In the present study, the interplay and higher-order terms of environmental and spatial variables are considered to evaluate the relations of environment and space-species richness rankings at global scale. Three taxonomic groups composed of mammals, birds and amphibians were analyzed for the study. Thek-means clustering method was introduced for richness rankings detection and analysis from published digital maps; and simple regression analysis and AIC criteria were used for identifying mostimportant correlated explanatory variables.When comparing each single variable, I found that latitude was the most important one influencing global vertebrate richness rankings. When onlyconsidering environmental variables, I foundthat precipitation was the only predictor of vertebrate richness rankings. However, when the interaction and high-order terms of different independent variables were considered, it was found that the interaction between latitude and temperature could better explain the global bird richness ranking, while the second-power effectof latitude was the best predictor for amphibianand mammalian richness rankings, as evidenced by the AIC model selection and comparison among the regression models. In conclusion, the inclusion of high-order and interaction terms of environmental and spatial variables could offer more insights into the understanding of global species diversity patterns.