## 4 Discussion
### Integration of Various Remote Sensing Metrics  
The effect mechanism of different environmental variables on species distribution is debatable [115], which limits the application of certain metrics to model the species distribution quantitatively. We applied three commonly used machine learning models in the integration of the remote sensing metrics. There were differences in the results generated from the three models; RF generally outperformed SVM and NN in our case study. In this study, SVM and NN exhibited high uncertainty in species richness modeling, with the estimated datasets showing higher r-square and lower RMSE than the training datasets. In consideration of the AIC values, the RF model provided a better representation of the metrics integration of remote sensing metrics in this study than the other two models. Previous studies have suggested that differences in the results of various machine learning models may be due to the sample size, or the ratio between the size of the training sample and the estimated sample. [116; 117]. However, there was no improvement in the performance of SVM and NN in species richness modeling, when we increased the proportion of the training sample and decreased the proportion of the estimated sample (Figure S3). RF has broader scope than SVM and NN, because it has no limitation on the distribution pattern of the training data. The complexity of the parameter setting may limit the performance of SVM and NN for model training [118]. Although, SVM has the advantage on solving non-linear problems, a major downside of SVM is that it can be painfully inefficient to train [119; 120]. Another main advantage of RF is that it handles very well with a large number of training examples, and it is not recommended to use SVM to handle large training examples, which might lead to a better performance of the RF. In the training process, we observed a large gap between RF, SVM, and NN. In addition, the computation time required for modelling differed considerably among the three machine learning models (Table 2). The computational efficiency of the SVM and NN models were much higher than that of the RF model. In this study, the multivariate integration index based on the RF model exhibited 20% more explained variance than the univariate metrics. Many species richness monitoring and modelling studies have been carried out in previous decades [3; 4]. Our result, using three categories of remote sensing metrics, exhibited twice the explained variance of previous studies, which used texture metrics and net primary productivity (NPP) [25]. Previous studies showed DHI components explained between 47% and 75% of total bird species richness (BBS) in Ontario (North America), and we extended the spatial scale from regional to global [61]. Although these studies selected different species richness \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Species** & **SVM** & **RF** & **NN** \\ \hline Mammal & 4.514s & 13.635s & 2.639s \\ Bird & 4.465s & 14.252s & 2.651s \\ Amphibian & 3.497s & 14.173s & 2.421s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The time statistics of the three machine learning models with 5000 training samples and 5000 prediction samples. datasets, a comparison of the correlations was still reasonable, and we asserted that the multivariate integration index had a better correlation with species distribution than univariate metrics on a global scale. Since the evolution of a species is a very slow process, the link between these remote sensing metrics and species characteristics is stable for decades [121]. Thus, the multivariate integration index we developed can be used for mapping the global species richness annually, which would provide great support for global biodiversity trend detection. At latitudinal and longitudinal zones, some differences between simulated species richness and in situ species richness were observed (Figure 8). There were two possible reasons that led to this disagreement.