SUPPORTING INFORMATION
Appendix S1
Spatial predictors
Spatial filter computation
To account for non-environmental spatial constraints on the marsh harrier distribution, we
used spatial variables obtained through eigenvector mapping (hereafter called spatial filters;
Griffith & Peres-Neto, 2006; De Marco et al., 2010). This method assumes that the spatial
arrangement of all points of the study area (i.e., sample locations or, as in our study case, the
regular grid cells of the whole study area) can be translated into a set of predictor variables,
which capture spatial effects at different spatial scales (Diniz-Filho & Bini, 2005; Václavík et
al., 2012). The inclusion of spatial filters in the models allowed us to account for the effect of
subjacent spatial structures that were not captured by the environmental factors considered
(De Marco et al., 2010).
We computed the spatial filters in SAM 3.0 (Rangel et al., 2006) by constructing a
pair-wise distance matrix amongst all grid cells of the study area using their Universal
Transverse Mercator coordinates (i.e., latitude and longitude). The distance matrix was
truncated at four times the maximum distance that connects all cells under minimum spanning
tree criterion, and from this modified distance matrix 481 positive spatial filters were
computed using principal coordinate analysis (Borcard & Legendre, 2002). Because of the
computational limitations of SAM (i.e., calculations could not be carried out for more than
about 4000 cells, Moriguchi et al., 2013), spatial filters were created using coordinates at a
coarse resolution (20x20 km) and then interpolated to the same resolution as environmental
variables (1x1 km) using the inverse distance weighted method (IDW) in ArcGIS 9.3 (BlachOvergaard et al., 2010; Moriguchi et al., 2013). We selected IDW because it is a good
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interpolator for phenomenon whose distribution is strongly correlated with distance,
particularly for closely packed, consistently spaced sample point sets (Kennedy 2009).
However, we acknowledge here that interpolation of the spatial filters from the 20-km
resolution to the 1-km resolution may result in more smoothed trends in the spatial
eigenvectors than using the data from the 1-km resolution directly. We presume that such
differences might be greater in more rugged landscapes than in more gently sloping regions
but due to the aforementioned computational obstacles this issue was not examined in this
study.
We then proceeded with a forward logistic regression procedure to select an adequate
number of spatial filters to be included as independent variables in SDMs (Griffith & PeresNeto, 2006; Peres-Nesto & Legendre, 2010). This way, only filters that in fact contain
important parts of the geometry of the data were used in SDMs. Filter selection was
conducted for the breeding and wintering seasons separately. For these analyses, we used the
occurrence data and 10,000 randomly selected points from areas from which the species is not
known to reside as pseudo-absences. We used Moran’s I coefficients and correlograms to
evaluate spatial patterns in selected filters as a measure of their spatial structure (Diniz-Filho
& Bini, 2005).
Spatial filters selected
In total, 17 filters were selected for the breeding season (Fig. 5a; for comparison with results
obtained according to a random subsample of the breeding period dataset, see Fig. S3 in
Supporting Information) and 19 for the wintering season (Fig. 5b) to describe spatial
variability in marsh harrier occurrence data. The spatial complexity and variable shape of
correlograms showed how selected filters reflected different spatial structures at different
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spatial scales (see Fig. S4 in Supporting Information for the map pattern of selected filters).
High levels of spatial autocorrelation in the first, intermediate and last distance classes
(represented by large positive and negative values of Moran’s I coefficients) tended to be
portrayed by a map pattern containing few major clusters of similar values as in the first
eigenvectors (e.g. F1, F4). As the degree of positive spatial autocorrelation decreased in filters
with lower eigenvalues, the map pattern became more fragmented (e.g. F30, F80),
representing finer-resolution spatial variation in the data. Overall, filters selected for the
breeding season had higher eigenvalues than those for the wintering season, meaning that
aggregation patterns of the species in the breeding season occur at broader spatial scales than
in winter (i.e., probability of occurrence differs more between sites that are further away from
each other during the breeding season than during the wintering season, thus the occurrence
patterns are patchier during the winters).
Supporting references
Blach-Overgaard, A., Svenning, J.C. Dransfield, J. Greve, M. & Balslev, H. (2010)
Determinants of palm species distributions across Africa: the relative roles of climate,
non-climatic environmental factors, and spatial constraints. Ecography, 33, 380-391.
Borcard, D. & Legendre, P. (2002) All-scale spatial analysis of ecological data by means of
principal coordinates of neighbor matrices. Ecological Modelling, 153, 51-68.
De Marco, P.Jr., Diniz-Filho, J.A.F. & Bini, L.M. (2010) Spatial analysis improves species
distribution modelling during range expansion. Biology Letters, 4, 577–580.
Diniz-Filho, J. A. F. & Bini, L. M. (2005) Modeling geographical patterns in species richness
using eigenvectorbased spatial filters. Global Ecology and Biogeography, 14, 177-185.
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Griffith, D.A. & Peres-Neto, P.R. (2006) Spatial modeling in ecology: the flexibility of
eigenfunction spatial analyses. Ecology, 87, 2603–2613.
Kennedy, K.H. (2009) Introduction to 3D Data: Modeling with ArcGIS 3D Analyst and
Google Earth, Ed. John Willings & Sons, Inc., Hoboken, NJ, USA.
Moriguchi, S., Onuma, M. & Goka, K. (2013) Potential risk map for avian influenza A virus
invading Japan. Diversity and Distributions, 19, 78-85.
Peres-Neto, P.R. & Legendre, P. (2010) Estimating and controlling for spatial structure in the
study of ecological communities. Global Ecology and Biogeography, 19, 174-184.
Rangel, T. F. L. V. B., Diniz-Filho, J.A.F., Bini, L.M. (2006). Towards an integrated
computational tool for spatial analysis in macroecology and biogeography. Global
Ecology and Biogeography, 15, 321-327.
Václavík, T., Kupfer, J.A. & Meentemeyer, R.K. (2012) Accounting for multi-scale spatial
autocorrelation improves performance of invasive species distribution modelling (iSDM).
Journal of Biogeography, 39, 42–55.
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FIGURES
Figure S1. The distribution of the six environmental variables: annual precipitation (PAN);
minimum temperature of the coldest month (TMIN); maximum temperature of the warmest
month (TMAX); slope (SLO); percentage of open vegetation (VEG) and percentage of aquatic
habitats (AQ).
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Figure S2. Model performance of univariate models based on 6 1x1 km environmental
variables containing information at 1km2 and 100km2 resolution: annual precipitation (PAN);
minimum temperature of the coldest month (TMIN); maximum temperature of the warmest
month (TMAX); slope (SLO); percentage of open vegetation (VEG) and percentage of
aquatic habitats (AQ). Mean AUC of 15 replicate Maxent runs and standard deviation are
shown.
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Figure S3. Spatial correlograms of spatial filters selected for the breeding distribution of
marsh harriers in peninsular Spain according to a random subsample of the breeding period
dataset (i.e., 284 locations). Correlograms were defined by Moran's I coefficients in 10
distance classes, indicating links among points of the study area successively separated by
100 km. Filters for the breeding season are: F1, F4, F5, F6, F7, F11, F12, F25, F30, F34, F37,
F42, F48, F49, F50, F55, F340; where increased number in the name of the filters indicates
subsequently lower eigenvalues.
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Figure S4. Example of geographic patterns of 9 of the selected spatial filters used in this
study. First spatial filters, such as F1 and F4, represented spatial correlation at broad spatial
scales. For example, the spatial pattern of F1 shows two major clusters of high and low
values, respectively, portraying a north-south gradient in Spain, while Filter 4 captures a
north-west / south-east gradient in the study area. Subsequent filters portray more oscillatory
patterns across Spain, representing aggregation patterns as subsequent lower scales.
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Figure S5. Observed and averaged predicted distributions of the marsh harrier in Spain in the breeding period according to a random
subsample of 284 localities of the breeding period dataset. Predicted distributions are based on Maxent models using different sets of
predictors: climate (CLIM model), climate and habitat predictors (CLIM+HAB model) or climate plus habitat and spatial filters
(CLIM+HAB+SPAT model). Note that models developed for each set of predictors were calibrated using 15 different randomly selected
subsamples of the data (averaged predictions are shown).
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TABLES
Table S1. Pearson correlation coefficient of the environmental variables and spatial
filters. Correlation is based on 10,000 randomly picked cells. Significant correlations
(P < 0.05) are shown in bold letters.
Variable
TMIN
TMAX
TAN
TMAX
0.448
TAN
0.897
0.78
SLO
-0.367
-0.518
-0.487
PAN
-0.045
-0.668
-0.368
0.494
VEG
-0.117
0.108
-0.036
-0.25
-0.329
AQ
0.162
0.08
0.153
-0.092
-0.016
10
SLO
PAN
VEG
-0.032
Table S2. Differences in model performance based on different sets of predictors for a random subsample of 284 localities of the breeding
period dataset. Model performance is assess using different measures of accuracy and model fit (AUC, AICc, BIC, sensitivity and specificity)
and modelling techniques (GLM and Maxent). Note that for each set of predictors, 15 replicate models with different subsets of the data were
conducted. The mean ± sd of the 15 replicate models conducted for each predictor set are shown. Comparisons are based on Mann-Whitney U
test. Letters indicate models that are not significantly different after Bonferroni corrections (i.e. at α ≤ 0.01). Best models are shown in bold.
GLM
AUC
AICc
BIC
Sensitivity
Specificity
Maxent
AUC
AICc
BIC
Sensitivity
Specificity
CLIM
HAB
CLIM+HAB
SPAT
CLIM+SPAT
HAB+SPAT
CLIM+HAB+SPAT
0.73 ± 0.03
1704 ± 18
1747 ± 18
0.70 ± 0.08a
0.66 ± 0.04a
0.82 ± 0.01a
1552 ± 10
1590 ± 12a
0.82 ± 0.05b,c
0.68 ± 0.04a
0.83 ± 0.02a,b
1514 ± 16
1587 ± 16a
0.77 ± 0.06a,c,d
0.74 ± 0.04b
0.85 ± 0.02b,c
1457 ± 22
1632 ± 25b
0.71 ± 0.10a,d
0.80 ± 0.07b,c
0.86 ± 0.02c
1403 ± 21
1613 ± 20b
0.77 ± 0.08a,c,d
0.76 ± 0.05b
0.88 ± 0.01c
1329 ± 20a
1539 ± 23c
0.83 ± 0.04b
0.83 ± 0.03c
0.88 ± 0.01c
1320 ± 18a
1549 ± 22c
0.78 ± 0.05a,b,c,d
0.81 ± 0.03c
0.72 ± 0.01
5129 ± 6
5146 ± 6
0.65 ± 0.04a
0.70 ± 0.02
0.81 ± 0.02a
4999 ± 17
5017 ± 18a
0.84 ± 0.03b
0.66 ± 0.01
0.83 ± 0.02a
4964 ± 15
4999 ± 16b
0.79 ± 0.05b,c
0.74 ± 0.02
0.82 ± 0.01a
4927 ± 14
5021 ± 13a
0.69 ± 0.05a
0.82 ± 0.04a
0.85 ± 0.02
4883 ± 21
4989 ± 22b
0.77 ± 0.05c
0.77 ± 0.03b
0.87 ± 0.01b
4819 ± 14a
4926 ± 14c
0.80 ± 0.08b,c
0.79 ± 0.05a,b
0.88 ± 0.01b
4822 ± 19a
4940 ± 20c
0.80 ± 0.08b,c
0.79 ± 0.06a,b
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