Differences in leaf thermoregulation and water use strategies between three co‐occurring Atlantic forest tree species

In the first study of leaf energy balance in tropical montane forests, we observed current leaf temperature patterns in the Atlantic forest, Brazil, and assessed whether and why patterns may vary among species. We found large leaf‐to‐air temperature differences that were influenced strongly by radiation and differences in leaf temperature between 2 species due to variation in leaf width and stomatal conductance. We highlight the importance of leaf functional traits for leaf thermoregulation and also note that the high radiation levels that occur in montane forests may exacerbate the threat from increasing air temperatures.

forests are particularly important in this regard as they are a considerable store of terrestrial carbon (Pan et al., 2011), potentially already function near their maximum temperature (Doughty & Goulden, 2008) and given their location cannot be replaced by species from lower latitudes. The biodiversity of tropical montane forests, which house many endemic species with restricted ranges, may be at particular risk from higher temperatures due to limits on upslope migration, especially for tree species in forests occurring on mountaintops (Phillips, 1997). Modelling studies suggest increasing temperatures are also likely to have a negative effect on tropical forest vegetation carbon; however, the extent of projected impact varies greatly between different models (Galbraith et al., 2010;Huntingford et al., 2013) as do the physiological mechanisms behind the declines (Galbraith et al., 2010).
Temperature can impact plant physiology both directly, by influencing rates of photosynthesis and respiration and indirectly by altering the ambient vapour pressure deficit (D; Lloyd & Farquhar, 2008). D increases with an increase in air temperature (T A ) if relative humidity (h) stays constant, and stomatal conductance (g s ) typically declines with increasing D (Leuning, 1995) to avoid excessive water loss. The reduction in g s with D has the consequence of reduced CO 2 concentration within the leaf. The photosynthetic optima of plants are typically near the mean maximum ambient temperature, showing the acclimation of plants to their environment (Slot & Winter, 2017). The temperature of the leaf tissue itself is the relevant temperature for the control of leaf physiological processes rather than T A .
High leaf temperatures (T L ) can induce damage to photosynthetic machinery; above c. 35°C thylakoid membranes have been observed to structurally change (Gounaris, Brain, Quinn, & Willams, 1983, 1984, and above 40°C photosystem II (PSII) may become deactivated and the electron transport rate reduced (Allakhverdiev et al., 2008).
Chlorophyll fluorescence parameters to assess heat tolerance of PSII show critical temperature thresholds in the region of 45-60°C, with significant variation between species (O'Sullivan et al., 2017;Sastry & Barua, 2017). Irreversible thermal damage to photosynthetic machinery has been observed to occur at 52°C in a tropical species (Krause et al., 2010).
Extremes of microclimate can lead to leaf temperatures that are markedly different from T A . For example, leaf temperatures up to 10°C above air temperatures when leaves were brightly lit have been observed in the Amazon (Doughty & Goulden, 2008) and in Panama (Rey-Sanchez, Slot, Posada, & Kitajima, 2016), and Slot, Garcia, and Winter (2016) found leaf temperatures of a Ficus insipida regularly exceeded 40°C and even reached 48°C during a 3-week period in Panama. Yet despite these striking patterns of leaf temperatures, and the on-going and anticipated increases in air temperatures, there are few datasets examining fluctuations of leaf temperatures in situ in tropical forests and, to our knowledge, none in tropical montane forests.
Leaf energy balance theory can be used to address the drivers of T L in a mechanistic approach (e.g., Michaletz et al., 2016). Developed from the Penman energy balance approach to evapotranspiration (Penman, 1948), the leaf energy balance equation (see Section 2, Equation (3)) estimates the leaf-to-air temperature difference (ΔT) for given microclimatic and leaf-specific variables (Jones, 1992). The leaf energy balance shows that ΔT is dependent on the net energy provided (or lost) by radiation and the energy lost through transpiration. The effects of these fluxes on ΔT depend on leaf shape and physiology through the boundary layer and stomatal resistances to water transport. Stomatal resistance is dependent on stomatal activity and boundary layer resistance increases with leaf width (see Section 2). Hence, although ΔT is strongly influenced by microclimatic conditions (in particular radiation and D), leaf traits (width and stomatal conductance) can also play a role in regulation of leaf temperature.
In addition, leaves can alter their physical position through changes in angle and/or orientation to increase or decrease the amount of radiation received.
Leaf structural traits (leaf mass per area [LMA] and leaf dry matter content [LDMC]) and stomatal conductance (g s ) influence the time required for leaf temperature to change following a change in the environment (the thermal time constant [τ]; Jones, 1992). Leaves with a long τ will show smaller temperature changes in a fluctuating environment, maintaining the leaf temperature closer to the mean air temperature than a leaf with a small τ, which will track fluctuation in air temperature (Michaletz et al., 2015).
Given the diversity of leaf structures and physiology observed within and among tropical forest species (e.g., variation in leaf[let] area over five orders of magnitude for a large sample of tropical species; Wright et al., 2017), it is possible that there will be diversity in leaf strategies with regard to temperature (Michaletz et al., 2015). This means that the impacts of potential future environmental changes may vary between species even within a single biome. Future combined atmospheric changes of increasing CO 2 and increasing T A could be particularly important for T L , as plants tend to respond to increasing CO 2 by reducing g s (Way, Oren, & Kroner, 2015).
Reducing g s decreases water use but also has the consequence of increasing leaf temperature (Barker et al., 2005;Drake, Gonzàlez-Meler, & Long, 1997) and can lead to premature leaf senescence under heat wave conditions (Warren, Norby, & Wullschleger, 2011). Increases in T A could be particularly important under fluctuating and extreme conditions (e.g., heat waves), increasing the occurrence of leaves reaching or exceeding threshold temperatures resulting in leaf damage.
We present an observational study of leaf temperatures in a highly threatened tropical forest region-the Atlantic forest, among the most diverse and threatened of biodiversity hotspots (Colombo & Joly, 2010;Myers, Mittermeier, Mittermeier, da Fonseca, & Kent, 2000). Our mountaintop study site is home to many endemic species.
Humans have exploited the Atlantic forest for 500 years resulting in a highly fragmented landscape (Joly, Metzger, & Tabarelli, 2014) that reduces possibilities for species migration. Hence, a greater understanding of forests in this region is of great interest given their high threat level. We focus here on determining and understanding interspecific differences in leaf temperatures caused by differences in leaf traits. Our approach aims to begin to reveal whether or not trees are likely to be able to cope with future conditions, and the extent to which species identity is likely to be important. This is a step towards an understanding of the resilience of tropical trees and is part of a broader effort to assess the effects of stressors on remaining Atlantic forests and their ability to recover.
We used a narrow canopy tower to access leaves of three  (Marchiori, Rocha, Tamashiro, & Aidar, 2016). The forest is classified as montane moist dense forest (Vieira et al., 2011), mean annual precipitation is 2,300 mm with a dry season in July and August, mean annual temperature is 17°C , and fog occurs frequently (Rosado, Oliveira, & Aidar, 2010). Canopy height of emergent trees reaches 30 m. Data collection was carried out between October 1, 2016 and October 10, 2016.

| Microclimate measurements
A narrow 27-m-high tower was used for access to the canopy and microclimate measurements (T A , photosynthetically active radiation [PAR], relative humidity [h], and wind speed [U]) were collected to detail the microclimate vertical profile ( Figure 1). As the tower is just 30 cm wide and tree branches are within arms reach of the tower (see Figure S2d), we consider that the presence of the tower likely has only minimal influence on the microclimate of the sampled leaves.  Figure 1). PAR and T A data were measured and recorded at 10-s intervals using two CR800 data loggers with AM 16/32 multiplexers (Campbell Scientific, Utah, U.S.A.). Four datalogging h sensors (RHT10, Extech, Massachusetts, U.S.A.) measured and recorded at 1-min intervals at heights 2, 8, 12.5, and 18 m. Four sonic anemometers (Sonicwind) measured U every 0.5 s at heights of 1.5, 6.5, 11.5, and 25 m, and 10-s averages were produced for each height. U for leaves positioned above 11.5-m height was linearly interpolated between the 25-and 11.5-m measurement.
Vapour pressure deficit (D) was calculated from T A and h (Campbell & Norman, 1998), where T A is in°C, h is relative humidity (as a proportion), e sat is saturating vapour pressure in kPa, and a, b, and c are constants (a = 0.611, b = 17.502, c = 240.97).
Due to a sensor fault, h was available only from October 5, 2016 to October 10, 2016. To estimate D within the profile for measurement days prior to this, we estimated h within the profile based on the observed relationship between T A and h at the four measurement heights (R 2 , .76-.87) from the available data collected over 6 days.

| Sampled species
Both Alchornea and Miconia are overstorey species, whereas Guapira is found in the subcanopy (Guilherme, Morellato, & Assis, 2004), and the species are ranked second, fifth, and sixth, respectively, in terms of abundance in the plot (Marchiori et al., 2016). All species are early successional (Marchiori et al., 2016) and are found in nearby old-growth  Rosado, Oliveira, Joly, Aidar, & Burgess, 2012). The species cover a range of leaf sizes; Guapira has the smallest leaves (notophyll), followed by Alchornea (mesophyll), with the largest leaves for Miconia (platyphyll).

| Leaf temperature measurements
To measure leaf-to-air temperature differences (ΔT, also called leaf temperature excess in the literature) we followed the two-junction thermocouple design of Singsaas and Sharkey (1998). This approach has the advantage of more accurately measuring ΔT than performing measurements of absolute T L and T A separately. Two long ( Guapira leaves. Selected leaves were fully expanded and mature, but not senescent, within reach from the canopy tower, and spread through the vertical profile ( Figure 1). The thermocouple junction to measure leaf temperature was secured to the abaxial mesophyll surface (avoiding any large veins) near to the midrib using surgical tape (Transpore, 3M, Minnesota, U.S.A.). The second junction was suspended in the air c. 2 cm below the leaf. Additional cabling was cable tied to a twig near to the leaf (or the petiole in the case of Miconia) and to the tower. This attachment procedure enabled the majority of thermocouples to remain attached to leaves during wind and rain (see Figure S2 for photographs of the equipment installation).
The petioles of two leaves, both of Miconia, snapped during the monitoring period. Table S1 gives details of the sampled leaves. ΔT was measured and recorded at 10-s intervals using a CR800 data logger with AM 16/32 multiplexer (Campbell Scientific, Utah, U.S.A.) until October 11, 2016.

| Leaf trait measurements
All sampled leaves were collected and stored in moist plastic bags for 24 hr before fully rehydrating and measuring structural traits in the laboratory at the Instituto de Botânica, São Paulo. Measurements were performed of leaf thickness (mm) with a digital calliper, leaf area (cm 2 ) with leaf area meter (LI-3100, LI-COR, Nebraska, U.S.A.), leaf mass (g), leaf width (cm), and leaf length (cm). Petioles were removed before measurements. Subsequently, leaves were dried at 70°C and dry-weight measured. These measurements were used to calculate LMA (g/m 2 ) and LDMC (g/g). For Guapira, the sample size for leaf traits was 6 (rather than 4 as for leaf temperature).

| Leaf energy balance
With input of measured microclimate, stomatal conductance and leaf width the leaf energy balance (Equation (3), Jones, 1992) can be estimated to predict the leaf-to-air temperature difference (ΔT e ,°C). It is important to note that the leaf energy balance assumes no leaf heat storage and that the leaf energy balance is considered to be in a steady state. ΔT e was estimated from spot measurements to test if ΔT e matched observations of ΔT when leaf surface PAR and g s were directly measured, and from the continuous microclimate data with g s estimated from the observed species-specific relationships between g s and D in order to assess the influence of microclimate and leaf specific variables on leaf temperatures using a large dataset. As the Guapira leaves were not exposed to a large range of microclimates due to their position in the understorey, we only consider ΔT e of Miconia and Alchornea in the latter analysis.
where T L and T A are the leaf and air temperatures, respectively (°C), R ni is the net isotropic radiation (W/m 2 , assuming the sky temperature is equal to T A measured at the nearest T A sensor to the leaf and sky emissivity of 0.97), γ is the psychrometric constant (Pa/K), r b,HR is the boundary layer resistance to heat and radiation and r b,W and r l,W are the boundary layer and leaf resistances to water, respectively (all resistances in seconds per metre), ρ a is the density of dry air (kg/m 3 ), c pa is the specific heat capacity of dry air (1,012 J·kg −1 ·K −1 ), s is the slope of relationship between temperature and saturated vapour pressure evaluated at T A , and D is the vapour pressure deficit (Pa).
Leaf traits (g s and leaf width) are included in Equation (3) through the leaf and boundary layer resistances. Leaf resistance to water, r l,W , is the inverse of g s . Boundary layer conductance to heat or water, g b,H , which is included in the determination of both r b,HR and r b,W , which are both used in Equation (3), is dependent on leaf width (W, m) and wind speed (U, m/s) Further details on the estimation of leaf energy balance are given in Appendix S1.
The thermal time constant (τ, s) was defined following Michaletz et al. (2016) as where φ, the ratio of projected to total leaf area, is 0.5 for flat leaves; LMA is in kilograms per square metre; c pw is the specific heat capacity of water (4,181 J·kg −1 ·K −1 ); and c pd is the specific heat capacity of dry leaf matter (J·kg −1 ·K −1 ). c pd varies by species and, here, we use 2,814 J·kg −1 ·K −1 , the mean of seven tropical tree species from Jayalakshmy and Philip (2010). H is a heat transfer coefficient (W·m −2 ·K −1 ) accounting for convection, radiation, and transpiration (Michaletz et al., 2016).
where g b,H and g b,R are the boundary layer conductance to heat and radiation, respectively (both are in metres per second; see Appendix S1). τ varies over time due to its dependence on g s and boundary layer resistance and was estimated from spot measurements.

| Leaf boundary layer resistance
Initial estimations of the leaf energy balance using Equation (3) showed that when ΔT e was evaluated at low wind speeds (<0.5 m/ s), the values were overestimated compared with the observed ΔT.
Using Equations (4) and S5 to estimate the boundary layer resistance to water (r b,W ), there is a steep increase in r b,W below wind speeds of 0.5 m/s ( Figure S3). To test if these high resistances were supported by the data, we solved the leaf energy balance equation for r b,W and estimated r b,W using the observations of ΔT (see Appendix S2). Plotted against wind speed, the estimated r b,W was lower than predicted by Equations (4) and S5 at low wind speeds ( Figure S3). Hence, we reparameterized constants from Equation (4) using the r b,W estimated from the leaf energy balance and observed wind speed and leaf width (see Appendix S2). Parameter estimation was performed separately for Miconia and Alchornea (there was not sufficient data for parameter estimation of Guapira) using non-linear least squares (R function nls).
In order to have accurate estimates of r b,W from the energy balance, it is essential that all microclimate inputs are correct. PAR was measured at various points from the tower (Figure 1). Examination of the spot measurement data showed that PAR measured by the nearest sensor suspended from the tower (maximum 1-m distance from leaf) occasionally strongly overestimated or underestimated leaf surface PAR ( Figure S4) as they are not measured at precisely the same location, angle, or orientation, and PAR shows high spatial vari-

| Data analysis
Linear mixed-effects models with leaf as a random factor were used for all statistical analyses including repeated measurements of the same leaf using the R package nlme (Pinheiro, Bates, DebRoy, Sarkar, & Core Team, 2017). R 2 for mixed-effects models are given using either the marginal pseudo R 2 that accounts for fixed factors only or conditional pseudo R 2 (Nakagawa & Schielzeth, 2013). The marginal pseudo R 2 is used unless otherwise stated, and R 2 values were calculated using the function provided in the R package MuMIn (Bartoń, 2016). Statistical analyses comparing between species using single values for each leaf used analysis of variance for three species comparisons and t test for two species comparisons.
Relationships between g s and D were analysed for each species using a linear mixed-effects model with leaf as a random factor. The relationships produced were used to estimate a time series of g s for each leaf based on D. The intercept of the g s -D relationship was thus leaf specific and the slope species specific.
To compare leaf temperatures under comparable microclimate conditions data were first selected for 20-min periods where ΔT e matched measured ΔT to ensure that microclimate variables are representative of the leaf surface, as for leaf boundary layer resistance (see above) but using the species-level parameterization of r b,W to estimate were significantly different from 1 for only three leaves, where the thermocouples slightly underestimated T L by up to 9% ( Figure S5).
Overall, the close agreement between the two measurement methods gives confidence in the thermocouple data.

| Microclimate during the monitoring period
Microclimate during the monitoring period is shown in Figure S6 and for a single sunny day in Figure 2. The first 7 days (October 1 to October 7) were predominately overcast with low PAR, high h, and low D,

| Patterns of leaf temperature
Leaves occasionally reached much higher temperatures than the ambient air, over 10°C above T A . The maximum T L for each leaf observed over the monitoring period ranged from 22.5 to 37.2°C and was above 35°C for five of the 23 leaves. Miconia leaves had significantly higher maximum temperatures than Alchornea leaves (Table 1). Daytime mean T L showed less variation than maximum T L between leaves   Figure S7). Leaves of Guapira, which were all at the bottom of the canopy, had lower maximum and mean T L (not tested for significance due to low sample size). Distributions of T L show positive skew ( Figure S7), which was significantly higher for leaves of Miconia than Alchornea (Table 1), showing that they reached high temperatures more often than Alchornea. During daylight hours ΔT was positive for leaves of Alchornea and Miconia and was close to 0 for all Guapira leaves ( Figure S8, Table 1). The maximum ΔT observed was 18.3°C, recorded from Miconia leaf M1. As for T L the distributions of ΔT were positively skewed, with significantly higher skewness for Miconia than Alchornea (Table 1). Minimum daytime ΔT was significantly lower for Alchornea than Miconia leaves (Table 1).
Night-time ΔT was typically negative but close to 0 and was significantly lower for Alchornea than Miconia (Table 1).
T A set a rough minimum bound on T L (Figure 3), with many excursions above T A due to high radiation (see Section 3.6) and a small number of excursions below T A , likely occurring when leaf surfaces were wet during/after rain or in fog. T L excursions above T A occurred more often for leaves positioned higher in the canopy.

| Leaf temperatures under specific microclimates
We compared leaf temperatures under specific microclimatic conditions. Under low light and temperature conditions, leaves of Guapira were significantly colder than those of Alchornea and Miconia Miconia than Alchornea (Figure 4c). Under the highest light conditions analysed, ΔT was again higher for Miconia than Alchornea; however, the difference was not quite significant ( Figure 4d).

| Thermal trait variation between species
Stomatal conductance (g s ) significantly declined with increasing D, and the relation varied significantly between species ( Figure 5, Table 2). At low D, g s was highest for Miconia and lowest for Guapira. Miconia showed a significantly stronger negative relationship between g s and D than Alchornea; hence, at higher values of D, Miconia leaves had lower g s . Conditional R 2 for the overall mixed model including the random factor for leaf was 0.49.
The thermal time constant (τ) ranged over two orders of magnitude from 9 to 350 s ( Figure 7a) and varied significantly between species (linear mixed effects model, F = 48.1, df = 20, p < .0001). τ for Guapira were significantly longer and more varied (mean ± SD 155.4 ± 84.0) than both Alchornea (mean ± SD 276.5 ± 11.1) and Miconia (mean ± SD 46.4 ± 14.4). τ decreased with increasing g s and was particularly high under very low g s (Figure 7b). For a given g s , τ increased in the order Alchornea < Miconia < Guapira (Figure 7b). These differences were driven by the leaf structural traits LMA and LDMC ( Figure S9). When estimated using a fixed LMA value the differences between Alchornea and Miconia are lost ( Figure S9b Miconia and Alchornea, where Miconia has higher ΔT and T L for a given PAR (Figure 9 and S13). Although the absolute values of ΔT e and T Le are somewhat higher than the observations, the differences between the species are maintained in the energy balance estimations. Relationships between ΔT and ΔT e and other microclimate variables (T A , D, and U) were much weaker than for PAR with all R 2 values below 0.3 (Figures S10-S12), whereas T L and T Le were strongly related to T A and D with R 2 values above 0.7 (Figures S14-S16).
To determine what causes the differences between ΔT of Miconia and Alchornea, we applied traits (leaf width and stomatal conductance strategy) of Miconia sequentially to Alchornea and reestimated ΔT e using the observed microclimate data. As shown in Figure S17, applying the larger leaf width of Miconia acts to increase the Alchornea ΔT e for a given PAR, almost to the extent that it matches the high ΔT e of Miconia. If the higher intercept of the g s -D relationship for Miconia is applied, the Alchornea ΔT e for a given PAR decreases. In contrast, if the steeper g s -D slope for Miconia is applied, the Alchornea ΔT e for a given PAR increases.
The effect is not as strong as the effect of leaf width ( Figure   S17). Applying both the Miconia intercept and slope results in an intermediate Alchornea ΔT e for a given PAR, slightly higher than for Alchornea with its original parameterization. If all Miconia traits are applied (leaf width and stomatal conductance strategy) Alchornea ΔT e for a given PAR increases to a greater extent than for any trait alone and even exceeds the ΔT e of Miconia. This is likely due to the higher D that the highest six Alchornea leaves are exposed to due to their position above the Miconia leaves ( Figure 1).   -Sanchez et al., 2016] and in the Amazon [Doughty & Goulden, 2008], 7°C for three species in tropical China [Dong, Prentice, Harrison, Song, & Zhang, 2017]). This could be due to high sampling frequency used in this study (every 10 s) compared with others ( The distributions of T L and ΔT collected over the 10-day period were significantly skewed ( Figures S7 and S8 and Table 2). This is because under the predominant microclimatic conditions of relatively low PAR and D, ΔT is low (<1°C) and T L is similar to T A . However, due to fluctuating conditions-especially PAR, which alters rapidly with cloud movements and wind and varies with sun angle, leaf angle, and orientation-large increases in ΔT occur. The duration of high ΔT excursions depends on how long the microclimate is sustained. The extent of high ΔT excursions is important because during high leaf temperatures beyond the photosynthetic temperature optima primary productivity will reduce carbon gain and very high leaf temperatures can cause irreversible thermal damage (e.g., above 50-53°C for a Panamanian tree species; Krause et al., 2010). Our data suggest that, at least during our measurement period, tree leaves at this Atlantic forest site are not approaching thresholds of irreversible damage but do reach temperatures known to affect thylakoid membrane structure (35°C; Gounaris et al., 1983;Gounaris et al., 1984) and reduce electron transport rates (40°C; Allakhverdiev et al., 2008)  Within the range of conditions during the study period, radiation was the most important microclimate variable for determining ΔT (Figure 9, Figures S10-S12). This has also been shown in other studies (e.g., Doughty & Goulden, 2008;Rey-Sanchez et al., 2016) and is understood biophysically (Jones, 1992). For absolute T L , PAR, T A , and Variation in leaf structural traits between species. Letters represent significantly different groups calculated using analysis of variance and Tukey post hoc tests T A at which ΔT = 0 and above which ΔT is negative. We found no evidence of a crossover T A , likely due to the relatively low T A during our study. The light levels observed in the study were high, occasionally exceeding 3,000 μmol·m −2 ·s −1 . We consider the light levels recorded in the profile to be accurate as they were highly comparable with an independent dataset from a weather station mounted at 27 m on the same tower ( Figure S18). The values are higher than the PAR observed in similar studies from lowland forests with typical maximum PAR of 2,000 μmol·m −2 ·s −1 (Doughty & Goulden, 2008;Rey-Sanchez et al., 2016). Again, measurement frequency may be important here for recording extreme instantaneous values. In fact, this maximum quantity of PAR is equivalent to more radiation than the solar constant (incoming light at the top of the atmosphere, 1.353 kW/m 2 ), which is possible in mountains when light is reflected from clouds (Stoutjesdijk & Barkman, 2014). Incoming radiation increases by 8% for every 1,000-m increase in elevation (Blumthaler, Ambach, & Ellinger, 1997).
Montane forests are therefore likely to experience higher maximum radiation loads than lowland forest, as has been measured at this site (Rosado, Joly, Burgess, Oliveira, & Aidar, 2016). Given the importance of radiation for T L , trees at high elevation may have greater risk of hitting damaging T L thresholds if air temperatures increase with climate change. At this specific site, in additional to increased radiation, D also increases with elevation and trees show more conservative water use (Rosado et al., 2016), which will further influence leaf temperatures.
Mountaintop species are already considered to be more greatly threatened than lowland species by increased temperatures as there is no cooler place for species to move to. The high radiation load increasing leaf temperatures may exacerbate this problem.
As microclimate is a key driver of leaf temperature, it is important to consider the vertical gradient in microclimate ( Figure S6). We found that all microclimate variables displayed vertical gradients, especially during sunny days when the differences between the top and bottom of the canopy exceeded 5°C T A , 2,200-μmol·m −2 ·s −1 PAR and 1.3-kPa D. The difference in T A leads to a larger difference in T L than the values of ΔT we typically found (Table 1). Although vertical gradients of PAR are often accounted for in vegetation models, often the gradients of other key variables are not considered, which would lead to error in quantification of leaf temperatures below the canopy top.

| Differences in leaf thermoregulation between species
We found striking differences in leaf temperature patterns between species that were attributable to differing leaf traits. Miconia leaves more commonly experienced high ΔT excursions than Alchornea, with higher skew in T L and ΔT distributions, higher maximum ΔT, and less negative minimum ΔT (Table 1) stress (higher PAR, T A , and D). The lack of significance at the highest PAR/T A subset tested is likely due to low data availability and higher PAR measurement errors at high PAR. As PAR was not measured directly at the leaf surface, it was difficult to ensure correspondence between PAR as measured by the nearest sensor and received at the leaf surface; this is more problematic under direct light conditions where leaf angle, orientation, sun angle, and within-canopy shading greatly impact leaf surface PAR. We recommend all studies of leaf temperature attempt to measure PAR at the leaf surface despite the higher efforts required.
The higher leaf temperatures displayed by Miconia can be accounted for by lower transpirational cooling due to two reasons.
Firstly, the wider leaf width increases boundary layer resistance, which lowers the evaporation from stomatal pores. Secondly, Miconia leaves showed a strong negative relationship between g s and D, which lowers transpiration under conditions of high thermal stress (as high D typically occurs concurrently with high PAR and T A ). Using the leaf energy balance equation, we find that the physical difference in leaf width is the dominant factor in producing the variation in ΔT between Miconia and Alchornea ( Figure S17). Miconia leaves get hotter than Alchornea leaves and, hence, may have a higher risk of thermal damage. However, this increased heating may come with a water use advantage, as, under high D conditions, transpiration rates per leaf area will be lower for Miconia than Alchornea. This could reduce the risk of xylem cavitation under water stress conditions. Differing thermoregulation strategies of trees likely arise in combination with trade-offs in terms of water use.
The study species only showed differing relationships between PAR, and T L and ΔT, with similar responses to other microclimatic variables (Figure 9, Figures S10-S16). This shows that it is the consequences for input solar energy that varies between the species, rather than differing mechanisms in response to T A . It is not to say that other microclimatic variables are not important for T L or ΔT but that the response of T L and ΔT to other variables is the same for the two species, at least under the measurement conditions. Night-time ΔT were consistently negative for all species. However, ΔT of Alchornea leaves were more negative than the other species (Table 1). The cause may be that many of the sampled Alchornea leaves were at the outer canopy, and therefore, heat radiation to space may be more effective for them due to the lack of obstacles (other leaves or canopies), resulting in greater cooling. Another factor may be that transpiration is maintained at night in this species more so than Miconia and Guapira. Observations from Rosado et al. (2012) do show night-time transpiration occurring for Alchornea trees at this site, but Alchornea did not show higher transpiration than other measured species.
Leaf temperatures of the subcanopy Guapira tree were consistently similar to air temperatures and showed little variation (Table 1) likely due to the canopy position receiving very little light ( Figure 1). However, when the data were subsetted for low PAR conditions only, leaves of Guapira still showed a lower ΔT than the two other species (Figure 4a). This could be due to the narrower leaf width of Guapira leaves (Figure 6), though the width is not significantly different from Alchornea. It could also be due to the unusual leaf angles displayed by the Guapira leaves that were hanging near vertically (Table S1, Figure 6e), which would limit the amount of light received and result in over estimates of the light environment from using a horizontally orientated sensor. Another potential contributor is the long τ values estimated, as T L is expected to vary less when τ is long (Ball, Cowan, & Farquhar, 1988). The long τ for Guapira leaves were a result of the combined low g s and low LDMC (Figure 7, Figure S9); because Dash line-modelled relationship for the alternative species. Statistical models are linear mixed-effects model with leaf as a random factor. R 2 is the marginal pseudo R 2 . To account for uneven sampling with respect to PAR data was subsampled for 1,000 points in 250 μmol·m −2 ·s −1 bins for points below 1,000 μmol·m −2 ·s −1 water has a higher specific heat capacity than dry leaf matter, the higher water content of Guapira leaves causes a longer τ (Vogel, 2009

| Towards a better understanding of tropical leaf temperature behaviour
The link between functional traits and leaf thermoregulation has been highlighted in recent work (Michaletz et al., 2015(Michaletz et al., , 2016. Here, we provide field-based evidence for this link in the most detailed study of leaf energy balance in tropical montane forests to date and include variation in water use as a key component. The traits that we find important (leaf width, g s at high D, and LDMC) may possibly connect other axes of plant functional variation (Reich, 2014)-the leaf economics spectrum (Wright et al., 2004) and plant hydraulics. Species that are able to maintain transpiration under high thermal stress conditions (high T A , PAR, and D) will require water to supply the transpiration stream from an efficient hydraulic system or from high water capacitance to avoid hydraulic failure. Avoiding extremes of T L and maintaining open stomata will then have the benefit of keeping T L closer to the temperature optima of photosynthesis, maintaining a CO 2 supply, and all this while PAR is high to drive a high photosynthetic rate (Ball et al., 1988). Conversely, lower transpiration under high thermal stress conditions will prevent excessive water loss and therefore avoid risk of hydraulic failure through xylem embolism but increase risk of the leaf reaching a damaging high temperature threshold. Critical thresholds of photosynthetic activity vary by species (O'Sullivan et al., 2017). A recent study of critical thresholds of 41 co-occurring tropical species found that variation was related to the leaf economics spectrum (Wright et al., 2004), with high LMA species showing higher temperature tolerance (Sastry & Barua, 2017). Miconia has significantly higher LMA than Alchornea (Figure 6), and it would be parsimonious if it also displays a higher critical temperature for damage to photosynthetic machinery. In summary, we hypothesize that trees at the slow end of the life-history spectrum (Reich, 2014) are likely to reach higher leaf temperatures, have lower g s and photosynthesis under high thermal stress conditions, have lower risk of hydraulic failure, and have a higher threshold for thermal damage, with the converse true of fast species.
If we are to understand the implications of climate change for tropical forests, it will be crucial to understand mechanisms of leaf thermoregulation and how this varies between species. We have based our findings on only a small, if detailed, dataset. There are very few comparable datasets available for tropical forests. More datasets exploring the full energy balance of tropical leaves from multiple sites with varying climatologies, and ideally over extended time periods, would certainly aid this. Beyond understanding current patterns of leaf temperatures, it is also necessary to understand the response of energy balance parameters to high T A and CO 2 . For example, herbarium data for an Australian shrub species showed a reduction in leaf width over the last century (Guerin, Wen, & Lowe, 2012), which could mitigate increases in T L due to increased T A . Conversely, declines in g s are a common response of tree species to increased CO 2 , which, although potentially reducing water use, could lead to higher T L (e.g., Barker et al., 2005;Warren et al., 2011). However, the extent of reductions in g s under elevated CO 2 varies with species (Way et al., 2015). In a study of seedlings of 10 tropical species, Cernusak et al. (2011) found reductions in g s in all species in response to elevated CO 2 , but the reductions were larger for species with high g s in ambient conditions. Warming may also cause changes in g s ; results from warming experiments show a variety of responses-increases, decreases, and no change (Way et al., 2015)-and a recent meta-analysis found decreases in stomatal density with higher T A in trees but not in herbs (Yan, Zhong, & Shangguan, 2017). If trees do indeed decrease g s under higher growth temperatures, this could result in further leaf warming beyond T A increases but only if transpiration declines as well as g s , which is not certain given the expected rise in D with increased T A . Our understanding of the effects of combined CO 2 and warming is even more limited. If both cause a decline in g s separately, would the combined effect be additive leading to even greater reductions? The limited experimental data do not paint a clear picture (Way et al., 2015). A final question is whether leaves that reach higher temperatures are better adapted to cope with high temperatures and, therefore, increasing T L would be less consequential than for low-temperature species, or does the fact that leaf temperatures are already high mean that high-temperature species are more at risk?

| CONCLUSIONS
In this study, we made detailed measurements of leaf energy balance for three tree species in the montane Atlantic forest, Brazil. Our results show surprising high leaf-to-air temperature differences given the relatively low air temperatures, which we attribute to the high light conditions during the study. The higher radiation levels occurring at high elevations may contribute to the risks of climate change to tropical montane forests. We find differences in leaf thermoregulation between leaves of Alchornea and Miconia, which is attributable to lower transpiration under high thermal stress conditions for Miconia due to its wider leaves and stronger reduction of g s with increasing D. Leaf energy balance modelling can be a powerful tool to understand variation between species in leaf thermoregulation, which will be necessary to model the impact of climate change on leaf physiology.

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