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.