3 RESULTS
Goldenrod species were observed in 60.5% of the squares (in 3544 out of
5850 finally examined squares). Solidago gigantea was the most
frequent species (53.1%, 3107 squares) followed by S. canadensis(21.4%, 1255 squares).
Solidago gigantea localities were widespread throughout almost
the entire area, aside from the higher altitudes in the southern part of
the study region. The S. canadensis was concentrated in the
western part of the study area, while being sporadically dispersed in
the eastern part and also avoiding the southern fragment with higher
altitudes (Figure 2).
The average value of AUC was 0.836 for S. candensis and 0.786 forS. gigantea . Despite some differences in model evaluations of
particular spatially blocked folds (Figure 3), the models for S .canadensis generally performed better than those for S.
gigantea . The parsimonious (simplified) model for S. canadensisrelied on a higher number of explanatory variables than those forS. gigantea .
FIGURE 2. Distribution of invasive Solidago species
(orange color) in studied region. The light gray color show distribution
of squares with confirmed Solidago absence. Squares excluded from
analysis, are not shown (left blank).
FIGURE 3. The values of area under curve (AUC) for simplified
models of S. canadensis and S. gigantea distributions,
with spatially blocked, 5-fold cross-validation.
Both species reacted to climatic conditions, expressed by the annual
average temperature (Tam) and temperature seasonality (Ts), as well as
the distance from the initial introduction sites (Figure 4). Moreover,
the spatial pattern of distribution of S. canadensis was also
explained by anthropogenic factors, such as population density as well
as the percentage of agricultural lands (cropland). The full list of all
variables included in the final models, along with their relative
influence, is shown in Figure 4.
FIGURE 4. Variables importance for each variable involved in
the simplified models. The whiskers denote the standard deviation
calculated basing on spatially blocked cross-validation.
The modelled response of species on particular variables is shown in
Figure 5. The distribution of both species was climatically limited,
with the species being unlikely to occur in regions with an average
annual temperature below 5.5°C. The probability of S. canadensisoccurrence increased with human population density (Figure 5), as well
as distance from its introduction site, with squares placed 100 km
distant from the initial sites of introduction having the highest
probability. The distribution of S. gigantea was also correlated
with the pattern of its initial introduction, and the probability of its
occurrence generally decreased with the distance (Figure 5), reaching
the lowest value at about 40 km and fluctuating above it.
FIGURE 5 The modeled responses of Solidago species for
particular environmental variables. The shape of the response was
modelled using the evaluation strips method (Elith et al., 2005), with
spatially blocked, 5-fold cross-validation. The graphs are sorted
according decreasing value of variables’ importance, upper panel forS. canadensis , lower – for S. gigantea .
Finally, the projection of the modelled probability of the presence of
the invasive Solidago species was performed, employing the
‘projection’ function in the Biomod2 package. The projection was
performed five times, for each spatially blocked fold in
cross-validation, and then averaged. The results of the projections are
presented on Figure 6. The average cutoff values, calculated basing on
the AUC values, were 0.205 for S. canadensis and 0.539 forS. gigantea .
FIGURE 6 The projected probability of presence of the invasiveSolidago species. The optimal cutoff value was 0.205 for S.
canadensis and 0.539 for S. gigantea .