Modeling complex nonlinear responses of shallow lakes to fish and hydrology using artificial neural networks

Abstract

Mathematical abstractions may be useful in providing insight that is otherwise very difficult to obtain due to complex interactions in the ecosystems. The difficulty associated with the nonlinearity and complexity of ecological processes and interactions can be avoided with artificial neural networks (ANN) and generalized logistic models (GLMs) which are practically ANNs without hidden layer. An ANN and a GLM were developed to determine the probability of submerged plant occurrence in five shallow Anatolian lakes, and both models were tested on an spatially and temporally independent test set consisting of data collected from another Anatolian lake, Lake Mogan. Independent variables included the ratio of carp biomass to total fish biomass (carp ratio), the amplitude of water levels, water level z-scores, morphology indices of the lakes and a period index. We optimized different ANN architectures to optimize the performance, and used bootstrapping to determine the maximum number of epochs to train the model. Cross-entropy measure ( c-index) was used to assess the performance of the models, which is approximately the area under the receiver–operator curve (ROC) and equivalent to log likelihood measure for binary outcome events. Following optimization, both ANN and GLM models explained the data effectively (corrected c-indices 0.99 and 0.95, respectively), and both models explained the independent test data set completely ( c-indices 1.00 for both models). Both models predicted a very strong impact of carp ratio on the occurrence of submerged plants, and relatively strong impacts of the amplitude, water level z-score and morphology index. In that sense, the predictions of the models were consistent with the field observations regarding the study lakes, as well as with alternative stable states theory of shallow lakes. In general, both models have been successfully predicted the state shifts in shallow lakes included in the model, and identified the thresholds for inducing those shifts from mainly hydrological variables. However, ANN model was more successful in capturing the relationships and interactions among input variables compared to the GLM model. To best of our knowledge, current study is the first ANN-based approach to predict the state shifts in shallow lakes and to identify the corresponding threshold value of the control factors. The model has been robust in being generalizable over distinct shallow lake ecosystems, at least in the same climatic zone as the study lakes.