## 2 Materials and Methods
### Developing a Nomadic Landscape Model: Climate-Vegetation-Livestock Interactions  
Together, Mongolian summer and winter pastures make up a peculiar nomadic landscape where pastures feed livestock and livestock move seasonally between pastures [21]. Livestock fatten in summer pastures with fresh biomass and survive in winter pastures with standing dry biomass (i.e., residue). Summer temperature, precipitation, and aridity determine summer vegetation growth, while winter temperature and precipitation affect the accessibility of livestock foraging to the residue forage in winter pasture [1]. Here, deep snow or ice cover prevent livestock from foraging the residue in winter pasture (i.e., low accessibility), and cold stormy weather can restrict the foraging range nearby winter shelter (i.e., low mobility). Winter mortality and summer reproduction are the primary causes of interannual changes in livestock numbers in Mongolia. With favorable winter and summer conditions, reproduction (i.e., _birth_) exceeds mortality (i.e., _loss_), causing net livestock increase. However, in harsh winter conditions, sometimes following poor summer pasture conditions, livestock loss is high and usually peaks in mid or late winter (i.e., January or later); this may last until the spring gestation period, resulting in a low birth rate. Emergency migration, _otor_, is a rapid and sometimes long-distance movement of herders and their pastoral household in autumn to seek better pastures or to flee bad weather and poor foraging in a coming _Dzul_[11; 34]. Because of the complex social and administrative factors that influence this migration [34], it is difficult to predict the timing, magnitude, and destination of _otor_. Hence, this study excludes the _otor_ effect in our analyses. Though slaughtering (i.e., slaughter) is performed for meat consumption and the income of local herders, it is marginal for herders who live remote and obtain major income from dairy and cashmere productions. By varying the slaughter rate for each livestock, herders use slaughter to increase goat numbers relative to sheep. We summarize the key features on nomadic pastoralism described above into a simplified schematic landscape model suggested, Figure 2. The schematic model was designed to illustrate the climate-vegetation-livestock interactions occurring in summer and winter pastures and their seasonal connectivity through nomadic movements at the level of the herder's nomadic landscape in Mongolia. Figure 2: A schematic nomadic landscape model describing the climate–vegetation–livestock interactions in Mongolian pasturelands. The subscripts of s and w means summer and winter variables,respectively; T, temperature; P, precipitation; ET, evapotranspiration; GPP, gross primary production; NPP, net primary production; R\({}_{\rm w}\), autotrophic respiration; biomass, a summation [\(\Sigma\)] of growing season NPP; residue, dead standing biomass; sheep, livestock numbers in a sheep unit; _loss_, natural mortality (the winter _loss_ is subject to _Dzud_); _slaughter_, meat production; _otor_, emergency long-distance migration. The bold arrows highlight the different biomass conversion processes in summer and winter pastures. The seasonal perspectives connecting summer and winter conditions were used in earlier studies investigating _Dzud_ phenomena [9; 10; 16]. By combining the seasonal perspective with the spatial perspective of separating and connecting the seasonal pastures, our model provides a more mechanism-oriented explanation on the natural seasonal mechanisms inherent in nomadic landscapes. The schematic model describes key state variables (i.e., biomass, residue, sheep), control variables (e.g., dryness, accessibility, mobility, sheep quality), and external forcing variables (T and P). Additionally, the model distinguished and expressed two explicitly flux variables (_otor_ and _slaughter_) that are affected by socioeconomic factors such as governance or markets.