Marc Delacoste

Application of neural networks to modelling nonlinear relationships in ecology

Abstract Two predictive modelling principles are discussed: multiple regression (MR) and neural networks (NN). The MR principle of linear modelling often gives low performance when relationships between variables are nonlinear; this is often the case in ecology; some variables must therefore be transformed. Despite these manipulations, the results often remain disappointing: poor prediction, dependence of residuals on the variable to predict. On the other hand NN are nonlinear type models. They do not necessitate transformation of variables and can give better results. The application of these two techniques to a set of ecological data (study of the relationship between density of brown trout spawning sites (redds) and habitat characteristics), shows that NN are clearly more performant than MR (R2 = 0.96 vs R2 = 0.47 or R2 = 0.72 in raw variables or nonlinear transformed variables). With the calculation power now currently available, NN are easy to implement and can thus be recommended for modelling of a number ecological processes.

Stochastic models that predict trout population density or biomass on a mesohabitat scale

Neural networks and multiple linear regression models of the abundance of brown trout (Salmo trutta L.) on the mesohabitat scale were developed from combinations of physical habitat variables in 220 channel morphodynamic units (pools, riffles, runs, etc.) of 11 different streams in the central Pyrenean mountains. For all the 220 morphodynamic units, the determination coefficients obtained between the estimated and observed values of density or biomass were significantly higher for the neural network (r2 adjusted= 0.93 and r2 adjusted=0.92 (p<0.01) for biomass and density respectively with the neural network, against r2 adjusted=0.69 (p<0.01) and r2 adjusted = 0.54 (p<0.01) with multiple linear regression). Validation of the multivariate models and learning of the neural network developed from 165 randomly chosen channel morphodynamic units, was tested on the 55 other channel morphodynamic units. This showed that the biomass and density estimated by both methods were significantly related to the observed biomass and density. Determination coefficients were significantly higher for the neural network (r2 adjusted =0.72 (p<0.01) and 0.81 (p<0.01) for biomass and density respectively) than for the multiple regression model (r2 adjusted=0.59 and r2 adjusted=0.37 for biomass and density respectively). The present study shows the advantages of the backpropagation procedure with neural networks over multiple linear regression analysis, at least in the field of stochastic salmonid ecology.