2.3 Statistical analysis
To calculate statistical correlations and differences between
populations at the 5% level of significance, we performed
Kruskal-Wallis H and Wilcoxon rank tests for multiple groups, and
Mann-Whitney U-tests for two groups, using R (R Core Team). We also
compared numerical data of colour variable populations to non-variable
conspecifics that are less constrained by population and / or habitat
size. In our analyses, the dependent variable (genetic diversity) and
independent variables (body size, population size, and level of habitat
fragmentation) were compared. However, because the species included in
our study are mainly found in three different taxonomic families, the
data lacks independence, due to which we calculated the difference
between variable and non-variable populations for each metric for each
species, assuming that what happens within each species in terms of
population divergence is independent of what is happening in other
species. From this difference data for each species we calculated 95%
Confidence Intervals (CI) with an independent T-test to determine
whether the mean difference was different from zero. This was done for
allelic richness, expected heterozygosity, and inbreeding coefficients.
All significant correlations were visualized with ggplot2 in R (Wickham
et al., 2016).
We also tested how body weight influenced colour variants in species
with a phylogenetic generalized linear mixed models (PGLMMs), which
estimates regression coefficients for binary and continuous data while
incorporating interspecific relatedness (Ives & Halmus, 2011). A
phylogeny and data frame of 70 carnivore species (Datafile S1) were
adopted from Diniz-Filho & Tôrres (2002), to which colour variant
presence / absence data were added (Datafile S2). We evaluated PGLMMs in
‘phyr’ 1.0.3 R package (Li et al., 2020), to test whether body weight
(log-transformed) was associated with the presence of colour variants.
Log transformation normalizes the strong right skew in metrics, which is
recommended for comparative approaches (Ives & Garland, 2014). Because
species only occur once as tips of the phylogeny, we used the
pglmm_compare() function. Range size (log-transformed), and
phylogenetic covariance were set as a random factor in our models, and
results were presented with standard error (SE). We calculated
R2 for PGLMM models using the package ‘rr2’
1.0.2 (Ives, 2019).