Finding the right thermal limit: a framework to reconcile ecological, physiological and methodological aspects of CT_max in ectotherms

Thermal tolerance and performance are critical in defining the fundamental niche of ectothermic animals and, consequently, limits of thermal tolerance are strong predictors of the biogeographical distribution of ectotherms (Addo-Bediako et al., 2000; Bennett et al., 2021; Buckley and Huey, 2016; Deutsch et al., 2008; Kellermann et al., 2012; Pinsky et al., 2019; Sunday et al., 2012; Sunday et al., 2019). Projected increases in average temperature as well as increases in seasonal and daily temperature variation (Easterling et al., 2000; IPCC, 2021; Rahmstorf and Coumou, 2011; Seneviratne et al., 2014) underscore the importance of reaching a consensus on how to measure and analyse thermal tolerance estimates. In this process, it is important to understand the biological basis of thermal tolerance traits, e.g. critical thermal maximum (CT_max; see Glossary), and also to recognize how these acute tolerance traits relate to more chronic thermal performance traits, e.g. optimal temperature (T_opt; see Glossary). Such an understanding will ideally improve our ability to deliver relevant and consistent predictions of species’ responses to climate change (Clusella-Trullas et al., 2021; Deutsch et al., 2008; Jørgensen et al., 2022; Kingsolver et al., 2013; Parmesan, 2006; Sinclair et al., 2016; Stoks et al., 2017).

There is currently little consensus on how to measure CT_max as this ‘trait’ can be determined with different endpoints, such as loss of coordination, onset of spasms, coma or death (Lutterschmidt and Hutchison, 1997a,b) and it is a source of confusion that CT_max is determined in assays with different time frames or heating rates, because the duration and intensity of heat exposure will invariably affect the CT_max estimate (Bates and Morley, 2020; Chown et al., 2009; Jørgensen et al., 2019; Kilgour and McCauley, 1986; Peck et al., 2009; Terblanche et al., 2007). An even bigger source of confusion comes from terminology, because CT_max is also often used to describe the upper endpoint of the thermal performance curve (TPC; see Glossary) for traits such as growth, metabolism or activity (in this Review, we define such upper limits as TPC_max) (Deutsch et al., 2008; Huey and Stevenson, 1979; Kellermann and van Heerwaarden, 2019). The somewhat indiscriminate use of the term CT_max results in ambiguity, which is problematic for comparison of CT_max across large comparative meta-analyses, and when CT_max is used in trait-based modelling to forecast the consequences of climate change (Cooper et al., 2008; Hoffmann et al., 2003; Jørgensen et al., 2022; Kellermann and van Heerwaarden, 2019; Sunday et al., 2012; Sunday et al., 2019; Woodin et al., 2013).

Some of the methodological challenges concerning CT_max have recently been addressed by (re)introducing the concept of the thermal death time (TDT) model (see Glossary), which combines information on the severity and duration of stressful temperature exposure (Fry et al., 1946; Jørgensen et al., 2019; Jørgensen et al., 2021b; Kilgour and McCauley, 1986; Maynard Smith, 1957; Rezende et al., 2014). However, these temperature–time models of critical tolerance have yet to be discussed extensively in relation to model boundaries and in relation to other measures of thermal performance, such as TPCs. Further, the physiological origin of TDT models is not well described (see discussion in Jørgensen et al., 2019 and Jørgensen et al., 2021b) nor have the models been properly integrated with the historical and ongoing debate on the mechanistic causes of CT_max (Bowler, 2018; Cossins and Bowler, 1987; González-Tokman et al., 2020; Jutfelt et al., 2018; Neven, 2000; Pörtner and Farrell, 2008; Schulte et al., 2011; Sørensen et al., 2003; Vornanen, 2020).

With this Review, we first discuss the current state of CT_max measurements and propose a common framework that can reconcile and differentiate the classic TPC model with the TDT model as models capturing how temperature affects rates of ‘life’ and ‘death’, respectively. We then establish an integrative model of thermal tolerance that is based on the balance between disruptive and homeostatic biological processes, providing a framework for understanding exposure to high temperature under naturally fluctuating thermal conditions, as it allows for the inclusion of repair in the assessment of cumulative heat stress. Together, this relatively simple and consistent view of critical thermal limits enables improved experimental design and a coherent understanding of animal heat tolerance in comparative, ecological and mechanistic studies.

When discussing thermal limits of ectotherms, it is important to differentiate between the temperature range that permits completion of the life cycle, i.e. development, maturation and reproduction, and the temperatures that acutely limit the survival of the organism as a result of acute thermal stress (Fig. 1; Fry et al., 1946; Hollingsworth, 1969; Fry, 1971; Woodin et al., 2013; Kellermann and van Heerwaarden, 2019; Bates and Morley, 2020; Parratt et al., 2021; van Heerwaarden and Sgrò, 2021). Fry and colleagues (Fry, 1947; Fry, 1971; Fry et al., 1946) distinguished between these temperature domains as the ‘zone of tolerance’ and the ‘zone of resistance’, respectively. Here, we refer to these as the ‘permissive’ and ‘stressful’ temperature range, respectively (see Glossary), to avoid confusion with effects of acclimation on heat stress tolerance or resistance. An important aspect of the proposed framework is the introduction of the critical temperature (T_c; see Glossary), which separates the permissive temperature range from the upper stressful temperature range.

The effects of permissive temperatures on ectotherm performance/fitness have traditionally been described by the TPC (Fig. 1; Angilletta, 2009; Huey and Stevenson, 1979; Huey et al., 2012). As Darwinian fitness is difficult to assess directly, a proxy related to fitness is usually used instead, e.g. egg-laying capacity, developmental speed (Huey and Berrigan, 2001; Huey et al., 2012; MacLean et al., 2019; Overgaard et al., 2014) or rates of biochemical or physiological processes, such as growth rate or feeding rate (Angilletta, 2009; Cossins and Bowler, 1987; Hochachka and Somero, 2002; Schulte et al., 2011; Sinclair et al., 2016). The TPC is most often left-skewed with an initial positive effect of increasing temperature on performance (Buckley et al., 2022; Dell et al., 2011; Gilchrist, 1995). After the maximal rate of performance is reached at T_opt, the rate of performance quickly decreases when temperature increases further. The upper and lower endpoints of TPCs are frequently termed CT_max and CT_min, respectively, which can be confusing because the temperature limits of the TPC are not necessarily related to acute failure (Fig. 1). Thus, a complicating feature of TPCs is that the performance of some traits, e.g. speed of locomotion, oxygen consumption rate and heart rate, clearly span both the permissive and stressful temperature range, while TPCs for population growth and chronic behaviours are restricted to only the permissive temperature range. To illustrate this, we compiled estimates of thermal performance of various biological processes and acute thermal limits in three ectothermic species: vinegar fly, brook trout and zebra mussel (Fig. 1). Note that heat failure and heat knockdown are used interchangeably to describe either onset of heat coma or heat mortality (Lutterschmidt and Hutchison, 1997a,b). For all three species, the TPCs of fitness proxies and growth are restricted to the permissive temperature range and always decline to zero before the temperature reaches the stressful temperature range above T_c (Fig. 1). In contrast, TPCs for processes related to movement or metabolic rate span both the permissive and stressful temperature range such that the observed decline in these traits coincides more with the decrease in survival time conveyed by the TDT model (secondary axes in Fig. 1). The distinct nature of TPCs for different traits is partly a result of the time scales at which the performance is measured as fitness proxies of growth and reproduction inherently operate over long time frames, whereas locomotion and metabolic rate are instantaneous measures (Cossins and Bowler, 1987; Hoffmann and Todgham, 2010; Kellermann and van Heerwaarden, 2019; Kellermann et al., 2019; Kingsolver and Woods, 1997; Kingsolver and Woods, 2016; Schulte et al., 2011, 2020; Sinclair et al., 2016). Traits such as metabolic rate or movement are obviously indirectly related to Darwinian fitness and remain important and functional at temperatures above T_c, where they may be critical for escaping the heat stress. Even so, the optimal and critical temperature limits of these ‘indirect’ fitness traits may be confusing if their TPCs are interpreted as direct correlates of Darwinian fitness, e.g. the ‘optimal’ temperature for metabolic rate or running speed is clearly not aligned with the optimal temperature for population growth (Fig. 1).

The distinction between the permissive and stressful temperature range is also highlighted by the differential impact of temperature on lifespan (Fig. 2). In the permissive temperature range, lifespan is not limited directly by acute thermal injury but decreases with increasing temperature simply as a consequence of the thermal effect on metabolic rate (rate-of-living hypothesis; Brown et al., 2004; Munch and Salinas, 2009; Shaw and Bercaw, 1962) or through differences in the temperature-specific ageing threshold which precedes death (described in the threshold hypothesis; Maynard Smith, 1963). Irrespective of the mechanism, the rate of ageing/senescence/mortality (calculated as the inverse of lifetime) in the permissive temperature range has temperature quotients (Q₁₀; see Glossary) that are typical for ‘normal’ biological processes (Q₁₀=1.1–3.1; Fig. 2) (Dell et al., 2011; Doudoroff, 1945; Loeb and Northrop, 1916; Munch and Salinas, 2009; Seebacher et al., 2014). These Q₁₀ estimates of ageing/senescence/mortality rates are in marked contrast to the very high Q₁₀ values that characterize rates of heat failure conveyed in the TDT model (see below).

In the stressful range, temperature poses an acutely limiting factor on survival and does so in a dose-dependent manner where the severity of the thermal stress dictates survival time, i.e. faster heat death at higher temperature. As exemplified in Fig. 2, the slope between temperature and survival time is much steeper in the stressful temperature range than in the permissive range. The lethal domain of high temperatures therefore only spans a few degrees before survival time becomes extremely brief (Brown and Crozier, 1927; Cossins and Bowler, 1987; Fry et al., 1946; Jørgensen et al., 2019; Jørgensen et al., 2021b; Kilgour and McCauley, 1986; Rezende et al., 2014). Consequently, in all eight species examined here, Q₁₀ values for heat failure rates (see Glossary) are much higher in the stressful temperature range (median Q₁₀=4953) compared with those for ageing rates in the permissive range (median Q₁₀=1.87; Fig. 2). These examples are in accordance with recent and historical evidence showing that the thermal sensitivity of processes related to heat failure are characterized by extreme Q₁₀ values in the range 100–100,000 (Hollingsworth, 1969; Jørgensen et al., 2019; Jørgensen et al., 2022; Maynard Smith, 1957). To put this in perspective, a Q₁₀ of 1500 (close to the median Q₁₀ of heat failure rate in 112 ectotherm species; Jørgensen et al., 2022) causes a ∼100% increase in injury rate per 1°C in the stressful temperature range, causing the knockdown time to be halved for each 1°C increase. Contrastingly, in the permissive range, where Q₁₀ is ∼2, lifespan is reduced by a modest 7% per 1°C increase as a result of accelerated biological activity. Importantly, the extreme thermal sensitivity in the stressful temperature range implies that the increase in intensity and frequency of heat waves associated with global warming could greatly amplify heat mortality for many ectotherms (Jørgensen et al., 2022).

The extreme thermal sensitivity of heat failure in the stressful temperature range is conveyed by the TDT model, which describes the exponential decline in survival time with increasing temperature (Fig. 3A,B; Fry et al., 1946; Kilgour and McCauley, 1986; Rezende et al., 2014; Jørgensen et al., 2019). Although the focus here is on heat tolerance, we emphasize that the TDT model can also be applied to cold stress (Chen and Walker, 1994; Nedvěd et al., 1998; Salt, 1966; Tarapacki et al., 2021).

Here, we define a critical temperature (T_c) that separates the permissive and stressful temperature domains (Fig. 1). Philosophically, T_c can also be considered as a narrow temperature range, rather than a specific temperature, where thermal relationships of the organism transition from mainly temperature effects on ‘processes supporting life’ to those on ‘processes causing injury and death’. Although it is difficult to empirically measure T_c (see ‘Concluding remarks and future perspectives’, below), this parameter is conceptually important for defining, parameterizing and reconciling measures of heat tolerance. For example, it is evident that any measure of acute heat failure will always be above T_c (Fig. 1). This definition helps separate measures of acute heat failure (often termed CT_max) from the upper thermal limits of TPCs (TPC_max) that must be below T_c for traits directly related to fitness and growth. The T_c concept presented in this review is largely analogous to ‘the upper incipient lethal temperature’ (UILT) defined by Fry and co-workers in their seminal studies on lethal temperatures in fish (Fry, 1947; Fry, 1971; Fry et al., 1946) or to the long-term survival temperature T_s, defined more recently by Richard et al. (2012) in marine ectotherms. These transition temperatures (UILT, T_s or T_c) all represent the highest temperature that allows for chronic survival, and above these transition temperatures, heat stress accumulates with increasing intensity as temperature is raised further (as in Fig. 2). Importantly, modelling studies of heat tolerance in fish (Kilgour and McCauley, 1986; Kilgour et al., 1985) and insects (Kingsolver and Umbanhowar, 2018; Jørgensen et al., 2021a,b) have all concluded that inclusion of a critical thermal limit (T_c) is needed for models of heat stress to disregard the time spent below T_c during the gradual temperature increase in a ramping assay, as this time does not contribute to the accumulation of heat injury.

Heat tolerance is typically measured using either static assays, where time to heat failure is measured under exposure to a constant temperature, or dynamic/ramping assays, where the heat failure temperature under incrementally increased temperature exposure is assessed. Both static and dynamic protocols have been widely discussed (Overgaard et al., 2012; Rezende et al., 2011; Terblanche et al., 2007), and in particular it is debated whether static and dynamic measures of heat tolerance are comparable or even ecologically relevant (Bak et al., 2020; Cooper et al., 2008; Kingsolver and Umbanhowar, 2018; Rezende et al., 2014; Santos et al., 2011; Sgrò et al., 2010; Terblanche et al., 2011). Much of this methodological discussion can be settled by the TDT model (Fry et al., 1946; Jørgensen et al., 2019, 2021b; Kilgour and McCauley, 1986; Maynard Smith, 1957; Rezende et al., 2014; Willot et al., 2022) and here we elaborate on this discussion by reviewing the foundation and boundaries of the TDT model.

The TDT model is based on the understanding that heat failure rate increases exponentially with temperature (Fry et al., 1946; Jacobs, 1919; Jørgensen et al., 2019, 2021b; Kilgour and McCauley, 1986; Kilgour et al., 1985) and that, at temperatures above T_c, the animal can only withstand a finite amount of accumulated heat injury before it succumbs to heat stress, here termed ‘thermal dose’ (see Glossary; Td in Fig. 3). This thermal dose is the same for all exposure temperatures above T_c and can graphically be represented as equal area rectangles in a plot of heat failure rate versus time to heat failure (Fig. 3A). As heat failure rate increases exponentially with temperature, it is clear that time to heat failure will decrease exponentially with temperature, as depicted in the classical TDT curve (Fig. 3B; Bigelow, 1921; Fry et al., 1946; Jørgensen et al., 2021b; Kilgour and McCauley, 1986; Maynard Smith, 1957). Time to heat failure is traditionally log₁₀ transformed such that the TDT curve becomes a simple linear relationship described by the slope and a point on the line, e.g. the temperature causing heat coma after a 1 h exposure (Jørgensen et al., 2019, 2021b; Willot et al., 2022). In the TDT model, the slope represents the thermal sensitivity factor, z=−1/slope, describing the temperature change resulting in a one order of magnitude change in heat failure time (Rezende et al., 2014). TDT model parameters are typically derived from experiments where time to failure is measured under exposure to three or more static temperatures (Fig. 3B) and, once established, the TDT model can be used to estimate heat failure time at a given temperature or failure temperature for a given exposure duration.

If the thermal dose is truly independent of temperature, then the injury sustained at different static temperatures should be completely additive as is well supported empirically (Fry, 1947, 1971; Fry et al., 1946; Jørgensen et al., 2021b; Kashmeery and Bowler, 1977). This additivity suggests that the same physiological mechanisms are responsible for heat injury sustained under both intense and moderate heat stress at temperatures above T_c (see below). Consequently, it is possible to use TDT model parameters derived from static experiments to accurately predict heat failure time during (i) combinations of different static exposures, (ii) gradually increasing temperature where a linear temperature increase results in an exponentially increasing heat failure rate and/or (iii) fluctuating temperature exposure (Fig. 3C). These predictions of heat stress additivity above T_c have, to our knowledge, only been comprehensively tested experimentally in two species – the brook trout and vinegar fly – but here the predictions have been fully validated (Fry et al., 1946; Jørgensen et al., 2021b). First, using only static exposure temperatures, TDT models were parameterized. Subsequently, the TDT parameters were used to predict time to heat failure during several static, ramping or fluctuating conditions, and these predictions were then compared with actual experimental measures of time to heat failure (Fig. 3D). As is clear from these examples, the time to heat failure during variable temperature exposures can be accurately predicted from TDT model parameters by simply integrating heat failure accumulation over time (Fry et al., 1946; Jørgensen et al., 2021b). Importantly, in these experiments, additivity was not affected by the order of exposure (high or low intensity heat first), and the stressful temperatures were always above T_c, preventing the animals from repairing thermal injury, which could occur in the permissive zone (see below). Although these two examples provide strong support for the additivity of heat stress above T_c, it remains relevant to test this prediction broadly among ectotherms.

A consequence of additive heat stress accumulation above T_c is that static and dynamic assay types can be reconciled by considering that both assays report the heat failure endpoint once a given amount of heat stress (the thermal dose) has accumulated (Fry et al., 1946; Jørgensen et al., 2019, 2021b; Kilgour and McCauley, 1986). In other words, the model essentially claims that all static and dynamic measures of acute CT_max measure the same trait! It is simply the progression towards CT_max that differs when different static and dynamic protocols expose the animal to different failure rates (Fig. 3C). Consequently, it is mathematically possible to convert one assay type to another using the parameters from a TDT model (Fig. 3C,D; Fry et al., 1946; Jørgensen et al., 2019, 2021b; Kilgour and McCauley, 1986; Kilgour et al., 1985). Further, this reconciling model can explain the frequent observation that in dynamic assays, CT_max decreases with slower ramping rates, as the slower ramping invariably increases the duration of exposure to stressful temperatures above T_c (Chown et al., 2009; Jørgensen et al., 2019; Kingsolver and Umbanhowar, 2018; McMahon and Ussery, 1995; Mitchell and Hoffmann, 2010; Peck et al., 2009; Richard et al., 2012; Terblanche et al., 2007).

A TDT model can be parameterized from several static experiments (a classic TDT model) or using several dynamic assays with different temperature ramping rates (Jørgensen et al., 2021b; Kilgour and McCauley, 1986). In previous work (Jørgensen et al., 2021b), we introduced the mathematical framework and R-scripts allowing researchers to directly obtain TDT parameters enabling conversion and comparison of thermal tolerance measurements within and between static and dynamic experiments (see https://github.com/MOersted/Thermal-tolerances for scripts and guidance). Furthermore, TDT parameters can be used to investigate the accumulation of heat stress under fluctuating temperatures (Fig. 3D). However, as with all models, considering limitations is crucial. Firstly, to establish a good TDT model, we recommend using several static experiments covering temperatures that result in a wide range of experimental durations as model extrapolation can be problematic (Jørgensen et al., 2019, 2021b). Secondly, it is important to consider the model boundaries as the TDT model is only valid at temperatures above T_c (Fig. 2; Jørgensen et al. (2021b)). Thus, TDT model parameters should never be used to assess temperature effects on thermal performance below T_c as tolerance and performance in the permissive temperature range are related to biological rates of life with different thermal sensitivities (Figs 1 and 2; Jørgensen et al., 2022).

Considering the additive effects of heat stress outlined above, it is reasonable to assume that a single biological disruption rate accelerating above T_c is the cause of heat failure in ectotherms or that several processes leading to heat failure converge in a common disruptive process (Bowler, 2018; Schmidt-Nielsen, 1997). Further, the extreme and unconventionally high Q₁₀ of the heat failure rate is indicative of a shared mechanistic cause of heat failure in ectotherms. However, at present there is little consensus regarding the physiological causes of heat failure. Below, we discuss how heat failure probably originates from a mismatch between rates of homeostatic and disruptive biological processes.

In the simplest model, the relationship between temperature and survival duration conveyed by the TDT model (Fig. 3) could be explained by a single temperature-dependent biological process that disrupts homeostasis with exponentially increasing intensity as temperature increases (‘disruption rate’ see Glossary; red curve in Fig. 4). However, heat injury only accumulates above a critical temperature threshold (T_c), necessitating the inclusion of an additional temperature-dependent biological rate representing the ‘capacity for homeostatic regulation’ (‘homeostatic capacity rate’ see Glossary; blue curve in Fig. 4). Introduction of this homeostatic capacity rate establishes T_c as the temperature where the rate of disruption exactly equals the capacity for restoration of homeostasis, i.e. with no net accumulation of heat injury or repair (for a comparable discussions of repair versus failure, see Colinet et al.; 2015;,Kovacevic et al., 2019). According to this view, T_c defines the permissive temperature range as the range where the homeostatic capacity rate is greater than the disruption rate, and the stressful range as the range where the homeostatic capacity rate is less than the disruption rate (Figs 1–4). Accordingly, it is actually the net difference (ΔLoss of homeostasis) between the rate of disruption (‘injury’, red curve in Fig. 4) and the rate of homeostatic capacity (‘repair’, blue curve in Fig. 4) that determines the exponential increase in heat failure conveyed by the TDT model.

A model with two antagonistic processes representing loss and re-establishment of homeostasis allows for modelling how net repair and net injury accumulation vary when ectotherms experience fluctuating temperatures (Colinet et al., 2015; Kovacevic et al., 2019; Nedvěd et al., 1998). Heat injury accumulates exponentially with temperature above T_c and even if an ectotherm survives a period above T_c and evades the stressful conditions, it will have accumulated a ‘load’ of heat stress (equivalent to a fraction of the thermal dose Td illustrated in Fig. 3A). This load of heat stress is additive (see above) in subsequent stressful exposures unless homeostasis is restored during exposure to temperatures below T_c. Accordingly, heat stress accumulated during a warm day can be partially or completely repaired during a cooler night (Colinet et al., 2015; Dillon et al., 2007; Fry et al., 1946; Kovacevic et al., 2019; Speights et al., 2017).

The potential for net repair at temperatures below T_c depends on the relative strength of the antagonistic processes determining repair and disruption of homeostasis, respectively (Fig. 4). The literature on repair rates is surprisingly scarce but studies indicate that net repair rate is temperature dependent with increasing repair rates found at higher temperatures (Bowler and Kashmeery, 1979; Dingley and Maynard Smith, 1968; Iandolo and Ordal, 1966). This observation is not fully compatible with the pattern in Fig. 4, where the rate of net repair should decrease at the highest permissive temperatures (because of an increasing disruption rate) and repair should converge to zero at T_c. It can also be argued that net repair capacity will not continue to increase indefinitely as temperatures decrease below T_c (Fig. 4). Ultimately, low temperatures will limit the capacity for repair and further it is assumed that at sufficiently low temperatures other processes will start to disrupt homeostasis as a result of cold stress (MacMillan and Sinclair, 2011; Nedvěd et al., 1998; Overgaard et al., 2021).

To briefly exemplify the thermal sensitivity of repair we used ‘split-dose’ experiments inspired by Kashmeery and Bowler (1977) where two stressful exposures are separated by a period at a permissive temperature allowing for repair. With this protocol, we examined the temperature dependence of repair in four species of Drosophila (Fig. 5A,B) by varying the temperature of the ‘repair’ period between the two stress exposures. The preliminary results support that net repair occurs when flies are allowed a period at permissive temperatures, and further that repair rate is temperature dependent (Fig. 5C) such that repair capacity declines at both low (probably due to slowed metabolism) and high temperature (due to the increased proximity to T_c and increased disruption rate).

There is currently no consensus on a single physiological dysfunction that is considered the proximal cause of acute heat failure in all ectotherms (Jutfelt et al., 2018; Pörtner, 2001; Somero et al., 2017; Vornanen, 2020). Several hypotheses have been proposed to explain ectothermic heat failure, and most of these can be linked to one or more of the five biological processes highlighted by Schmidt-Nielsen (1997): (i) protein denaturation, (ii) thermal inactivation of enzymes, (iii) inadequate oxygen supply, (iv) unbalanced temperature effects on interdependent metabolic reactions or (v) membrane dysfunction. These five ‘heat failure hypotheses’ are not mutually exclusive and several physiological dysfunctions may operate in unison to cause the high thermal sensitivity that characterizes heat failure (Fig. 2). For this review, we emphasize that these heat failure hypotheses easily integrate with a simple model balancing homeostatic capacity versus homeostatic disruption (Fig. 4). Specifically, we discuss this in relation to three examples: (i) oxygen limitation, (ii) protein denaturation and (iii) membrane effects on cellular excitability.

The much-debated ‘oxygen- and capacity-limited thermal tolerance’ hypothesis (OCLTT; Pörtner and Farrell, 2008; Clark et al., 2013; Verberk et al., 2016; Jutfelt et al., 2018) poses that ectotherms reach their critical thermal limit when the capacity for aerobic mitochondrial ATP production no longer matches the requirements of the standard metabolic rate (Pörtner, 2001). Limitations to aerobic ATP production at high temperature have often been linked to insufficient oxygen transport, including inadequate cardiac function (Pörtner, 2001; Pörtner and Farrell, 2008). However, compromised mitochondrial coupling and ATP production at high temperature are increasingly being discussed in relation to this hypothesis (Blier et al., 2014; Chung and Schulte, 2020; Hraoui et al., 2020; Iftikar and Hickey, 2013; Jørgensen et al., 2021a; Michaelsen et al., 2021). The OCLTT hypothesis has received mixed experimental support, particularly for terrestrial ectotherms (Fobian et al., 2014; Verberk et al., 2016). Nevertheless, the central tenets of the OCLTT hypothesis are easily integrated with a model of a temperature-sensitive (im)balance of homeostatic capacity (ATP synthesis rate) versus homeostatic disruption (ATP demand) (Fig. 4). The OCLTT hypothesis further aligns because it explains that reduced performance (declining TPC) at the highest permissive temperatures results from decreasing aerobic scope caused by the reduced difference between the antagonistic rates (ATP synthesis versus ATP demand) (Pörtner, 2001; Pörtner and Farrell, 2008; Ern, 2019).

A second hypothesis relates to increased expression or translation of heat shock proteins (hsps) which is a hallmark of heat stress in ectotherms (Feder and Hofmann, 1999; Parsell and Lindquist, 1993; Ritossa, 1962; Tomanek, 2010). The expression of inducible hsps during heat stress is somewhat proportional to net protein denaturation and heat stress can therefore be viewed as an (im)balance of homeostatic disruption (denaturation rate) versus homeostatic capacity (removal rate of denatured protein or rate of de novo protein synthesis). The imbalance between these antagonistic rates can be assessed from the magnitude of hsp expression, and several studies support that accumulated protein denaturation is tightly linked to heat failure. For example, (i) cumulative hsp expression is proportional to accumulated heat stress during fast and slow heat ramping in Drosophila, although the temperature of heat failure is different between ramping rates (Sørensen et al., 2013), (ii) heat hardening through a brief pre-exposure to heat stress increases hsp expression which subsequently augments the homeostatic capacity rate and therefore increases heat tolerance (Feder and Hofmann, 1999; Parsell and Lindquist, 1993; Sørensen et al., 2003; Tomanek, 2010), and (iii) protein degradation is extremely sensitive to temperature (Q₁₀=10–1000; Ushakov, 1964; Cossins and Bowler, 1987; Tattersall et al., 2012), which is similar to the very high Q₁₀ found for organismal failure beyond T_c (Fig. 2; Jørgensen et al., 2022).

A third hypothesis compatible with the model outlined in Fig. 4 relates to the imbalance of membrane processes strengthening or weakening cellular excitability. In insects, it is well described that heat knockdown is associated with a shutdown of the central nervous system (CNS). This is caused by a surge in extracellular [K⁺], resulting from an imbalance between active and passive ion transport, that ultimately depolarizes the neurons, causing neuronal silencing (Armstrong et al., 2009; Jørgensen et al., 2020; Robertson et al., 2020; Spong et al., 2016). Similar perturbations in CNS function are also found in other ectotherms at temperatures close to CT_max (Andreassen et al., 2022; Friedlander et al., 1976; Hamby, 1975; Jutfelt et al., 2019; Orr, 1955) and loss of ion balance in the extracellular fluid surrounding muscle has also been implicated in ectothermic heat failure (Gladwell et al., 1975; Grainger, 1975). Finally, Vornanen (2016, 2020) argues that heat tolerance is governed by the ‘temperature-dependent deterioration of electrical excitability’ (TDEE) hypothesis, which poses that unbalanced thermal sensitivity of excitatory (Na⁺ current) and inhibitory currents (K⁺ current) compromises the generation of cardiac action potentials, which eventually causes cardiac failure. From these examples, a temperature-sensitive antagonistic interaction between passive/active or excitatory/inhibitory ion transport across membranes could also explain why heat failure rates increase exponentially with increasing temperature.

Collectively, these three examples show that it is both straightforward and appropriate to integrate leading physiological hypotheses of heat failure with a model of two temperature-sensitive antagonistic rates. One rate determines the capacity for maintenance/restoration of homeostasis (e.g. ATP synthesis rate, protein synthesis rate or active ion transport) and the other rate, increasing faster with temperature, acts to disrupt homeostasis (e.g. ATP use, protein denaturation or passive ion leak). In the permissive temperature range, homeostatic capacity exceeds the disruption rate allowing for chronic survival, whereas the acutely stressful temperatures are dominated by disruption rates accumulating imbalance, which directly dictates survival duration (Figs 2, 3 and 4). The balance between these antagonistic rates will therefore also determine the critical transition temperature T_c and the potential for repair (Fig. 5).

Estimates of thermal tolerance are frequently compared within or between species to infer eco-physiological patterns (Addo-Bediako et al., 2000; Ghalambor et al., 2006; Hoffmann et al., 2013; Kovacevic et al., 2019; Pinsky et al., 2019; Sunday et al., 2011; Sunday et al., 2019). Such comparisons are complicated by the variable use of static and dynamic protocols to assess tolerance limits (Bak et al., 2020; Kovacevic et al., 2019; Rezende et al., 2014; Santos et al., 2011; Terblanche et al., 2007; Terblanche et al., 2011). However, as outlined above, tolerance measures can be reconciled and converted to a common estimate using the TDT parameters, e.g. the maximal static temperature tolerable for 1 h (sCT_max(1h)). To illustrate this, Jørgensen et al. (2021b) compiled and recalculated heat tolerance measures using data obtained from different sources of static or dynamic assays. Despite the original measures being based on very different protocols, populations and acclimation statuses, the recalculated sCT_max(1h) values were remarkably similar within species (Fig. 6A; for more examples, see Jørgensen et al., 2021b), suggesting that the TDT model has promising applications in meta-analyses where a standardized measure of heat tolerance allows direct comparison.

The TDT model represents a powerful tool for designing experiments to test the heat tolerance of different species, populations, acclimation groups, etc. (Fig. 6B). Comparing groups with different heat tolerance limits and T_c can be problematic, as it may be difficult to find a treatment suitable for all groups. For example, if groups are tested at the same temperature and duration, this treatment may be above T_c for some groups, but below T_c for others (line a in Fig. 6B). Even above T_c, the level of stress inflicted on the groups may differ considerably for a given duration at the treatment temperature (line b in Fig. 6B). Accordingly, the associated behavioural or physiological responses of the groups may represent different information on chronic and acute temperature effects (see also Fig. 2). However, using information from the TDT model, it is possible to expose treatment groups to the same stress intensity (same level of homeostatic failure) using temperatures (or durations) specific to each group (line c in Fig. 6B). Such an approach will allow for more targeted experiments investigating the physiological mechanisms of thermal failure even if the experiments are performed on experimental groups that differ widely in thermal tolerance (Tarapacki et al., 2021).

Finally, the TDT model offers a framework to examine how temperature acclimation and adaptation (re)shape heat tolerance (Willot et al., 2022) or how nutritional status, water status and pathogens affect the heat stress response. In the context of the presented framework, we here discuss how acclimation or adaptation can affect heat susceptibility by changes in either resistance or tolerance to heat stress (Fig. 6C). Increased resistance can be achieved through modification of one (or both) of the two antagonistic rates determining net heat stress (rates of disruption and homeostatic maintenance, respectively; Fig. 4). Changing the rate of either disruption or homeostatic maintenance will increase T_c (compare solid and dashed red line in Fig. 6C). Heat stress susceptibility can also change by altering tolerance, which is equivalent to increasing Td (graphically an increased area of the thermal dose rectangle; Figs 3 and 6C). In this scenario, tolerance time increases even when homeostasis is lost at the same rate and above the same T_c (Fig. 6C). The difference between increased tolerance and resistance can be discerned by examining putative changes in T_c following acclimation/adaptation (Angilletta, 2009; Cossins and Bowler, 1987; Fry et al., 1946; Hoffmann and Todgham, 2010). Furthermore, increases in tolerance can be inferred from evaluating how markers of heat stress have accumulated at different levels of heat stress, e.g. indicated by higher lactate levels, hsp levels or the level of ionic imbalance (Sørensen et al., 2013;,Tarapacki et al., 2021).

The framework presented here (summarized in Fig. 7) separates permissive and stressful temperature ranges and allows for ecological and physiological assessment of heat stress based on the balance between two antagonistic biological processes (thermal injury and repair; Fig. 7A). This model therefore also provides an understanding of how temperature sensitivity of different biological processes underpins the TPC and the TDT model. Central to this framework is a clear boundary, T_c, which separates the permissive and stressful temperature ranges (Fig. 7). Acknowledging these temperature ranges with vastly different thermal sensitivities therefore allows for better integration of observations across studies and provides a conceptual model to study the temperature tolerance traits that are essential for predicting species’ responses to climate change (Jørgensen et al., 2022).

Future efforts should investigate how T_c is best determined experimentally. Our suggestions for experiments that potentially may uncover this include; (i) creating TDT curves over sufficiently wide temperature ranges to uncover the actual breakpoints between permissive and stressful temperatures ranges (Fry, 1971; Fry et al., 1946; Hollingsworth, 1969) (Figs 2 and 7B), (ii) initiating dynamic assays at different temperatures, where a start temperature >T_c would result in increased CT_max, whereas start temperatures <T_c should have negligible effects on the CT_max estimate (Kingsolver and Umbanhowar, 2018), (iii) measuring CT_max at gradually slower ramping rates as the resulting CT_max estimates should then approach T_c asymptotically (Richard et al., 2012) and (iv) estimating T_c as the ‘resting’ temperature where thermal injury is equal to the repair capacity during experiments of alternating stressful and benign temperatures (compare species repair capacities in Fig. 5C).

Another perspective resulting from this synthesis concerns the temperature fluctuations that many ectotherms experience naturally. Fluctuations that occur only above or below T_c are easy to integrate into the TDT or TPC model, respectively (Colinet et al., 2015; Deutsch et al., 2008; Fry et al., 1946; Jørgensen et al., 2021b; Sinclair et al., 2016). However, the situation is much more complex when fluctuations occur between the permissive and stressful temperature ranges as they are dominated by different thermal sensitivities, and especially for TPCs, different traits can span the two temperature ranges (Fig. 7C,D). Studies on the thermal sensitivity of heat stress repair are still scarce (Bowler and Kashmeery, 1979; Dillon et al., 2007; Dingley and Maynard Smith, 1968; Kovacevic et al., 2019) and currently it is difficult to distinguish repair from rapid hardening processes which can increase heat resistance/tolerance during subsequent exposures to heat stress (Bowler, 2005; Krebs and Loeschcke, 1994; Sørensen et al., 2003). Although not the focus of this Review, many similar conceptual observations can also be applied to cold limits of ectotherms as these limits are also the result of unbalanced antagonistic processes (MacMillan and Sinclair, 2011; Overgaard et al., 2021). It may therefore be relevant to consult the cold tolerance literature, where the repeated transition from stressful to benign temperatures associated with ‘fluctuating thermal regimes’ and ‘repeated cold exposures’ has been investigated (Colinet et al., 2015; Colinet et al., 2018; Koštál et al., 2007; Marshall and Sinclair, 2012; Nedvěd et al., 1998).

Finally, the physiological rates underlying homeostatic capacity and disruption that ultimately determine CT_max are still intensely debated (Bowler, 2018; González-Tokman et al., 2020; Andreassen et al., 2022; Jutfelt et al., 2018; Neven, 2000; Pörtner and Farrell, 2008). We hope that appropriate integration of the TDT model in future experimental designs can help to identify the proximal physiological causes of heat stress susceptibility (Fig. 6B,C). The framework presented here will, for example, allow for a systematic approach to experimentally associate homeostatic capacity rate and/or perturbation rate with physiological mechanisms hypothesized to cause heat death in ectotherms (oxygen limitation, protein denaturation, membrane dysfunction, neurological failure, etc.).

We thank Jeppe Bayer and Loisa D. Bonde for laboratory assistance in repair experiments. We are grateful for the many discussions on temperature biology of animals with our colleagues at Section for Zoophysiology, Aarhus University, and we thank David Vasseur, Ray Huey and the anonymous reviewers for constructive feedback.