Statistical analyses – Variation in rates of phenotypic
plasticity
Comparisons of exponential and linear decay models showed that the
former was superior to the latter in most cases (see Results). Thus, the
following statistical analyses use estimates ofλE as the dependent variable.
Inspection of the distribution of standard errors (SE) for estimates ofλE were used to exclude experiments that had poor
model fit for the exponential decline models (Fig. S3). This was based
on judgement, trading-off maintaining sample size while excluding
potentially biased estimates. Using a threshold SE value of 0.01 enabled
us to retain 78% of the experiments (n = 240 out of 308). The
statistical analyses described below use estimates obtained below this
threshold. Increasing the threshold SE value to 0.02 increased the
inclusion rate to 88% (n = 271) without resulting in qualitative
changes in the results (Table S1). The bias in estimatedλE for experiments with SE > 0.02
and within the range 0.01-0.02 can be observed by comparingλE in experiments within different SE bins (Fig.
S4).
Variation in λE was analysed using
meta-analytical models, fitted using the function rma.mv in the
package metafor v.3.8-1 (Viechtbauer, 2010), while accounting for
the sampling variances (i.e. the squared standard error of theλE estimates). The full model contained the fixed
effects of taxonomic class, body mass, acclimation temperature, type of
thermal tolerance measure, and slope of the estimated exponential decay
function at tn . Life stage was given in less than
one third of the identified experiments, and was therefore not included
in the model. Random effects included effects of species, study, and
experiment. The latter was included because up to several experiments
were included per species and study, and meta-analytical models do not
contain an error term. In addition, we included the possibility for a
phylogenetic signal in λE beyond that imposed by
taxonomic class. This was done by building a tree using the packagerotl v.3.0.12 (Michonneau et al., 2016) and the Open Tree of Life
(Open Tree et al.) which was made ultrametric using the functioncompute.brlen in package ape v.5.6-2 (Paradis & Schliep,
2019). This tree was used to compute the species relatedness
variance-covariance matrix which was included as a second species-level
random effect. Thus, this model accounts for heterogeneity in estimatedλE due to differences between species unrelated
to phylogeny, and a random species effect that accounts for the
influence of phylogenetic relatedness within taxonomic classes. All
statistical analyses were conducted in R v.4.1.2 (R Core Team, 2021)
The evidence for the full model relative to simplified ones was
evaluated by comparing AICc values. We first evaluated the relative
support for a model that included the phylogenetic random effect against
one that did not contain this term (fitted using REML). After choosing
the appropriate random effect structure we proceeded by comparing the
relative support for all alternative models (fitted using ML) with
simpler fixed structures using the function dredge from the
package MuMIn v.1.47.1 (Barton, 2022). Since we found no evidence
for a body mass effect (see Results), and several experiments lacked
this information (Table S2), we repeated the comparison of models with
different fixed effect structures while excluding the body mass variable
to allow for the potential inclusion of alternative fixed effects.
Finally, we present the estimated model parameters from the model
receiving the strongest support (fitted using REML). For all analyses,
inspection of residual plots suggested that assumptions of their
normality and homogeneity were satisfied.