Species distribution models (SDMs), which evaluate species-environment relationships, are one of the key topics in ecology and biogeography. These models evaluate the current status of target ecosystems and potential impacts in both time and space. Although species distributions are often calculated based on the composite habitat suitability of several variables, there are no guidelines for calculating them. The present study assessed the effects of model formulation on habitat suitability evaluation and the accuracy of species distribution modelling. We employed a genetic algorithm (GA)-optimized fuzzy habitat preference model (FHPM) for evaluating habitat suitability of topmouth gudgeon (Pseudorasbora parva) in the Northwestern part of Kyushu Island in Japan. Four operations were used to calculate the composite habitat suitability from multiple habitat variables: arithmetic mean, geometric mean, product and minimum. To transform model outputs to presence/absence, four threshold criteria were compared based on model accuracy: prevalence, conventional 0.5, minimization of the sensitivity-specificity difference threshold (MDT), and maximization of the sensitivity-specificity sum threshold (MST). The models were first calibrated and validated based on the mean squared error (MSE) between composite habitat suitability and the observed presence-absence of the fish, and then evaluated using confusion matrix-derived measures such as the area under the receiver operating characteristics (ROC) curve (AUC), correctly classified instances (CCI), kappa and true skill statistic (TSS). The results clearly illustrated the effects of model formulation and threshold criteria on habitat suitability curves (HSCs) and accuracy in modelling species distributions. The use of the product model formulation led to the best accuracy in terms of MSE and AUC, and consistency in the shape of HSCs. The two threshold criteria of MST and MDT are also recommended for the consistently higher performance in terms of CCI, kappa and TSS. This case study of topmouth gudgeon illustrates the need for further studies on the model behaviour with regard to data characteristics (i.e., sample size and prevalence) and model structure (i.e., fuzzy sets and parameter settings of the GA).
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