Phylogenetic path analysis
Because the feather wear hypothesis is a multiple-step
hypothesis, it is important to be able to parse direct and indirect
relationships between variables. We investigated these direct and
indirect relationships using a phylogenetic path analysis, following the
method outlined by and von Hardenbeg and Gonzalez-Voyer (2016) as
explained in Garamszegi, Ed. (2014). Phylogenetic path analysis has
several advantages when assessing multivariate relationships, especially
in its ability to discriminate between direct and indirect effects
between variables, and in its consideration of multiple interactions at
once. To evaluate the multivariate interactions in this system, we used
results from PGLS analyses to inform 12 separate hypotheses of direct
and indirect effects within prealternate molt, seasonal dichromatism,
migration distance and foraging stratum (supplemental fig. 1). We used a
d-sep based path analysis to build sets of phylogenetic-controlled model
equations, which we evaluated using the package caper (Orme et al. 2013)
in R. We then used an information theory approach based on a C statistic
(Sjipley 2016) to rank candidate models. The C-statistic evaluates ranks
the conditional independencies within the models and produces
CICc score for each model. We used P-values and CICc
(Von Hardenberd and Gonzales-Voyer 2013) scores to evaluate the
probability and information content of the C-statistic, respectively. We
used P-values of the C statistic to identify a subset of models that we
were not able to reject, and then ranked models by their CICc score to
evaluate the likelihood of each candidate model.