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).