Catastrophic-like shifts in shallow Turkish lakes: a modeling approach

A generalized logistic model (GLM) was developed to determine occurrence of submerged macrophytes in shallow Lake Eymir, and the model was tested independently on the upstream shallow Lake Mogan using the data collected fortnightly from both lakes during 1997-2002. The independent variables included concentrations of chlorophyll-a (chl-a), suspended solids (SS) and total phosphorus (TP), Secchi disc transparency and z-scores of water levels. The dependent variable was the binary index of submerged plant occurrence. We used bootstrapping to determine the maximum number of epochs to train the model and to execute training when the corrected average cross entropy (c-index) leveled off. The model predicted that SS concentration, z-scores of water levels and TP concentration were the most important variables for determining occurrence of submerged plants. Sensitivity analyses showed that the probability of submerged plant occurrence followed a strong hysterisis response to varying water levels and the concentrations of SS and TP, with the break points being ±50 cm, 12-17 mg l−1 and 200-300 μg l−1, respectively. This observed sensitivity was in accordance with the alternative stable states hypothesis of shallow lakes. For occurrence of submerged plants, chlorophyll-a concentration and Secchi disc transparency had low significance. This was in concert with both relevances of input variables and the field results. The model gave a good definition of the system since the c-index and corrected c-index on the training data were high (0.970 and 0.963, respectively). Testing the model on Lake Mogan produced a c-index of 0.815 with around 80% of the cases being correctly classified. This showed that the model had a high ability to generalize over a spatially independent test set; therefore, it had a great reliability as well. In addition, the predictive power of the model was indeed very high. Consequently, the model captured the relationships between the input and output variables successfully and consistently with alternative stable states hypothesis.