Statistical analyses
Our first set of analyses using univariate mixed-effects models examined
individual differences in trait expression and how trait expression
changed with age or time within a day. Our second set of analyses using
bivariate mixed-effect models estimated within-sex among- and
within-individual correlations between traits.
Univariate models. The univariate models fitted individual
identity as a random effect and (within-individual mean-centred)
observation day and (mean-centred) time of day as covariates. We used
the following error structure for the response variable: body mass was
modelled with Gaussian errors, plant use (found in narrow-leafed plants
(1) or not (0)) and calling activity (exhibiting calling (1) or not (0))
were modelled with binomial errors. Despite including a quadratic term
of observation day (i.e., age) as an additional covariate in the
univariate models, we did not observe quadratic ageing patterns in any
of the traits (results not included). Consequently, the univariate
models did not include a quadratic term of observation day. In addition
to the random intercept model, we used a random slope model to estimate
among-individual variation in age-related plasticity. We found no
variation in the age-related slopes (results not included).
All univariate mixed-effects models were implemented in ASReml (version
4.1, VSN Interaction, Hemel Hempstead, UK) and solved using the
restricted maximum likelihood method. The significance of fixed
effects was assessed through conditional Wald F tests. Statistical
significance for variance was determined using a likelihood-ratio test
(LRT). To examine deviations from zero variances, LRTs were conducted,
involving the difference in deviance (-2 × log likelihood) between the
full model and a model where the variance was removed. The P
value was computed under the assumption of an equal combination of P
(χ2, df = 0) and P(χ2, df = 1)
(hereafter, χ20/1).
Bivariate models. We constructed sets of bivariate models, where
we fitted two traits from plant use, calling activity, and body mass as
the response variables. These models included individual identity as a
random effect and had no fixed effects. In the bivariate models, we
constrained the among-individual covariance between plant use and other
traits to zero because the among-individual variance in plant use was
not significantly positive (see Results). The within-individual
variances in plant use and calling activity were fixed to one because
they were not estimable with binary data. Thus we were not able to
calculate a within-individual covariance between calling activity and
plant use. We fitted the bivariate models within a Bayesian framework
using the MCMCglmm package (Hadfield 2010) in R (version 3.2.0). To
minimise autocorrelation among samples, 1,300,000 Markov Chain Monte
Carlo (MCMC) iterations were performed, which were sampled at
1,000-iteration intervals after an initial burn-in period of 300,000
iterations, using Gamma priors. This resulted in a total of 1000 samples
from the posterior distribution. Convergence was attained by visual
inspection of output plots and by ensuring that autocorrelation between
consecutive samples did not exceed 0.1 (Hadfield 2010).