Estimation of environmental optima and tolerances of diatoms using multifactor multiplicative modeling

• Multiplicative regression model was demonstrated for the study of diatom ecology.
• A local mean estimator and kernel functions were used to construct the model.
• The bell-shaped curve with a single optimum proved to be fitting only for few taxa.
• Multiplicative regression is found to be a powerful tool to study autoecology.
• Further optimization of the model is required including additional factors

We demonstrated the use of a multifactor multiplicative regression model to study the ecology of diatoms. A dataset of 174 samples of diatoms matched with environmental variables, which were collected from similar typology streams of three major watersheds in Ethiopia was used to build the model. Tropical rivers experience wet and dry season dynamics with highest levels of pollution at low water levels. In extreme polluted sites, diatoms are still present whereas other bio-indicator groups such as fishes, macrophytes and even macro-invertebrates are absent. The distribution of selected model diatom taxa (widely known pollution tolerant and sensitive taxa) in relation to environmental descriptors was studied by fitting non-parametric multiplicative regression (NPMR) to species relative abundances. A local mean estimator and Gaussian kernel functions were used to construct the models. The models reported here are those showing the best fit for particular number of predictors. Predictors were added until the cross-validated coefficient of multiple determination (×R2) increased at least by 5% so that the model with the highest number of predictors had the highest ×R2. We used bootstrap sampling to validate the model. NPMR a powerful model to study autoecology allows us to question the assumption that a suitable indicator species exhibits approximately bell-shaped curve with a single optimum for the probability density function of a species along environmental gradients. Only a few number of taxa showed such an optima whereas multi-interaction of diatom species could cause linear, skewed or non-unimodal, bimodal and multimodal responses. Therefore, modeling of species response to environmental gradients can be best explored without predefining the response curve and considering simultaneous multiple factor interaction in a multiplicative way.