## 2 Materials and Methods
### Understanding Factors of Vegetation Cover: Stepwise Backward Regression
#### 2.2.2 Model Variables  
In order to understand the factors of vegetation health in and around national parks of southern Africa, the normalized difference vegetation index (NDVI) was used as a measure of vegetation health and abundance. NDVI is calculated as: \(\frac{NIR-R}{NIR+R}\), where R is the red band and NIR is the near infrared band [46]. This index works on the principle that NIR is highly reflective in healthy vegetation and red is highly absorptive in healthy vegetation. NDVI values range from \(-1\) and \(+1\), with any value above 0 indicating vegetation and above 0.9 saturating out in dense healthy vegetation [46]. The NDVI product from the Moderate Resolution Imaging Spectroradiometer (MODIS) MOD13Q1.006 Terra Vegetation Index (250 m spatial resolution) was used in this research. This NDVI product was obtained from Google Earth Engine (GEE) and had been atmospherically corrected on a per-pixel basis and was also pre-masked for water, clouds, heavy aerosols, and cloud shadows. The data has also been through the quality assessment check with the provided pixel reliability band. These products are 16 day MODIS observation composites where the pixel value is equal to the NDVI value of the observation closest to nadir view. This is determined between the top two NDVI observations during a 16 day period. The monthly product used spanned from March 2000-November 2016. This data was aggregated into seasons: December, January, February (DJF)--boreal winter/southern Africa wet season; March, April, May (MAM)--boreal spring/southern Africa wet season; June, July, August (JJA)--boreal summer/southern Africa dry season; and September, October, November (SON)--boreal autumn/southern Africa dry season. This study focuses only on the wet seasons (DJF and MAM), given that during the dry season, NDVI values in this region are very low. Over the 21 st century, these seasons were broken into finer temporal periods of 2000-2004, 2005-2008, 2009-2012, and 2013-2016 to determine if different factors were important at different times across the overall time period of 2000-2016. The seasonal mean NDVI during each time period was used as the dependent variable in the following regressions. The independent variables in these regressions were: country (X1), land cover (X2), area (X3), mean annual precipitation (X4), human population (X5), elevation (X6), and transfrontier (X7). All of the variables except for country (coded) and transfrontier (yes or no) were at the 1 km spatial resolution, and were extracted at the park/buffer scale. The country variable is designated in the model to accountfor management type, depending on the country name and boundaries, which were obtained from the Thematic Mapping website [47]. The land cover variable is designated in the model depending on the cover type [42]. Within a park or buffer, the land cover type at a pixel level occurring most often was used as a representation of the respective area. Generally, land covers across these national parks are varying types of savannas [1]. This land cover data was obtained from the Global Land Cover Facility at the University of Maryland [42]. The area variable represented the size of each park and buffer zone. Precipitation, gathered from the Global Historical Climatology Network, represents longer-term climate, and was calculated by creating the mean annual precipitation (MAP) across the parks and buffers over 30 years [41]. The population density variable is measured in people per km\({}^{2}\) and was obtained from the WorldPop 2015 dataset [48]. Elevation, which has a complex relationship with vegetation (at extreme highs there is little vegetation, but at mid-level vegetation trees may be the most productive vegetation types and grasses may be less productive, and shrubs may decline consistently with increasing vegetation) is potentially an important explanatory variable [49]. The average elevation was calculated (m) for each park and buffer with data from the Shuttle Radar Topography Mission [50].