INTRODUCTION

The use of critical endpoints or thresholds as thermal tolerance metrics has gained considerable momentum over the last two decades. For example, Deutsch et al. (2008) showed that tropical animals lived at temperatures closer to their physiological limits and were, therefore, more vulnerable to global warming. These authors originally used intrinsic rates of increase to estimate the temperature at which fitness dropped to zero and populations were no longer sustainable. Subsequent analyses have adopted the temperature at which an organism collapses and/or dies during a ramping experiment as a more indirect proxy of tolerance limits (Clusella-Trullas et al., 2011; Huey et al., 2009; Pinsky et al., 2019; Sunday et al., 2010, 2014). These so-called ‘critical thermal limits’, which presumably describe the lower and upper temperatures that an organism can tolerate, have been measured in thousands of species (Bennett et al., 2018) and have a long history in plants (see Sachs, 1864). However, these estimates are not directly comparable to thermal effects on fitness and are highly sensitive to experimental conditions such as initial temperatures and rates of temperature changes (Lutterschmidt & Hutchison, 1997; Terblanche et al., 2007). These limitations, concomitantly with increasing use of these estimates to predict species' resilience to warming, have sparked debate on the mechanistic basis of thermal tolerance as a trait and the adequacy of critical endpoints as tolerance proxies (Huey & Kearney, 2020; Ørsted et al., 2022; Rezende et al., 2011; Rezende & Santos, 2012, Rezende et al., 2014; Santos et al., 2011; Terblanche et al., 2011).

The fundamental concern is that critical limits, quantified as a single temperature value, ignore the cumulative nature of physiological stress, which includes both the intensity and duration of a thermal challenge. Empirical studies have shown that the logarithm of survival time varies linearly with temperature, a relationship well established for microorganisms such as bacteria and fungal spores (Bigelow, 1921; Watkins & Winslow, 1932), molluscs (Ansell et al., 1980), insects (Jørgensen et al., 2019; Maynard-Smith, 1957) and vertebrates (Brett, 1956; Somero & DeVries, 1967). These thermal death time (TDT) curves are widely used in the pest control and food processing industry (Stumbo, 1973; Tang et al., 2007 and references therein). Related approaches, such as thermal tolerance landscapes (sensu Rezende et al., 2014) that describe TDT effects across different survival probabilities, have been recently employed to predict heat mortality under constant and fluctuating temperature conditions in animals (Jørgensen et al., 2019; Molina et al., 2023; Rezende et al., 2020). There is a growing consensus in animal studies that TDT curves and tolerance landscapes provide a more accurate framework to estimate thermal tolerance in ecological settings (Huey & Kearney, 2020; Jørgensen et al., 2022; Rezende et al., 2020), yet the potential to apply this framework to plants remains virtually unexplored (but see Neuner & Buchner, 2023).

Thermal tolerance metrics such as the T₅₀ threshold, which describe the temperature required for a 50% drop in physiological function, are now being used to estimate potential vulnerability of a given plant species under a warming climate (Cook et al., 2021; Curtis et al., 2016; Marchin et al., 2022; Perez & Feeley, 2020; Sastry & Barua, 2017). These metrics usually are based on photosynthetic thermal threshold assays to determine the point of failure based on the physiological response of photosystems to applied thermal stress. All else being equal, such metrics allow the comparison of tolerance among leaves, individual plants, species and environmental effects (e.g. Curtis et al., 2014, 2016; Drake et al., 2018; Feeley et al., 2020; French et al., 2017, 2019; Knight & Ackerly, 2003; Perez & Feeley, 2020; Sastry & Barua, 2017; Slot et al., 2019). However, use of these critical endpoints involves the same conceptual pitfalls discussed in the animal literature, prompting lively discussion regarding their adequacy and application in plant thermal tolerance (Lancaster & Humphreys, 2020, 2021; Perez et al. 2021a). Indeed, several studies have shown that damage to plants caused by heat is not only determined by the stress temperature but also the duration at a given temperature or heat dose (Bilger et al., 1984; Colombo & Timmer, 1992; Hüve et al., 2011). Furthermore, at a constant temperature, increasingly longer periods of the same stress temperature cause more damage to photosystems measured by a range of physiological techniques (Dascaliuc et al., 2007; Hüve et al., 2011; Li et al., 2014; Marias et al., 2016; Valladares & Pearcy, 1997). These results highlight that critical limits in the plant literature likely exhibit limitations similar to those discussed in animal studies. Accordingly, Neuner and Buchner (2023) recently revealed the typical association between heat intensity and duration described by the TDT curve for leaf damage and photosynthetic dysfunction across five alpine plant species, suggesting that a unified approach to study thermal tolerance across organisms is not only desirable but also feasible.

Another key limitation of fixed duration heat thresholds is their application for modelling predicted vulnerability under future scenarios. Currently, plant thermal vulnerability is assessed by comparing plant physiological thresholds to average maximum leaf or air temperatures to produce thermal safety margins (Cook et al., 2021; Krause et al., 2010; Leon-Garcia & Lasso, 2019; O'Sullivan et al., 2017; Perez & Feeley, 2020; Sastry & Barua, 2017; Zhu et al., 2018). However, the fluctuating nature of leaf temperature (Leigh et al., 2012) and cumulative heat exposure are not accounted for in this approach. Here we aim to bridge this gap. The application of TDT curves combined with the dynamic survival model developed for animal thermal tolerance (Rezende et al., 2020) offers a methodological framework to predict cumulative heat stress in plants. Addressing this central issue opens the avenue not only to compare thermal tolerance across plant populations and species, but also to employ predictive tools that utilise realistic thermal tolerance landscapes in this group. With this purpose, we investigated the impact of heat stress on plant photosystem function (maximum quantum yield, F_V/F_M) in two Australian arid zone species, the shrub, Myoporum montanum R.Br., and tree, Eucalyptus socialis F.Muell. ex Miq. First, we examined whether the 50% decline in function of Photosystem II (PSII), often employed in plant studies to assess response to heat stress (T₅₀), exhibits the expected relationship between temperature intensity and duration (Figure 1). Second, we analysed how this relationship varied within M. montanum longitudinally over multiple trials to estimate intraspecific variability via potential changes in heat tolerance over the course of the summer. Third, we compare our empirical results against recently published estimates by Neuner and Buchner (2023) to illustrate how thermal adaptation may explain differences in heat tolerance across plant species with this framework. Finally, we applied a dynamic model of thermal damage (Rezende et al., 2020) to illustrate how temperature–duration relationships obtained in the laboratory can be employed to forecast the effect of heat stress on leaf function under natural conditions.

MATERIALS AND METHODS

RESULTS

Estimates of overnight F_V/F_M for each temperature and time combination are provided in the supplementary information (Table S1). The model comparison approach shows that logistic regressions including only main effects and exposure time in logarithmic scale provide the best fit to the data (Table 1). This result suggests that the slopes of the temperature–duration relationships remain relatively constant across trials and/or species, and also provides support to the log-linear relationship predicted by the framework (Figure 1). To assess how well the best model fits the empirical observations, we performed a regular linear regression between predicted values against observed F_V/F_M and obtained an R² = 0.77 (F_1,638 = 2134, p < 2.2 × 10⁻¹⁶). Thus, the best logistic model explains roughly 77% of the variance in F_V/F_M observed across leaf samples. Results were qualitatively similar when we repeated the analysis including only M. montanum and removing species as a categorical factor (results not shown), and in this instance, the model with only main effects and log-transformed exposure time had an even stronger support based on Akaike weights (w_i = 0.96). Also, in this analysis the fit of the model improved, based on the stronger regression between predicted and observed F_V/F_M (R² = 0.79, F_1,478 = 1848, p < 2.2 × 10⁻¹⁶).

As we hypothesised, empirical values of overnight F_V/F_M exhibit the response predicted by the temperature–duration framework and a large fraction of the unexplained variance can be attributed to variation in F_V/F_M within each temperature and exposure time combination (Figure 2). Thus, the temperature–duration framework appears to describe the overall response of PSII to heat stress remarkably well, with some of the unexplained variation involving differences across leaves and/or individual plants within each sample (Figure 2; Figures S3 and S4). Accordingly, most of the variation around mean estimates was detected at intermediate F_V/F_M (Figure S5), which is expected as all leaves are likely either unharmed or completely damaged at extremely low and extremely high temperatures, respectively.

We then estimated T₅₀ as the inflection point of the logistic regression (Figure 2), as well as its standard deviation, with the bootstrap analysis (Table S2). Linear regressions between T₅₀ estimates and log time (Equation 2) performed separately for each trial and/or species resulted in a very good fit (Figure 3). For M. montanum, the R² ranged between 0.95 and 0.98 across the three trials (F_1,3998 = 80,970 to 188,700 and p < 2.2 × 10⁻¹⁶ in all cases), with the 1-min exposure time (intercept), $$$ {T}_{50}^{\prime } $$$, varying between 59.6 and 56.2°C across trials and the thermal sensitivity (slope), z remaining virtually constant and corresponding to 6.5°C (z range 6.45–6.53, Figure 3b). In contrast, for E. socialis we obtained a $$$ {T}_{50}^{\prime } $$$ of 63.2°C and a z of 8.3°C with the linear regression, though with a lower goodness of fit, resulting in an R² = 0.86 (F_1,3998 = 24,320, p < 2.2 × 10⁻¹⁶). This illustrates how the higher variability in F_V/F_M across leaf samples and a T₅₀ falling often outside the experimental temperatures for this species results in a lower precision in the estimation of its heat tolerance (Figure S5). Accordingly, the standard deviations associated with the temperature–duration parameters were substantially larger for E. socialis than for M. montanum (+ ~1 SD, Figure 3b; Table S3), and their overlapping z supports a single slope across these two species and temporally within M. montanum trials as suggested by the model comparison analysis of the F_V/F_M responses (Figure 3a; Table 1, M. montanum and E. socialis). Parameter estimates for the temperature–duration curves are listed in Table S3.

Photosynthetic function (F_V/F_M) in the field

Simultaneously measured air and leaf temperatures had a robust linear relationship: T_leaf = 1.63 (±0.02 SE) + 0.91 (±0.0006 SE) T_air obtained with a linear regression (R² = 0.98, F value = 2.5 × 10⁶ (160,478 df) and residual error = 0.75, Figure 4b). This fit was then employed to convert past recorded air into predicted leaf temperatures for our estimation of PSII heat stress in the field (Figure 4) using the ‘dynamic’ model (Rezende et al., 2020). Simulations from the dynamic model suggest that summer temperatures could often be stressful for M. montanum, though there were pronounced differences from year to year. Interestingly, heat tolerance seemed to decrease from trials 1 to 3, resulting in higher vulnerability at relatively lower temperatures. This temporal change in heat tolerance for M. montanum was used to create three scenarios when simulating potential heat damage. When we analysed the data on 24-h bins, we detected a regular sigmoidal association between daily thermal damage as a function of maximum daily temperatures (Figure 4), which provided a relatively straightforward rule of thumb to diagnose differences in thermal stress based on the temperature–duration curve. For instance, for M. montanum, the probability of thermal damage may begin to rise in days reaching maximum temperatures of approximately 40, 38.5 and 36°C based on thermal tolerances derived from summer trials 1, 2 and 3, respectively, but would near 100% when temperatures reach 45, 43 and 41°C (Figure 4).

DISCUSSION

Here we show that the temperature–duration TDT framework developed to study thermal tolerance in microorganisms and metazoans can be successfully employed to quantify heat tolerance of photosynthetic tissue in plants. It is not entirely surprising, as multiple studies have reported that higher stressful temperatures or longer exposure durations increase damage to photosystems (Agrawal & Jajoo, 2015; Dascaliuc et al., 2007; Hüve et al., 2011; Königer et al., 1998; Marias et al., 2017; Valladares & Pearcy, 1997; Yan et al., 2011). Importantly, this general relationship between temperature and exposure time has also been reported for other plant traits, such as visual cell death in seedlings (Colombo & Timmer, 1992), leaf weight loss in green beans (Yarwood, 1961) and visual leaf damage and PSII dysfunction in alpine species (Neuner & Buchner, 2023). Here we demonstrate how these findings might be analysed within a single framework for plants for application in climate change ecology.

Our analyses also demonstrate how variation in heat tolerance can be quantified and compared within and across plant species and subsequently how to employ this knowledge to estimate heat stress in natural populations. For the limited subset employed here, analyses detected differences in heat thresholds corresponding primarily with shifts in the elevation of the temperature–duration curves rather than changes in their respective slopes (M. montanum and E. socialis, Table 1; Figure 3a). The shift in threshold temperature perhaps reflects that of the environmental conditions. Photosystem heat tolerance can rapidly change with local environmental conditions and water status (Buchner & Neuner, 2003; Cook et al., 2021; Ghouil et al., 2003; Havaux, 1992; Knight & Ackerly, 2003; Sumner et al., 2022; Valladares & Pearcy, 1997; Zhu et al., 2018). It is also a protective mechanism, in that it increases with high leaf temperatures (Perez & Feeley, 2020), along with other leaf mechanisms such as membrane fluidity (Zheng et al., 2011), solute and sugar concentration changes (Hüve et al., 2006), heat shock factor and protein expression (Driedonks et al., 2015; Heckathorn et al., 1999; Milner, 2020; Wang et al., 2004). Once heat shock has passed however, these mechanisms and PSII heat tolerance can de-acclimate within hours to days (Aspinwall et al., 2019; Charng et al., 2006; Drake et al., 2018). Over the course of summer sampling in our study, there was a decline in heat thresholds across trials, while air temperatures decreased and rainfall increased for trials 2 and 3 (Figure S1). As such, progressively lower heat tolerances over the trials in our study most likely reflected the increasingly benign conditions over summer.

Several inferences can be made through comparing parameters for our temperature–duration curves with those recently reported by Neuner and Buchner (2023). First, that variation in heat tolerance within a single species is far from negligible [also see Cook et al. (2021), for a single genotype M. montanum variation with environment] and this may be lower than variation across species ($$$ {\Delta T}_{50}^{\prime } $$$ 3.3°C within trials vs. 14.2°C across species; Δz 0.03 vs. 4.6; Table S3). Second, perhaps not surprisingly, our species inhabiting Australian desert environments exhibited higher tolerance to heat stress than the alpine plants considered (Figure 3b). Third, for the species compared here, higher thermal thresholds tended to also equate to higher thermal sensitivity (Figure 3b). The higher sensitivity means that tolerance decreased faster with a longer heat exposure. Higher critical limits with higher thermal sensitivity have been found across kingdoms (Arthropoda, Mollusca, Chordata, Echinodermata, Brachiopoda; Rezende et al., 2014; Molina et al., 2023), supporting the idea that the phenomenon also may be present in the plant kingdom. Across kingdoms, thermal sensitivity ranges from 1 to 9 in insects, bivalves and fishes (Rezende et al., 2014). The seven plant species represented here range from distinct and ecologically diverse environments (desert vs. alpine) and reflect a relatively wide range in thermal sensitivity (4–8) compared to that of animal kingdom (Rezende et al., 2014). Additional data are clearly required to fully understand how heat tolerance landscapes vary across plant lineages, distribution limits, habitats and functional groups. Importantly, while these analyses may not necessarily contradict large-scale global trends detected with critical thermal limits (Lancaster & Humphreys, 2020), they may dramatically increase the statistical and predictive power of analyses at smaller spatial scales by controlling for the confounding effects of exposure duration (e.g. see Table 1 in Rezende et al., 2014).

Just as with animal studies, many of the limitations of the theoretical framework apply to plants. For example, thermal tolerance studies on plants often neglect the synergistic impact of other stressors, such as dehydration, or how heat tolerance may change during different stages of the lifecycle (Geange et al., 2021). Similarly, simulations employing the dynamic model for animals ignore spatial heterogeneity in light and temperature, physiological history before the stress, the existence of microhabitats and, importantly, short- and long-term physiological recovery following a thermal stress (Huey & Kearney, 2020). However, one aspect unique to plants is that, because they are modular organisms, studies often work with indirect proxies of temperature stress at the leaf level such as photosystem function via F_V/F_M, and arbitrary thresholds such as T₅₀, instead of thermal mortality of the whole plant. While this approach is crucial for comparative purposes (Lancaster & Humphreys, 2020, 2021; Perez, Feeley, et al., 2021), it remains to be determined how different thresholds are indicative of heat tolerance in natural plant populations. For instance, the temperature–duration curves from Neuner and Buchner (2023) suggest that 50% visual leaf damage is attained at temperatures on average 3.7°C higher than those required for a 50% drop in F_V/F_M; hence, caution is warranted when comparing curves obtained with different methods (Table S3). Here, we were able to predict the probability of M. montanum leaves of reaching T₅₀ (Figure 4), but like Neuner and Buchner (2023), are yet to translate this probability into leaf death and, subsequently, plant survival, reproduction and ultimately Darwinian fitness. Future research should seek to bridge the gap between physiological proxies of thermal stress and their demographic consequences by calibrating predictive models with measures of crown dieback, plant mortality and decreased seed production following heat waves (Breshears et al., 2021; Marchin et al., 2020; Milner et al., 2023) and relationships between CO₂ assimilation and T₅₀ thresholds (Perez et al. 2021b). Finally, exploration across plant taxa, vegetation systems and environmental growth conditions will determine common trends in thermal sensitivity. For example, there may be a relationship among species differing in their underlying biological mechanisms for temperature stress response, such as those capable of rapid isoprene production (Siwko et al., 2007) and changing membrane lipid compositions (Zheng et al., 2011).

CONCLUSIONS AND IMPLICATIONS

Our analyses show how the theoretical framework currently employed to study heat tolerance in animal research can be successfully employed in plants. Modelling thermal sensitivity in the way we present here incorporates an important dimension to estimating plant thermal tolerance in a thermally changing environment. Coupling thermal tolerance with the dynamic model enables the identification of conditions predicted to be damaging to leaves. Until now, the use of thermal thresholds has been limited to thermal safety margin estimation using static maximum temperatures to derive parameters. We demonstrate how this approach can greatly overestimate heat tolerance for predictive purposes. For instance, M. montanum static T₅₀ estimates obtained following a 15-min exposure were roughly 10°C higher than predicted stressful temperatures in the field (peak temperatures in Figure 4a). The presented framework estimates plant thermal vulnerability considering the changing nature of temperature rather than static durations, resulting in more realistic probabilities of reaching damaging temperatures (Figure 4c,d). Estimates of heat stress through TDT curves and the dynamic survival model have recently been applied to predict acclimation in fish under various environmental scenarios (Verberk et al., 2023). For plants, the accurate prediction of leaf temperature is complicated (Blonder et al., 2020; Blonder & Michaletz, 2018), but has rapidly advanced [e.g. tealeaves (Muir, 2019) and NicheMapR (Leaf Temperature Hindcaster, [https://camel.science.unimelb.edu.au/biological-forecasting-and-hindcasting-tools/])]. Combining leaf temperature modelling with our framework could forecast plant responses to nuanced environmental shifts, such as altered humidity with climate change. This approach has the potential to not only identify vulnerable species or populations, but also predict their thermally vulnerable periods in greater detail and with greater precision than current methods. This opens the prospect for meaningful predictive comparisons of thermal limits, not only among plants, but also across biological kingdoms.

AUTHOR CONTRIBUTIONS

AMC, KP and AL designed the research. AMC collected the data. AMC and ELR analysed the data, and AMC, ELR and AL wrote the first draft. All authors contributed to the final draft.