Model Selection and Phylogenetic Signal
We fit models of evolution to molt and dichromatism to understand how
phylogenetic history and selection may interact with these traits, as
well as to inform phylogenetic comparative analyses involving these two
traits. To select models of evolution for molts and dichromatism, we fit
various models of evolution to the data and phylogeny. We fit models of
character evolution using Brownian motion (BM), Orstein-Uhlenbeck (OU),
and Early-burst (EB) (Butler 2004) models in the package geiger in R
(Harmon et al. 2008). We fit models of continuous traits for feather
regions and extent of molts and dichromatism, and models of discrete
traits for presence of molts and dichromatism. We extracted the sample
size-corrected AIC (AICc) values and parameters from the BM, OU, and EB
models for cross-model comparisons and converted these values to AIC
weights to compare models (Revell 2012). We compared the AICc weights
for these three models by calculating AICc weights for each feather
tract and for presence and extent of prealternate molt, and seasonal
dichromatism. To assess the best model across body regions, we
calculated AICc weighted parameter values across feather regions by
weighting rate parameters by AICc weights and summed these weighted
parameters for molts and dichromatism. We calculated phylogenetic signal
as Pagel’s Lambda in phytools (Revell 2012) for each molt and sexual and
seasonal dichromatism for each body region, as well as presence and
extent of molts and dichromatism.
The difference between gains and losses of traits can be important to
understand how traits change and interact over evolutionary time. We
were interested in knowing when and how often seasonal dichromatism and
prealternate molt were gained and lost, and whether these transitions
provided insight into the relationship between prealternate molt and
seasonal dichromatism. We evaluated the number of transitions and the
probability that rates of gains and losses were significantly different
for presence of molts and dichromatism by reconstructing ancestral
states under equal rates (ER) and all rates different (ARD) models; we
compared the log-likelihoods of each model using a likelihood ratio test
to obtain a p-value for rejection of the ER model in favor of the more
complex ARD model. This method allowed us to ask if rates of gains and
losses of molts and dichromatism were significantly different from
equal. We used a similar test, based on Pagel (1994) to test if the
evolution of prealternate molt is dependent on long-distance migration,
through comparison of likelihood ratios of dependent and independent
models of evolution (Figure 1g).