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∞ )/(z0 –z∞ ), 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.