Statistical analyses
Full codes for statistical analyses are presented in ESM 4. Life history
variables exhibited a variety of correlations that suggested substantial
collinearity, so variable reduction was necessary. We thus conducted a
principal components analysis (PCA) using the R package FactoMineR
(Lê, Josse, & Husson, 2008) to extract
independent orthogonal eigenvectors (PC axes) for later phylogenetic and
generalized linear mixed modelling analyses (ESM 4). We investigated the
inter-specific relationships between TL variables and life-history axes
as represented by the first three PC axes. We evaluated how phylogeny
accounted for overall variance of TL variables and the species scores on
PC1, PC2 and PC3, using linear mixed models in a Markov chain Monte
Carlo environment (MCMCglmm) (Hadfield,
2010). MCMCglmm allows inclusion of phylogenetic tree files in glmm
models, in a Bayesian framework. MCMCglmm also statistically
“controls” for phylogenetic dependence among variables that is due to
the pattern of shared evolutionary ancestry of the species, so that
“phylogeny-adjusted” patterns among variables are revealed (see
(Dunn & Møller, 2014). An additional
random factor that adjusted for variance in sample sizes of measurements
of variables among species was included, by inserting sampling variances
into the mev argument of MCMCglmm.
We conducted univariate analyses of associations of telomere variables
and each of the principle component axes (body size, pace of life, and
parental care), and then multivariate analyses of all 3 life-history
axes. The life-history axes were applied in MCMCglmm models that
separately examined Adult TL , Chick TL and TROC(see ESM 4). Phylogeny was entered as a random factor: TL
variables = [PC1 or PC2 or PC3] + 1|phylogeny +
1|mesd [adjustment for standard errors of sample sizes,\(mesd=\ \sqrt{\frac{1}{N-3}}\)] + error . These models
produced estimates of phylogenetic associations of Adult TL, Chick
TL, TROC , and of each of the life-history axes in the univariate
analyses. Also, we examined the magnitude and significance of
correlations between the 3 telomere variables and all 3 life-history
axes, in multivariate analyses. Posterior distributions of covariances
were transformed into correlations (using the posterior.cor()function in package MCMCglmm). We were then able to evaluated the part
of the correlation explained by the phylogenetic tree (i.e.phylogenetic correlation) or not (i.e. residual correlation) for
each paired association of life history PC axes and telomere variables.
Finally, using Pearson’s correlation test we examined associations of TL
and the PC axes in 3 different bird orders (where the sample size
> 8, i.e. Passeriformes, Procellariiformes,
Charadriiformes). These last analyses allowed a preliminary examination
of correlative relationships of TL and life-history PC axes within
specific categories of birds that shared both history and ecological
features. Effect sizes of correlations followed Cohen’s (1988) suggested
criteria: r = 0.1, small; r = 0.3, medium; r = 0.5, large).