Figure 1

Accuracy of the regression models for K₀: adjusted R². In all panels the number of variables from 1 through 8 corresponds to increasing sets of environmental predictors in the following order: {EVI, PRE, TMP, LND, ELV, LON, POP, LAT}. (A) Multi-linear regression (MLN), (B) multi-linear regression with linear cross terms (GLC), and (C) second order polynomial with linear cross terms (GPC). In each boxplot, the tick mark inside the box indicates the median value of the adjusted R², while the vertical extensions of the box above and below the median are the 25^th and 75^th quartiles, respectively. The height of the box stands for the interquartile range. The whiskers (dashed lines) indicate the spread of points outside the interquartile range. Outliers more than 1.5 times the interquartile range away from the median are indicated by circles. As the number of variables increases, both whiskers and interquartile ranges reduce, indicating that the robustness of the regression improves. The median value of the normalized residual standard error (RSE) for MLN, GLC, and GPC models with five predictors are 35.0%, 27.0%, and 27.0%, while the adjusted R² values are 0.62, 0.78, and 0.79, respectively.