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).