A comparison between two GAM models in quantifying relationships of environmental variables with fish richness and diversity indices

Various regression methods can be used to quantify the relationships between fish populations and their environment. Strong correlations often existing between environmental variables, however, can cause multicollinearity, resulting in overfitting in modeling. This study compares the performance of a regular generalized additive model (GAM) with raw environmental variables as explanatory variables (regular GAM) and a GAM based on principal component analysis (PCA-based GAM) in modeling the relationship between fish richness and diversity indices and environmental variables. The PCA-based GAM tended to perform better than the regular GAM in cross-validation tests, showing a higher prediction precision. The variables identified being significant in modeling differed between the two models, and differences between the two models were also found in the scope and range of predicted richness and diversity indices for demersal fish community. This implies that choices between these two statistical modeling approaches can lead to different ecological interpretations of the relationships between fish communities and their habitats. This study suggests that the PCA-based GAM is a better approach than the original GAM in quantifying the relationship between fish richness and diversity indices and environmental variables if the environmental variables are highly correlated.