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.