Data analysis
We tested for an effect of sex on plumage coloration characters using generalized linear models (GLM) in the R package lme4 (Bates et al., 2015). We included the hybrid index score as a fixed factor in the model. In particular, we tested the extent to which differences in plumage scores for forecrown, supercilium, and wing bar, as well as the calculated hue and chroma from spectrophotometry of forecrown feathers, were associated with sex. False discovery rates were calculated to account for the five comparisons (Benjamini & Hochberg, 1995). We also tested for the direction of asymmetric backcrossing by comparing the hybrid index of the whole genome and the Z chromosome for individuals with a hybrid index between 0.2 and 0.8 using a paired t-test in R. All analyses were performed in R version 3.6.2 (R Core R Core Team, 2019).