2.9 Path analysis of the effects of male ornamental traits and female body size on parental investment during incubation
To investigate whether an individual’s investment in incubation depended on its or its mate’s body size or ornamentation, we conducted a series of path analyses. We recorded incubation behavior at 3-hour intervals, as parents typically alternate incubation every 46.725 ± 3.383 minute (mean ± SE). Using data from 80 nests (also including the nest with less than 24 hours of records), we employed GLMMs in the ’nlme’ package , with nest ID and population ID as random effects for each model structure. We tested whether female tarsus length, male body mass, female ornament color (FPC1), and male ornament color (MPC1) had directional effects on male and female incubation investment within a 3-hour period. As female plovers typically dominate diurnal incubation and males usually incubate at night , we transformed the time for each scan from a 24-hour clock to a continuous time variable that spans across midnight using a cosine transformation.
We constructed a series of alternative path models to examine the effects of ambient temperature, parents’ body size, and ornament traits on their incubation behavior. Since the total amount of time required for incubation varies with time of day and ambient temperature, we included the time that the nest was empty also as a dependent variable in our path models. To account for correlations among parents’ body size and ornamentation (FPC1 and MPC1), we used thepiecewiseSEM package to construct models in which these four variables were intercorrelated. We also included correlations between female and male incubation time.
To investigate the factors affecting male and female incubation time, we initially developed a full path model that included ambient temperature, time of day, female ornament (FPC1), male ornament (MPC1), female tarsus length (according to Table 3), and male body mass as predictor variables. Subsequently, we built 85 candidate path models by removing one to four predictor variables among parents’ body size and ornamentation from the original model while keeping ambient temperature and time of day as fixed predictors. We then evaluated the candidate models based on their Fisher C-test and AICc values and selected the best-supported path model. The final model provides insights into the parental incubation investment strategy (for more details, please refer to the supplementary material).
To investigate the impact of ambient temperature on parental incubation investment strategy, we partitioned the data based on mean ambient temperature (mean ± SE: 23.782 ± 0.160 ℃, with a range from 3.97 ℃ to 40.54 ℃) and implemented a bootstrapping procedure to minimize the impact of sampling error on female incubation data. We utilized the ‘phyr’ package to construct PGLMM models and the ‘piecewiseSEM” package in R version 3.6.3 to conduct the path analysis.