## 3 Results
### Performance of Modelling Algorithms  
All modelling algorithms for Acacia _decurrens_ identification were generally effective in terms of both AUC and TSS values (Figure 3 and Table 2). AUC values ranged between 0.84 (GLM and CART) and 0.93 (RF). TSS ranged from 0.64 to 0.81 (Table 2). RF received the highest TSS, and GLM received the lowest TSS among all SDM algorithms. GLM, CART, and MARS had the lowest performance out of all six algorithms based on both AUC and TSS values, and RF achieved the highest performance. ROC plots are graphical representations of sensitivity (the true positive rate) plotted against 1-specificity (the false positive rate). In these plots, an algorithm that exhibits a curve closer to the top-left corner demonstrates superior performance compared to an algorithm with the curve closer to the 45-degree line within the ROC space. For instance, the ROC plots generated using the GLM and CART algorithms (Figure 3) exhibit a section of the plot that leans closer to the 45-degree line, indicating relatively lower performance. These results are different from the RF ROC plots, which illustrate relatively higher performance. Sensitivity and specificity scores were high across all algorithms, signifying the effective identification of both the presence and absence areas of Acacia _decurrens_ (Table 2). This indicates that the proportion of correctly classified samples was maximum.  
The presence values of Acacia _decurrens_ plantation forest for the GLM, MARS, BRT, RF, SVM, and CART algorithms were 19.07%, 23.56%, 19.09%, 23.48%, 24.15%, and 24.72%, respectively. The best performing RF algorithm shows that Acacia _decurrens_ covered an area of approximately 15,818.53 ha within the study area.  
Ensemble modeling was employed to combine all the selected algorithms, reducing bias, and providing a relative evaluation of the significance of each predictor variable across all chosen modeling algorithms, with the intention of enhancing prediction performance [45]. According to the ensemble model result, 14,203.97 ha (22.44%) of the district was covered by Acacia _decurrens_, with a higher prevalence in the Southcentral and Central regions (Figure 4).  
\begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Variables** & **VIF** \\ \hline
1 & ARVI & 7.414995 \\
2 & Aspect & 1.190828 \\
3 & CVI & 6.169403 \\
4 & Elevation & 3.323751 \\
5 & GI & 3.797256 \\
6 & mSAVI & 3.771155 \\
7 & Rainfall & 3.080133 \\
8 & Road & 1.192230 \\
9 & Slope & 1.220056 \\
10 & Soil type & 1.724052 \\
11 & Temperature & 5.638469 \\ \hline \end{tabular}
\end{table}
Table 1: VIFs of the predictive variables after multicollinearity test with a cut-off threshold of 10.  
portance of each variable for Acacia _decurrens_ identification determined and variables with below 1% contribution (Aspect and Soil type) were excluded from the final modelling [95].  
The optimal environmental conditions that best represent the occurrence probability of Acacia _decurrens_ concerning both the vegetation indices and environmental variables are presented in Figures 6 and 7, respectively. They provide a quantitative representation of the relationship between predictors and the logistic probability of an Acacia _decurrens_ distribution. These curves assist in comprehending the ecological niche of the Acacia _decurrens_ within the predictor's range. Peaks in each curve indicate the values that influenced optimal model performance. The shape, the location of the peak, and the range of values around the peak provide valuable information that influences the distribution of Acacia _decurrens_. Among vegetation indices, the response curves with the highest peak value were observed for CVI, with a high probability in areas that have a value between \(\sim\)30 and 40, followed by GI (\(\sim\)0.8 and 0.9) and ARVI (\(\sim\)0.4 and 0.7). The response curve for temperature values exhibited the highest peak among the environmental variables, with a high probability in areas that have a temperature \(\sim\)28 \({}^