Using external information and GAMs to improve catch-at-age indices for North Sea plaice and sole

G. J. Piet 0 0 G. J. Piet: Netherlands Institute for Fisheries Research , PO Box 68, 1970 AB IJmuiden , The Netherlands External information and Generalized Additive Models (GAMs) are used to improve the indices provided by the BTS survey for the stock assessment of plaice and sole. These ancillary data consist of the following variables: Depth, Sediment grain-size, Surface temperature, Latitude, Longitude, Time of day and Day of year. Three approaches that predict the catches of four age-groups of plaice (1-4+) and sole (1-4+) were studied: (1) a ''basic'' GAM that incorporated the external variables; (2) A GAM where the catches of fish species other than the two target species were represented by three Principal Components (PC's) and added to the ''basic'' model; (3) The predictions of the basic model were applied to a regular grid covering a slightly expanded index area. The results are validated using two criteria: one is that of internal consistency, the other compares the estimates with the results of the stock assessments of plaice and sole without the tuning of the BTS index. Both in terms of internal consistency and correlation with the stock assessments all three methods involving GAMs performed better than the actual observed catches. The approach where the predictions of the basic model were applied to a grid performed best of all for both plaice and sole. 1054-3139/02/060624+09 $35.00/0 - Introduction Several sources of information are used for the tuning of the stock assessment of plaice and sole: data from commercial fisheries (UK and Netherlands) as well as two research vessel surveys (e.g. Beam Trawl Survey, BTS and Sole Net Survey, SNS) (ICES, 2000). The primary objective of these surveys is to provide indices of the year-class strength of the younger age-groups (14+) of plaice and sole. During these surveys, catches of these two target species are recorded as are those of other fish species as well as several physical and chemical variables encountered at each site. In a survey, the catches depend on the behaviour and distribution of the species which in turn may be determined by environmental factors such as water depth, salinity, sediment granulometric characteristics, light or food availability (Rogers, 1992; Gibson, 1994, 1997). Generalized Additive Models (GAMs) have previously been applied to relate distributions of abundance from fish survey data to locational and environmental covariates (Swartzman et al., 1992, 1994, 1995; Augustin et al., 1998; Borchers et al., 1997). In the present study ancillary data are incorporated as covariates in GAMs to improve the catch-at-age indices provided by the BTS survey for the stock assessment of plaice and sole. The objectives were to (1) compare several methods that incorporate external data using GAMs and (2) determine whether this approach helps in improving the indices required for the stock assessments of plaice and sole. For this, the catches per haul of four age-groups (14+) of plaice and sole are predicted using GAMs and the results are evaluated using two criteria: one is that of internal consistency, the other compares the estimates with independent data (i.e. the results of the stock assessments of plaice and sole without the tuning of the BTS index). Material and methods The BTS survey was initiated in 1985 and is carried out in international cooperation covering both inshore and BTS index area offshore areas throughout the North Sea, Channel and western waters of the UK. The survey is conducted over five weeks during August and September. The fishing gear used to collect data for the North Sea plaice and sole indices is a pair of 8 m beam trawls rigged with nets of 120 mm and 80 mm stretched mesh in the body and 40 mm stretched mesh cod-ends. A total of eight tickler chains are used, four mounted between the shoes and four from the groundrope. The survey was designed to take between one and three hauls per ICES rectangle depending on the rectangle. The stations are allocated over the fishable area of the rectangle on a pseudorandom basis to ensure that there is a reasonable spread within each rectangle. No attempt is made to return to the same tow positions each year. Towing speed is 4 knots for a tow duration of 30 min and fishing occurs during daylight only. From the start of BTS in 1985 until present the same research vessel (RV Isis) was used. At each station all fish species are measured and recorded together with physical/chemical variables such as surface and bottom temperature, depth and position in latitude and longitude. For the present study 1155 hauls within and just outside the expanded Index area were used (Figure 1). To model the catches of plaice and sole in the BTS, Generalized Additive Models (GAMs) were applied. GAMs are an extension of Generalized Linear Models (GLMs) because they allow nonparametric functions to estimate the relationship between the response and the predictors (Hastie and Tibshirani, 1990). The nonparametric functions are estimated from the data using smoothing operations. Several error distributions of the data can be modelled such as a binomial, normal/ gaussian or poisson. Because of the skewed distribution of the catches per haul and high proportion of 0 catches of most species-at-age it was necessary to use a two-stage GAM: first the probability that species-at-age was present (Pp) was modelled using a binomial distribution, then the log-transformed positive catches (logC) were predicted using a gaussian model. Pp or logC=Year+Depth+Time+Day+Grain-size+ Latitude+Longitude+Period*Depth+Period* Grain-size+Period*Latitude+Period*Longitude+ Latitude*Longitude+Surface Temperature*Depth Year was added as a factor for the effect of the difference between years. More gradual change in modelling the Bold values are significant at p 0.05. fishes distribution over time was incorporated by distinguishing three five-year periods (i.e. 19851989, 1990 1994 and 19951999) using a factor Period. The relationship of the catch with the external factors was modelled using a cubic smoothing spline. In order to acquire relatively smooth and interpretable relationships with all external factors except for the geographical position the degrees of freedom were restricted to 3 (grain-size, time of day and day of year) or 5 (depth). This two-stage GAM was used for each species-at-age. In order to correspond to the arithmetic mean of the untransformed data the predicted catch (Ce) was calculated as follows: Ce=Pp*exp(logC)*exp(0.5 where is the square root of the deviance divided by the degrees of freedom. Three different approaches were studied using the basic two-stage GAM. (1) The first approach used only the basic two-stage GAM. (2) In addition to the basic GAM the catches of fish species other than the two target species, represented by three Principal Components (PCs), were used as linear explanatory variables in both the binomial and gaussian part of the model. (...truncated)