Choice of selectivity coefficients for cation exchange using principal components analysis and bootstrap anova of coefficients of variation

Modellers of the exchange of sodium, potassium, calcium and magnesium in soils have to choose from up to six different equations based on the mass action law paradigm (mainly Gapon, Vanselow, Gaines-Thomas and Kerr) and up to six different binary cation combinations. In this article a methodology to choose the most appropriate equation and binary cation combinations is presented. The combination of six equations with six binary cation combinations resulted in 36 selectivity coefficients. Each one of these was assessed for 133 calcareous illitic soil samples. Six principal components analyses (PCA) were carried out to find out which three binary cation combinations accounted most for the variance of the soil exchange selectivity. Then a bootstrap anova and multiple comparison (MC) procedure with orthogonal contrasts were carried out to compare the coefficients of variation of the selectivity coefficients calculated with each equation. According to the PCA, the three binary cation combinations involving calcium, and expressed with whichever of the equations of Kerr, Vanselow and Gaines-Thomas, accounted most efficiently for the variance of the soil exchange selectivity. According to the bootstrap anova and MC analysis, the Gapon equations, either in analytical concentrations or activities of aqueous cations, provide significantly larger coefficients of variation than the equations of Kerr (either in analytical concentrations or activities of aqueous cations), Vanselow and Gaines-Thomas. The use of the Kerr, Vanselow or Gaines-Thomas equations and the three binary cation combinations involving calcium resulted in the most effective way of modelling the exchange equilibria of sodium, potassium, calcium and magnesium in calcareous illitic soils.