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.