Research Article: An ecologically constrained procedure for sensitivity analysis of Artificial Neural Networks and other empirical models

Date Published: January 30, 2019

Publisher: Public Library of Science

Author(s): Simone Franceschini, Lorenzo Tancioni, Massimo Lorenzoni, Francesco Mattei, Michele Scardi, Thilo Gross.


Sensitivity analysis applied to Artificial Neural Networks (ANNs) as well as to other types of empirical ecological models allows assessing the importance of environmental predictive variables in affecting species distribution or other target variables. However, approaches that only consider values of the environmental variables that are likely to be observed in real-world conditions, given the underlying ecological relationships with other variables, have not yet been proposed. Here, a constrained sensitivity analysis procedure is presented, which evaluates the importance of the environmental variables considering only their plausible changes, thereby exploring only ecological meaningful scenarios. To demonstrate the procedure, we applied it to an ANN model predicting fish species richness, as identifying relationships between environmental variables and fish species occurrence in river ecosystems is a recurring topic in freshwater ecology. Results showed that several environmental variables played a less relevant role in driving the model output when that sensitivity analysis allowed them to vary only within an ecologically meaningful range of values, i.e. avoiding values that the model would never handle in its practical applications. By comparing percent changes in MSE between constrained and unconstrained sensitivity analysis, the relative importance of environmental variables was found to be different, with habitat descriptors and urbanization factors that played a more relevant role according to the constrained procedure. The ecologically constrained procedure can be applied to any sensitivity analysis method for ANNs, but obviously it can also be applied to other types of empirical ecological models.

Partial Text

Fish assemblage diversity in freshwater ecosystems constitutes a valuable natural resource in economic, scientific, cultural and educational terms [1]. Its conservation and management face threats as overexploitation of inland waters, flow modification, water pollution, habitat degradation and invasion by exotic species [2], [3]. Identifying the relationships between fish species richness and habitat complexity at a local scale is one of the primary concerns in understanding how environmental descriptors actually affect fish biodiversity [4], [5], [6].

While several methods are available to test the sensitivity of ANNs or of any other type of model, we based our analysis on the perturbation method, because it is the one that most closely matches the rationale of the procedure we propose. However, the same rationale may be adapted to any other method (e.g. Partial Derivatives or Lek’s profiles method), as its only goal is to avoid data patterns that are not likely to occur in real-world conditions and that therefore are not really useful to open the ANN “black-box” as well as any other type of empirical model and to elucidate the way it worked and the ecological relationships it captured.




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