Statistical analyses - Comparison of linear vs. exponential decay
functions
For each experiment, we fitted both linear and exponential decay models
to the observed data. For the linear decline we fitted a piecewise
regression with an intercept of 1 (at t = 0), which estimates the
breakpoint b (i.e. the time at which Dtreaches 0), from which the rate λL can be
calculated as 1/b . Thus, both models estimate a single parameter,
and their relative fits for a given experiment can be compared directly
using their residual standard errors. Models were fitted using the
function nls_multstart from the nls.multstart package
v.1.2.0 (Padfield & Matheson, 2020) in R v.4.1.2 (R Core Team, 2021).
For most studies, z0 was measured in individuals
prior to transfer to the new temperature. It was often less clear
whether experimenters had been able to measure a ‘true’ value ofz∞ , i.e. thermal tolerance after full acclimation
to the new temperature had been obtained. This is a key point when
measuring rates of plasticity because estimates ofλE will be biased if full acclimation to the new
environment has not been achieved (Fig. S2). However, an advantage of
the exponential decay function is that achievement of full acclimation
can be assessed by calculating the slope of the estimated function (i.e.\({{-\lambda}_{E}e}^{\lambda_{E}t}\)) at the final acclimation time
point tn (this slope has an asymptotic value of
0). Thus, this value was calculated for each experiment and included as
a covariate in our analysis (see below) to control for any bias
introduced by variation in maximum acclimation time among studies.