Appendix S1. Addressing Spatial Autocorrelation
Introduction
A common challenge in interpreting species distribution patterns deals with spatial autocorrelation.
Spatial autocorrelation (SA), resulting from spatial dependence between species presences or as a
response to a spatially autocorrelated environmental factor, can lead an increased risk of a type I
error (i.e. falsely reject null hypothesis) (Lichstein et al., 2002; Dormann et al., 2007). Various
analytical techniques are currently available to test and to account for the occurrence of SAR in
ecological data. Most of such techniques, however, require continuous data or parametric error
estimates of species environment relations to assess the effect of SAR (Moran’s I test, Conditional
Autoregressive model s, Simultaneous Autoregressive models, etc) (Rangel et al.; Legendre, 1998;
Lichstein et al., 2002; Dormann et al., 2007; Allouche et al., 2008). Yet, when species absence data is
not available and species-environment relations are predicted by using presence-only data, such
techniques are not applicable. Hence, to investigate whether elephant presence data used in this
study and the resulting niche model was affected by spatial dependence between elephant
observations or spatially autocorrelated environmental predictors, we used an alternative approach.
Methods
First, to investigate whether the observed pattern of elephant occurrences in the north of
Aceh were clustered in space, Ripley’s L function was used (Ripley, 1977; Wiegand & Moloney,
2004). This method compares the observed pattern of species presences in space to the pattern of
points as expected based on a complete spatial randomness over a range of distances (Wiegand &
Moloney, 2004). If species occurrences are not completely random, the observed pattern could
either be a result of (1) spatial dependence of localities (i.e. presences are more likely to be
observed in adjacent transects) or (2) a response of the elephants to a spatially autocorrelated
environment (Legendre, 1998). On the other hand, if the observed pattern of elephant presences
does not deviate from the expected pattern of complete spatial randomness, the observed
distribution of elephant presences is accepted to be a result of a random process and hence can be
considered to encompass a spatially independent data sample. In other words, in absence of spatial
clustering, the observed presence of elephants at one transect is unlikely to be a result of elephant
presence in any adjacent transect.
The Ripley’s L statistic was calculated several times for increasing distance classes
incrementing by 100 meters up to a maximum of 5000 meters, corresponding to the maximum
distance between sample plots. In order to produce unbiased estimates of point clustering within
and between sample plots the extent of the analysis was constrained by the outlines of the sampled
area. Significance intervals of the obtained statistic were determined by means of 99 random Monte
Carlo simulations. For each trial, a number of points corresponding to the number of observations
within the original dataset, were randomly positioned to the analysis window and Ripley’s L statistic
was calculated. The point pattern of elephant presences was considered to be random if the
corresponding L-statistic fell within the 95% confidence envelope of the simulated trials.
Secondly, to assess whether the predictor variables used for elephant niche model
construction were spatial autocorrelated, possibly affecting the results of the ENFA analysis, spatial
correlograms were calculated (Rangel et al.; Rossi et al., 1992; Bellehumeur & Legendre, 1998). The
average similarity between elephant presence points was calculated by means of the Moran’s I
statistic (and 95% confidence interval) and plotted over 10 classes of increasing between-point
distance intervals (500m increments). As such, this method allows determining at what distance
spatial autocorrelation exists and pseudo sampling of species distributions might occur (Anselin,
1995).
Finally, to assess whether spatial autocorrelation in the predictor variables influenced the
niche model predictions, the ENFA analysis was repeated separately using two pruned datasets.
Therefore, elephant presence points occurring within 500 or 1000 meters of any adjacent presence
point were omitted, resulting in two datasets relating to plot and site level presence observations.
Data analysis was conducted using the R statistical computation environment version 2.11.1
(packages: adehabitat, maptools and spatstat).
Results and conclusions
Of all possible point-pair combinations within the extent of the analysis (i.e. 5000m from a focal
point) 42 (15%) of all point-pairs were within 500m and 65 (23%) point-pairs were within 1000m
distance of each other. The results of the point pattern analysis showed that the observed pattern of
elephant presences across the north of Aceh did not differ significantly from a pattern expected
based on complete spatial randomness. Therefore observed pattern of elephant presences can be
considered spatially independent (Figure S1).
The analysis of spatial autocorrelation in the predictor variables used to describe the
elephants’ niche in the north of Aceh showed that all variable except for the variable Landscape
curvature over 500m were significantly affected by spatial autocorrelation (Figure S2). One variable
(Landscape curvature over 5000m) showed significant spatial autocorrelation at a 500 meter
interval, two variables (NDVI, Slope) were autocorrelated at distances up to 1000 meter and 4
variables (Elevation, Ruggedness, Road density and Forest cover) were autocorrelated at distances of
more than 1000 meter.
Figure S1 Plot of the observed point clustering (black dots) and the 95% confidence interval of 99
Monte Carlo trials of complete spatial randomness (black lines) against the between-points distances
Figure S2 Correllograms for each of the eight ecogeographical predictors included in the ENFA
analysis. Each diagram shows the relative spatial autocorrelation indicated by the Morans I statistic
for over ten distance intervals incrementing by 500 meters (0-5000 meters). Error bars indicate the
95% confidence interval around the average value.
Since the model predicted by the ENFA analysis showed high correlation with both Landscape
curvature over 5000m as well as the predictors: NDVI, Road density and Forest cover, the results
could potentially be biased due to pseudo replication. Yet, since elephant presence observations
showed no apparent pattern of spatial dependence between points, any inference about elephant
habitat preferences in response to the environment is expected to solely reflect habitat selection
processes.
This hypothesis is confirmed by the results from the additional ENFA analysis. The elephants’
niche model appears to produce consistent results at different spatial scales. Hence, predictors
which most strongly correlated to the elephants’ niche under the initial model were also the
predictor variables shaping the elephants’ niche using the datasets in which adjacent points were
omitted (Figure S3). Model performance was good (AUC=0.830.02, N=48) under the 500m dataset
and reasonable under the 1000m dataset (AUC=0.780.02, N=41).
Since no significant clustering was found between elephant presence points and the fact
that the ENFA analysis produced consistent results even when the predictor variable were spatially
autocorrelated in some cases, the niche model presented is believed to be valid. Our results have
shown that the survey design used to collect invaluable data on elephant habitat produces robust
results on elephant habitat selection and habitat suitability, also at different spatial scales.
Figure S3. Bi-plots of the first two factors extracted by the ENFA analysis showing the marginality
scores on the x-axis and the first specialization factor scores on the y-axis. The background
environment of the whole study area is indicated by light grey polygons and the area used by
elephants is indicated by dark grey polygons. The relative correlation between the two factors
(marginality and specialisation) and each of the eight predictor variables are indicated by arrows.
The niche model predicted by the ENFA analysis using the elephant presences pruned at 500m
distance (A) does not deviate from the niche model predicted based elephant presences pruned at
1000m (B)
A
B
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