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Supporting Information: Figures S1-S9
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Figure S1: Number of bivariate models used to build ESMs (a) for different sample sizes (N1 ≤ 25; 25 <
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N2 ≤ 50; N3 > 50) and variable importance for ESMs (b and c) and standard SDMs (d). The plots show
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the number of times a predictor was considered in a bivariate model for ESMs based on GLMs, GBMs
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and Maxent (b) and the mean Somers' D of the bivariate models per predictor which was used as
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weight for ESMs (c). The variable importance for standard SDMs (d) is 1 minus the correlation
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coefficient between models including and excluding a variable.
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The median number of bivariate models considered to build ESMs (considered if Somers’ D > 0) was
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50 with a minimum of 20 bivariate models (a). For some species more than half of the bivariate
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models were skipped from ESMs, however, for each ESM every predictor was kept at least 2 times in
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a bivariate model (b). Contrary to ESMs, every modelling technique of standard SDMs frequently
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dropped variables completely (i.e. variable importance is 0 in d). The overall pattern of variable
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importance for ESMs is the same compared to standard SDMs, however, each of the 11 predictors
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were always kept for the ensemble (c). This means that ESMs are not superior to standard SDMs
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because they use cross-validation to drop non-informative predictors, rather they are superior
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because they do not drop but keep them (although down-weighted) for the ensemble. Thus, ESMs
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are much more informative than standard SDMs where a variable is either in or out.
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Figure S2: Correlation matrix and histograms of model performance based on the five evaluation
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indices used: Area under the Curve (AUC), True Skills Statistics (TSS), sensitivity (Se), specificity (Sp)
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and Boyce index. Both standard SDMs and ESMs, as well as each of the three modelling techniques
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and their ensemble, are included in the figure. TSS, Se and Sp were highly correlated with AUC (|r| ≥
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0.7, provided in bold). Only the Boyce index was negligibly correlated with the other indices.
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Figure S3: Model performance according to True Skills Statistics (TSS), sensitivity (Se) and specificity
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(Sp) and its relationship with different modelling strategies (Standard and ESM) and techniques
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(GBM, GLM and Maxent) as well as their ensemble prediction (EP).
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Fig. S4: Boxplots of Pearson correlation coefficients between predictions of two modelling techniques
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when used as standard SDMs and within the ESM framework. The predictions of different techniques
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were clearly more similar with ESMs.
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Fig S5: Evaluation of the species distribution models by AUC (top) and the Boyce index (bottom) using
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the calibration dataset of the transferability assessment. For the transferability assessment only the
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34 species in the group 25 < n ≤ 50 (Fig. 3) were considered and split into one halve for calibrating
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and one halve for independently evaluating the models. Significant differences (***: p ≤ 0.001, **: p
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≤ 0.01, *: p ≤ 0.05, ƚ: p < 0.1) between standard SDMs and ESMs are indicated for each technique
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(GBM, GLM and Maxent) and the ensemble prediction (EP).
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Figure S6: Mean AUC score (left) and Boyce index (right) as well as the standard error bars of ESMs
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and standard SDMs evaluated with the transferability assessment. The evaluation measures on the x-
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axes are based on 50-fold split sampling of the calibration dataset (western partition of Switzerland,
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see Fig. S4), while evaluation measures on the y-axes are based on the independent test dataset
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(eastern partition of Switzerland, see Fig. 4).
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Figure S7: AUC against an increasing number of averaged bivariate models to build an ESM evaluated
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on the test dataset of the transferability assessment for three species. Bivariate models were
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randomly added to the ESM until the ESM contained all 55 possible bivariate models. The grey lines
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in each row of panels represent 20 random runs, the red lines in each panel indicate the mean of the
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20 runs and black lines represent the standard error. The horizontal black lines show the AUC of the
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corresponding standard SDM. The species shown are a) Asplenium adulterinum, b) Sedum rubens and
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c) Typha minima.
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Figure S8: Boxplots of the performance of Ensemble Small Models (ESM) in comparison to different
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approaches to build standard SDMs. In addition to the approach used in the main text (BIC variable
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selection for GLMs and without further variable selection for Maxent), for both techniques models
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were built following an all subset approach and selecting the best performing model based on cross-
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validated (CV) AUC scores. 50-fold split sampling of the training data from the transferability
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assessment was used for model evaluation. Model performance was not significantly improved by an
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all subset approach and cross-validated variable selection compared to a selection using stepwise BIC
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for GLM and no pre-selection for Maxent. Performance of variable selection using cross-validation
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was even smaller when evaluation was based on Boyce index. These results do also hold when
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models were evaluated using the test data of the transferability assessment (Fig. S9).
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Figure S9: Performance of Ensemble Small Models (ESM) in comparison to different approaches to
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build standard SDMs analogous to Table S2 but evaluated with the testing data from the
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transferability assessment. The model performance was always highest for ESM.
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