Black locust seedlings (Robinia pseudoacacia L.) were grown in a controlled greenhouse facility in Garmisch-Partenkirchen, Germany (708 m a.s.l.). The trees had been planted in individual large pots (120 L) filled with a mixture of humus and sand (ratio of 2:3) in September 2012. In 2014, when the experiment was conducted, trees were 4 years old. As the experiment was part of a 3-year campaign, which sought to evaluate the long-term effects of repeated heatwaves and heat–drought waves on tree growth and performance, the trees in the stress treatments had already been exposed to two experimental heat/heat–drought waves during summer 2013. The basal area in the previously stressed trees was slightly lower than that of the control trees before the experiment was initiated in 2014 (heat: -13 % and heat–drought -16 %), although basal growth rates and photosynthesis recovered to prestress conditions 3 weeks after stress relief in 2013 (Ruehr et al., 2016). After the experiment in 2013 ended, the trees were pruned to 1.80 m height, kept outside during winter and transferred back into the greenhouse in May 2014, where the measurements were performed from 6 July to 26 August.

Black locust trees were kept in two adjacent, separately controllable compartments of the greenhouse facility from May onwards. The environmental conditions in the greenhouse (equipped with UV-transmissive glass) were regulated by a computer (CC600, RAM Regel- und Messtechnische Apparate GmbH, Herrsching, Germany) and air temperature settings followed outside conditions measured in front of the greenhouse, while relative humidity was set to mimic the diurnal cycle of long-term (20-year) monthly averages from a meteorological station close by. Photosynthetically active radiation (PQS1, Kipp & Zonen, Delft, the Netherlands), air temperature and relative humidity (CS251, Campbell Scientific Inc., Logan, UT, USA) in each greenhouse compartment were monitored by two sensors each. During nonstress conditions, differences in environmental conditions between the two compartments of the greenhouse were generally small during both years of the experiment (Ruehr et al., 2016; Duarte et al., 2016). Prior to the first heatwave, the black locust trees grew under the same environmental conditions from 7 May to 13 June and none of the environmental drivers differed by more than 2 % (see Table 1). While in one compartment of the greenhouse, trees were always kept under the ambient conditions as described above (control trees, n=6), trees in the second compartment (heat and heat–drought trees, n=12) were periodically exposed to two consecutive heatwaves simulated by a +10 ∘C increase of temperature lasting between 14 and 15 days. During the heatwaves, relative humidity in the heat compartment of the greenhouse was controlled to decrease so that vapor pressure deficit increased. Each heatwave was followed by a recovery phase of 7 days. While control and heat-treated trees received on average 2.6 L tree-1 day-1 irrigation, heat–drought-treated trees received (starting 6 days before heat stress) only 1.3 L tree-1 day-1. Recovery periods were initiated by supplying each tree once with a larger amount of water (10.8 L) which increased soil moisture and largely reduced soil water deficit. Isoprene emissions were measured in parallel with the CO2 and H2O gas exchange using leaf chambers attached to three different trees per treatment. After the experiment, leaf biomass within each chamber was harvested, dried and weighed, and half-sided leaf area was determined via previously determined specific leaf area. In one case, when an enclosed leaf wilted and dried, the corresponding chamber was installed on an intact leaf of the same tree. To determine leaf biomass losses, leaf litter was collected, dried and weighed. Leaf area was calculated from dry weight and treatment-specific leaf area (data not shown).

The bottom of each tree pot was equipped with a coiled water pipe to provide soil cooling to mimic predefined soil temperatures at a depth of 50 cm (corresponding to air temperature averaged over the previous 20 days). Soil water content (10HS, Decagon Devices, Inc, Pullman, WA, USA) and soil temperature (T107, Campbell Scientific Inc., UT, USA) were measured in each pot at a depth of 10 cm and in additional pots at 30 and 50 cm depth. The volumetric soil water content (SWC) was used to determine the daily relative extractable soil water (RSW, in %) according to the following relationship: RSW=100×SWC-SWCminSWCmax-SWCmin, with SWCmin and SWCmax being experimentally derived minimum values of daily soil water content at 30 cm depth during drought and maximum values of mean daily SWC per sensor. In order to get an average value per tree pot, RSW from three different depths were averaged.

Since isoprene emissions from plants are temperature and light dependent, leaf level isoprene fluxes can be estimated from a light-dependent function fQ, a temperature-dependent function fT and an isoprene emission factor ES, which is assumed to be a constant, but plant-specific factor which describes the isoprene emissions at reference conditions (e.g., a temperature of 30 ∘C and PAR = 500 µmol m-2 s-1). Eiso=ESfQfT Temperature and light response functions are usually normalized to unity at standardized conditions and describe the shape of the isoprene emission curve. The response functions were first developed by Guenther et al. (1991, 1993). These models use a hyperbolic function to describe the light response function as follows: fQ=CL1αQ1+α2Q2, where CL1 is a scaling constant and α the quantum yield of isoprene emission; here, both parameters were optimized for each treatment separately in order to best describe the light response function of the measured isoprene fluxes.

The temperature dependence of isoprene emissions is usually characterized by an exponential increase with leaf temperature until an optimum temperature Tm is reached followed by a subsequent exponential decrease (Guenther et al., 1991, 1993). fT=eCT1TL-TsRTsTL1+eCT2TL-TmRTsTL Ts is standard temperature (usually 30 ∘C, or 303 K) at which the normalized response curve is one, R is the gas constant (8.314 J mol-1 K-1), TL is the leaf temperature in Kelvin and CT1 and CT2 are parameters which can be interpreted as activation and deactivation energy of isoprene emissions (in J mol-1), respectively. Later on, a third parameter, CT3, was introduced to force the temperature response curve through one at the chosen standard temperature (Guenther et al., 2006). We did not normalize temperature and light response curves to one under standardized conditions, thus providing the original parameterized emission factor (Es). However, to allow better comparisons with other studies, we tested whether the original parameterized emission factor differed compared to the emission factor when the curve was forced through one and found that both values were identical within the given standard errors (maximal difference of 0.2 nmol m-2 s-1). The experimentally derived average temperature response of the control, heat and heat–drought-treated trees was used to optimize the parameters CT1, CT2 and Tm using a nonlinear weighted fitting algorithm (see Sect. 2.4) for each treatment separately. For the control treatment we did not have enough data points in the high-temperature range to constrain the optimum temperature, and therefore we set the optimum temperature to a fixed value of 311.8 K (see Guenther et al., 1991) in order to optimize the remaining parameters.

The data post-processing and statistical calculations were performed using the commercial software package Matlab^® (Version R2013b, Math Works^®, MA, USA). To estimate leaf isoprene emissions we largely followed the standardization criteria (except for light control) for leaf-scale emission measurements recommended by Niinemets et al. (2011). Because temperature control was performed within the separate compartments of the greenhouse, temperatures within the leaf chambers were recorded but not controlled separately.

Increases or decreases in isoprene emissions and photosynthesis during the heatwaves were calculated as treatment effect (treatment-controlcontrol). To test for differences between treatments and time periods, we used a linear mixed effects model (using fixed effects for time period and treatment and random effects for tree and measurement day) to test for significant changes in isoprene emissions for each treatment and during the different time periods of the experiment (Ruehr et al., 2016). A p < 0.05 was considered statistically significant.

To determine light and temperature relationships of isoprene emissions in each treatment and during both stress periods, we grouped the data into 8 bins according to PAR levels (< 5, 5–50, 50–100, 100–150, 150–200, 200–400, 400–650 and > 650 µmol m-2 s-1) and temperature conditions (15–20, 20–24, 24–28, 28–32, 32–35, 35–40, 40–45 and > 45 ∘C) within the chambers. The parameterization of the light and temperature response functions (Eq. 7 and 8) was carried out for each treatment as follows. In an initial step, the bin-averaged isoprene data (PAR > 100 µmol m-2 s-1 with temperature bins defined above) were fitted to the temperature-response function (Eq. 8) using a nonlinear fitting algorithm weighted with the inverse standard deviation. The temperature fit (parameter ES, CT1, CT2 and Tm) was then used to normalize the measured isoprene emissions to a standard temperature of 30 ∘C before fitting isoprene data bin-averaged for PAR to the light response function (Eq. 7). The light response fit (parameter ES × CL1 and α) was then used to normalize the measured isoprene flux data to standard light levels (PAR = 500 µmol m-2 s-1), which were again fitted to the temperature-response function. This procedure was repeated in an iterative way until all fitting parameters changed by less than 1 % between subsequent iterations. Since we deliberately included ambient diurnal and day-to-day temperature variations in our study, it was not possible to keep the number of data points constant in each temperature bin and treatment. To warrant comparability among the bin averages of each treatment, the same temperature bins were used in each treatment. As a consequence some bins at the upper end of the temperature distribution included only a few data points, while some had only one. In the case that the standard deviation could not be calculated, we assumed a conservative value of 100 (seven times higher than the highest standard deviation observed) to reduce the weight of this point for the temperature fit.

To exclude nighttime fluxes, which were always zero in all treatments, daytime averages were calculated exclusively for data when PAR was higher than 50 µmol m-2 s-1. The fraction of recently assimilated carbon emitted as isoprene was calculated by dividing the isoprene carbon flux by the assimilated carbon and calculating bin averages after classifying the isoprene fluxes into 8 temperature bins as mentioned above.

With a maximum of 34.7 ∘C and a minimum of 27.8 ∘C, daytime average air temperatures during the heatwaves were considerably warmer than under ambient conditions (daytime-averaged maximum 23.2 ∘C and minimum 13.7 ∘C). Along with warmer temperatures, daily averaged vapor pressure deficit (VPD) increased up to 3.0 kPa, while it remained below 1.0 kPa under ambient conditions (Fig. 2b). Outside the stress periods, air temperature and VPD did not differ between the greenhouse compartments (Fig. 2a, b).

While the daily averaged relative extractable soil water content (RSW) remained above 40 % in the control trees, it decreased to 20 % in the heat and 15 % in the heat–drought treatment (Fig. 2c). After watering at the first day of the recovery, the soil water content in the stress treatments increased considerably and RSW during the recovery remained between 50 and 70 % in both stress treatments. During the heat periods, the RSW of the heat-stressed trees was slightly higher than the RSW of heat–drought-treated trees. Heat and heat–drought stress caused a large decline in midday leaf water potential (-1.7 MPa in the control compared to -2.3 MPa in both stress treatments, data not shown). In both treatments, we observed pronounced leaf shedding during the first heatwave and estimated that about 80 % of the leaves were shed in the heat treatment and 90 % in the heat–drought treatment, averaging to a leaf area of about 2.4 m2 m-2 lost in both treatments. Leaf shedding reduces water loss and protects the integrity of the hydraulic system in black locust (Ruehr et al., 2016). The relatively larger leaf shedding in the heat–drought trees together with a smaller biomass (indicated by reduced basal area due to last year's experiment; see Methods) than under heat-stress only, might explain the small differences in RSW between the heat and heat–drought treatment (Fig. 2c), although irrigation in heat–drought trees was halved compared to the heat and control trees.

Along with increased temperatures and reduced RSW during the stress periods, average daytime stomatal conductance in heat–drought-stressed trees decreased to values below 0.01 mol m-2 s-1 (Fig. 3a). The stomatal conductance of heat trees during the heatwaves was higher compared to heat–drought trees, with daily averages between 0.01 and 0.03 mol m-2 s-1, but still lower than in the control trees (Fig. 3a). Compared to the control, net photosynthesis during the first heatwave decreased on average by 44 % in the heat and 67 % in the heat–drought treatment (Fig. 3b). During the second heatwave, this decrease was smaller with 41 % in the heat and 46 % in the heat–drought treatment. Following stress release, net photosynthesis in heat and heat–drought trees recovered quickly and reached values similar to the control trees after a few days. A linear mixed effects model comparing net photosynthesis during the stress periods to prestress control conditions confirmed the significance of these changes (Table 2), and that before the first heatwave, net photosynthesis did not differ significantly among treatments (see pretreatment values, Table 2).

Daytime isoprene emissions of black locust in the heat treatment were on average higher by 153 and 142 % than in the control trees during the first and second heatwave, respectively (Fig. 3c). In the heat–drought-stressed trees isoprene emissions were 171 % higher than in the control trees during the first heatwave and 333 % during the second heatwave. During both recovery periods, isoprene fluxes decreased rapidly to values comparable to prestress conditions, suggesting a quick and complete recovery. Except for the heat–drought trees during the second heatwave the significance of changes in isoprene emissions in the heat and heat–drought treatment during stress phases was confirmed by a linear mixed effects model (Table 2), while before stress and during the two recovery phases isoprene emissions did not differ significantly between the treatments and control (Table 2).

We found isoprene emissions of the heat and heat–drought-treated trees during the recovery periods to be clearly related to net photosynthesis (A) following an exponential function Eiso= exp(a×A)-b (p < 0.05; Fig. 4). Such a relationship was also visible in control trees as long as temperatures did not exceed 30 ∘C (Fig. 4). In control trees, net photosynthesis was on average 4.5 µmol m-2 s-1 and isoprene emission 1.5 nmol m-2 s-1. During the heatwaves, isoprene emission was not related to net photosynthesis in heat and heat–drought-treated trees. Net photosynthesis decreased to 2.5 µmol m-2 s-1 on average in the heat and 2.1 µmol m-2 s-1 on average in the heat–drought treatment, while isoprene fluxes increased sharply to 11.2 nmol m-2 s-1 in the heat and 5.9 nmol m-2 s-1 in the heat–drought treatment on average.

In the temperature range from 28 to 32 ∘C, control trees emitted an equivalent of 1.6 % of assimilated carbon as isoprene (Table 3). In the same temperature range, heat and heat–drought-stressed trees emitted the equivalent of 0.8 % (t-test compared to control resulted in p<0.05) and 1.2 % (p>0.05) of the photosynthetic carbon as isoprene, respectively. With increasing temperatures, heat-stressed trees emitted an equivalent of up to 12 % (temperature > 45 ∘C) and heat–drought stressed trees up to 20 % of the assimilated carbon as isoprene (temperature range of 40–45 ∘C).

The light and temperature relationships of isoprene emissions were parameterized for all treatments including only measurements taken during the period of the heatwaves (Table 3). Details for all parameters optimized by recursively fitting the nonlinear light and temperature equations (Eqs. 7 and 8) to the bin-averaged isoprene data are given in Table 3. Except for the parameter CT1 in the heat–drought treatment all fitted values were statistically significant.

When comparing isoprene emissions of the stress treatments with the control, isoprene emissions at light saturation (and 30 ∘C) were approximately 45 % lower in the heat and 24 % lower in the heat–drought treatment (Fig. 5b). Compared to literature values, isoprene emissions of all trees reached light saturation at relatively low values of photosynthetically active radiation (e.g., PAR between 200 and 300 µmol m-2 s-1 for the control and heat–drought-stressed trees), most probably because of the relatively low levels of PAR (see Table 1) in the greenhouse. Response curves of isoprene versus environmental conditions obtained in this study will thus be more comparable to lower canopy conditions where leaves are not constantly under light saturation. To reflect this, we normalized temperature responses of isoprene to a PAR of 500 µmol m-2 s-1 (typically values of 1000 µmol m-2 s-1are used in the literature). Normalized temperature response curves revealed, similarly to light response curves, that control trees emitted (in the temperature range that overlapped among all treatments) more isoprene than stressed trees at similar temperatures (Fig. 5a). The 95 % confidence bounds for the fitted curves (dashed lines) indicate that above 30 ∘C temperature functions of the heat and heat–drought trees were statistically different to the temperature function of the control trees. At a standard temperature of 30 ∘C, for example, the control trees emitted 16.0 ± 0.2 nmol m-2 s-1 of isoprene, while the heat-stressed trees and heat–drought-stressed trees emitted 8.7 ± 0.5 and 12.1 ± 1.2 nmol m-2 s-1, respectively (see also Table 4). However, not only the emission factor ES but also other parameters (CT1, CT2 and Tm) related to the shape of the temperature response function changed during heat and heat–drought stress (see Table 4). For temperatures above 28 ∘C, average values of isoprene emissions differed significantly between the control and stress treatments (Appendix B, Table B1).

Measured isoprene emissions were assessed against modeled values (for model parameters, see Table 4). As expected the heat stress (slope = 0.95 and R2 = 0.89) and control models (slope = 1.01 and R2 = 0.87) performed quite well in estimating the isoprene emissions over the whole temperature range covered by the measurements. The model derived for combined heat–drought stress was, however, less successful in estimating measured isoprene emissions (slope = 0.73 and R2 = 0.65) and tended to underestimate high isoprene emission rates (Fig. 6).

To assess the possibility of simulating isoprene emissions of heat or heat–drought-treated trees based on the parameters from the control treatment, we derived a correction factor from the difference of isoprene emission rates from treatment-based model parameterization versus the control-based model (Fig. 7a). The derived correction factors are similar for both treatments (0.47 for the heat treatment and 0.49 for the heat–drought treatment; Fig. 7a). However, when applying the correction factor, the thereby modified models failed to simulate the measured isoprene emissions for heat and heat–drought trees (Fig. 7b), in particular in the higher flux range. This indicates that a simple linear adjustment represents a poor substitute for a stress-specific parameterization that is used to simulate isoprene emissions.

In our study, heat and heat–drought-stressed trees showed reduced stomatal conductance along with lower rates of net photosynthesis during the heatwaves (Fig. 3). While net photosynthesis in black locust is limited by stomatal closure during heat and heat–drought stress (Ruehr et al., 2016), isoprene emission is mostly insensitive to the degree of stomatal opening (i.e., high Henry's law constant; see Niinemets et al., 2004). Additionally the temperature optimum of net photosynthesis is usually reached at much lower temperatures than that for isoprene synthase activity (Rennenberg et al., 2006), resulting in an earlier inhibition of photosynthesis compared to isoprene emissions (Loreto and Fineschi, 2015). In our experiment, heat and heat–drought-stressed black locust trees showed a temperature optimum of net photosynthesis at about 25 ∘C, while peaks in isoprene emissions were reached at much higher temperatures (42.4 ∘C in the heat and 41.2 ∘C in the heat–drought treatment), similar to what has been reported for other tree species (Guenther et al., 1991, 1993; Monson et al., 1992). The temperature optima of isoprene synthase and other enzymes, as well as the availability of the isoprene precursor dimethylallyl pyrophosphate, are likely responsible for this threshold (Niinemets et al., 2010a) and we can expect isoprene emissions to increase unless these temperature optima are reached or carbon substrate for isoprene synthase has become depleted (Grote and Niinemets, 2008). In agreement with our study, earlier studies on heat stress responses found elevated isoprene emissions (Sharkey and Loreto, 1993; Singsaas and Sharkey, 2000). This is in stark contrast to patterns of isoprene emissions during drought, where most studies found no change or even reduced emissions (Pegoraro 2004a; Brilli et al., 2007; Fortunati et al., 2008). In our study, however, the effects of drought were apparently dominated by the responses of isoprene emissions to the high temperatures as both, heat and heat–drought-stressed trees showed similar emissions. This may indicate that hotter droughts as predicted with climate change could lead to enhanced leaf level isoprene emissions in black locust.

Upon stress release, isoprene emissions recovered more quickly (within about 2 days) than net photosynthesis to prestress levels. After periods of drought stress, a quick recovery of isoprene emissions seems to emerge as a common feature that has also been observed in previous studies (Sharkey and Loreto, 1993; Pegoraro et al., 2004b; Velikova and Loreto, 2005; Brilli et al., 2013) and may help isoprene emitting plants to cope with abrupt and repeated temperature changes as commonly observed under natural conditions. However, studies on isoprene dynamics following stress release are scarce and there is to our knowledge only one study that considers dynamics of isoprene emissions during and following prolonged combined heat–drought stress (Vanzo et al., 2015). Vanzo et al. (2015) found that isoprene-emitting poplars recovered rapidly from stress and even increased photosynthesis during recovery in contrast to nonisoprene-emitting trees, which showed weaker recovery of photosynthesis. Net photosynthesis in our study recovered quickly, too. By comparing isoprene and nonisoprene emitting poplars, Vanzo et al. (2015) could demonstrate a positive effect of isoprene emissions on the trees' performance during and following heat–drought stress. Such a beneficial effect of isoprene during high-temperature stress and a quick recovery thereafter has also been reported by other studies (Velikova and Loreto, 2005; Behnke et al., 2007). Thus, the fast recovery of both isoprene emission (reduction) and photosynthesis (increase) could be related to the beneficial effects of isoprene synthase in protecting the photosynthetic apparatus. Further, a fast recovery of photosynthesis and isoprene emissions after stress suggests that no irreversible damage to the unshed leaf tissues as a consequence of high temperature or drought had been induced (Niinemets, 2010).

Photosynthesis supplies most of the carbon, as well as energy for isoprene synthase during unstressed conditions (Delwiche and Sharkey, 1993; Sharkey and Loreto, 1993; Niinemets et al., 1999; Karl et al., 2002). Assuming that all the carbon incorporated into isoprene originates directly from photosynthesis, approximately 1.6 % of the carbon assimilated during net photosynthesis was used for isoprene emission in control trees at temperatures between 28 and 32 ∘C. This value is in the same range as the 2 % which were proposed for other major isoprene emitting trees at a temperature of 30 ∘C (Sharkey and Yeh, 2001; Sharkey et al., 2008). The ratio of photosynthesis to isoprene emission can, however, change dramatically during stress conditions. In a coppice poplar plantation at ambient temperatures only 0.7 % of assimilated carbon were emitted as isoprene (Brilli et al., 2016), while in response to high temperature or drought stress, the ratio of isoprene emission to assimilated C may increase up to 50 % or even more (Sharkey and Loreto, 1993; Pegoraro et al., 2004b). In our experiment we found a decoupling of isoprene emissions from photosynthesis and thus the equivalent of up to 13 % of C assimilated in the heat and 20 % in the heat–drought treatment to be emitted as isoprene (Table 3). The divergence between isoprene emissions and photosynthesis is most likely a consequence of the different temperature optima for isoprene emissions and photosynthesis. While above 30 ∘C isoprene emissions are still increasing exponentially with temperature, photosynthesis is already decreasing (Ruehr et al., 2016), leading to discrepancies between photosynthesis and isoprene emissions. Although we assume that isoprene is mainly formed from current photosynthates, we cannot exclude that C for isoprene formation might have originated from other carbon sources such as sugars and starches (Affek and Yakir, 2003). Especially under conditions of limited photosynthesis, like severe drought, it has been reported that plants use increasing amounts of stored C to supply isoprene synthesis (Brilli et al., 2007; Fortunati et al., 2008). The divergence between photosynthesis and isoprene emissions during stress as found in our study could indicate that remobilized C might have been used to supply isoprene synthesis, originating from nonstructural carbohydrates in leaves or other tissues (Schnitzler et al., 2004).

It is still a matter of debate as to why some plants invest substantial amounts of carbon to maintain isoprene emissions even under severe stress when C demand for maintenance might be higher than C supply. One likely explanation is that isoprene acts as an antioxidant in the plants, eliminating reactive oxygen species produced during stress in order to prevent oxidative damage (Vickers et al., 2009). Further, isoprene is discussed to protect the chloroplasts under high temperatures or drought (Velikova et al., 2011, 2016) which was explained with a stabilizing effect of isoprene on the thylakoid membranes (Velikova et al., 2011). This in turn has been again reported to reduce the formation of reactive oxygen species (Velikova et al., 2012). However, Harvey et al. (2015) found that the concentration of isoprene within the leaves is lower than expected and thus unlikely to alter the physical properties of the thylakoid membranes. Thus, the exact pathways leading to the thermoprotective effect of isoprene are still to be discussed.

Common knowledge of the temperature response function of isoprene (Niinemets et al., 2010) would suggest that the higher isoprene emissions for stressed plants found here are solely due to increased temperatures. However, heat and heat–drought-stressed trees showed somewhat different temperature and light response curves and had 45 and 25 % lower isoprene emissions relative to the control trees at the chosen standard temperature of 30 ∘C. If isoprene emissions of the stressed trees are calculated with the parameter values of the control trees, the average isoprene emissions during stress would have been overestimated by roughly 50 % in both stress treatments. At a first glance, the apparent lower isoprene emissions in stressed trees compared to unstressed trees at the same temperature is surprising. Intuitively one would expect heat and heat–drought-stressed plants to emit – in comparison to control trees at the same temperature – more isoprene during periods of stress because of the thermoprotective role of isoprene (Vickers et al., 2009; Ryan et al., 2014). However, there are indications that the quantities of emissions have little influence on the thermoprotective effect, as long as isoprene emissions are maintained. Vickers et al. (2009) stated that even low isoprene emissions should be sufficient for the stabilization of membranes under heat stress. A fact which supports this theory is that external isoprene fumigation of nonisoprene-emitting plants increases their thermotolerance (Velikova and Loreto, 2005), while it has no effect on isoprene-emitting species (Logan and Monson, 1999).

The overestimation of isoprene emission rates simulated by the Guenther et al. algorithm (control treatment parameterization) in our study during prolonged stress episodes agrees with observations at the ecosystem scale: Potosnak et al. (2013) and Seco et al. (2015) found that isoprene emissions from an oak- and hickory-dominated deciduous forest and a broadleaf temperate forest were overestimated by the Guenther et al. algorithm during severe drought events. Brilli et al. (2016) reported that during a high-temperature period, isoprene emissions of a poplar plantation simulated with the Guenther et al. algorithm were higher than the observed emissions. A reduction of isoprene emission rates under prolonged but moderate stress does not only hold for drought stress, but has been found for several abiotic stressors (Niinemets, 2010). It is also known that the severity and duration of stress plays a crucial role in the actual stress response, especially in the case of irreversible damage (Niinemets, 2010).

While the basic shapes of temperature and light response functions of isoprene emissions have been manifested quite early (Guenther et al., 1993), recent research reports that these response functions can vary with previous environmental conditions (Niinemets et al., 2010b) and may critically depend on the experimental conditions (e.g., how long isoprene emissions were allowed to equilibrate after changing the temperature). The standard isoprene emission factor is not necessarily a species-specific constant, but may change in response to stress, leaf age, or CO2 concentration (Niinemets et al., 2010a). Thus we assessed the response of isoprene emissions to changes in temperature and light. In contrast to most studies this was not done on the basis of discrete changes in temperature and light but under fluctuating environmental conditions (following outside temperature and humidity), which may naturally occur. We were able to simulate measured isoprene emissions using treatment-specific model parameters (Table 4) with large confidence (R2 > 0.87 and slope close to one); only under heat–drought conditions were the highest isoprene emissions underestimated by the treatment-specific model. In summary, our finding that the isoprene emission factor ES reduces during heat and heat–drought stress agrees well with current findings (Niinemets et al., 2010a; Geron et al., 2016). However, by applying a simple correction factor the standard-parameterized (control) model did not allow the stress-induced changes in emissions to be simulated. This is because not only the emission factor, but also the shape of the temperature response function changed with stress. This expands findings which have been reported recently by Geron et al. (2016) for several oak species during drought. However, while for most oak species the ES was, similarly to our study, reduced during drought, in one out of five oak species isoprene emission rates increased (Geron et al., 2016). This shows on the one hand that such stress effects may be species specific and on the other hand that neither a general direction of the change in ES nor the change in the shape of temperature or light response functions is known. Therefore, further field and laboratory studies will be required to reach a level of process understanding that allows stress-driven isoprene emissions to be described. In any case, the results of this study clearly show the need to critically reassess temperature response functions during stress and, in a further step, incorporate stress-specific response functions into BVOC emission models in order to provide reliable estimates.