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 .