## 3 Results
### Factors Influencing Changes in Livestock Numbers
#### 3.2.2 RF and SMR Modeling and Primary Factors  
The RF model estimated the percent change in livestock number in a better linear fit with the reported percent change than the SMR, while the RF underestimated the change, resulting in a higher RMSE than the SMR (Figure 6a,b). Consequently, the RF and SMR explained 89% and 82% of the temporal and spatial variations found in the reported percent change in livestock numbers, respectively. Moreover, in the _soun_-level comparisons, the RF depicted the interannual livestock changes very well, showing high R\({}^{2}\) values of over 0.9 in most _soums_ investigated (Figure 7a). In contrast, the SMR was successful for 203 _soums_, equivalent to 70% of the _soums_ investigated, but failed in the other 30% _soums_. Additionally, the SMR showed relatively low _soun_-level R\({}^{2}\) values with 0.81 on average (Figure 7b).  
Figure 5: Scatter plots of primary and secondary principal components of the PCA. The same result is illustrated with different categories of (**a**) year and (**b**) rate of change in livestock numbers.  
Figure 6: Evaluation and statistics of stepwise multiple regression (SMR) analyses: (**a,b**) _soum_-level comparison of observed and predicted annual rate of change in livestock numbers (%) from the FRand SMR models for 2003-2010, respectively; (**c,d**) percent relative frequency of _soum_-level primary factors from the FR and SMR models, respectively, using data for 2003-2009 (blue circles, without 2009-2010 _Dzud_ data) and 2003-2010 (dark yellow bars).  
The factors that had the greatest impact on the percent change in livestock numbers had similar proportions by season at both modeling analyses (Figure 6c,d). The ratios between summer winter variables were 61% vs. 39% and 51% vs. 49% for RF and SMR, respectively. However, the proportions of winter variables decreased when the _Dzud_ year data was excluded in the modeling from 39% to 36% and from 49% to 30% for RF and SMR, respectively. Looking at the importance of each factor, winter temperature (T\({}_{\rm w}\)) was the most frequent primary factor across _soum_s in both model studies. These results imply that the impacts of winter conditions on the _Dzud_ occurrence becomes important, but that summer conditions also have an equally large influence, and even more so in normal years.  
In the spatial patterns of primary factors, RF and SMR produced spatial patterns somewhat differently locally but similar regionally (Figure 7c,d). In the RF model, the summer water conditions such as P\({}_{\rm s}\) and dryness were the prevailing primary factors of the Gobi in the south; winter temperature (T\({}_{\rm w}\)) in the northern mountainous regions and in the eastern plain steppe; and NDVI\({}_{\rm s}\) in the Altai region in the west (Figure 7c). In contrast, T\({}_{\rm s}\) and P\({}_{\rm w}\) appeared somewhat randomly scattered across Mongolia. The SMR model produced similar regional patterns but a new lumped pattern of P\({}_{\rm w}\) in mid-western mountainous areas (Figure 7d).  
Figure 7: Results of RF (**a,c**) and SMR (**b,d**) modeling for 2003–2010: (**a**) R\({}^{2}\) of RF models; (**b**) R\({}^{2}\) of SMR models; (**c**) primary factors of RF models; (**d**) primary factors of SMR models. The dashed areas are _soum_s excluded from the modeling due to data gaps. The blank areas in (**d**) are _soum_s where the SMR model was not created.