2.2 Field Methods and Calculation of Independent Variables
To examine changes in species diversity from before to after the 2011 Horseshoe Two Fire, we remeasured vegetation during the summers of 2017 and 2018 in 138 plots established and first measured in 2002 and 2003 (Poulos et al., 2007; Figure 1). The distribution of plots was initially stratified using vegetation cover types (Kubler, 2000; Taylor et al., in press). Sample points were placed in the center point of homogeneous areas of a cover type larger than 1800 m2. Highly dissected terrain with vertical rhyolitic towers made random or systematic sampling impossible, as we were limited to sites < 30° slope that were accessible by foot. Nevertheless, the plot network spanned gradients of vegetation types, topography, and fire severity arising from the Horseshoe Two Fire (Figure 2).
In the initial 2002-3 survey, woody vegetation at each selected point was sampled in 5 x 25 m belt transects established parallel to the slope contour. The location (GPS) and azimuth (º) of each belt transect were recorded. We measured the basal diameter of all shrubs and trees of each genet > 10 cm, counted individual juvenile plants (<10 cm basal diameter), tallied shrubs including cacti (stems), and estimated percent cover of each woody species in one of six cover classes (<1, 1-4, 5-24, 25-49, 50-74,75-100 %). Post-fire plot remeasurements in 2017-18 were identical to those employed in 2002-3 in the same 5 x 25 m belt transects.
Using Ward clustering with NbClust (3.0) in the vegan package (2.5-7) in R (R Core Team, 2020), 138 plots were clustered into three vegetation types: juniper woodlands (n=59), piñon woodlands (n=39), and pine-oak forest (n=40) (M. Freiburger et al., personal communication). Juniper woodlands were characterized by alligator juniper (Juniperus deppeana Steud.), Emoryi oak (Quercus emoryi Torr.), three-leaved sumac (Rhus trilobata Nutt.), Palmer’s century plant (Agave palmeri Engelm.), catclaw mimosa (Mimosa aculeaticarpa  Benth.), and twistspine pricklypear (Opuntia macrorhiza Englem.). Piñon woodlands were dominated primarily by border piñon (Pinus discolor Bailey and Hawksw), Toumey oak (Q. toumeyi Sarg.), pointleaf manzanita (Arctostaphylos pungensKunth), Wheeler’s sotol (Dasylirion wheeleri Wats.), Garry’s silktassel (Garrya wrightii Torr.), and sacahuista (Nolina macrocarpa S. Watson). Pine-oak forests were composed mainly of Chihuahua pine (P. leiophylla var. chihuahuana (Engelm.) Shaw), Apache pine (P. engelmannii Carr.), Arizona pine (P. arizonica Engelm.), Arizona white oak (Q. arizonica Sarg.), silverleaf oak (Q. hypoleucoides Camus), Arizona madrone (Arbutus arizonica (Gray) Sarg.), and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco).
We estimated fire severity of the 2011 Horseshoe Two Fire for each of the 138 plots using raster delta normalized burn ratio (dNBR; Eidenshink et al., 2007), a Landsat ETM+ derived product that estimates absolute change in fire severity from before to after a fire. The Normalized Burn Ratio is calculated from ETM+ bands 4 and 7 as (ETM4 – ETM7)/ (ETM4 + ETM7); ETM4 represents the near-infrared spectral range (0.76 -0.90 μm) and ETM7 the shortwave infrared spectral range (2.08 – 2.35 μm). Differenced NBR images (pre-fire NBR minus post-fire NBR) are referred to as dNBR images. Pre-fire Landsat ETM+ images are from the month before the fire and post-fire images are from 6 months after the fire for dNBR calculation. We selected dNBR rather than a relativized remotely sensed fire severity estimator because absolute change provides a more reliable measure than relative change for asessing vegetation cover change occurred in response to the Horseshoe Two Fire. We acquired dNBR data from the Monitoring Trends in Burn Severity data distribution site (https://www.mtbs.gov/), extracting a value for each plot with the point sampling tool in QGIS (QGIS Development Team, 2020). In some cases, dNBR was used as a continuous independent variable; in others, dNBR fire severity classes (none, low, moderate, and high; MTBS, www.mtbs.gov) were employed for analyses.
We used elevation and the topographic relative moisture index (TRMI; Parker 1982) as independent woody plant diversity predictors, as past research has revealed their importance of in regulating woody plant species composition (Poulos et al., 2007). Elevation was extracted in QGIS (QGIS, 2020) for each plot from 30-m resolution digital elevation models (DEM) (https://lpdaac.usgs.gov); TRMI was calculated from field measured topographic position (ridge, upper elevation, mid elevation, lower elevation, and valley), slope direction (in degrees), slope steepness (in degrees), and surface shape (convex, convex-straight, straight, concave-straight, and concave). TRMI provides a quantitative xeric to mesic continuum among plots, independent of elevation. We also extracted and used the terrain ruggedness index (TRI) from the 30-m DEMS in QGIS, which is defined as the mean difference between a central plot pixel and its surrounding 8 pixels.