Larson, E.R., R.V. Gallagher, L.J. Beaumont and J.D. Olden.
Generalized “avatar” niche shifts improve distribution models for invasive species
Appendix S4. Species characteristics and native range climates for narrowing avatar ensembles
Predicting Niche Shifts by Species Traits
We evaluated the suggestion of Larson & Olden (2012) that similarity of ecological traits,
phylogenetic similarity, or other species characteristics (e.g. native range, residence time since
invasion) could be used to match avatars to emerging invaders and improve transferability of
niche shifts. We first classified our 26 focal species into a set of niche shift groups based on
observed changes in means, variances, and covariances for four climate predictors between
native and total ranges. We then attempted to predict membership to these niche shift groups
based on plant species characteristics given by Table 1 in Gallagher et al. (2010). Our intent was
to find species characteristics that could a priori predict niche shift types for invaders and
consequently improve performance of avatar models for emerging invaders. In particular, we
sought to improve on the relatively poor performing median avatar models, anticipating that
avatar niche shifts using reduced ensembles might produce models that could approximate the
reduction in errors of omission found for extreme avatar models without the accompanying
increase in errors of commission.
We first classified niche shifts into a reduced set of groups for better matching avatar
ensembles to emerging invaders. We used the Bray-Curtis dissimilarity coefficient to create a
cluster dendrogram (Appendix S4 Figure 1) based on changes in mean, variance, and covariance
between native and total ranges for our 26 invasive plants (Figure 1). From this cluster
dendrogram, we identified four general niche shift groups, although two of these groups had few
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species (two and three species; Appendix S4 Figure 1). We also visualized these niche shift
groups using a principal coordinates analysis (PCoA) on the same Bray-Curtis dissimilarity
coefficients (Appendix S4 Figure 1). All multivariate analyses were conducted using the vegan
library in R. Of the four niche shift groups, one group had small niche shifts as measured by changes in
minimum temperature variance, covariance between minimum temperature and minimum precipitation,
and mean maximum precipitation (Group 1; Appendix S4 Figure 1). Two other groups (Group 3; Group
4) had large niche shifts as changes in these same climatic variables. A final group (Group 2) had large
niche shifts as measured by changes in maximum temperature variance, covariance between maximum
temperature and minimum temperature, and covariance between maximum precipitation and minimum
precipitation (Group 2; Appendix S4 Figure 1).
A resource manager modeling the potential distribution for an emerging invader would
want to anticipate which such niche shift group the emerging invader was likely to belong to
based on species characteristics. We used characteristics compiled for our 26 focal species from
Gallagher et al. (2010) to attempt to predict membership to niche shift groups. These
characteristics included: seed dispersal mode (assisted or unassisted; assisted seeds disperse by
wind, water, or animals), growth form (grass, herb, shrub, tree, vine), longevity (annual or
perennial), seed mass (g), weed status (invasive or naturalized; see Diez et al., 2009), residence
time (years since introduced to Australia), province of native range (Afrotropic, Nearctic,
Neotropic, Palearctic), and extent of native range size (10-arcminute grid cells occupied in the
native range). The selection of these characteristics draws from theory and empirical study of
invasion success and pattern; for example, native range size is often an effective predictor of
invasiveness (Pysék et al., 2009; Shah et al., 2012), whereas time since introduction influences
invasion success (Dawson et al., 2009) and might set the extent to which a species has spread,
which could influence observed niche shift type (Václavík & Meentemeyer, 2012). The
2
functional traits of species have also been shown to provide some capacity for predicting
invasions success (see Van Kleunen et al., 2010 for a review). For example, species with annual
life-cycles, which tend to possess smaller seeds and an herbaceous growth form, have been
shown to be disproportionately represented in the invasive species pool (Sutherland, 2004). We
used these species characteristics in a classification tree to attempt to predict membership to the
four identified niche shift groups (see above). The classification tree model was developed in the
rpart library in R following the methodology of De’ath & Fabricius (2000), with a minimum end
node size of two species to accommodate our smallest niche shift group (Group 2). We identified
the best performing tree using the one standard error rule based on 10-fold cross-validation
(De’ath & Facricius, 2000).
The best performing tree used a single split (province of native range) to produce two end
nodes assigning species membership to either niche shift Group 1 or Group 4 (Appendix S4
Figure 1). Species predicted to belong to Group 1 had Nearctic or Neotropical native ranges,
whereas species predicted to belong to Group 4 had Afrotropical or Palearctic native ranges. This
simple classification tree correctly assigned 8 of 11 species to Group 1 and 9 of 15 species to
Group 4 (Appendix S4 Figure 1). Two species belonging to Group 3 and one species belonging
to Group 4 were misclassified as belonging to Group 1. Three species belonging to Group 1, two
species belonging to Group 2, and one species belonging to Group 3 were misclassified as
belonging to Group 4. A resource manager concerned with predicting the potential distribution of
an emerging invader would not have information available to know if a misclassification to niche
shift group had occurred. Accordingly, we used classification to these two niche groups (Group
1, Group 4) including misclassifications to develop reduced sets of ensemble avatar models for
comparison to our full ensemble avatar model (see main text). As noted above, we made this
3
comparison only for the median avatar model. We repeated the avatar modeling methodology
from the main text specific to classification tree assignments to Group 1 (11 total species) and
Group 4 (15 total species; Appendix S4 Figure 1). Performance was evaluated as errors of
omission, errors of commission, and AUC for Group 1 and Group 4 avatar models relative to the
total median avatar model from the main text, with single-sample t-tests used to evaluate whether
the mean difference between the two models deviated significantly from zero (no change).
Classification by species characteristics to reduced avatar ensembles that shared niche
shift types did not improve model performance over median avatar models from the full
ensemble of species (Appendix S4 Figure 2). The Group 1 avatar model did not differ
significantly from the total median avatar ensemble by errors of omission (t = 1.797, P = 0.103),
commission (t = 0.714, P = 0.492) or AUC (t = -0.798, P = 0.444). Likewise, the Group 4 avatar
model did not significantly differ from the total median avatar ensemble by errors of omission (t
= -1.967, P = 0.069), commission (t = 1.288, P = 0.219), or AUC (t = -1.746, P = 0.103). Failure
to find improved model performance for reduced, characteristic-based avatar ensembles might
relate to misclassifications from the tree, although our misclassification rate of 35% is plausible
for what a resource manager implementing our approach might encounter. Further, for
consistency with the main text, we did not incorporate the infrequently observed sign changes in
covariance between native and total ranges in characterizing niche shift groups by cluster
dendrogram and PCoA. Including greater niche shift detail may improve identification of and
assignment to niche shift groups, although preliminary data investigation including sign changes
in covariance did not suggest this to be the case. Similarly, preliminary investigations evaluating
whether a phylogeny built for our 26 focal species might better predict to niche shift groups was
similarly discouraging.
4
Predicting Niche Shifts by Native Range Climates
An alternative approach might be to attempt to anticipate niche shifts by considering only
the native range climates of focal species. One advantage of this approach over that investigated
above is that emerging invaders would not need to be assigned via species traits to a potential
niche shift group, which carries an associated risk of misclassification. Emerging invaders could
instead be directly assigned to avatar invader groups with which they share similar native range
climates. However, this approach is dependent on the assumption that the character and
magnitude of subsequent niches shifts is dependent on starting climatic conditions for each
species (i.e. species with similar native range climates will experience similar niche shifts during
invasion). We evaluated a native range climate-based approach via a process similar to that
above. We first identified similar groups of our study species based on the climates in their
native ranges, with a specific focus on mean values of maximum and minimum temperature and
precipitation to identify a climatic center for each species. We then used both a cluster
dendrogram (on Euclidean distance) and visualization by Principal Components Analysis (PCA)
to assign our study species to four groups based on these native range climates. These groups
spanned gradients of warmer native range climates with higher maximum precipitation values to
cooler native range climates with higher minimum precipitation values (Appendix S4 Figure 3).
Generalized avatar niche shifts were then transferred to “emerging” invaders in each group from
the remaining species in their native range climate ensemble (as in main text and above). As
previously, performance was evaluated as errors of omission, errors of commission, and AUC for
the reduced groups relative to the total median avatar model from the main text, with single-
5
sample t-tests used to evaluate whether the mean difference between the two models deviated
significantly from zero (no change).
Performance of avatar niche shifts by native range climate groups was more variable than
observed for avatar niche shifts as predicted by ecological traits (above). Group 1 did not differ
significantly from the total median avatar ensemble by errors of omission (t = -0.431, P =
0.685), errors of commission (t = -1.953, P = 0.108), or AUC (t = -0.829, P = 0.449).
Alternatively, Group 2 experienced marginally more errors of omission (t = 2.215, P = 0.069),
significantly fewer errors of commission (t = -2.763, P = 0.033), and a marginally lower (or
worse) AUC (t = -2.431, P = 0.051). Group 3 performed better than the total median avatar
ensemble by errors of omission, which reduced significantly (t = -5.930, P = 0.002); performed
worse by errors of commission, which increased significantly (t = 3.932, P = 0.011); and did not
differ by AUC (t = 0.026, P = 0.981). Similar to Group 1, results for Group 4 differed little from
the total median avatar ensemble. Group 4 did not differ significantly by errors of omission (t =
0.949, P = 0.379), experienced a small but significant reduction in errors of commission (t = 2.798, P = 0.031), and did not differ significantly by AUC (t = 0.527, P = 0.617).
Ultimately, avatar niche shifts based on similarity of native range climates failed to
reliably improve on model performance of the total median avatar ensemble – although the
significantly reduced errors of omission for Group 3 (above) suggest that in some cases (or for
some climates) avatar ensembles defined by native range climates may improve on larger,
indiscriminate ensembles. Yet in general, these results suggest that similarity of native range
climates between emerging invaders and their avatars does not assure similarity of the niche
shifts (or their absence) that they experience. To directly evaluate this, we performed a Mantel
test seeking to evaluate the relationship between native range climate similarity (Euclidean
6
distance; above) and niche shift similarity (Bray-Curtis dissimilarity; above) as pairwise
comparisons between all of our focal species (Appendix S4 Figure 5). Although this Mantel test
was significant (P = 0.037; 999 permutations), it had little explanatory power (Mantel r = 0.137;
Appendix S4 Figure 5), as similarity of native range climates between species does not seem to
assure that they will experience niche shifts of similar character or magnitude during the invasion
process.
Conclusions and Future Directions
We conclude by suggesting that idiosyncrasies of the invasion process might impede
matching avatar species to emerging invaders by species characteristics like native range
climates, ecological traits or phylogenetic relatedness. For example, both Gallagher et al. (2010)
and Petitpierre et al. (2012) similarly failed to predict niche shift types by the same or similar
sets of ecological traits used here. We agree with many of the explanations from those authors
for this phenomenon: data quality issues may erratically misrepresent the niche for either the
native or non-native range independent of any species characteristics, and the invasion process is
likely ongoing for many species and accordingly different proportions of the total niche are being
represented (e.g. Václavík & Meentemeyer, 2012). As such, large ensembles of avatar invaders
may be preferable over small ensembles or single avatars matched by species characteristics,
because larger ensembles may average out the invasion idiosyncrasies of individual species and
represent a more generalizable niche shift. Further, these large ensembles seem to buffer against
implausible niche shifts that violate relationships between variance and covariance and produce
impossible correlation values (see main text).
7
However, we conclude by urging researchers to continue to explore better methods to
predict the magnitude and character of niche shifts for anticipating the potential distribution of
emerging invaders. As a recent example, Donaldson et al. (in press) demonstrate that discordance
between native and invasive range climates observed in invasive species may be predictable by
invasion pathway and associated locations (urban vs. natural) of initial introduction. Such
developments hold promise to further improve the avatar invader concept discussed here,
although we emphasize that we believe our extreme avatar niche shifts (main text) already
provide a useful “worst case scenario” of niche shift that may be applied for precautionary
distribution models of emerging data-poor invaders.
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Appendix S4 Figure 1. A cluster dendrogram of niche shift attributes (Main Manuscript Figure
1) using Bray-Curtis dissimilarity, identifying four candidate niche shift groups: Group 1 (white),
Group 2 (light gray), Group 3 (dark gray), and Group 4 (black). Color scheme is used to refer to
niche shift groups throughout the figure. Niche shift groups are also visualized by principal
coordinates analysis (PCoA) on Bray-Curtis distances with niche shift attributes that load
significantly on components (axes) plotted as vectors in the top panel, and species identities
provided as the first letter of the genus and first three letters of the specific epithet in the bottom
panel. A simple classification tree is used to assign membership to the four niche shift groups by
species characteristics (see Appendix S4 text), with classification to Group 1 signified by a
square end node and classification to Group 4 signified by a circle end node. These end node
symbols are provided in the PCoA to further clarify instances of correct classification to niche
shift groups or misclassification, which is also given by histograms in each of the two
classification tree end nodes.
10
Appendix S4 Figure 2. Comparisons of Group 1 and Group 4 avatar niche shifts as assigned by
classification tree (Appendix S4 Figure 1) to the median avatar niche shift from the main text for
errors of omission, errors of commission, and AUC. A dashed line signifies no difference
between models.
11
Appendix S4 Figure 3. A cluster dendrogram of native range climates using Euclidean distance,
identifying four native range climate groups: Group 1 (white), Group 2 (light gray), Group 3
(dark gray), and Group 4 (black). Color scheme is used to refer to native range climate groups
throughout the figure. Native range climate groups are also visualized by principal components
analysis (PCA) with native range climate attributes (maximum and minimum temperature and
precipitation) plotted in a correlation circle in the top panel, symbols as Group 1 (squares),
Group 2 (circles), Group 3 (triangles), and Group 4 (diamonds) in the top panel, and species
identities provided as the first letter of the genus and first three letters of the specific epithet in
the bottom panel.
12
Appendix S4 Figure 4. Comparisons of native range climate groups (one through four) to the
median avatar niche shift from the main text for errors of omission, errors of commission, and
AUC. A dashed line signifies no difference between models.
13
Appendix S4 Figure 5. Niche shifts as Bray-Curtis dissimilarity (Appendix S4 Figure 1)
regressed against native range climates as Euclidean distance (Appendix S4 Figure 3) for all
pairwise comparisons of study species. Similarity of native range climates significantly predicts
similarity of observed niche shifts (P = 0.037; 9999 permutations) but with low explanatory
power (Mantel r = 0.137).
14