Correlative species distribution models (SDMs) often involve some degree of projection into novel covariate space (i.e. extrapolation), because calibration data may not encompass the entire space of interest. Most methods for identifying extrapolation focus on the range of each model covariate individually. However, extrapolation can occur that is well within the range of univariate variation, but which exhibits novel combinations between covariates. Our objective was to develop a tool that can detect, distinguish and quantify these two types of novelties: novel univariate range and novel combinations of covariates.
Global, Australia, South Africa.
We developed a new multivariate statistical tool, based on the Mahalanobis distance, which measures the similarity between the reference and projection domains by accounting for both the deviation from the mean and the correlation between variables. The method also provides an assessment tool for the detection of the most influential covariates leading to dissimilarity. As an example application, we modelled an Australian shrub (Acacia cyclops) widely introduced to other countries and compared reference data, global distribution data and both types of model extrapolation against the projection globally and in South Africa.
The new tool successfully detected and quantified the degree of dissimilarity for points that were either outside the univariate range or formed novel covariate combinations (correlations) but were still within the univariate range of covariates. For A. cyclops, more than half of the points (6617 of 10,785) from the global projection space that were found to lie within the univariate range of reference data exhibited distorted correlations. Not all the climate covariates used for modelling contributed to novelty equally over the geographical space of the model projection.
Identifying non-analogous environments is a critical component of model interrogation. Our extrapolation detection (ExDet) tool can be used as a quantitative method for exploring novelty and interpreting the projections from correlative SDMs and is available for free download as stand-alone software from http://www.climond.org/exdet.