Statistical analysis
We used generalized linear modelling (GLM; family = Gamma; g(µi) = 1/µi; R package ’lme4’; Bates et al. 2012) to explore the effects of longitude (east or west) on the extent of moult. We also tested the possible effects of the moulting year as an independent variable due to changes in climate conditions over time (Kiat et al. 2019b). A model that included an interaction between the effects of longitude and year was also tested. Each species was tested separately, and we selected the best model based on the Akaike Information Criterion, modified for small sample sizes (AICc; Akaike 1987). A specific model was selected only if it exhibited a ΔAICc > 2.00 compared to other models. Model selection was performed using the R package ’MuMIn’ (Barton & Barton 2019) and r 2 was calculated using the R package ’rsq’ (Zhang 2018).
In addition, we used a comparative approach to test the effects of three independent variables that may affect bird moulting properties (de la Hera et al. 2009; Kiat & Sapir 2017; Kiat et al. 2019a). These variables included the difference in migration distance between Western and Eastern Palearctic, the species-specific mid moulting latitude and body mass. We specifically tested their effects on the intensity of the relationship between the longitudinal effect and moult extent (dependent variable), calculated as the difference (Δ) in the extent of passerine wing moult between the Eastern and Western Palearctic. Because species traits are known to be phylogenetically conserved, and thus data from closely related species are not statistically independent, we repeated the analysis following the independent contrasts method which identifies evolutionarily independent comparisons (Felsenstein 1985). To account for phylogenetic non-independence, we conducted this analysis using Phylogenetic Generalized Least Square (PGLS) regression (Freckleton et al.2002). We examined the strength of phylogenetic non-independence using the maximum likelihood value of the scaling parameter Pagel’s λ (Pagel 1997) implemented in the R package ’caper’ (Orme 2013). Pagel’s λ is a multiplier of the off-diagonal elements of the variance-covariance matrix, which provides the best fit of the Brownian motion model to the tip data and ranges between zero (no phylogenetic signal) and one (phylogenetic signal that depends on branch lengths as in the analysis of phylogenetically independent contrasts). We then corrected for the effects of shared ancestry using the maximum likelihood value of λ. The phylogenetic tree (Figure 2) was obtained from an analysis of global bird diversity (Jetz et al. 2012) using 10,000 trees that were generated from BirdTree.org (Rubolini et al. 2015). The consensus tree was built using BEAST version 1.8.4. Analyses (two-tailed, criticalα = 0.05) were performed using R (version 3.6.2; R Development Core Team 2019).