Rate and capacity of acclimation of temperature tolerance in ectothermic animals

Organisms experience environments that change by different amounts and at different rates throughout their lives. Phenotypic plasticity helps organisms respond to such change because it can facilitate a ‘match’ between the phenotype of the individual and the phenotype that is optimal in its present environment. Here we evaluate the ability of organisms to match both the amplitude and tempo of environmental fluctuations by asking whether a relationship exists between the capacity and rate of phenotypic plasticity, and if so, in what direction? We re-analyze published data from experiments documenting the temporal dynamics of acclimation in thermal tolerance to temperature change. Across species of reptiles, amphibians, fish, insects and crustaceans, we find that the rate and the capacity with which thermal tolerance can respond plastically to temperature change is negatively correlated. In other words, when plastic adjustment of the phenotype is large, the rate at which that adjustment can be realized is slow.. Our results indicate that if changes in the environment occur rapidly and are large in magnitude, an example being the extremes in weather brought about by climate change, it may be difficult for organisms to evolve plasticity that is rapid enough and of sufficient capacity to counteract them.

Methods
We utilized the existing database of plasticity time course experiments provided by Einum and Burton (2023), https://doi.org/10.5061/dryad.gtht76hqq. This database contained data from 308 experiments from 60 studies. The procedure for compiling studies, eligibility criteria for inclusion, and the method applied for estimating rates of plasticity is given in detail in (Einum & Burton 2023). Briefly, though, these studies consisted of experiments where animals, having been acclimated to a given initial temperature, were abruptly shifted to a new acclimation temperature (either lower or higher). Thermal tolerance was measured prior to and at different time steps t (in h) after this shift. Measures of thermal tolerance were either critical maximum temperature (CTmax) or critical minimum temperature (CTmin). The data set also contained a lower number of experiments that had measured the time to some defined response such as immobility or death when exposed to a detrimental high or low temperature (TTD). However, for the current work TTD measurements were excluded, as the approach we used estimated plasticity capacity on the original scale of the data (see below), and thus these were not comparable for measurements of critical temperatures and TTD. This left data from 277 experiments from 47 studies. The model fitted to each dataset (see below) estimates two parameters, and thus to avoid overparameterization we excluded 36 experiments with less than three time points of observation following the initial value measured at time = 0. Finally, we removed another 36 experiments that were missing acclimation temperatures (required for calculating capacity, see below). Thus, the data set available for estimation of rate and capacity consisted of 205 experiments originating from 39 studies. For each experiment, a time series of phenotypic values, zt, charting the time-course of the acclimation response were obtained, typically from figures showing the mean tolerance of groups of individuals that had experienced the ‘new’ temperature for differing lengths of time.

Einum and Burton (2023) provided a method to calculate a single parameter that describes the rate of phenotypic plasticity. In the current analysis, we required estimates of plasticity capacity that corresponded to estimates of the rate of plasticity. To obtain estimates of both plasticity rate and capacity we first rescaled each experimental dataset to have a critical temperature of 0°C at the first measurement timepoint and with a subsequent increase, i.e.  , where Zt is the rescaled critical temperature at time t (in hours). We then fitted the model Zt = Z∞(1-e-λt), where Z∞ is the rescaled asymptotic critical temperature when acclimation is complete (i.e. plasticity capacity), and λ (h-1) is the plasticity rate (Fig 1). The model was 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), and for each data set we extracted the estimated means and variances of the capacity and rate parameters. The model failed to converge for ten of the 205 experiments, and these were excluded from further analyses. To make plasticity capacity comparable among experiments that varied in the difference between the initial and new acclimation temperatures, we transformed each Z∞ estimate into an acclimation response ratio, or ARR (e.g. Claussen 1977). The ARR is given as the absolute change in critical temperature per degree difference in temperature between the initial temperature (i.e. the first temperature the experimental organisms are completely acclimated to) and the new acclimation temperature once the plastic response is completed, i.e. |Z∞/(acclimation temperature – initial temperature)|. The variance associated with each Z∞ estimate was also divided by the difference between the initial and new acclimation temperatures so that plasticity capacity variances were expressed on the same scale as the ARR values.