2.3 Statistical Analysis
General Approach. We analyzed γ, α, and β for (1) changes over the two sample periods for all plots, for each vegetation type separately, and for burned vs. unburned plots separately and (2) their continuous relationships with dNBR and the three topographic variables. Where interaction terms were integral to an explicit hypothesis, we retained significant and insignificant interactions; otherwise, insignificant interactions were dropped from models. For continuous independent variables, we first tested second-degree polynomial models, dropping the quadratic term when it was insignificant; first order terms were retained in cases of a significant quadratic component. Separate from the diversity analyses, we used correlation analysis to identify relationships among gradients of fire severity (dNBR), elevation, TRMI, and TRI.
Gamma Diversity. For landscape diversity (γ), we used rarefaction (“EstimateS” 9.10; Colwell and Elsensohn, 2014) to estimate species richness (with 95% confidence intervals) and test for changes in γ from pre-fire to post-fire for all plots combined and for each of the three vegetation types separately. We tested whether temporal change in γ was tied to the Horseshoe Two Fire and, if so, at which fire severities, by analyzing each of the four fire severity classes (no fire and low, moderate, and high severity). If the fire drove temporal changes, we would expect change for one or more of the classes of burned plots but not for unburned plots.
Alpha Diversity. For α, we used the “vegan package” (Oksanen al., 2020) in R (R Core Team, 2020) to calculate species richness, evenness, inverse Simpson diversity index, Shannon-Weiner diversity index, Simpson index, and unbiased Simpson index for each plot for before and after the Horseshoe Two Fire. We used paired t-tests (in R) to compare 2002-2003 vs. 2017-2018 α metrics for all plots combined and for each of the three vegetation types separately.
We tested whether temporal changes in α could be attributed to fire and, if so, at which severities, with paired t-tests for sets of plots that did not burn and those that experienced low, moderate, and high severity fire. We used “lme4” (Bates et al. 2013) and “lmertest” (Kuznetsova et al., 2020) in R to test linear and polynomial mixed effects models for the influence of fire severity as a continuous variable (dNBR) on α and the interaction of timestep and dNBR, with the prediction that fire severity would affect α under post-fire conditions only. Mixed effects models were used to account for nesting across time within plots. We examined whether vegetation types differed in the shape (linear, hump-shaped, etc.) of the species richness-fire severity relationship by running linear and polynomial regressions of the change in the number of species over time for each plot vs. dNBR for each vegetation type separately.
We used linear and polynomial mixed effects models to examine the relationship of α metrics with the topographic variables, elevation, TRMI, and TRI. The interaction term (timestep*topographic variable) of these models tested for shifts in these relationships from the pre-fire to post-fire period.
Beta Diversity. For β, we used “vegan,” “betapart” (Baselga et al., 2020), and “ecodist” (Goslee & Urban, 2007; Goslee et al., 2020) in R to calculate a variety of Sorensen dissimilarity statistics among plots on species presence-absence matrices. We partitioned total β into nestedness and turnover components (Baselga, 2010, 2012) to assess which process best explained spatio-temporal patterns. Nestedness occurs when communities with smaller numbers of species are subsets of richer ones, whereas species turnover refers to the replacement of some species with others (Baselga, 2010, 2012). Where appropriate, we tested whether a second-degree polynomial model provided a better fit than a linear one for continuous independent variables.
We used three different approaches to test hypotheses about β—all focused on the roles of time, fire, vegetation types, and topography. First, we calculated pairwise dissimilarities among all plots (“pairwise plots”; mission V4 of Anderson 2011) for the pre-fire and the post-fire sample periods separately. We tested hypotheses with these dependent variables using the adonis2 test in vegan, which employs the permutational MANOVA approach of McArdle & Anderson (2001). Classical statistical tests were inappropriate for these data because of the lack of independence among pairwise plot dissimilarities. We statistically tested for changes in total β, species turnover, and nestedness across the two sample periods for all plots and for each of the three vegetation types separately. To assess the extent to which the Horseshoe Two Fire drove these temporal changes in β, we separately analyzed plots that did not burn (control) vs. those that experienced low, moderate, and high severity fire. Finally, we used the adonis2 test to develop the best model for the role of elevation, TRMI, and TRI in controlling β.
As a second and complementary approach (Legendre & De Cáceres, 2013), we calculated pre-fire vs. post-fire dissimilarities separately for each plot (“matched plots”; mission T2 of Anderson et al., 2011). We used general linear effects models (Hothorn et al., 2015) to test for differences in prefire-postfire dissimilarities among the three vegetation types, among the four fire severity categories, across dNBR, and with respect to topography (elevation, TRMI, and TRI). We examined whether vegetation types differed in the shape (linear, hump-shaped, etc.) of the β-fire severity relationship by running linear and polynomial regressions of dissimilarities for each plot vs. dNBR for each vegetation type separately.
Finally, we used Mantel tests to examine whether post-fire plot dissimilarities in species presence were correlated with Euclidian distances for fire severity (dNBR) and each of the topographic variables (“mantel tests”; mission T3 of Anderson et al., 2011). Additionally, we carried out a mantel test on the relationship between a matrix of pre-fire minus post-fire pairwise plot species dissimilarities vs. the Euclidian dNBR distance matrix in order to assess whether temporal changes in plot species dissimilarities were positively related to variability among plots in fire severity. These mantel tests of fire severity test the hypothesis that pyrodiversity promotes β. For these mantel tests, we also evaluated whether any of the significant relationships could be explained simply by differences between plots in geographic distance. We calculated pairwise plot geographic distances using the Geographic Distance Matrix Generator (Ersts, 2021), which were then subjected to a mantel test between beta diversity and distance and to partial mantel tests using each independent variable with distance as a second explanatory variable.
We examined the overall contributions of α and β to γ for before vs. after the fire using rarefied γ for all plots, mean α richness per plot, and β calculated as Whittaker’s β (1972) βw = γ / α.