Supplemental S1. Species Distribution Modeling Methodology
We adopted Araújo and News’s (2007) approach and niche models and their
associated geographic projections were built using a series of combinations of methods,
variables combinations and the climatic scenario defined above. Four different methods
were used for modeling the species’ distribution: BIOCLIM, Mahalanabis Distances,
Genetic Algorithm for Rule Set Production (GARP) and Maximum Entropy (MAXENT).
The BIOCLIM (Hijmans et al., 2002; Busby, 1991) is based on the production of
envelopes that should contain the presence points in the multidimensional environmental
space. The Mahalanobis Distance method (Farber and Kadmon, 2003) determines the
distance of each point in multivariate space to the centroid of this space (optimum of the
species), taking into account the covariance structure among explanatory variables. The
GARP method (Stockwell and Noble, 1992) is based on artificial intelligence that works
by combining rule sets with the purpose of getting the most accurate prediction to the
considered region. The MAXENT (Phillips and Dudik, 2008) is a method for making
predictions based on incomplete information, and estimates a target probability
distribution by finding the distribution of maximum entropy which is closest to the
uniform one. This optimization is subjected to a set of constraints representing the
incomplete information about the target distribution.
For each of the climates (i.e. current time, 6 kyr BP and 21 kyr BP), a total of 1,400
different models were generated, using distinct combinations of dataset partition and
variable selection. The SDMs were processed in the integrated computing platform
BioEnsembles (Diniz-Filho et al., 2009). The BioEnsembles platform, available by
request from the authors, is software for optimization and takes advantage of high-speed
parallel processing. First, the full dataset was randomly partitioned into two subsets
(training and projection), with 70% and 30% respectively, and this procedure was
replicated 50 times. For each subset, we obtained a total of 7 models by performing all
combination of the three environmental variables (2n-1, n = 3). Each model was truncated
based on the ROC curve (see Allouche et al., 2006), transforming quantitative predictions
of some models (e.g., distances from species’ niche centroids in Malahanobis distances)
into a binary vector of 0/1, indicating absence or presence of the species in each cell
(Diniz-Filho et al., 2009). Following Allouche et al. (2006), the evaluation of models was
done by the True Skill Statistics (TSS) and, because our analyses are based on presenceonly data, we also focused on the specificity (which is the proportion of correctly
identified presences in the validation data set). Models with TSS < 0.5 were not used to
obtain final ensemble projection (Table 2). The final variable analyzed for each SDM was
then the frequency with which D. alata is predicted in each cells, called here Estimated
Occurrence Frequencies (EOF). This EOF indicates the more climatically suitable areas
for the species. Each of the EOF vectors was then averaged and weighted (by TSS) and
consensus of the frequencies was produced.
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