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Supplementary Material:
David A. Keith, Jane Elith, Christopher C. Simpson
'Predicting distribution changes of a mire ecosystem under future climates'
Appendix S2. Model diagnostics
Figure S1. Modelled response functions for the 4-factor Boosted Regression Tree model. Percentage figures
show variable importance in the model. Pann = Mean Annual Precipitation (mm); TR250 = Topographic
roughness index within 250m neighbourhood (metres); Tmin = Minimum Temperature of Coldest Period
(C); Mmin = Mean Moisture Index of Lowest Quarter MI (index). Black is mean response; grey shows 95%
confidence intervals (bootstrapped).
% deviance explained = 64.5; AUC = 0.978. 1100 trees.
Figure S2. Modelled response functions for the 4-factor Generalised Additive Model. (a) Pann, Mean
Annual Precipitation (mm). (b) TR250, Topographic roughness index within 250m neighbourhood (metres)
(c) Tmin, Minimum Temperature of Coldest Period (C). (d) Mmin, Mean Moisture Index of Lowest Quarter
MI (index). Y axes as above – ie logit probability of observing swamp. Dotted lines show 2*standard errors
(a)
(b)
(c)
(d)
Figure S3. Modelled response functions for the 3-factor Boosted Regression Tree model. Percentage figures
show variable importance in the model. Pann = Mean Annual Precipitation (mm); TR250 = Topographic
roughness index within 250m neighbourhood (metres); Mmin = Mean Moisture Index of Lowest Quarter MI
(index). Black is mean response; grey shows 95% confidence intervals (bootstrapped).
Deviance explained = 64.0%; AUC = 0.977; 1300 trees.
Figure S4. Modelled response functions for the 3-factor Generalised Additive Model. (a) Pann, Mean
Annual Precipitation (mm). (b) TR250, Topographic roughness index within 250m neighbourhood (metres)
(c) Mmin, Mean Moisture Index of Lowest Quarter MI (index). Y axes as above – ie logit probability of
observing swamp. Dotted lines show 2*standard errors
(a)
(c)
(b)
Fig. S5. Interactions between predictors for 4-factor Boosted Regression Tree Model
Fig. S6. Geographically stratified 7-fold cross-validation. Colours are absence points in the 7 folds
structured by catchments. Black points are the presence sites assigned to the fold where they lie – e.g. most
northern ones in red.
The table below shows the allocation of absences (0) and presences (1) to the 7 folds.
#
1
2
3
4
5
6
7
# 0 388 445 272 198 263 137 257
# 1 16 18 38 59 35 14 16
The results show little any difference in cross-validation deviance explained and AUC to the full
unstructured model (see model diagnostics in Figs S1 & S3).
4 variable model:
mean total deviance = 0.609
mean residual deviance = 0.153
estimated cv deviance = 0.264 ; se = 0.022
training data correlation = 0.863
cv correlation = 0.709; se = 0.049
training data ROC score = 0.991
cv AUC score = 0.965; se = 0.008
3 variable model:
mean total deviance = 0.609
mean residual deviance = 0.137
estimated cv deviance = 0.25 ; se = 0.026
training data correlation = 0.878
cv correlation = 0.716; se = 0.05
training data ROC score = 0.993
cv AUC score = 0.964; se = 0.009
Fig. S7. Spatial predictions from geographically stratified subsets of the data.
These maps show variation in predictions that arises from using data from fewer than all occupied catchments – specifically, from using datasets from the
spatially explicit cross-validation. Predictions are from the 4-variable BRT model, to either A. Current, or B Future (2050, GCM=CSIRO, Scenario=A1FI)
conditions. The models were fitted to the different sets of training data using fixed settings determined as optimal on the full dataset – i.e.: learning rate = 0.003,
bag fraction = 0.75, tree complexity = 5, number of trees = 1200. Fixed settings will tend to increase variability, if anything, but is a realistic set-up across
subsets of data. Most variability in predictions is in predictions to current times, though even for that the main patterns are stable. This result is consistent with
the estimates of predictive performance on the left-out training points (above).
A.
Predictions to current climate from subsets of data used in the spatially structured 7-fold crossvalidation
B.
Predictions to 2050 CSIRO A1FI from subsets of data used in the spatially structured 7-fold crossvalidation
Fig. S8. Comparison of climates at sample sites in current time with those projected in the study region for
2070 using CSIRO-Mk3 AIFI emission scenario (i.e. the most extreme combination examined) using
multivariate environmental similarity surfaces (MESS) in MaxEnt (Phillips et al. 2006; Elith et al. 2010;
2011). On left, novel climates for the study region are shown in red. On right the variables is “responsible”
for the novel climates are shown:– Tmin, Minimum Temperature of Coldest Period (C) on coast (orange);
Mmin, Mean Moisture Index of Lowest Quarter MI in north (green).