Eel catches in the River Tevere (in prep.). 

° Stazione Zoologica "A. Dohrn" di Napoli, Villa Comunale, 80121 Napoli, Italy
* Dipartimento di Biologia, Università di Roma "Tor Vergata", Roma, Italy
 
 

Eel catches in the Tevere river were empirically modeled using an EBP neural network. A five years data set was used for model training (1991, 1993 and 1995, n=532) and validation (1992 and 1994, n=283). The NN model had only one output daily eel catches (CPUE) and six input (precictive) variables. Three input variables included a two days "memory", i.e. they were splitted into three different inputs at time=0, time=-1 and time =-2 (in days). therefore, the NN structure was: 

All the input variables were scaled into the [0,1] interval, so obviously the NN output had to be scaled back to the original units.

The NN model returned a fairly good estimate of the daily catches (r²=0.572, MSE=0.447), as shown in the following figures, where model outputs vs. observed values are plotted. The largest errors in NN estimates were recorded for high (>1.5 CPUE) observed values. This probably depends on the fact that a stochastic or unexplained component plays a major role in determining very high and very low catches. Low catches have a finite limit (i.e. 0 CPUE), so they do not contribute to the overall error as much as high catches do, even though they play a similar role (see log-log plot on the right). However, extreme catches had probably a stochastic component (our samples were too small?) or they were correlated to predictive variables that were not included in the model: in both cases they could not be accurately estimated by a NN model (as well as by other models!).

The error distribution (see next figure) was good enough, since it was not too asymmetrical and almost unbiased (mean error = -0.015). About 90% of the errors were smaller than 1/10 of the range of the observed values (from 0 to 7.5 CPUE).
 
 

The observed (dashed line) and predicted (solid line) time series are shown in the following figure. The overall fitting of the NN model is quite good, not only for the years that were used for training, but also for the two years (1992 and 1994) that were only used for the NN model validation. 
 
 

The yearly estimates of eel catches are quite accurate, even when only validation years are taken into account.
 
 

Even though NN sensitivity analysis is not as straightforward as it may appear, an estimate of the relative importance of each predictive variable was obtained. However, it has to be stressed that these results account only for first order relationships between predictive variables, because interactions between predictive variables are not taken into account. The sensitivity analysis was carried for each precictive variable by using a random value instead of the observed value in all the input patterns: the resulting mean square error (MSE) and its variation with respect to the original MSE are shwon in the following figure. Rainfall during the day before sampling was the most sensitive variable in affecting the NN estimates.
 
 

Even though our results are preliminary, NNs seem a very promising tool for empirical modeling of eel (as well as other species) catches. These applications were already developed for small pelagic fishes, but they are probably even more interesting in freshwater environments, where predictive variables are much more difficult to identify and to measure. Of course, the selection of the best predictive variables and a right balance between accuracy in reproducing catch variations and good generalization will play a very important role in improving these NN models.