Comparison of three spatial interpolation methods in predicting time-dependent toxicities of single substances and mixtures

Abstract

This study aims to optimize the time-dependent toxicity assessments for both single substances, particularly those causing hormesis, and mixtures that exhibit toxicological interactions. To achieve this, three time-dependent toxicity prediction methods were developed using geologic interpolation techniques: Inverse distance weighted (IDW), Kriging, and linear interpolation based on Delaunay triangulation (LDT). The toxicity of 7 single substances and 80 mixtures on Vibrio qinghaiensis sp.-Q67, along with 6 single substances and 19 mixtures on Microcystis aeruginosa, were assessed to evaluate the predictive accuracy of these methods. The coefficient of determination (R²), mean absolute error (MAE), and root-mean-square error (RMSE) were employed as performance metrics during cross-validation. The results showed that IDW underperformed LDT and Kriging in terms of both RMSE and MAE, indicating that LDT and Kriging had superior accuracy compared to IDW. Although LDT and Kriging demonstrated comparable predictive capabilities, LDT was identified as the more practical option for time-dependent toxicity prediction due to its simplicity and no requirement for parameter tuning. Consequently, LDT was presented as a new, efficient, and user-friendly tool for assessing the time-dependent toxicity of both individual chemicals and chemical mixtures. LDT will help to better assess the ecological risks of chemicals.