Use of Neural Networks to Forecast the Abundance of Argentine Hake in the Southwest Atlantic

Not to be cited without prior reference to the author

ICES CM 2010/A:12

Use of neural networks to forecast the abundance of Argentine hake in the Southwest Atlantic

Darriba, M., González, L., Martínez, G., Torres, J.M.

Departamento de Física Aplicada. Facultad de Ciencias del Mar, Universidad de Vigo. Box 36310, Vigo, Spain, tel. +34 986812631, fax. +34 986812556. [email protected], [email protected], [email protected], [email protected].

Abstract

The Argentine hake (Merluccius hubbsi) is one of the most important commercial species in the Patagonian-Malvinas shelf. In this work, we propose a predictive model of abundance for this species based on a Multilayer Perceptron (MLP) neural network. The network was developed using fishery data that were collected on board Spanish commercial vessels operating in the area between 1989 and 2006 and environmental data provided by the oceanographic model implemented by MERCATOR Ocean. The MLP output is the cpue (catch per unit effort; kg h- 1), which is used as an abundance index. As input variables we included latitude, longitude, Julian day, temperature and salinity at three depth levels, sea surface temperature gradient and moon phase. The whole dataset was split into two independent sets, one to train the network and the other one to validate it. GIS techniques and statistical methods were used to analyse and visualize the data and the results. Model results show a good fitting between the observed and estimated cpue (r=0.74 using the validation set). This tool might be useful to implement an operational forecasting system.

Keywords: Argentine hake, MLP, neural networks, prediction model

Contact author: J.M. Torres Palenzuela, Departamento de Física Aplicada, Universidad de Vigo. [email protected].

Introduction

The Argentine hake (Merluccius hubbsi) is an important target species for the fisheries fleet operating in the southwest Atlantic. The main aim of this paper is the implementation of a catch per unit effort (cpue) predictive model for this species based on an artificial neural network, in particular a multilayer perceptron (MLP). Different statistical methods were applied to analyse the relationship between the different environmental variables and cpue in a previous step to the development of the MLP. Geographic Information Systems (GIS) were used to visualize and analyze the results. Fisheries data were collected by the Galician trawlers operating in the southwest Atlantic area between 1989 and 2006, although only data between 1993 and 2006 were used in this study. Artificial neural networks are computer algorithms that work in a similar way to the human brain (Sugiyama and Ogawa, 2001), and are a powerful tool for modelling multivariate, complex and non-linear data (Chen et al., 1992), so that it is the ideal technique to be applied in fisheries forecasting problems (Guegan et al., 1998). Artificial neural networks have been successfully applied to model fishery variables and Pacific herring (Clupea pallasi) recruitment (Chen and Ware, 1999), to predict the relative abundance of bigeye tuna (Thunus obesus) from catch and effort data (Maunder and Hinton, 2006) or to estimate fishing set positions from vessel tracks derived from vessel monitoring system (VMS) data (Bertrand et al., 2008).

The study area lies in the Patagonian Shelf, between longitudes 64ºW and 54ºW and between latitudes 55ºS and 40ºS. This area is characterized by the presence of a permanent thermohaline front located at the border of the shelf. The exact geographical location and the density gradient across the front depend on the dynamic of the two currents dominating the ocean circulation in the area— the warm southward flowing Brazil current and the cold northward flowing Falkland (Malvinas) current—which converge at approximately 36–38ºS (Peterson, 1992). As a consequence of the active regional and local circulation with frequent coastal fronts and upwelling zones, the waters in the southwest Atlantic area are highly productive and sustain important pelagic and demersal fisheries (Wang et al., 2007).

Figure 1: Location map of the study area, showing the Falkland Islands. The numbered rectangles (from 1 to 3) enclose the zones used in the statistical study. In order to facilitate the spatial analysis, the study area was divided into three sub-areas (Figure 1). These zones coincide with the areas where the Spanish fleet is operating. Area 1 (around 42ºS) and Area 2 (between 43º30'S and 48ºS) are the portions of the continental shelf and slope which fall outside the Argentinean Exclusive Economic Zone (EEZ). The Area 3 is located around the Falkland Islands and cover approximately the same area as that of the Falkland Islands Interim and Outer conservation zones (FICZ and FOCZ respectively), but it was redesigned as rectangles to facilitate the integration into the model.

Hakes (Merlucciidae) are abundant nektonic fishes inhabiting shelf and continental-slope waters of the Atlantic Ocean, eastern Pacific, and south-western Pacific off New Zealand. The Argentine hake inhabits waters over the Argentine and Uruguayan continental shelves between 28ºS and 54ºS, and between 50 and 800 metres depth (Buratti and Santos, 2010). The species lives in temperate-cold waters associated to the Malvinas current system and to the upwelling of sub-Antarctic waters along the southern coast of Brazil (Bezzi et al., 1994). Two main stocks have been identified, the northern one, between 34ºS and 41ºS, and the southern one, located between 41ºS and 54ºS (Bezzi et al., 1995). Our data are mostly concentrated in Area 2 (43º30'S - 48ºS) and therefore they mainly correspond to the southern stock. Although the species was one of the most abundant fish resource during the study period, during the last years there was a drastic decrease in its total biomass due to an over-exploitation of both stocks (Renzi and Irusta,2006; Cordo, 2006).

Data sources

Fishery data were collected on board commercial vessels operating in the southwest Atlantic area between 1989 and 2006, although only data between 1993 and 2006 were used in this work due to the environmental variables were only available after 1993. These vessels are part of the Fishing Vessel Owners´ Cooperative of the Port of Vigo (ARVI) fleet. The use of commercial ships to evaluate fisheries status requires caution because factors such us license conditions, commercial priorities or the knowledge and experience of the crew can influence the characteristics of the recorded data. In spite of these inconveniences, data from commercial vessels provide the most extensive and representative datasets available for these fisheries.

Physical and biological parameters were recorded on board by trained observers working for the Instituto Español de Oceanografía, Vigo, Spain (IEO) and Falkland Islands Government Fisheries Department, Stanley. In a later step all these data were integrated into a database, including the following variables for each haul: temporal parameters (date, year, month, week of the year and Julian day, defined as the number of days elapsed since the 1st of January of the corresponding year), the fishing location (in latitude and longitude) recorded during the shooting operation, the fishing hours, the total catch estimated from processed fish by applying conversion factors [in kilograms (kg)] for each species and cpue, computed as the total catch per fishing hours, which were adopted as an index of effort. Unfortunately, there was insufficient available information to apply any correction factor for the variable catching power of individual vessels or the increasing fishing power over time, introducing some additional noise into the data.

Environmental variables were derived from the MERCATOR model (from 1993 to 2006) and associated with the fisheries database. Operational forecasting systems developed by MERCATOR Ocean are based on three-dimensional (3D) ocean models described by primitive equations obtained from applying the Navier–Stokes equations in a stratified fluid. The formulation requires some physical approximations, and variables such us diffusion or viscosity are included by parameterizations. The model runs using medium-range weather forecasting models to generate the atmospheric forcing, in addition to a constant climatology and bathymetry. Moreover, for operational requirements and also for validation and reanalysis it receives, in real time, ocean measurements from satellite and in-situ observation systems. As output, it computes several ocean parameters, including temperature, salinity or currents, inside a 3D grid so that it is possible to evaluate the longitudinal, latitudinal and by-depth parameter variations (Drévillon et al., 2008).

The following seven variables were obtained from the MERCATOR data set: Sea Surface Temperature (SST); Sea Bottom Temperature (SBT); Sea Surface Salinity (SSS); Sea Bottom Salinity (SBS); Thermocline Temperature (TT); Thermocline Salinity (TS) and SST gradient (GSST). All these parameters were linked to the fisheries database using the date and the geographic location of the hauls, so that the values of the grid cell containing these locations were extracted and correctly associated with the fisheries data.

Daily temperature (in Celsius) and salinity (in psu) data at surface and bottom were directly provided by MERCATOR. The thermocline temperature and salinity required a previous determination of the thermocline depth, which was obtained for each grid cell in the model from the vertical temperature profile, computing the temperature gradient between each two consecutive vertical levels and selecting as the thermocline the deepest layer of the pair with the maximum gradient between them. Regarding the SST gradient, which defines the maximum rate of change in SST from a grid cell to its neighbors, was computed using the average maximum technique (Burrough, 1986) in a 3 x 3 grid-cell neighborhood. The output units are degrees of slope ranging from 0 to 90.

Finally, moon phase data were available from U.S. Naval Observatory (USNO) web page by specifying the date and a fix location on the centre of the study area (50 ºS 60ºW). An integer number from one to eight was assigned to each traditionally recognized stage of the Moon in the same order as the sequence of occurrence: New Moon; Waxing Crescent; First Quarter; Waxing Gibbous; Full Moon; Waning Gibbous; Last Quarter and Waning Crescent. Each one of these Moon phases is characterized by the degree of illumination (maximum at Full Moon and minimum at New Moon) and the geometric appearance of the visible part.

Methodology: Neural network models

Artificial neural networks are powerful tools that can model complex non-linear systems (Chen and Ware, 1999) and do not require assumptions about the relationships or data distributions. A MLP is a feed-forward artificial neural network which uses a back-propagation learning algorithm with the aim of approximating a set of input data to the corresponding output data. A MLP network is composed of non-linear computational elements, named neurons or nodes, arranged in multiple layers: an input layer, which only distributes the input signals into the network; one or more hidden layers and an output layer. Each individual neuron in the hidden layers and the output layer transforms its input signal by an activation function.

The layers are interconnected in a feed-forward way, so that each neuron of a layer is connected to the nodes of the successive layer but has no connections to neurons in the previous layers. The relationship between the input and the output depends on the weights that define each connection. These values are established by a supervised learning technique, using a priori information about the actual output corresponding to a set of input data to adjust the network so that the best approximation possible to the actual output is achieved. In this particular case a back-propagation training procedure is used: the weights are iteratively adjusted, layer by layer in a looping pattern, starting with the output layer and ending with the input layer. This adjustment continues until no more significant variations in the overall error are observed. Weighting adaptations are produced using a non-linear optimization method called gradient descent, which requires a differentiable activation function.

In this work, we developed two different MLP networks in order to forecast the cpue for Argentine hake in the complete study area and other two ones considering only the Area 2, where approximately 86% of the total catches were recorded. For both cases, we designed two MLP nets: one including all the input variables and the other one with only environmental variables. All the networks were designed with two hidden layers and an output layer with a unique neuron associated to the desired output, i.e. the log-cpue. Note that cpue data were log transformed to avoid the influence of very high values on the model fitting. The activation function for both hidden layers and the output layer is a non-linear sigmoid function, which yields values in the range from 0 to 1.

The variables we used to predict the cpue were chosen considering two characteristics: they should be predictable in the short term, so that the model could be applied in an operational way; and they should be linked to the response variable. So, latitude and longitude are indicative of the fishing location, which is related to the spatial variability of the catches in a given instant. The Julian day can reflect the intra-annual variability of the cpue. The thermocline depth is related to the depth of the surface mixed layer and the phytoplankton development as a function of the light and the nutrient concentration. The temperature and the salinity (recorded at three depth levels) define the different water masses in the ocean, which are associated with the circulation patterns responsible for the distribution of species included in the same trophic chain. Moreover, cold surface waters can be related to nutrient-rich waters due to an upwelling event. The Moon influences on the life cycle of some marine species including the Argentine hake and finally the SST gradient is used as an indicator of the presence of local thermal oceanic features such us fronts or currents, which can be related to the nutrients and marine species distribution. A correlation between the abundance of Argentine hake and the presence of thermal features in the southwest Atlantic area was found in previous works (Wang et al., 2007).

Table 1 shows a summary of the main characteristics of the designed neural networks. Topology indicates the number of nodes in each layer, including the input layer, both hidden layers and the output layer. Note that MLP#1 and MLP#3 included all the input variables, whereas MLP#2 and MLP#4 only environmental variables.

MLP#1 MLP#2 MLP#3 MLP#4 Area Complete study area Area 2 (number of (13176 records) (7310 records) records) Topology 11 30 15 1 8 12 8 1 11 30 15 1 8 12 8 1 Latitude Latitude Longitude Longitude SST SST Julian Day Julian Day SSS SSS SST SST TT TT SSS SSS Input TS TS TT TT variables SBT SBT TS TS SBS SBS SBT SBT GSST GSST SBS SBS Moon Moon GSST GSST Moon Moon Output log-cpue variable Training 8999 5000 records set Validation 4177 2310 records set Activation Sigmoid function function Table 1: Summary of the main characteristics of the designed MLP. In order to train each neural network, the corresponding dataset was divided into two independent parts: a training set, including approximately two thirds of the records and used to train the neural model by a cross-validation method, and a validating set, consisting of the remaining records, and necessary to validate the network. Both subsets must be random and representative of the whole dataset; hence, they were created including records over the entire spatial, temporal and cpue ranges.

For a better performance a 10-fold cross-validation was performed to train the neural models. First, the training sample was partitioned into 10 subsamples, and then the neural net was trained ten times, so that each time nine different subsamples were used to train the net and the remainder one to test it.

Finally, the validation dataset was used to evaluate the performance of the predictive neural networks. The criteria we use to evaluate the model fitting are:

 Coefficients of correlation (R) and determination (R2) between the observed log-cpue and the predicted log-cpue.

 Mean prediction error (MPE) between the observed (log-cpueO) and predicted (log- cpueP) log-cpue:

MPE is defined as: MPE= (1/n) (PE1 + PE2 + . . . + PEi + . . . PEn-1 + PEn)

where PEi is the prediction error (i.e. log-cpueOi – log-cpuePi ) and n is the number of records of the validation set.

 Variance of the prediction errors (VAR):

2 2 2 VAR = [1/(n-1)] [(PE1 – MPE) + . . . + (PEi – MPE) + . . . + (PEn-1 – MPE) + (PEn – MPE)2 ]

 Mean absolute percent error (MAPE) between the observed and predicted log-cpue, defined as:

MAPE = (1/n) [(|log-cpueO1 – log-cpueP1|/log-cpueO1) + ...... + (|log-cpueOn – log-cpuePn|/log-cpueOn)] Although the performance measurements are more significant when computed using the validation set, they are also obtained using the training dataset. R and R2 are measurements of the correlation between the observed and the predicted data set. MPE made it possible to find out if the model tends to underestimate (high positive values) or overestimate (high negative values) the observed log-cpue values. MAPE was used in this work as measurement of absolute error, while VAR was used to quantify error variability.

Several simulations were performed with a varying number of hidden layers and different activation functions. Since MLP results may vary slightly at different runs, each simulation was also run 10 times and then an average was computed from all the experiments. The final architectures (Table 1) were selected considering four parameters that define the MLP network performance (R, MPE, VAR and MAPE), in a similar way to Chen and Ware (1999). Then, results shown in this work correspond to the optimal forecast neural models.

Results

The whole fisheries dataset from 1993 to 2006 includes a total of 103711 records. There are catches from 34 vessels of 93 different species. For the Argentine hake, the complete dataset includes 13176 records, with 7310 records in Area 2. Figure 2 shows the spatial distribution of the Argentine hake. The high concentration of hauls with high cpue in Area 2 is notable. Around 86% of the total catches are recorded in this zone. Regarding temporal distribution, an increase of the monthly average cpue from April to August was observed, with a peak over 750 kg h-1 in July. The relationships between cpue and the features used as input in the forecasting neural models are non-linear and without clear trends.

Table 2 shows the results of the parameters that define the model fitting and the forecasting quality, all of them computed from the validation set and the training set. As it was expected, results computed from the validation set were worse than the ones obtained from the training set.

Figure 2: Location of the hauls with CPUE greater than 100 kg h-1 Figure 3 depicts the relationship between the observed and predicted log-cpue values for each haul in the validation set for all the neural models. The identity line (line y=x) is also shown in these graphics to observe the deviations of the forecasted log-cpue values with respect to the expected ones.

Figure 3: Correlation between the observed and the predicted output for all the neural models. a) MLP#1 b) MLP#2 c) MLP#3 d) MLP#4

Figure 4 shows histograms with the distribution of the prediction errors in the validation set for the four neural models. If the model fitting were good, it would be expected a normal distribution with the most of the prediction errors between -1 and +1.

Figure 5 shows the mean prediction error (MPE) for each range of observed cpue considering only the validation set, and the distribution (relative abundance) of observed cpue in the training set. These graphics were obtained for all the models and used to analyse the over and/or underestimation of the models as a function of the observed cpue and the influence on the mean error of the abundance of hauls with a given cpue range in the training procedure.

Discussion

The neural model that performed best according to the all the validation criteria (Table 2) was MLP#1, which was trained using observations from the complete study area and considering all the possible input variables (R= 0.74 in the validation set). In this model, the similarity of the performance measures computed from the validation and training datasets is notable, with correlations between the observed and model output around 0.75 and the same value of MPE. This is indicative of the representativeness of the validation set.

Figure 3a shows a clear linear trend between the observed and the model output, although deviations of the forecasted log-cpue values with respect to the expected ones (line y=x) are observed: they tend to be positive when observed log-cpue is low and negative when observed log-cpue is high. Therefore, as it is also seen in Figure 5a, MLP#1 tends to overestimate the predicted values with low log-cpue values (negative MPE values) and to underestimate with high observed log-cpue values (positive MPE values). In summary, MLP#1 tends to smooth the output and performs better with medium log-cpue. It might be explained by the imbalance of the training set, with 76% of the hauls with medium log-cpue values between 3 and 7. Hauls with peaks of low or high observed log-cpue values are not well detected by the model and prevent a higher correlation. Globally, it tends to underestimate slightly the log-cpue values (MPE = 0.04 in both the training and the validation set). Distribution of the prediction errors shows values between -1 and +1 in approximately 60% of the hauls (Figure 4a), with a MAPE of 0.36 (0.33 in the training set).

Figure 4: Histograms showing the error distribution for all the neural models. a) MLP#1 b) MLP#2 c) MLP#3 d) MLP#4

MLP#2 shows results clearly poorer that the obtained using MLP#1 (Table 2). Therefore, the selected environmental variables do not explain all the temporal and spatial variability observed in the dataset, since the inclusion of latitude, longitude and Julian day implies a significant improvement of the neural model. Specifically, the main drawback with respect to MLP#1 is an increase of the problems to detect peaks of high and low log-cpue. As seen in Figure 5b, the overestimation and underestimation effect with low and high observed log-cpue values is more marked. As a consequence, MLP#2 shows a poorer correlation (R = 0.47) without a clear linear trend (Figure 3b) and a greater variability of the prediction errors (VAR=2.23 versus VAR=1.30, using the validation set). Regarding the errors distribution considering the validation set (Figure 4b), only around 50% of the hauls show prediction errors between -1 and +1, while a high percentage of hauls (21.2%) with PE between 1 and 2. However, the global effect is not very strong and MLP#2 only shows a slight underestimation (MPE = 0.07 in both the training and the validation set) and an acceptable MAPE (0.50 in the validation set) due to the model still performs well for medium log-cpue values.

Dataset from Area 2 is slightly different from the complete dataset, since the mean cpue is greater (5.28 versus 4.75) and the imbalance in the cpue distribution is more marked (Figure 5) with a smaller percentage of hauls with low cpue (only 9.2% of hauls with log-cpue lower than 3, 19% if the complete dataset is considered). As a consequence of this imbalance, the neural models trained with Area 2 dataset (MLP#3 and MLP#4) are expected to show more problems to detect peaks of low cpue and poorer correlations. According to the validation criteria (Table 2), these neural models are not as good as MLP#1, although they outperform MLP#2. MLP#1 MLP#2 MLP#3 MLP#4 Training Valid. Training Valid. Training Valid. Training Valid. set set set set set set set set R 0.78 0.74 0.53 0.47 0.73 0.67 0.65 0.52 R2 0.61 0.55 0.28 0.22 0.54 0.45 0.42 0.27 MPE 0.04 0.04 0.07 0.07 0.01 -0.12 0.02 -0.27 VAR 1.11 1.30 2.02 2.23 1.03 1.53 1.29 2.07 MAPE 0.36 0.33 0.55 0.50 0.24 0.37 0.28 0.45 Table 2: Model fitting parameters computed from the training and validation sets for all the neural models.

Although differences between MLP#3 and MLP#4 are not as marked as the ones between both neural models trained with the complete dataset, the inclusion of latitude, longitude and Julian day also causes an improvement of the performance of the model. In this way, MLP#3 show a better correlation, with a clearer linear trend (Figure 3c, 3d) and a error distribution more balanced (Figure 4c, 4d), with approximately 64% of the hauls with PE between -1 and +1 in contrast to 55% in MLP#4. Both models show MAPE values lower than 0.5 computed from both the training and the validation set (Table 2).

Figure 5: Mean prediction error (MPE) for each range of observed CPUE computed from the validation set (blue columns, left axis) and relative abundance of hauls for each range in the training set (black line, right axis). a) MLP#1 b) MLP#2 c) MLP#3 d) MLP#4

These models also tend to smooth the output, showing overestimation with low cpue values and underestimation with high cpue values (Figure 5c, 5d). However, the global result is not so clear. While MPE computed from the training set reflects a slight underestimation (MPE = 0.01 in MLP#3; MPE = 0.02 in MLP#4), results from the validation set show a clear overestimation for both models. These high negative MPE values are due to the overestimation of a small number of hauls with low cpue values. The lack of enough training data with low cpue values prevent the neural models from performing better within these ranges.

Conclusions

The results of this work show the potential of neural models based on MLP artificial network for forecasting cpue of Argentine hake in the southwest Atlantic area. The tool is based on environmental variables and it might be useful to implement an operational forecasting system based on maps of predicted cpue for a species for a given day, with a prediction horizon of so many days as the available oceanographic model. An operational system would allow continual improvement of the neural networks by training those using new recorded data as they became available.

The inclusion of new input variables, not only more environmental parameters but also information related to the life cycle of a species or its interactions with other species, would improve the neural models. It is also probable that an important part of the unexplained variability in the observed cpue could be caused by fishing effort effects, which we could not evaluate since we only have data from a part of the Spanish fleet, and fishing data from other vessels operating in the same area and time is not available. The application of a conversion factor to the cpue values to take into account the catching power of each individual boat or the use of an alternative algorithm to predict the peaks of maximum cpue would allow us to improve the results. The same methodology could be applied to other species with an important presence in our fisheries database.

Acknowledgements

This research was supported by the Galician government (Xunta de Galicia). Authors wish to thank ARVI and MERCATOR for the provision of data.

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