Phylogeny and comparative analyses
We built a supermatrix phylogeny of the Amphibolurine Agamidae based on
2 mitochondrial (ND2 and ND4) and 3 nuclear (BDNF, RAG-1 and BACH1)
genes, built around a multi-locus nuclear gene backbone taken from the
Zheng & Wiens supermatrix dataset (Pyron et al. 2013; Zheng &
Wiens 2016). Full details of the supermatrix assembly, alignment and
phylogenetic analysis are given in Supplementary Information
(Supplementary methods, Table S6, Figure S6). We used a subset of 1300
post-burnin trees (subsampled using logcombiner (Bouckaert et al.2019) and pruned of all non-focal taxa (Phytools R package; Revell 2012)
in subsequent phylogenetic comparative analyses.
We tested whether variation in the concentration of carotenoids and
pteridines was associated with environmental gradients of habitat
productivity (indirect compensation) or indices of sexual selection. The
response variables in these models were: 1) total carotenoids; 2) total
pteridines; and 3) the ratio of carotenoids to pteridines. The predictor
variables were environmental PC1 and PC2, sexual size dimorphism and
sexual dichromatism (which are uncorrelated, r2 =
0.05, Estimate = -0.003 – 0.009). Given that information on sexual
selection indices only exists at the level of species rather than the
individual, we also ran species-level models (27 species). We calculated
total carotenoids, total pteridines and the ratio of carotenoids to
pteridines based on average pigment concentration per species. We used
these measures as the response variables and the two indices of sexual
selection as predictors.
We next tested for associations between the concentrations of specific
carotenoid and pteridine pigments (direct compensation). The variables
in these models were the concentrations of: 1) dietary yellow-orange
carotenoids (lutein/zeaxanthin, 3’-dehydrolutein, β-carotene); 2) red
ketocarotenoids (astaxanthin, canthaxanthin); 3) yellow pteridines
(xanthopterin); 4) red pteridines (drosopterin); and 5) colourless
pteridines (pterin, 6-biopterin, isoxanthopterin, pterine-6-carboxylic
acid).
Lastly, we tested whether the concentration of pigments present in skin
tissue was associated with its colour. The response variables were
luminance (the brightness of the colour), saturation (the intensity of
the colour) or hue. For luminance and saturation, we ran two models with
the following predictors: 1) total carotenoids; and 2) total pteridines.
For hue we ran four models with concentrations of pigment subcategories
as predictors: 1) dietary carotenoids (yellow-orange); 2) xanthopterin
(yellow); 3) ketocarotenoids (red); and 4) drosopterin (red). Using
these same subcategories of pigments, we tested for concentration
differences between tissues with a yellow to red component (150 tissues,
including browns) and those without (36 tissues that were black, grey,
white or cream; total 186 samples). Lastly, we tested for associations
between colour (luminance, saturation and hue) and environmental
gradients of habitat productivity (PC1 and PC2).
All models were run as phylogenetically controlled mixed models in the R
package MCMCglmm (Hadfield 2010). We sampled 1300 phylogenies from the
posterior distribution of possible phylogenies generated in the Bayesian
phylogenetic analyses. The trees employed had 28 tips, which
corresponded to the 27 species sampled and two tips from the two
populations of Ctenophorus pictus . For all models we used
phylogeny as a random factor to control for phylogenetic relatedness
between species. Given that we had several individuals per species and
all individuals had more than one tissue sampled, we also included as
random effects the individual and species ID (except in species-level
models). We followed Ross et al. (2013) and sampled a tree at iteration
t, and ran the MCMC mixed model for 1500 iterations, saving the last
sample. This process was repeated for 1300 iterations (one per tree),
and the first 300 runs were discarded as burn-in. Inverse Wishart priors
(weakly informative) were used for the covariances and we used parameter
expanded priors for the random effects. We ensured that all effective
sample sizes were above 1000 and visually assessed convergence in the
models using the command plot(model). We used custom code to extract a
statistic that quantifies the percentage of variance explained by the
fixed factors in our models (equivalent to r2). The
graphs presented were generated using ggplot and the predicted fit lines
were obtained from simplified mixed models (same as described above but
only including significant variables). All pigment concentration
variables were loge transformed to facilitate
convergence, for variables with concentrations of zero we added 0.1 to
all samples to avoid infinite values. We present 95% confidence bounds
from the posterior distribution of the estimate based on phylogenetic
mixed models run on 1000 phylogenies, where cases in which the upper and
lower confidence bounds do not overlap zero indicate a significant
effect.