Robust methods are needed to resolve contradictions in species richness curves along ecological gradients

Abstract

Nonmonotonic changes in species richness along ecological gradients are frequently observed in nature. While theories support both symmetric and skewed unimodal relationships, related studies usually fit second-order polynomials, which assume symmetric relationships. These studies often apply various transformations of the predictor variable to reduce the effects of outliers or to meet assumptions of normality. We studied whether predictor transformation affects the shape of the fitted curves. To test the effect of predictor transformation on the shape of the fitted curves, we re-analyzed the dataset of a highly-cited global analysis on the productivity–species richness relationship without performing any data transformations and contrasted the results with those of the original analyses that used log-transformed productivity data. We found that predictor variable transformation, which was used in the original paper, changed the shape of fitted curves in 32 % of the sites as well as the shape of the global relationship compared to the use of untransformed data. Therefore, we propose the reconsideration of predictor transformation and suggest an alternative approach: the piecewise regression. We found that piecewise regression is robust against predictor variable transformation. It resulted in much fewer inconsistent shape categories between the transformed and untransformed cases compared to the original analyses (2 instead of 9). We suggest that studies applying untransformed and transformed predictors when studying the shape of species richness curves along gradients are not directly comparable. Using piecewise regression models may contribute toward resolving the ongoing debate on the change in species richness along ecological gradients in general, and the productivity-species richness relationship in particular.