2.5 Statistical analyses
To investigate variations in the color and size of plover ornamental traits, we conducted a principal component analysis (PCA) to reduce the number of variables. For male plovers, the color and size of the breast band, eye stripe, and crown were subjected to a PCA. We also included the color of the head stripe since males have a stripe on their forehead (see Figure S1 and Tables S2). A negative value for ”lightness” and a positive value for ”redness” indicated greater color saturation, resulting in a more colorful appearance (Tables S2). MPC1 captured the variation in color and was characterized by negative values for the lightness of the breast band, eye stripe, and head stripe, combined with a positive value for the redness of the crown. MPC2 captured the variation in size and was characterized by positive values for the size of the breast band, eye stripe, and head stripe. Together, MPC1 and MPC2 explained 71.0% of the total variance in male ornament traits (Table S2). For female plovers, we conducted a PCA on the color and size of the breast band, eye stripe, and crown (Figure S1). FPC1 captured the variation in color and was characterized by positive values for the redness of the breast band, eye stripe, and head stripe. FPC2 captured the variation in area and was characterized by positive values for the size of the breast band, eye stripe, and head stripe. Together, FPC1 and FPC2 explained 65.7% of the total variance in female ornament traits (Table S3). Finally, we tested the difference in ornamental traits between male and female plovers in four populations using one-way ANOVA.
To allow comparisons between Kentish and white-faced plovers, we first obtained the genetic relatedness among the four populations by calculating a genome-wide pairwise population differentiation (F st) using the dataset and methods of . Then, we incorporated the pairwise F st values in a covariance matrix representing the amount of shared evolutionary history between the four populations and performed phylogenetic generalized linear mixed models (PGLMM).
To account for sampling uncertainty in our estimates, we performed a bootstrapping procedure for all analyses. This involved randomly resampling the data with replacements for each bootstrap iteration (i), running 1,000 PGLMM analyses, and reporting the 95% confidence interval of the estimate. The PGLMM results, including the estimate, z value, and p value, as well as the 95% CI of the estimate based on the bootstrapping procedure, are presented throughout the results section.
2.6 Modellin g the relationships between male body size, ornamental traits, and temperature
To examine the impact of temperature on the correlation between male body size and ornamental traits, we employed phylogenetic generalized linear mixed models (PGLMMs). The models had male body mass as the dependent variable, and the independent variables were the ornament PCA values (coloration: MPC1; size: MPC2) and ambient temperature. By incorporating the interaction between males PCA values and ambient temperature, we aimed to investigate the potential moderating role of temperature in the relationship between male body size and ornamental traits. Moreover, we included both the breeding season and incubation duration as fixed effects in the models to control for possible variation in male body condition. Additionally, population and year were considered as random effects to account for any unobserved heterogeneity across different populations and years.
2.7 Modellingthe relationships between male