What is up? Testing spectral heterogeneity versus NDVI relationship using quantile regression

Environmental diversity and net primary productivity (NPP) are powerful indicators of local plant species richness (α-diversity). Remote sensing proxies of environmental diversity, such as spectral heterogeneity and NPP, are often used in modelling species richness variability, usually through regression analysis. As multicollinearity may affect analysis of species diversity, the interdependence of such proxies should be a major concern in their use. However, few attempts have been made to examine the interdependence between spectral heterogeneity and NPP proxies such as the Normalized Difference Vegetation Index (NDVI), in most cases using Ordinary Least Square (OLS) regression or Pearson correlations. We test the possible dependence of Landsat Enhanced Thematic Mapper (ETM+) local spectral heterogeneity versus NDVI using quantile regression and rejecting the main assumption of OLS regression, i.e. the symmetry of model residuals. A second-order polynomial function was fitted to the data and both OLS and quantile regression led to a humped-back relationship between spectral heterogeneity and biomass. Nonetheless while for most of the quantiles the humped-back curve was significant (with a negative and significant quadratic slope), for quantiles higher than 0.90, the parabola opened up until it reached an almost linear shape, showing that, at very low values of biomass, pixels may show high levels of local heterogeneity. Hence, patterns of spectral heterogeneity versus NDVI are possible when considering maximum potential spectral variability. We show that the investigation of all possible subsets within a scatter plot may lead to identification of patterns that remain hidden in OLS regression.