irish Sea, ICES sub-area VIIa, between 18 July 2015 and 21 July 2015. The trial vessel quad-rig trawled using a triple warp and centre clump arrangement with 4 identical nets each fitted with a diamond mesh cod-end with nominal mesh sizes of 70, 80, 90, or 100 mm (mesh size descriptors used henceforth). Cod-ends were constructed with single braided 6 mm (nominal) diameter polyethylene twine and were fitted with strengthening bags and lifting straps as is typical in this fishery. Cod-end mesh size was measured with the Omega gauge using the protocol of Fonteyne (2005). Mean cod-end mesh size values (with standard error in brackets) were the following: 70.8 (0.3), 80.8 (0.3), 92.6 (0.2), and 103.0 (0.3) mm. Codend circumference was 120 (70 mm), 120 (80 mm), 100 (90 mm), and 100 (100 mm) meshes which complies with the legal maxima under Regulations (EC) nos. 850/98 and 2602/2001 and conforms to normal fishing practice. Nominal mesh size in the main trawl body was 80 mm, while mesh size in the upper wing ends was 160 mm. Corresponding to the normal fishing practices in the area, square mesh panels of 120 mm mesh size were mounted 9–12 m from the cod-line. Here, “net” describes the whole trawl body. Net positions in relation to the vessel were fixed while cod-end positions were rotated daily to account for potential differences in fishing power without confounding cod-end mesh size and net position effects (Figure 1). Each cod-end was deployed on each net for 3 hauls which equates to one out of four fishing days, with data from 12 consecutive hauls analysed. Further information on the vessel and gear used in the trial is presented in Table 1. Fishing operations approximating normal commercial fishing practice were carried out with haul duration, towing speed, and depth of ground fished averaging: 04:47 h, 3.1 kn, and 48 m respectively. Table 1 Details of fishing vessel and gear. Vessel . Our Lass II (DA261) . Vessel Length Overall (m) 21.7 Engine power (kW) 484 Home port Howth, Ireland Trawl type Quad-rig for Nephrops Trawl manufacturer Pepe Trawls Ltd., Ireland Otter board manufacturer/type Dunbar 7’6” Fishing circle (mm) 380 x 80 Door weight (kg) 492 Clump weight type/weight (kg) Roller/680 Average door to clump spread (m) 34.4 Sweep length (m) 50 + 20 Vessel . Our Lass II (DA261) . Vessel Length Overall (m) 21.7 Engine power (kW) 484 Home port Howth, Ireland Trawl type Quad-rig for Nephrops Trawl manufacturer Pepe Trawls Ltd., Ireland Otter board manufacturer/type Dunbar 7’6” Fishing circle (mm) 380 x 80 Door weight (kg) 492 Clump weight type/weight (kg) Roller/680 Average door to clump spread (m) 34.4 Sweep length (m) 50 + 20 Open in new tab Table 1 Details of fishing vessel and gear. Vessel . Our Lass II (DA261) . Vessel Length Overall (m) 21.7 Engine power (kW) 484 Home port Howth, Ireland Trawl type Quad-rig for Nephrops Trawl manufacturer Pepe Trawls Ltd., Ireland Otter board manufacturer/type Dunbar 7’6” Fishing circle (mm) 380 x 80 Door weight (kg) 492 Clump weight type/weight (kg) Roller/680 Average door to clump spread (m) 34.4 Sweep length (m) 50 + 20 Vessel . Our Lass II (DA261) . Vessel Length Overall (m) 21.7 Engine power (kW) 484 Home port Howth, Ireland Trawl type Quad-rig for Nephrops Trawl manufacturer Pepe Trawls Ltd., Ireland Otter board manufacturer/type Dunbar 7’6” Fishing circle (mm) 380 x 80 Door weight (kg) 492 Clump weight type/weight (kg) Roller/680 Average door to clump spread (m) 34.4 Sweep length (m) 50 + 20 Open in new tab Sampling Random representative subsamples were obtained to estimate Nephrops catch at length for each codend mesh size. Nephrops carapace length was recorded to the nearest mm below using digital callipers connected to a wireless recording system (Cosgrove et al., 2015). Catch weight is known to influence the opening of cod-end meshes and affect cod-end size selection for a range of fish species (e.g. Robertson and Stewart, 1988; Campos et al., 2003; Herrmann and O’Neill, 2005; Herrmann et al., 2006) and the crustacean Aristeus antennatus (Campos et al., 2003). Hence, the total catch weight in each cod-end, “catch weight per cod-end”, was obtained for inclusion as a covariate in the model to determine its potential effect on Nephrops selectivity. Model development In the quad-rig trial, the response Yh,i,j was the count of Nephrops in a given haul (⁠ h=1,…,12 ⁠), carapace length-class (⁠ i=1,…,lh ⁠, where lh is the maximum number of length classes in haul h) and cod-end mesh size (⁠ j=70 mm,80 mm,90 mm,100 mm ⁠). For example, for the 30 mm carapace length bin in haul 5, the response was Yh=5,i=30mm=24, 12, 19, and 20 denoting that 24 Nephrops were counted in the 70 mm cod-end, 12 in the 80 mm, 19 in the 90 mm, and 20 in the 100 mm. The response data are multivariate counts for which interest lies in describing how the relative proportions retained per length-class in each of the cod-ends varies as a function of the cod-end mesh size and other explanatory variables. When trials result in counts per category (cod-end), a starting distribution is the multinomial (Agresti, 2002) with probability mass function pn1,n2,n3,n4=N!n1!n2!n3!n4!π1n1π2n2π3n3π4n4(1) where nj is the count in the jth cod-end and N=∑jnj ⁠; and πj is the probability of outcome j ⁠, ∑jπj=1. Covariates With a multivariate response, covariates can be either case-specific, which are common across categories or alternative-specific (also termed “choice-specific”), which differ for each category (MacFadden, 1973). Case-specific covariates Carapace length is the only case-specific covariate included in the model. A common model for case-specific covariates is the multinomial logit, where the probability of a given outcome depends on values of the case-specific explanatory variables for the h,ith observation: πh,i,j=eαj+βjCLi∑k=14eαk+βkCLi,(2) where CLi is the carapace length. Note that α1 and β1 are fixed at zero so that the first cod-end (70 mm control gear here) is set to the baseline (Greene, 2000). Alternative-specific covariates For a given haul, both catch weight per cod-end and net-position differ by cod-end mesh size and are, therefore, considered alternative-specific covariates. Parameters for alternative specific covariates can be either generic, i.e. common across cod-ends or alternative-specific, i.e., differing across cod-ends (Croissant, 2012). For example, the effect of catch weight per cod-end Wh,j could differ by cod-end mesh size. We, therefore, allowed the effect of catch weight to either differ by cod-end: Wh,jγj or be the same across cod-ends: Wh,jγ ⁠. Net position effects (port inside PI ⁠, starboard inside SI and starboard outside SO ⁠; port outside being the baseline) were modelled using generic coefficients, as to model them with cod-end-specific coefficients would require four parameters per net position, which would use excessive degrees of freedom from a relatively small number of hauls. We thus use a mixture of case-specific and cod-end-specific covariates leading to the fixed effects model (with cod-end-specific weight effects): πh,i,j=eαj+βjCLi+Wh,jγj+δPIPIh,j+δSISIh,j+δSOSOh,j∑k=14eαk+βkCLi+Wh,kγk+δPIPIh,k+δSISIh,k+δSOSOh,k,(3) where, for example, PIh,j=1 if mesh j was in the port inside position in haul h and PIh,j=0 otherwise. Two interactions were included in the model: catch-weight per cod-end and carapace length ρjWh,jCLi ⁠; and net-position and carapace length (e.g., ϕPIPIh,jCLi ⁠). The interaction between catch weight per cod-end and carapace length may capture changes in selectivity owing to mesh opening; whereas the interaction between net position and carapace length may reflect different selectivity over length caused by the whole net excluding the cod-end. Interaction coefficients and variables are not included in (4) for presentation purposes. All continuous covariates were scaled to have mean zero and standard deviation of one prior to fitting, which we found improves hessian matrix estimation. Subsampling offset As the counts are sub-sampled, it is also necessary to include an offset for the proportion of the catch in each cod-end sampled. In a twin-rig (two category) trial the offset is given by lnqt/qc where qt and qc are the proportions of the catch sampled in the test and control, respectively (Holst and Revill, 2009). In the quad-rig trial with the proportion qh,j of the jth cod-end in the hth haul sampled, the vector of offsets is given by Oh,j=0,lnqh,2qh,1,lnqh,3qh,1,lnqh,4qh,1 ⁠, where the first zero comes from lnqh,1qh,1 ⁠. The offset is incorporated as πh,i,j=eαj+βjCLi+Wh,jγj+δPIPIh,j+δSISIh,j+δSOSOh,j+Oh,j∑k=14eαk+βkCLi+Wh,kγk+δPIPIh,k+δSISIh,k+δSOSOh,k+Oh,k.(4) Multinomial random effects Counts for category j in a multinomial have an expected mean Enj=πjN and variance Varnj=πjN1-πj ⁠. However, there is often more variability in the counts than the mean-variance (and covariance) allows for, which is termed overdispersion (Hinde and Demétrio, 1998). This may reflect uncaptured variability or clustering, in particular haul-level variability not accounted for when the observations are treated as independent multinomials. Given that the observations are clustered by hauls, the approach we focus on for accounting for extra-multinomial variability is to include random effects in the model. Multinomial random effects include the baseline category logit random effects model (Hartzel et al., 2001). This model has a multinomial response distribution with the addition of random effects that more explicitly capture the variability attributable to hauls. The random effects multinomial model we test is an extension of (4) given by πh,i,j=eαj+βjCLi+Wh,jγj+δPIPIh,j+δSISIh,j+δSOSOh,j+Oh,j+uh,j∑k=14eαk+βkCLi+Wh,kγk+δPIPIh,k+δSISIh,k+δSOSOh,k+Oh,k+uh,k(5) where the random effects per haul have a multivariate normal distribution uh ∼ MVN0,Σ ⁠, where Σ is the covariance matrix of the random effects. The baseline category random effect is again set to zero, resulting in a trivariate normal distribution for uh ⁠. An arbitrary (six parameter) covariance matrix structure, as recommended in Hartzel et al. (2001) was implemented. The random effect structure we implemented introduces a random intercept for each cod-end and haul log-odds ratio. The model contained conditional logit, multinomial logit, and random effects, which does not facilitate model naming. For simplicity, we refer to the model as a “multinomial mixed effects model”. Model selection and prediction We define the full model as including the main effects (5) and the interactions between: catch-weight per cod-end and carapace length; and net position and carapace length. We fit all valid sub-models of this model with weight effects treated as either generic or cod-end-specific. As the models are estimated via maximum likelihood, we report both Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC). With a large number of samples (which is here the sum of the length bins per haul across all hauls: 338 rows) AIC can tend towards models of increasing complexity whereas BIC penalizes the number of parameters more severely. As the actual number of hauls is limited (12), we selected our final model using a pragmatic compromise between both information criteria. Overall predictions were obtained by setting the net position values in the predicted model matrix to ¼ (Fox and John, 2003). Catch weight per cod-end in the overall predictions was set to the mean per cod-end. Estimation The estimation of the multinomial random effects model necessitates integrating over the random effects to estimate the marginal likelihood. We did not find readily available software to fit Equation (7) we therefore wrote an estimation routine in Template Model Builder (TMB) (Kristensen et al., 2015) and R (R Core Team, 2015). Code for running the multinomial mixed effects model is stored at: https://github.com/mintoc/epif/tree/master/multinomial. Results A total of 15 443 Nephrops were measured during the experiment. Most of the carapace length measurements were in the range of 20–45 mm (Figure 2). Considerable between-haul variability was observed in the proportions retained at length with some hauls displaying consistently lower or higher retention across carapace lengths (Figure 2). The observed proportions at the extremes of the length distribution were more variable as they were derived from fewer observations (e.g. zero or unity proportions in Figure 2). Total Nephrops catch weights were 2093, 1837, 1642, and 1662 kg in the 70, 80, 90, and 100 mm cod-ends, respectively. Nephrops accounted for approximately 40% of the total catch weight across all hauls with the remainder of the catch primarily consisting of flatfish and gadoid species. Figure 2 Open in new tabDownload slide Proportion of Nephrops retained per length-class by diamond mesh size. Hauls are coloured to demonstrate the haul effects. The diameter of the points is proportional to the log base 10 of the raised counts to illustrate where the distribution of the counts. Separate inclusion of each of the main effects (carapace length, net positions, and catch weight per cod-end) resulted in decreases in both the information criterion relative to a model with fixed proportions (Table 2, models 2–4). Model 10 included the main effects of carapace length and catch weight per cod-end and their interaction had the lowest BIC, whereas model 13 including, in addition, net position effects and the interaction between net position and carapace length had the lowest AIC of those models treating the catch weight per cod-end effect as generic (Table 2, models 1–13). Including catch weight per cod-end effects as cod-end specific was not supported in any of the models, as judged by BIC (Table 2, models 14–21). The most complicated model was chosen by AIC (model 21). However, the model required 26 degrees of freedom from 12 hauls, which was deemed excessive. In addition, the parameter estimates of the catch weight per codend by carapace length effects for this model did not make sense. We, therefore, decided to treat the catch-weight per cod-end effect as generic and chose model 13 as the “best fitting” model used for inference. Table 2 Multinomial mixed effects model fit summaries. Model . CL . NP . W . WxCL . NPxCL . W alternative . Log likelihood . Model df . AIC . BIC . 1 −2106.85 9 4231.7 4318.51 2 + −2084.61 12 4193.22 4308.97 3 + −2075.63 12 4175.26 4291.01 4 + −2080.57 10 4181.14 4277.6 5 + + −2053.3 15 4136.6 4281.29 6 + + −2058.25 13 4142.5 4267.9 7 + + −2067.25 13 4160.5 4285.9 8 + + + −2044.49 16 4120.98 4275.32 9 + + + −2021.92 18 4079.84 4253.47 10 + + + −2039.97 14 4107.94 4242.99 11 + + + + −2013.11 19 4064.22 4247.5 12 + + + + −2026.28 17 4086.56 4250.54 13 + + + + + −2009.69 20 4059.38 4252.3 14 + + −2072.33 13 4170.66 4296.06 15 + + + −2049.76 16 4131.52 4285.86 16 + + + −2056.11 16 4144.22 4298.56 17 + + + + −2033.1 19 4104.2 4287.48 18 + + + + −2021.58 20 4083.16 4276.08 19 + + + + + −2001.13 22 4046.26 4258.47 20 + + + + + −2004.9 23 4055.8 4277.66 21 + + + + + + −1990.62 26 4033.24 4284.04 Model . CL . NP . W . WxCL . NPxCL . W alternative . Log likelihood . Model df . AIC . BIC . 1 −2106.85 9 4231.7 4318.51 2 + −2084.61 12 4193.22 4308.97 3 + −2075.63 12 4175.26 4291.01 4 + −2080.57 10 4181.14 4277.6 5 + + −2053.3 15 4136.6 4281.29 6 + + −2058.25 13 4142.5 4267.9 7 + + −2067.25 13 4160.5 4285.9 8 + + + −2044.49 16 4120.98 4275.32 9 + + + −2021.92 18 4079.84 4253.47 10 + + + −2039.97 14 4107.94 4242.99 11 + + + + −2013.11 19 4064.22 4247.5 12 + + + + −2026.28 17 4086.56 4250.54 13 + + + + + −2009.69 20 4059.38 4252.3 14 + + −2072.33 13 4170.66 4296.06 15 + + + −2049.76 16 4131.52 4285.86 16 + + + −2056.11 16 4144.22 4298.56 17 + + + + −2033.1 19 4104.2 4287.48 18 + + + + −2021.58 20 4083.16 4276.08 19 + + + + + −2001.13 22 4046.26 4258.47 20 + + + + + −2004.9 23 4055.8 4277.66 21 + + + + + + −1990.62 26 4033.24 4284.04 Explanatory variables are abbreviated: carapace length (CL); net positions (NP); catch weight per cod-end (W). W alternative denotes whether the catch weight effects were alternative specific (i.e., differ by cod-end), which are those models below the horizontal line. A “+” sign denotes inclusion in the model. The model degrees of freedom (Model df) includes 6 parameters parameterizing the trivariate covariance matrix of the random effects for all models. Final selected model is shaded. Open in new tab Table 2 Multinomial mixed effects model fit summaries. Model . CL . NP . W . WxCL . NPxCL . W alternative . Log likelihood . Model df . AIC . BIC . 1 −2106.85 9 4231.7 4318.51 2 + −2084.61 12 4193.22 4308.97 3 + −2075.63 12 4175.26 4291.01 4 + −2080.57 10 4181.14 4277.6 5 + + −2053.3 15 4136.6 4281.29 6 + + −2058.25 13 4142.5 4267.9 7 + + −2067.25 13 4160.5 4285.9 8 + + + −2044.49 16 4120.98 4275.32 9 + + + −2021.92 18 4079.84 4253.47 10 + + + −2039.97 14 4107.94 4242.99 11 + + + + −2013.11 19 4064.22 4247.5 12 + + + + −2026.28 17 4086.56 4250.54 13 + + + + + −2009.69 20 4059.38 4252.3 14 + + −2072.33 13 4170.66 4296.06 15 + + + −2049.76 16 4131.52 4285.86 16 + + + −2056.11 16 4144.22 4298.56 17 + + + + −2033.1 19 4104.2 4287.48 18 + + + + −2021.58 20 4083.16 4276.08 19 + + + + + −2001.13 22 4046.26 4258.47 20 + + + + + −2004.9 23 4055.8 4277.66 21 + + + + + + −1990.62 26 4033.24 4284.04 Model . CL . NP . W . WxCL . NPxCL . W alternative . Log likelihood . Model df . AIC . BIC . 1 −2106.85 9 4231.7 4318.51 2 + −2084.61 12 4193.22 4308.97 3 + −2075.63 12 4175.26 4291.01 4 + −2080.57 10 4181.14 4277.6 5 + + −2053.3 15 4136.6 4281.29 6 + + −2058.25 13 4142.5 4267.9 7 + + −2067.25 13 4160.5 4285.9 8 + + + −2044.49 16 4120.98 4275.32 9 + + + −2021.92 18 4079.84 4253.47 10 + + + −2039.97 14 4107.94 4242.99 11 + + + + −2013.11 19 4064.22 4247.5 12 + + + + −2026.28 17 4086.56 4250.54 13 + + + + + −2009.69 20 4059.38 4252.3 14 + + −2072.33 13 4170.66 4296.06 15 + + + −2049.76 16 4131.52 4285.86 16 + + + −2056.11 16 4144.22 4298.56 17 + + + + −2033.1 19 4104.2 4287.48 18 + + + + −2021.58 20 4083.16 4276.08 19 + + + + + −2001.13 22 4046.26 4258.47 20 + + + + + −2004.9 23 4055.8 4277.66 21 + + + + + + −1990.62 26 4033.24 4284.04 Explanatory variables are abbreviated: carapace length (CL); net positions (NP); catch weight per cod-end (W). W alternative denotes whether the catch weight effects were alternative specific (i.e., differ by cod-end), which are those models below the horizontal line. A “+” sign denotes inclusion in the model. The model degrees of freedom (Model df) includes 6 parameters parameterizing the trivariate covariance matrix of the random effects for all models. Final selected model is shaded. Open in new tab Case-specific parameter estimates were the log-odds ratios relative to the 70 mm (Table 3, rows 1 and 2). The baseline position was the port outside position and the intercept parameters implied that at mean catch weight per cod-end and mean carapace length, similar proportions of Nephrops were found across the cod-ends in the port outside position (Table 3, intercept). The log-odds carapace length slopes increased across cod-end mesh sizes reflecting that, for example, a bigger difference in the proportions retained between the 100 mm and the 70 mm than the 80 mm and the 70 mm (Table 3, row 2). The port inside effect was significantly negative (Table 3, row 3) implying a lower fishing power for this position in this trial. The starboard inside position also fished lower than the port outside position (Table 3, row 4), whereas the starboard outside had a similar retention to the port outside position (Table 3, row 5). Table 3 Best fitting model (model 13) parameter estimates table. Parameter . 70 mm . 80 mm . 90 mm . 100 mm . Intercept αj 0 0.01 (0.078) −0.079 (0.105) −0.071 (0.093) Carapace length βCL,j 0 0.094 (0.046) 0.196 (0.05) 0.21 (0.048) Port inside δPI −0.498 (0.091) Starboard inside δSI −0.16 (0.071) Starboard outside δSO −0.036 (0.084) Cod-end weight γ 0.204 (0.058) PI x CL ϕPI 0.195 (0.058) SI x CL ϕSI −0.029 (0.046) SO x CL ϕSO 0.165 (0.045) W x CL ρ −0.075 (0.029) Parameter . 70 mm . 80 mm . 90 mm . 100 mm . Intercept αj 0 0.01 (0.078) −0.079 (0.105) −0.071 (0.093) Carapace length βCL,j 0 0.094 (0.046) 0.196 (0.05) 0.21 (0.048) Port inside δPI −0.498 (0.091) Starboard inside δSI −0.16 (0.071) Starboard outside δSO −0.036 (0.084) Cod-end weight γ 0.204 (0.058) PI x CL ϕPI 0.195 (0.058) SI x CL ϕSI −0.029 (0.046) SO x CL ϕSO 0.165 (0.045) W x CL ρ −0.075 (0.029) Standard errors are in parentheses. Intercept and baseline carapace length effects pertains to the port outside net position. Open in new tab Table 3 Best fitting model (model 13) parameter estimates table. Parameter . 70 mm . 80 mm . 90 mm . 100 mm . Intercept αj 0 0.01 (0.078) −0.079 (0.105) −0.071 (0.093) Carapace length βCL,j 0 0.094 (0.046) 0.196 (0.05) 0.21 (0.048) Port inside δPI −0.498 (0.091) Starboard inside δSI −0.16 (0.071) Starboard outside δSO −0.036 (0.084) Cod-end weight γ 0.204 (0.058) PI x CL ϕPI 0.195 (0.058) SI x CL ϕSI −0.029 (0.046) SO x CL ϕSO 0.165 (0.045) W x CL ρ −0.075 (0.029) Parameter . 70 mm . 80 mm . 90 mm . 100 mm . Intercept αj 0 0.01 (0.078) −0.079 (0.105) −0.071 (0.093) Carapace length βCL,j 0 0.094 (0.046) 0.196 (0.05) 0.21 (0.048) Port inside δPI −0.498 (0.091) Starboard inside δSI −0.16 (0.071) Starboard outside δSO −0.036 (0.084) Cod-end weight γ 0.204 (0.058) PI x CL ϕPI 0.195 (0.058) SI x CL ϕSI −0.029 (0.046) SO x CL ϕSO 0.165 (0.045) W x CL ρ −0.075 (0.029) Standard errors are in parentheses. Intercept and baseline carapace length effects pertains to the port outside net position. Open in new tab The main effect of catch-weight per cod-end was positive (Table 3, row 6). This effect was not surprising in that there was a strong correlation (0.75) between the Nephrops catch weight per cod-end and (total) catch weight per cod-end. The interaction between catch weight per cod-end and carapace length was, however, negative (Table 3, row 10) indicating that the carapace length slope decreases with increasing catch weight per cod-end. The interactions between net position and carapace length (Table 3, rows 7–9) indicated that retention increased over carapace length in the port inside and starboard outside positions. Given the finding that the port inside had overall lower retention (Table 3, row 3), the interaction implied that this net retained lower numbers of smaller Nephrops, whereas the starboard inside net had lower retention over all lengths, and the starboard outside had increased retention over length relative to the port outside. From the best fitting model the estimated covariance and correlation matrices of the random effects were Σ^= (0.060.070.060.070.110.060.060.060.08) and corr(u)^= (10.810.880.8110.630.880.631), respectively. The magnitude of the variance of the random effects (e.g., Σ^1,1=0.06 ⁠) implied that having accounted for the fixed effects of carapace length, net position, and catch weight per cod-end (Table 3), the expected proportions varied in extremes by ±12% by haul (inverse logit of 95% intervals −0.5,  +0.5). Typically the variability was lower than this (Figure 3). The relatively low inter-haul variability estimated together with the model comparisons (Table 2) highlighted that a considerable amount of between-haul variability was captured by the fixed effects of net position and catch-weight per cod-end though some inter-haul variability remains, which was captured by the random effects (Figures 3 and 4). Dropping the random effects from model 13 resulted in a large decrease of the log likelihood to −2161.12, which when tested on a Chi-squared distribution with 6 degrees of freedom (random effect covariance matrix parameters) was highly significant in favour of the inclusion of the random effects. Figure 3 Open in new tabDownload slide Estimated trivariate random effects (log-odds ratios to the baseline 70 mm case: uh in (6) by haul. Figure 4 Open in new tabDownload slide Fitted multinomial mixed effects proportions by haul. Solid and dashed lines represent the predictions from the best fitting model with and without random effects respectively. The by-haul predictions fitted the data well in both the fixed effects and random effects models (Figure 4), although the random effects models expectedly fitted some haul and mesh combinations better (e.g., 70 mm and 80 mm in hauls 3 and 5). Overall predictions showed a higher proportion of small Nephrops retained in the 70 mm, with a decrease in the proportion of smaller Nephrops retained as cod-end mesh size increases (Figures 5 and 6). In addition, the slope of the proportion retained over length classes went from negative in the 70 mm and the 80 mm to positive in the 90 mm and the 100 mm (Figure 5). Higher proportions of larger Nephrops were retained in the 90 mm and 100 mm cod-ends (Figure 5). Figure 5 Open in new tabDownload slide Overall predicted proportions at length. Solid and dashed lines represent the mean and 95% confidence intervals on the mean respectively (see text for discussion on confidence intervals in this setting). Figure 6 Open in new tabDownload slide Pairwise odds ratios obtained by setting cod-end mean weights and equal position effects. 95% confidence intervals are pointwise Bonferroni corrected for the six comparisons made. The estimated confidence intervals on the mean proportions were narrow (Figure 5) reflecting the number of observations contributing to the mean with the considerable between-haul variability accounted for via the fixed and random effects (Figure 4). Note that confidence intervals on proportions should not be interpreted separately as the proportions at a given length retained in the four test cod-ends sum to one. Based on Bonferonni corrections to the confidence intervals, the catch ratios between the pairs of cod-ends (inter-mesh odds ratios) showed: uncertain differences of the 70–80 mm, no difference between the 90 mm and the 100 mm and larger differences among the others (Figure 6). The uncertain differences observed between the 70 mm and the 80 mm could be further investigated by removing non-significant parameter estimates from the best fitting model (Table 3). Discussion Our study developed a multinomial mixed effects model that included case-specific and alternative-specific covariates, cod-end specific sub-sampling, and multivariate random haul effects. The method is generally applicable to multi-gear catch comparison studies, as demonstrated in our analyses of a quad-rig trawling Nephrops fishery. Here, we discuss the model developments, main findings of the quad-rig application and fishery implications. Model developments Examples of the application of multinomial models to fisheries include analysis of egg stages (Stratoudakis et al., 2006; Ibaibarriaga et al., 2007), comparisons of age-length keys (Gerritsen et al., 2006), fleet behaviour (Ward and Sutinen, 1994), and discard survivability (Benoit et al., 2010). We extended the traditional multinomial logit model to include the specific requirements of a catch-comparison trial such as alternative-specific covariates (e.g. catch weight per cod-end) multiple sub-sampling ratios and haul-level random effects (to account for over-dispersion). The method is applicable to other catch comparison situations where multiple gears are tested concurrently. By incorporating these effects, we have developed a general multinomial modelling framework with applications beyond the field of fisheries science. Hartzel et al. (2001) conceptually develop the baseline logit multinomial random effects model but, to our knowledge, no readily available open source code exists for fitting this model. The use of TMB greatly facilitated model development as it converges quickly for the relatively complicated mixed effects models implemented here. Strong correlations observed in the random effects may result from the order the nets are hauled aboard for this trial but would require further investigation. The estimated random effects were odds ratios relative to the baseline 70 mm cod-end (Figure 3). Using another mesh-size baseline would imply different random effects and covariance matrices but the model would structurally be the same, given the implementation of an unconstrained covariance matrix (Hartzel et al. 2001). Future model developments A linear carapace length effect was fitted (Table 2). However, this assumption may result in an over-influence of smaller and medium carapace lengths on the proportions retained at larger lengths. Quadratic effects (results not shown) did not improve the model fit but they may not be supported at larger lengths simply because there are fewer observations. As a result, the fits for larger lengths should not be over-interpreted. Alternative approaches such as fixing the proportions above a certain carapace length to be equivalent or implementing smooth non-parametric curves could be used to address local changes more adequately (Fryer et al., 2003). The random effects implemented are additive random intercepts on the linear predictor scale, which alters the baseline proportion for each haul and cod-end mesh size (Figures 3 and 4). It is common in other settings to include random effects on additional parameters, e.g. carapace length effect. These can be incorporated into the present framework by implementing a 6×6 covariance matrix with the top-left 3×3 block representing the intercept and the bottom right 3×3 block representing the carapace length random effects covariance. A completely unconstrained covariance matrix would require 12 additional parameters (18 covariance parameters in total). However, it may be useful to only allow for covariance in the random intercept and random slope for a given odds ratio, restricting the intercept and slope random effects for different odds ratios to be independent. With each additional random parameter, the number of unconstrained covariance parameters triples relative to a single random parameter; therefore, care needs to be taken on what parameters are allowed to vary given the logistical constraints on the number of hauls in a trial. Using a Dirichlet-multinomial distribution (Thorsén, 2014) offers an alternative method for modelling count data with a response with two or more categories. The Dirichlet-multinomial model is a multivariate extension of the beta-binomial distribution and is used in cases where data exhibit variance greater than expected in a multinomial. Over dispersion in the Dirichlet-multinomial is accounted for by an additional set of parameters for the baseline category, allowing for an additional variability in the response counts (Mosimann, 1962; Thorsén, 2014). We chose to develop the multinomial mixed effects model rather than apply the Dirichlet-multinomial model, as a key component of over-dispersion here is likely at the haul-level. A combined Dirichlet-multinomial mixed effects model could be developed in the future. Covariate effects Carapace length, catch weight per cod-end and net position significantly affected the numbers of Nephrops retained in the different cod-end mesh sizes (Table 2). The significant effect of carapace length, and fewer smaller Nephrops retained as mesh size increased (Figures 5 and 6), corroborates the results of previous studies in the Irish Sea and Bay of Biscay (Briggs et al., 1999; Nikolic et al., 2015). This is also consistent with previous findings that increases in diamond cod-end mesh size do not generally affect the selection range of Nephrops, but do affect Nephrops catch at length (Catchpole and Revill, 2008). The significant negative interaction between catch weight per cod-end and carapace length confirms the influence of this covariate on retention of Nephrops norvegicus. The negative interaction is consistent with a moderation of the effect of catch weight per codend on carapace length as catch weight increases. Nephrops escapement is known to take place along the entire length of the trawl (Hillis and Earley, 1982). Catch weight is likely to affect mesh openings and Nephrops escapement in the codend, but may also affect whole-trawl Nephrops selectivity. Whatever the underlying process, the significant effect of catch weight on catch at length highlights the importance of accounting for this covariate in designing experiments or developing management measures for vessels targeting Nephrops with different gears and different catch profiles. Net position was an important variable explaining a considerable amount of inter-haul variability (Table 2). Position effects within a quad-rig likely result from differences in fishing power caused by variable net geometry associated with asymmetry of warps, sweeps, and doors. Net geometry is assumed to govern gear performance and fishing mortality for Nephrops (Sangster and Breen, 1998; Eigaard et al., 2011). Failure to address this issue could result in confounding mesh effects with position effects. We found that the simplest way to deal with these effects is to rotate the gears so that each gear has multiple opportunities to fish in each position. Logistical constraints limit the number of rotations but we found a rotation each night to be a feasible compromise between logistics and position mitigation. Assessment of position effects on quad-rigs using data from gear monitoring sensors (Sangster and Breen, 1998) or side-scan sonar (Lucchetti and Sala, 2012) could further assist in understanding this issue. The model allows for additional covariates to be included. Variables we did not incorporate in the model include haul duration, time of day, cod-end circumference, and other measurements of gear geometry, and environmental parameters such as depth, tidal effects, sea state, among others. The effects of these variables will be captured to some extent by the random effects estimated in the model (Figure 3). They could also be included as fixed effects but the number of covariates that can be included is limited by the number of tows and meshes in the trial (i.e. available degrees of freedom). Fishery implications The finding that catch weight influences codend catch at length for Nephrops has important implications for the development of gear specific management measures in Nephrops fisheries. Reductions in total catches of up to 61% of cod, 38% of haddock, and 59% of whiting were observed in trials which compared catches in quad and twin-rig trawls in the Celtic and North Seas. These reductions could be associated with lower headline height and altered sweep arrangements (Revill et al., 2009; BIM, 2014a). Significantly increased proportions of small Nephrops and cod were retained in the quad-rig compared with the twin-rig in the Celtic Sea study (BIM, 2014a). Results of the current and aforementioned studies suggest that lower catch weight associated with reduced fish catches in quad-rig trawling is likely to increase retention of smaller Nephrops compared with single or twin-rig trawling. Hence, management measures which consider the different catch profiles of single, twin, and quad rig trawling are required in Nephrops fisheries to optimize bycatch reduction and quota utilization under the EU landing obligation. An increase in minimum cod-end mesh size would make sense economically and biologically. In the context of the landing obligation, economic modelling of an increase in minimum cod-end mesh size from 70 mm to 80 mm on a quad-rig vessel, demonstrated that reduced catches of small Nephrops in the larger mesh size provided more opportunity to catch increased quantities of larger more valuable Nephrops. This lead to marginal increases in vessel profitability over the course of a fishing season (Cosgrove et al., 2015). Our finding that larger cod-end mesh sizes retained fewer small Nephrops provides firm biological justification for a mesh size increase. The confirmed effect of catch weight on codend catch at length for Nephrops suggests that any increase in minimum cod-end mesh size should take account of the different catch profiles associated with different numbers of trawling rigs. Such an approach would effectively reduce catches of undersize Nephrops, boost sustainability of the Nephrops stock, assist fishers in meeting EU landing obligation requirements, and optimize economic returns from the Nephrops fishery. Acknowledgements We are grateful to the owners Ivan and Eamon Wilde, skipper, and crew of MFV Our Lass II for their assistance during the cod-end mesh size gear trial. Thanks to Peter Tyndall, BIM, and Jennifer Doyle, Marine Institute, for technical advice, and Colm Lordan, Marine Institute for information on quad-rig activity in Irish waters. We especially thank Rob Fryer (Marine Scotland Science) and an anonymous reviewer for comments that greatly improved the methods, interpretation, and presentation. 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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. © International Council for the Exploration of the Sea 2017.
TI - A general catch comparison method for multi-gear trials: application to a quad-rig trawling fishery for Nephrops
JF - ICES Journal of Marine Science
DO - 10.1093/icesjms/fsw236
DA - 2017-05-01
UR - https://www.deepdyve.com/lp/oxford-university-press/a-general-catch-comparison-method-for-multi-gear-trials-application-to-cSEjtgF0MI
SP - 1458
EP - 1468
VL - 74
IS - 5
DP - DeepDyve
ER -