Aerial mapping: Bison wallows were mapped in 2011 using aerial photographs from Riley County Geographic Information Systems (https://gis.rileycountyks.gov/), and again in 2019 using aerial imagery obtained from the National Agriculture Imagery Program (United States Department of Agriculture Farm Service Agency, Salt Lake City, Utah).  We then used Esri (Environmental Systems Research Institute Inc., Redlands, California) ArcMap to identify wallows at scales of 1:669 (2011) and 1:663 (2019), using a fishnet grid to track areas that had been searched.  A wallow was identified as any oval area with bare or partially bare ground, or with a clearly defined border of vegetation different from that surrounding it.  For the purposes of this study, we used only those wallows with 50% or less plant cover, resulting in the identification of 3,231 wallows in the 2011 dataset and 2,936 wallows in the 2019 dataset.  Because of differences in scale and resolution, data from 2011 and 2019 were analyzed separately. Density of mapped wallows were analyzed based on fire frequency, elevation, and slope.  

Landscape descriptors (frequency of fire, elevation, and slope) were identified using using Esri ArcMap 10.8 software. Fire frequency is part of the overall experimental design of KPBS and is applied to each watershed within the bison-grazed enclosure at intervals of 1, 2, 4, or 20 years. Data on slope and elevation were obtained using a 2-meter digital elevation model generated from Lidar (LIght Detection And Ranging) data. Elevation was classified into quartiles, resulting in four levels of elevation corresponding to 333 to <360, 360 to <388, 388 to <415, and 415 to 443 meters above sea level. Slope was classified into three levels corresponding to 0 to <6, 6 to 12, and >12 degrees, allowing for absorption of small variations in slope into surrounding areas for smoothing purposes. The overlaid combination of fire frequency, elevation quartile, and slope levels defined 4,174 unique area polygons. We then counted the number of wallows in each polygon for the 2011 and 2019 datasets.

Physical characterization: Between 8 June and 13 August 2020, we surveyed a subset of wallows randomly selected from the 2011 dataset.  For each wallow surveyed, we collected two measurements of the longest axis and two measurements of the shortest axis of the wallow. We also took measurements of depth every 61 cm (i.e. 2 feet) along the longest axis of the wallow. Length and width (in meters) of each wallow were defined as the average of the two measurements collected of the longest and shortest axes, respectively. We calculated the surface area, A (m2), of each wallow using an elliptical approximation, such that A = π * (length/2) * (width/2), where π is the mathematical constant 3.14159. Wallow depth (in centimeters) was defined as the median depth measurement along the longest axis. Wallow volume, V (m3), was approximated using the formula for an ellipsoid divided by two, such that V = ½ (4/3 * π * (length/2) * (width/2) * (depth/2)). For each measured wallow, the slope (in degrees) of the surrounding terrain was obtained from ArcGIS data. We also recorded whether the wallow was located on a grazing lawn or not.  A grazing lawn was defined by the presence of short-cropped grasses and abundant forbs.  Finally, we recorded whether the wallow contained any aquatic or terrestrial vegetation in a binary yes/no manner.