Calculating rates of plasticity
Rates of plasticity were calculated according to the approach outlined by Burton et al. (2022). Thus, for each observation of temperature tolerance at times t we first calculated the proportion of the full plastic response that remained to be achieved,Dt , as (zt -z )/(z0z ), wherez0 is the first measurement of the phenotype (typically measured prior to the onset of acclimation), zt is the phenotype after acclimating for a time period t , and z is the fully adjusted phenotype. In theory, z is the final measurement of thermal tolerance. However, given measurement noise this may not be the case. Thus, we definedz as the maximum (for acclimation to higher temperature) or minimum (for acclimation to lower temperature) value for a given measurement of tolerance observed. For each experiment, we considered two potential responses in plasticity of thermal tolerance. First, Dt may have a value of 1 at t = 0 (first measurement) and decline linearly with time with a rateλL given by λL = (1-Dt )/t until it reaches 0, after which it will be constant. Alternatively, Dt may have a value of 1 at t = 0 and decline as an exponential decay function towards 0 with rate λE , such that\(D_{t}=e^{{-\lambda}_{E}t}\). Thus, for each experiment, we fitted these two types of 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 breakpointb (i.e. the time at which Dt reaches 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 functionnls_multstart from the nls.multstart package (Padfield and Matheson 2020).
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. S1). 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 included as a covariate in our analysis (see below) to control for any bias introduced by variation in maximum acclimation time among studies.