Modeling microalgal abundance with artificial neural networks: Demonstration of a heuristic 'Grey-Box' to deconvolve and quantify environmental influences

An artificial neural network (ANN)-based technology - a 'Grey-Box', originating the iterative selection, depiction, and quantitation of environmental relationships for modeling microalgal abundance, as chlorophyll (CHL) a, was developed and evaluated. Due to their robust capability for reproducing the complexities underlying chaotic, non-linear systems, ANNs have become popular for the modeling of ecosystem structure and function. However, ANNs exhibit a holistic deficiency in declarative knowledge structure (i.e. a 'black-box'). The architecture of the Grey-Box provided the benefit of the ANN modeling structure, while deconvolving the interaction of prediction potentials among environmental variables upon CHL a. The influences of (pairs of) predictors upon the variance and magnitude of CHL a were depicted via pedagogical knowledge extraction (multi-dimensional response surfaces). This afforded derivation of mathematical equations for iterative predictive outcomes of CHL a and together with an algorithmic expression across iterations, corrected for the lack of declarative knowledge within conventional ANNs. Importantly, the Grey-Box 'bridged the gap' between 'white-box' parametric models and black-box ANNs in terms of performance and mathematical transparency. Grey-Box formulations are relevant to ecological niche modeling, identification of biotic response(s) to stress/disturbance thresholds, and qualitative/quantitative derivation of biota-environmental relationships for incorporation within stand-alone mechanistic models projecting ecological structure.