Gradient forests: calculating importance gradients on physical predictors

Abstract

In ecological analyses of species and community distributions there is interest in the nature of their responses to environmental gradients and in identifying the most important environmental variables, which may be used for predicting patterns of biodiversity. Methods such as random forests already exist to assess predictor importance for individual species and to indicate where along gradients abundance changes. However, there is a need to extend these methods to whole assemblages, to establish where along the range of these gradients the important compositional changes occur, and to identify any important thresholds or change points. We develop such a method, called "gradient forest," which is an extension of the random forest approach. By synthesizing the cross-validated R2 and accuracy importance measures from univariate random forest analyses across multiple species, sampling devices, and surveys, gradient forest obtains a monotonic function of each predictor that represents the compositional turnover along the gradient of the predictor. When applied to a synthetic data set, the method correctly identified the important predictors and delineated where the compositional change points occurred along these gradients. Application of gradient forest to a real data set from part of the Great Barrier Reef identified mud fraction of the sediment as the most important predictor, with highest compositional turnover occurring at mud fraction values around 25%, and provided similar information for other predictors. Such refined information allows for more accurate capturing of biodiversity patterns for the purposes of bioregionalization, delineation of protected areas, or designing of biodiversity surveys.

Physico-chemical thresholds in the distribution of fish species among French lakes

“…A total of 500 trees were generated for each random forest. Individual variable importance was estimated using constrained permutations to reduce the influence of correlated variables (correlation coefficient > 0.5) (Strobl et al, 2008;Ellis et al, 2012). As required for regression tree analysis (De'ath and Fabricius, 2000), the variance of BPUE data was stabilized using a log-transformation after addition of the minimal strictly positive value for each species.…”

How well does random forest analysis model deforestation and forest fragmentation in the Brazilian Atlantic forest?

“…Model fitness is examined using validation data that is not in the training sub-sample; hence, cross-validation with external data is not necessary. The validation sample is also used to calculate measures of variable relative importance (Ellis et al 2012b). The outputs from all of the trees are then averaged, which provides predictive accuracy and low bias (Breiman 2001).…”

“…We used the R "extendedForest" library provided by the Gradient Forest project Ellis et al 2012b) to carry out RF analysis. This package was developed for use in ecological studies of species distributions.…”

“…This package was developed for use in ecological studies of species distributions. It integrates results from RF analyses for a number of individual species distributions into results that enable prediction of multiple species distributions Ellis et al 2012b). In addition, it is able to analyse large numbers of potential factors and to reduce bias when predictors are correlated .…”

“…RF is used widely in bioinformatics (Cutler and Stevens 2006), for land cover classification (Gislason et al 2006) and analysis of medical experiments, for example. Although there were few ecological applications, it has recently gained popularity in this area (Prasad et al 2006;Fu et al 2010;Gilbert and Chakraborty 2011;Bonilla-Moheno et al 2012;Ellis et al 2012a;Leal et al 2016).…”