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).