A framework for the standardisation of tropical tuna purse seine CPUE: application to the yellowfin tuna in the Indian Ocean

We revised the existing framework for tuna CPUE standardisation in light of the increasing literature that advocates the use of mixed effects models to account for the characteristics of logbook data. We apply the framework on yellowfin tuna (YFT) from the Indian Ocean, caught by the purse seine EU fleet (Spain and France) from 1984 to 2015. We used a comprehensive list of candidate covariates, including nonconventional covariates, and run exploratory models to assess the contribution of each covariate. Due to the large number of covariates, the lasso – least absolute shrinkage and selection operatormethod was applied for data mining and model selection purposes. The results are two standardised YFT CPUE time series for the period 1984-2015, one for large fish caught in free-school related sets, and one for mainly juveniles caught in floating object related sets. Issues on the usefulness of highly aggregated data (low resolution: annual and fleet wide) is discussed along with the need for more detailed information on the use of dFADs, preferably at the level of a fishing trip. Introduction This paper is the result of the Workshop for the development of indices of abundance for the EU tropical tuna purse seine fishery, held in Fuengirola, Spain, on July 2016. During the workshop, experts on tropical tuna fisheries set the foundations for the development of a CPUE standardisation framework for the EU tuna purse seine fleet. Indian Ocean yellowfin tuna was prioritised as a case study, due to its imminent stock assessment. The framework is based on the use of generalised linear mixed models, instead of the generalised linear models used to date. CPUE calculation and standardisation primarily uses data from logbooks. The inclusion of random effects in the standardisation model allows us to take into account the special characteristics of fisheries dependent data: i. Logbook data are longitudinal (Laird and Ware, 1982; Liang and Zeger, 1986), i.e. several observations are made over time on the same subjects, here the subject being the vessel and/or the skipper. ii. In contrast to the set sampling trajectory of a survey vessel, fishing vessels follow specific strategies and tend to aggregate in areas where fish abundance is high and stable. Thus, areas assumed to be poorer in abundance are not “sampled” by the fishing vessels, and the sampling area varies from one year to the next (Cao et al., 2011). iii. Closures of Exclusive Economic Zones (EEZs) to the fishery have been observed. Certain EEZs are avoided for other reasons, such as piracy. Hence, the sampling of EEZs is not a random process, but fishing sets are grouped within each EEZ (Fonteneau et al., 2016). iv. Fishing sets extend over different biogeographical provinces (Longhurst, 2010). We can assume that sets taking place in the same province are not independent observations. In this case the grouping factor is treated as a random effect (Snijders, 2011). The proposed framework includes the collation of a comprehensive list of new non-conventional variables as potential covariates in the standardisation model; these variables are possible drivers of catchability: fishing strategies technological advances, and environmental factors. The high value on the acquisition of data on covariates on fishing technology at a highly disaggregated scale has already been highlighted by (Bishop, 2006). The covariates constitute factors that affect fishing strategy and variables that describe changes in fishing technology. In the case of the European tropical tuna purse seine fishery attempts have been made to collate non-conventional information, specifically for dFAD-fishing, and to integrate it into the CPUE standardization procedure (Gaertner et al, 2016). The number of covariates and estimated coefficients can be significant (> 50, as categorical variables may have several levels) and is increasing as new fishing strategies and technologies evolve and more comprehensive data collection protocols are developed. The increasing number of covariates makes model selection a tedious and computationally intensive task. Stepwise selection becomes impossible due to the great number of models one needs to test (for 10 covariates there is 45 different combinations pairs of covariates at the 1 step of the forward stepwise regression). Furthermore, stepwise regression cannot deal with collinearity. Statistical procedures of model selection were adapted to the large number of available explanatory variables and the hierarchical structure of the data. For prediction accuracy and interpretation purposes we opt for the lasso – for least absolute shrinkage and selection operatormethod for data mining (to discover relationships between CPUE and explanatory variables) and model selection, within a parsimonious approach (Tibshirani, 1996). This approach has been used in the dFAD CPUE standardization of bigeye in the Indian Ocean (Katara et al, 2016). The selection of the final model is based primarily on expert opinion and secondarily on the results derived from the lasso regression and modelling experiments, pertaining to the inclusion/ exclusion of candidate covariates, and the examination of the model estimates and the explained deviance. With these steps we conform to the suggestions given by (Bishop, 2006), and aim for realistic model fits, paying relatively less attention to precision or maximizing explained variance, while adopting modern statistical methods to overcome known issues in fisheries-dependent data. Material and Methods The analysis was based on logbook data from two of the main fleets: the French and Spanish purse seiners targeting tuna in the Indian Ocean. The database was subset into 2 datasets: i. free-school sets, which capture large yellowfins and ii. floating object-related sets whose yellowfin component is mainly composed by juveniles. CPUE was calculated and standardised for each dataset. For details on the size frequencies caught per set type see annex I. The logbook database is managed by the Tuna Observatory of IRD and by the IEO), for the French and Spanish fleets, respectively. Complementary data from other sources were compiled, to be used as covariates in the CPUE standardization models. A full list of the covariates and their sources is given in table 1. CPUE was defined as the catch per set. Due to the zero-inflated nature of the response variable, a delta log-normal model was applied. The model comprises 2 sub-models: i. A binomial model that standardises the probability of a positive set, and ii. A lognormal model that standardises catch per positive set. The candidate covariates in table 1 were considered fundamental by the working group of experts that took part in the workshop on the development of indices of abundance for the EU tropical tuna purse seine fishery in Fuengirola, Spain. However, some variables were collinear or interacting, and overfitting was examined. The model selection exploration began by applying the lasso regression (GLM) in search of a simple model with high goodness of fit, but most importantly a model that accounts for changes in catchability. Variables with regression coefficients greater than 0 are selected and exploratory models are built based upon this original selection. In cases where the number variables selected in lasso regression was too large to allow for an ordinary least-squares (OLS) regression, a stricter regression coefficient cut off point was chosen. The basis for this choice was to balance the ratio of the number of necessary variables to the number of observations in the data. To test for this we run models with different numbers of variables based on different regression coefficient cut-off points. In conjunction with lasso regression we run some simple models and examined changes in the model fit, attributed to adding or excluding covariates. Such exploratory models are recommended when the inclusion of a variable is dubious. The final model was based on the results of these data mining techniques, on the hierarchical structure of the data and on prior knowledge of the fishery and its evolution in time. From the full list of covariates discussed by the working group in Fuengirola, Spain, some were ignored due to their low resolution and high collinearity. Annual time series of covariates that refer to whole fleets proved problematic, causing rank deficiency. The phenomenon is common when the variance of the predictor is inadequate for model estimation, i.e. there is no signal reflected in the dependent variable . In the binomial models, searching time was added as an offset. Lasso regression estimates can be biased; as recommended by (Friedman et al. (2009); Tibshirani ( 2011, 1996), after model selection, the final models were estimated using OLS. Predictions were made with lsmeans (Lenth, 2014). Memory leakage issues were dealt with by manually constructing the data reference grid (an array of factor and predictor levels, as described in Lenth, 2014) upon which predictions in lsmeans are based. Confidence intervals were calculated with the delta method (Sobel, 1982; Casella and Berger, 2002). The analysis was performed in R.