A unifying model to estimate thermal tolerance limits in ectotherms across static, dynamic and fluctuating exposures to thermal stress

Fitting tolerance time versus temperature to build a thermal death time curve

The high coefficients of determination found in the D. melanogaster TDT curves (Fig. 3A) are not uncommon and the exponential relation has consistently been found to provide a good fit of tolerance time vs. temperature in ectotherms^{3,15,20,22,23,24}. Tolerance time vs. temperature data are also well fitted to Arrhenius plots which are based on thermodynamic principles (see for example^15,36) and the absence of breakpoints in such plots provides a strong indication (but not direct proof) that the cause of coma/heat failure under the different intensities of acute heat stress is related to the same physiological process regardless whether failure occurs after 10 min or 10 h^2,3 (but see “Discussion” section below). Despite the superior theoretical basis of Arrhenius analysis, we proceed with simple linear regressions of log₁₀-transformed t_coma (TDT curve) as this analysis likewise provides a high R² and is mathematically more straightforward. The physiological cause(s) of ectotherm heat failure are poorly understood^37,38 but we argue that they are founded in a common process where heat injury accumulates at a temperature-dependent rate until a species-specific critical dose is attained (area below the curve and above T_c in Fig. 2). Thus, the organism has a fixed amount (dose) of thermally induced stress that it can tolerate before evoking the chosen endpoint. The experienced temperature of the animals then dictates the rate of which this stress is acquired, and accordingly when the endpoint is reached (Fig. 2) It is this reasoning that leads to TDT curves and explains why heat stress can be additive and thus also determines the boundaries of TDT curve modelling.

Injury is additive across different stressful assay temperatures

If heat stress acquired at intense and moderate stress within the span of the TDT curve acts through the same physiological mechanisms or converges to result in the same form of injury, then it is expected that injury is additive at different heat stress intensities. This hypothesis was tested by exposing flies sequentially to two static temperatures (different injury accumulation rates) and observe whether coma occurred as predicted from the summed injury (Fig. 2C). The accumulated heat injury at the two temperatures was found to be additive regardless of the order of temperature exposure (Fig. 3B,C). This finding is consistent with a conceptually similar study using speckled trout which also found strong support for additivity of heat stress at different stressful temperatures¹³. The exact physiological mechanism of heat injury accumulation is interesting to understand in this perspective, but it is not critical as long as the relation between temperature and injury accumulation rate is known.

If injury accumulation is additive irrespective of the order of the heat exposure, we can extend the model to fluctuating temperature conditions. We have previously done this by accurately predicting dynamic CT_max from TDT parameters obtained from static assays for 11 Drosophila species (Fig. 6A, see “Discussion” section below and¹⁵). Here we extend this to temperature fluctuations that cannot be described by a simple mathematical ramp function. Specifically, groups of flies were subjected to randomly fluctuating temperatures and the observed t_coma was then compared to t_coma predicted using integration of heat injury based on TDT parameters (Fig. 4). The injury accumulation (Fig. 4C) was calculated by introducing the fluctuating temperature profiles in the associated R-script and the observed and predicted t_coma was found to correlate well (R² > 0.94) across the 13 groups tested for each sex. These results further support the idea that injury is additive across a range of fluctuating and stressful temperatures and hence that similar physiological perturbations are in play during moderate and intense heat stress. It is important to note that in these experiments, temperatures fluctuated between 34.5 and 42.5 °C and accordingly the flies were never exposed to benign temperatures that could allow repair or hardening (see below).

In conclusion, empirical data (present study;^6,13,14,22) support the application of TDT curves to assess heat injury accumulation under fluctuating temperature conditions both in the lab and field for vertebrate and invertebrate ectotherms. Potential applications could be assessment of injury during foraging in extreme and fluctuating environments (e.g. ants in the desert³⁹ or lizards in exposed habitat⁴⁰) or for other animals experiencing extreme conditions^41,42. The associated R-scripts allow assessment of percent lethal damage under such conditions if the model is provided with TDT parameters and information of temperature fluctuations (but see “Discussion” section of model limitations below).

Model application for comparison of static versus dynamic data

There is little consensus on the optimal protocol to assess ectotherm thermal tolerance and many different types of static or dynamic tests have been used to assess heat tolerance. TDT curves represent a mathematical and theoretical approach to reconcile different estimates of tolerance as the derived parameters can subsequently be used to assess heat injury accumulation at different rates (temperatures) and durations^13,15,16. Here we provide R-scripts that enable such reconciliation and to demonstrate the ability of the TDT curves to reconcile data from static vs. dynamic assays we used published measurements of heat tolerance for 11 Drosophila species using three dynamic and 9–17 static measurements for each species⁴³. Introducing data from only static assays we derived TDT parameters and subsequently used these to predict dynamic CT_max that were compared to empirically observed CT_max for three ramp rates (Fig. 6A). In a similar analysis, TDT parameters were derived from the three dynamic (ramp) experiments to predict t_coma at different static temperatures which were compared to empirical measures from static assays (Fig. 6B). Both analyses found good correlation between the predicted and observed values regardless whether the TDT curve was parameterized from static or dynamic experiments (Fig. 6). However, predictions from TDT curves based on three dynamic assays were characterised by more variation, particularly when used to assess tolerance time at very short or long durations. Furthermore, D. melanogaster and D. virilis which had the poorest correlation between predicted and observed t_coma in Fig. 6B had values of z from the TDT curves based on dynamic input data that were considerably different from values of z derived from TDT curves based on static assays (Fig. 6B inset). In conclusion TDT curves (and the associated R-scripts) are useful for conversion between static and dynamic assessment of tolerance. The quality of model output depends on the quality and quantity of data used as model input, and in this example the poorer model was parameterized from only three dynamic assays while the stronger model was based on 9–17 static assays (see also “Discussion” section below).

Model application for comparison of published data

Thermal tolerance is important for defining the fundamental niche of animals^1,2,4 and the current anthropogenic changes in climate has reinvigorated the interest in comparative physiology and ecology of thermal limits in ectotherms. Meta-analyses of ectotherm heat tolerance data have provided important physiological, ecological and evolutionary insights^5,44,45,46, but such studies are often challenged with comparison of tolerance estimates obtained through very different methodologies.

Species tolerance is likely influenced by acclimation, age, sex, diet, etc.⁴⁷ and also by the endpoint used (onset of spasms, coma, death, etc.²⁷). Nevertheless, we expected heat tolerance of a species to be somewhat constrained⁴⁵, so here we tested the model by converting literature data for nine species to a single and species-specific estimate of tolerance, sCT_{max (1 h)}, the temperature that causes heat failure in 1 h (Fig. 5). The overwhelming result of this analysis is that TDT parameters are useful to convert static and dynamic heat tolerance measures to a single metric, and accordingly, the TDT model and R-scripts presented here have promising applications for large-scale comparative meta-analyses of ectotherm heat tolerance where a single metric allows for qualified direct comparison of results from different publications and experimental backgrounds. While this is an intriguing and powerful application, we caution that careful consideration should be put into the limitations of this model (see “Discussion” section below).

Practical considerations and pitfalls for model interpretation

As shown above it is possible to convert and reconcile different types of heat tolerance measures using TDT parameters and these parameters can also be used to model heat stress under fluctuating field conditions. Modelling and discussion of TDT predictions beyond the boundaries of the input data has recently gained traction (see examples in^48,49) but we caution that the potent exponential nature of the TDT curve requires careful consideration as it is both easy and enticing to misuse this model.

Input data

The quality of the model output is dictated by the input used for parameterization. Accordingly, we recommend TDT parameterization using several (> 5) static experiments that should cover the time and temperature interval of interest, e.g. temperatures resulting in t_coma spanning 10 min to 10 h, thus covering both moderate and intense heat exposure. Such an experimental series can verify TDT curve linearity and allows modelling of temperature impacts across a broad range of temperatures and stress durations^13,15,22. It is tempting to use only brief static experiments (high temperatures) for TDT parameterization, but in such cases, we recommend that the resulting TDT curve is only used to describe heat injury accumulation under severe heat stress intensities. Thus, the thermal sensitivity factor z represents a very powerful exponential factor (equivalent to Q₁₀ = 100 to 100,000;¹⁵) which should ideally be parametrized over a broad temperature range (see below). We also include a script that allows TDT parametrization from multiple ramping experiments and again we recommend a broad span of ramping rates to cover the time/temperature interval of interest. A drawback of ramping experiments is the relatively large proportion of time spent at benign temperatures where there is no appreciable heat injury accumulation. Thus, dynamic experiments can conveniently use starting temperatures that are close to the temperature where injury accumulation rate surpasses injury repair rate (see “Discussion” section of “true” T_c below, in Supplemental Information and¹⁹ for other considerations regarding ramp experiments).

A final methodological consideration relates to body-temperature in brief static experiments where the animal will spend a considerable proportion of the experiment in a state of thermal disequilibrium (i.e. it takes time to heat the animal). To avoid this, we recommend direct measurement of body temperature (large animals) or container temperature (small animals), and advise against excessive reliance on data from test temperatures that results in coma in less than 10 min.

Extrapolation

Most studies of ectotherm heat tolerance include only a single measure of heat tolerance which is inadequate to parameterize a TDT curve. However, a TDT curve can still be generated from a single measure of tolerance (static or dynamic) if a value of z is assumed (see Supplemental Information). As z differs within species and between phylogenetic groups (Table S1^15,20), choosing the appropriate value may be difficult and discrepancies between the ‘true’ and assumed z represent a problem that should be approached with care. In Fig. 7A we illustrate this point in a constructed example where a single heat tolerance measurement is sampled from a ‘true’ TDT curve (full line; t_coma = 40 min at 37 °C). Along with this ‘true’ TDT curve we depict the consequences for model predictions if the assumed value of z is misestimated by ± 50%. Extrapolation from the original data point is necessary if an estimate of the temperature that causes coma after 1 h is desired, however due to limited extrapolation (from 40 to 60 min), estimation of sCT_{max (1 h)} values based on the ‘true’ and z ± 50% are not very different (< ± 0.22 °C in this example). Accordingly, moderate extrapolations are associated with minor latent errors and such assumptions were the basis for many data points in our comparative analysis (Fig. 5). If extensive extrapolation is used (here 40-fold from 40 min to either 1 or 1600 min, Fig. 7A), the assumed z results in sCT_max estimates varying ± 2 °C from the true value and even more dramatic discrepancies are seen if t_coma is calculated for the temperatures resulting in the ‘true’ sCT_max for 1 min or 1600 min (41 and 33 °C, respectively, table in Fig. 7A). Due to the powerful exponential nature of the TDT curve, extrapolation to 41 or 33 °C with values of z ± 50% gives predicted t_coma of 1.5 s-3.42 min (‘true’ t_coma = 1 min) and 8 h-44 days (‘true’ t_coma ~ 1 day). Accordingly, excessive extrapolation of TDT curves should be avoided as even moderate errors in the estimate of z can result in dramatic output errors if the TDT curve is extrapolated beyond the domain of the input data.

Breakpoints and incipient lethal temperature

TDT curves are established at critically high temperatures and another cause of concern for extrapolation of TDT curves relates to the boundaries of the model. Below some temperature [incipient lethal temperature c.f.¹³, here termed T_c (see “Mathematical foundation” section], the processes related to acute heat injury will no longer determine the duration of survival, and graphically this is represented as a breakpoint on the TDT curve (analogous to an Arrhenius breakpoint) (Fig. 7B). The premise of the TDT curve is not valid below T_c and hence other processes will limit survival below this temperature resulting in a breakpoint. For most species T_c is unknown, and it is possible that this value (breakpoint) will also depend on other factors (acclimation, age, sex, diet, etc.)(compare Fundulus and Drosophila, Fig. 7B). Accordingly, extrapolation beyond the parameterized time–temperature domain of the TDT curve should be met with great caution for instance when modelling over diurnal temperature fluctuations as this likely includes temperatures below the incipient temperature.

The role of repair and acclimation

From the present study and historical data^{13,14,16,22,25} it is clear that damage attained within the boundaries of the TDT curve is additive and that this model can be used to assess heat injury accumulation during fluctuations. Additivity is, however, only empirically validated within the boundaries of the TDT curve (i.e. above T_c; Fig. 7B), and at temperatures below T_c it is likely that heat injury can be repaired (Fig. 7C). A study using split-dose heat exposures interspaced by benign temperature exposure found that breaks (> 6 h) between heat exposure disrupted additivity, suggesting that injury is repaired at benign temperature⁵⁰. Injury repair rate is largely understudied but repair rate is generally increasing with temperature^51,52,53. It is therefore an intriguing and promising idea to include a temperature-dependent repair function in more advanced modelling of heat injury. Until such repair processes are introduced in the model, we recommend that additivity of heat injury is evaluated critically if it involves periods at temperatures both above and below T_c (i.e. over consecutive days, see also¹³). An alternative, but not mutually excluding, explanation of increased heat resilience in split-dose experiments relates to the contribution of heat hardening as it is likely that the first heat exposure in a series can induce hardening responses that increase resilience (and thus change the TDT parameters) when a second heat exposure occurs. Such issues of repeated thermal stress have been discussed previously⁵⁴ but for the purpose of the present study the main conclusion is that simple TDT curve modelling is not applicable to fluctuations bracketing T_c unless this is empirically validated. Future studies could address this issue as inclusion of repair functions would add further promise to the use of TDT curves in modelling of the impacts of temperature fluctuations.

Source: Ecology - nature.com