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.