This is the accepted version of the article: Kováč, Daniel; Veselá, Barbora; Klem, Karel; [et al.]. «Correction of PRI for carotenoid pigment pools improves photosynthesis estimation across different irradiance and temperature conditions». Remote sensing of environment, Vol. 244 (July 2020), art. 111834. DOI 10.1016/j.rse.2020.111834 This version is avaible at https://ddd.uab.cat/record/224227 under the terms of the license 1 Correction of PRI for carotenoid pigment pools improves photosynthesis estimation across different 2 irradiance and temperature conditions 3 Daniel Kováč1, Barbora Veselá1, Karel Klem1, Kristýna Večeřová1, Zuzana Materová Kmecová2, Josep 4 Peñuelas1,3,4, Otmar Urban1 1 5 Global Change Research Institute of the Czech Academy of Sciences, Bělidla 986/4a, 603 00 Brno, 6 Czech Republic 2 7 Faculty of Science, Ostrava University, 30. dubna 22, 701 03 Ostrava 1, Czech Republic 3 8 CSIC, Global Ecology Unit CREAF-CSIC-UAB, E-08193 Bellaterra (Catalonia), Spain 4 9 CREAF, E-08193 Cerdanyola del Vallès (Catalonia), Spain 10 Abstract 11 We studied the influence of changing carotenoid pigments on the sensitivity of the photochemical 12 reflectance index (PRI) to photosynthesis dynamics. The goal of the measurements was to examine 13 how the introduction of ΔPRI into the working dataset can improve the estimation of photosynthesis. 14 Spectral and photosynthetic characteristics of European beech and Norway spruce saplings were 15 periodically measured in growth chambers with an adjustable irradiance and temperature. Patterns of 16 environmental changes inside the growth chambers were created by periodic changes in irradiance 17 and temperature. Four general irradiance periods lasting 10-12 days each were established. Introduced 18 irradiance regimes varied in the sum of daily irradiance and amplitude of irradiance changes. 19 Temperature was changed with more complex patterns to induce changes in xanthophyll cycle 20 pigments at various time scales within these regimes. Our measurements confirmed the PRI linkage to 21 photosynthetic light use efficiency (LUE). However, the strength of this connection was found to be 22 dependent on changing pigment concentrations, specifically on the change in the ratio of chlorophylls 23 to carotenoids. Furthermore, a negative interference in photosynthesis estimation from PRI was 1 24 recorded if the temperature was lowered overnight to 12° C. The differential PRI (ΔPRI), calculated as 25 the simple difference between the PRI value measured during the daytime period and in early morning 26 (PRI0), revealed a decreased effect from pigments and cold temperature on LUE estimation. The 27 regression analysis among all measured data identified an increased association between PRI and LUE 28 following the introduction of ΔPRI from R2 = 0.26 to 0.69 in beech and from R2 = 0.61 to 0.77 in spruce 29 data. The analyses showed that both leaf carotenoid concentrations and the conversion state of 30 xanthophyll cycle pigments played a significant role in determining PRI and PRI 0 values and that the 31 accurate assessment of these pigments in PRI across multiple levels of stress from irradiance and 32 temperature might improve estimations of LUE through ΔPRI. In our data, ΔPRI appeared to be a good 33 measure of photosynthesis, the dynamics of which differed between beech and spruce saplings upon 34 switching temperatures. 35 KEYWORDS: photochemical reflectance index, proximal sensing, irradiance, temperature, carotenoids, 36 xanthophyll cycle, light use efficiency 37 1 | INTRODUCTION 38 The usefulness of a photochemical reflectance index (PRI) approach to link plant photosynthetic CO2 39 uptake efficiency in changing light (light use efficiency, LUE) and remotely sensed data has been widely 40 reported (Garbulsky et al., 2008; Peñuelas et al., 2011). PRI is based on our understanding of the 41 photoprotective role of xanthophyll cycle pigments within plants. When plants absorb more light 42 energy than can be used by chlorophyll to produce glucose, excessive light energy is either transferred 43 to xanthophyll molecules and emitted as heat or emitted as fluorescence (Gamon et al., 1992; Rascher 44 et al., 2009). Variations in xanthophyll cycle pigment concentrations and conversions produce 45 reflectance changes at a wavelength of 531 nm. Comparing this reflectance with a reference 46 wavelength (typically 570 nm) can be used to detect stress (Gamon et al., 1997, 1992; Peñuelas et al., 47 1995). Examination of empirical work has determined a fundamental relationship between plant 48 photochemistry and PRI that is based on the responsiveness of photosynthesis to irradiance. 2 49 The variability of factors that may affect canopy-measured PRI can produce confusion in interpreting 50 PRI, in addition to the desirable effects introduced by changing pigments. In field applications, sun– 51 canopy–sensor geometry can exert a strong effect on the resulting PRI values, as light fields may vary 52 in complex ways with canopy structure (Middleton et al., 2009; Sims et al., 2006). Wu et al. (2015) 53 examined crops and found the structural dependence of PRI on leaf area index (LAI). In addition, these 54 authors proposed a solution for removal of the structural signal, and their results imply that LAI change 55 as a consequence of a change in the illumination angle can impact the measured PRI of the canopy. 56 The results reported by Wu et al. (2015) and Gitelson et al. (2017) suggest that canopy structure- 57 related LAI interferences should be considered when evaluating PRI responses between canopies with 58 lower LAI. 59 The foliar ratio of chlorophylls to carotenoids (Chla+b/Carx+c) has a strong impact on the observed PRI 60 variability (Filella et al., 2009). Decreasing Chla+b/Carx+c may be related to photosynthesis 61 downregulation in stressed plants, but the changes in pigments may also cause impairment of the PRI– 62 LUE relationship over the long term. Attempts have been made to eliminate the Chla+b/Carx+c 63 variability in the measured signal by deconvoluting the influence of pigments. Gamon and Surfus 64 (1999) have shown an opportunity to detract the extent of xanthophyll cycle pigment conversions by 65 subtracting measured PRI value from the starting PRI value in introduced ΔPRI (ΔPRI = PRI0 – PRI). 66 Following this work, Gamon and Berry (2012) characterized differences in ΔPRI between sun and shade 67 leaves as induced with pigment changes. This study has shown that PRI0 represents a PRI state to which 68 PRI values can be related if the comparison of diurnal changes and plant groups is required. Ideally, 69 PRI0 is measured at low irradiance on leaves with inactivated protective functions to isolate the slow 70 changing component of PRI most likely related to Chla+b/Carx+c and the concentration of lutein 71 pigments. Magney et al. (2016) determined that the ΔPRI does respond to diurnal physiological 72 changes resulting from changes in VPD, air temperature, and stomatal conductance and suggested 73 that these changes may be dependent on the observed pigment dynamics. Nitrogen availability 74 affecting amounts of chlorophylls was considered a primary driver of ΔPRI sensitivity in this study, 3 75 defining the slope of the observed dependency. ΔPRI yields better correlations in nutrient-deficient 76 plots, thereby indicating the importance of carotenoid levels in observed relationships. There are 77 several good examples showing the opportunity to better estimate LUE from PRI measured at the top 78 of the canopy, if the value of PRI is corrected to the morning PRI0 (Hmimina et al., 2015, 2014; Ripullone 79 et al., 2011; Soudani et al., 2014). The presented studies often involve drought stress in the 80 experimental design as the main factor driving photosynthesis declines and the magnitude of PRI 81 response (Magney et al., 2016). We intend to further study the basics of the improved relationship 82 between photosynthetic LUE and ΔPRI, and the desirable role of changing pigments in developing 83 these relationships under conditions involving induced changes in irradiance and temperature. 84 Differences in the sensitivity of photosynthetic processes to light and temperature stress among 85 species suggest the occurrence of interactive effects on photosynthetic pigments. An insufficient 86 understanding of the associated reflectance signature in relation to the measure of photosynthesis is 87 consequential (Ollinger, 2011; Sims and Gamon, 2002). The co-variation of environmental drivers in 88 the upper canopy suggests that leaves in the upper canopy are often exposed to greater stress 89 originating from exposure of leaves to direct light (Niinemets and Valladares, 2004). Upper canopy 90 leaves may suffer from a variety of additional stresses, among which temperature stress may play a 91 particularly substantial role (Williams et al., 1996). The upper canopy crown, usually accounted for in 92 spectrometric measurements, may represent a substantial portion of the canopy involved in the 93 observed gas exchange (Coops et al., 2017). However, the functional trait attributes of plants may not 94 be the only features able to explain changes in PRI in a given environment. It may also be necessary to 95 account for the PRI variations with changing Chla+b/Carx+c that determines the constitutive (slow- 96 changing) component of the PRI. It has been suggested that the finer definition of the facultative 97 process (fast-changing with xanthophyll cycle) can help to detect LUE and responses to summer stress, 98 such as heat and drought (Gamon and Bond, 2013). Our previous development provided elementary 99 knowledge of PRI changes in relation to dynamic fluctuations of photosynthetically active radiation 100 (PAR) and temperature (Kováč et al., 2018). This study suggests large improvement in estimating LUE 4 101 from ΔPRI, with measurements of PRI0 that correspond to the xanthophyll cycle pigment conversion 102 state in the dark. Changes in PRI–LUE and ΔPRI–LUE relationships have yet to be investigated with 103 dynamic irradiance increases and temperature changes occurring on a daily scale. 104 We aimed to study further the sensitivity of both PRI and ΔPRI to decreasing and increasing 105 photosynthesis in fluctuating environments. In this study, we focused on observations of the effect of 106 mutual interactions among the plant pigments and overall canopy LAI on the developing relationship 107 between PRI and LUE in changing temperature conditions. Understanding the aspects of LUE 108 estimations using PRI would improve the applicability of PRI measurements in remote-sensing 109 applications. We aimed to overcome the canopy structural effect on measured PRI by fixing the 110 illumination–observation setup of the measurement by measuring canopies within the closed 111 environment of a growth chamber. We thus compared responses in photosynthesis, pigments and PRI 112 of tree species with distinctive sensitivities to low and high temperatures. Norway spruce trees, which 113 prefer cold regions and higher altitudes, were compared with European beech trees, which show 114 tolerance to higher temperatures and grow at lower altitudes. We established four regimes that varied 115 in their daily sum of irradiance income even as the trees were undergoing similar periodic changes in 116 temperature on a daily scale. We measured how the changes in pigments within these regimes 117 affected the observed PRI–LUE relationship and examined the role of established pigment 118 concentrations in the developing sensitivity of PRI and ΔPRI to LUE. 119 2 | MATERIALS AND METHODS 120 2.1 | Setup of the experiment 121 For the study, we selected two tree species with different habitat preferences: European beech (Fagus 122 sylvatica) and Norway spruce (Picea abies). These species are widespread within the Czech Republic 123 and the Central European region, with a distribution generally occurring according to their contrasting 124 climate and temperature demands. Seedlings of the selected tree species aged 3–4 years old (0.5–0.6 125 m tall) were grown in pots in the garden of the Global Change Research Institute from early spring until 5 126 the new leaves or needles were well developed. Thereafter, the trees were moved to the experimental 127 setting of growth chambers FS-SI-4600 (Photon Systems Instruments, Drásov, Czech Republic), where 128 they were processed for reflectance data acquisition, foliar photosynthetic pigments estimation and 129 photosynthesis measurements under changing conditions of irradiance (PAR) and temperature. The 130 initial acclimation period lasting 1 week (photoperiod 14 hours, irradiance 100 µmol m−2 s−1, day/night 131 temperatures set to 23/18°C and relative air humidity of 65%/80%) was followed with individual 132 regimes that differed in the sum of daily irradiance income, daily amplitude of irradiance changes and 133 temperature dynamics. Four periods of 10–12 days were established that varied in daily irradiance 134 amplitudes of 300–600–1200 (IRR1), 600–900–1500 (IRR2), 900–1200–1500 (IRR3), and 300–600–900 135 (IRR4) µmol m−2 s−1. Detailed descriptions of irradiance and temperature changes according to time of 136 day within each regime are provided in the attached research data. The second day of each irradiance 137 period IRR1–IRR4 was established as a control day to measure plant responses to what can be termed 138 “standard” temperature changes following the irradiance fluctuations. The last 2 days of each 139 irradiance period were devoted to measuring parameters in fluctuating temperatures. The first day of 140 this 2-day measurement period started with the same temperature as on the previous day. The 141 temperature was then experimentally lowered at midday to 16 °C. This decreasing temperature was 142 started after the trees had been heated for half an hour during the midday period of highest PAR. The 143 temperature decrease to 16 °C was gradual over a period of 2 h (12:00 to 14:00). Temperature was 144 lowered compared to previous days as well as during the dark (night) period to 12°C. Cold period 145 temperatures remained the same for each irradiance regime. Heating after a cold period was started 146 during the morning of the following day. During that following day, the temperature was increased 147 compared to the previous control days while the irradiance level remained unchanged. Ranges of the 148 temperature change on normal days of IRR1–IRR4 were 20–26° C, 24–30° C, 25–35° C, and 19–24° C. 149 In the morning of each measuring day before the lights in the growth chambers were switched on, the 150 leaves and needles of beech and spruce saplings were collected for the estimation of foliar 151 photosynthetic pigments (Chla+b, Carx+c) and individual carotenoid concentrations (antheraxanthin 6 152 (A), violaxanthin (V), zeaxanthin (Z)). Concentrations of chlorophylls and carotenoids were estimated 153 spectrophotometrically using a Specord 500 spectrophotometer (Analytik Jena, Jena, Germany). 154 Pigment concentrations in pigment extracts have been estimated from absorbance curves using 155 Lichtenthaler equations (1987). Amounts of xanthophyll cycle pigments were estimated by the HPLC 156 method (Kurasová et al., 2003), and the conversion state of the xanthophyll cycle pigments (i.e., de- 157 epoxidation state, or DEPS) was calculated according to Gilmore and Björkman (1994) as DEPS = (A + 158 Z) / (V + A + Z). The maximum quantum yield of photosystem II photochemistry (Fv/Fm) was estimated 159 from measurements using a PAM-2500 portable chlorophyll fluorometer (Heinz Walz, Effeltrich, 160 Germany) for dark adapted leaves. The Fv/Fm was calculated as Fv/Fm = (Fm − F0)/Fm, in which F0 and 161 Fm represent the minimum (F0) and maximum (Fm) chlorophyll fluorescence of darkness-adapted 162 leaves. 163 Reflectance factors of canopies created by four saplings of either beech (in July-August) or spruce 164 (September-October) species were measured in the growth chambers using a custom-made system 165 for measuring reflectance that is based on two JAZ spectrometers (Ocean Optics, Dunedin, FL, USA). 166 The spectrometric system is used for measurements in the dual field of view configuration. The trees 167 that were measured with a spectrometer were not moved throughout the measurement period. Each 168 JAZ unit measures data in spectral range between 340 and 1025 nm in 2048 channels with a spectral 169 resolution (FWHM) of 1 nm for each channel. The reflectance estimation was based on comparisons 170 between the radiant flux reflected from the measured canopy and incident (reference) irradiance at 171 each measuring wavelength similar to Gamon et al. (2015). Optimization of the measurement system 172 for measurements in growth chambers was performed using a spectralon panel reflecting a down- 173 welling radiant flux at PAR of 1500 μmol m-2 s-1. In addition, the radiance data estimation accounts for 174 the optimization of the signal measured using each unit to integration time to strengthen the signal- 175 to-noise ratio, conversion of the measured digital photon count signal to radiometric units, and dark 176 current spectrum correction of this signal. All the supporting information for the calculations of 177 reflectance factors from the measured data using the current establishment of the spectrometer, 7 178 optical fibres (2-meter-long QP600-UV-VIS optical fibres), and cosine reduction (CC-3-UV-T) was 179 estimated prior to initiating the measurements. The correction data were loaded into the measuring 180 system (on a desktop computer attached to the spectrometer), which processed the measured data 181 automatically while saving as text files the basic outputs from each data measurement. The 182 spectrometric method used for measuring reflectance factors is described in greater detail by Kováč 183 et al. (2018). The system setup ensured automatic data acquisition, starting in the morning and 184 continuing at a 1-minute frequency throughout the day. The computer connected to the 185 spectrometers via the USB port controlled simultaneous measurements by both spectrometers. The 186 LED Fyto-Panels (Photon Systems Instruments) that create the light environment inside the growth 187 chambers (Fig. 1) also served as the light source for measuring canopy reflectance factors. The linear 188 change in the light intensity produced by the Fyto-Panels enabled the measurement of canopy 189 reflectance factors without impacting the illumination directions and shadow fractions of vegetation 190 while changing the irradiance. As a result, we could attribute the variability in reflectance to pigment 191 changes in the measured leaves rather than to changes in canopy shadows as a consequence of 192 changing illumination angles. The sampled area covering four tree crowns was ca. 44 cm in diameter, 193 which was provided by the optical-fibre tip’s 23° field of view and the 1-metre distance between the 194 trees and measuring optics. Examples of measured reflectance curves are shown in Fig. 1. PRI was 195 calculated following Gamon et al. (1997) as PRI = (R531 – R570)/(R531 + R570) from reflectance at 196 wavelengths of 530.37, 530.73, 531.08, 531.44, 531.79 nm (average used to estimate the value of R531), 197 and 570.31, 570.67, and 571 nm (R570). Development of PRI during the day period on control days 198 within each IRR regime is shown in Fig. 2. The average of the PRI data in the final 5 minutes of the initial 199 low-PAR period (under 100 µmol m−2 s−1) was taken as a PRI0 value because a small rise in PRI was 200 always observed in response to activating the photosynthesis functions in the morning. Based on the 201 PRI0 value, a differential PRI was later calculated as ΔPRI = PRI0 – PRI (Gamon and Berry, 2012) for each 202 PRI acquisition during the day. 8 203 The main focus of the gas-exchange measurement was to estimate the actual photosynthesis rate (A), 204 stomatal conductance (Gs), and transpiration (Tr). Measurements were collected five times per day at 205 PAR set at 300, 600, 900, 1200, or 1500 µmol m−2 s−1 and at temperatures that were adjusted 206 accordingly. A portable photosynthesis system LI-6400 XT (LI-COR Biosciences, Lincoln, NE, USA) was 207 used to measure the photosynthetic dynamics of leaves in the upper crown. Leaves were measured 208 inside an LI-6400-02B leaf assimilation chamber. The light use efficiency (LUE) was calculated as LUE = 209 A/PAR. Within each IRR regime, gas exchange and chlorophyll fluorescence were initially measured on 210 the second day, referred to as the control day, and later on two consecutive days with induced cooling 211 of trees towards the end of each irradiance regime. The actual quantum yield of photosystem II 212 photochemistry (ΦPSII) was calculated from PAM-2500 estimated values of steady state fluorescence 213 (Fs) and light-adapted maximum fluorescence (Fm′) as ΦPSII = (Fm′ − Fs)/Fm′ (Genty et al., 1989) for 214 each gas exchange data acquisition. Similarly, non-photochemical fluorescence quenching (NPQ) was 215 calculated as NPQ = (Fm − Fm′)/Fm′. Photochemical fluorescence quenching (qP) was calculated as qP 216 = (Fm′ − Fs)/(Fm′ − F0′) from Fs, Fm′ and light-adapted minimum fluorescence (F0′). A database was 217 created of spectrometric and physiology data measured under irradiances ranging from 300–1500 218 µmol m−2 s−1 and temperature ranging from 14–35° C. The core data are available online. 219 2.2 | Data analysis 220 All analyses of the collected data were performed using R 3.5.1 (R Foundation for Statistical Computing, 221 Vienna, Austria). To visualize and quantitatively summarize the multivariate covariation of optical 222 variables (PRI and ΔPRI), major vectors of environmental factors, leaf pigment concentrations, and 223 physiology measures, we performed a principal component analysis (PCA). Principal component 1 and 224 2 scores were plotted in a PCA biplot. PCA analysis and visualization were conducted using the R 225 “factoextra” and “ggplot2” packages. The data for the individual parameters were tested for normality 226 using the Kolmogorov–Smirnov test. Tukey’s HSD post hoc (p < 0.05) multiple range test was performed 227 using the HSD.test function in the “agricolae” package to evaluate differences between individual 9 228 treatments. Data for the Tukey analyses are displayed in bar plot figures. A logarithmic regression 229 model was used to study the relationships among PRI, ΔPRI, and LUE at probability levels p < 0.05, p < 230 0.01, and p < 0.001. Scores of regression analyses among the data within the individual IRR regimes 231 and between all data are shown in Table 1, and fitted logarithmic equations for pairs of data are shown 232 in Table 2. Dependency graphs between these key variables are displayed in Fig. 8. 233 3 | RESULTS 234 3.1 | Relationships among environmental, optical, and physiological variables 235 Principal component 1 (PC1) explained 37.6% of the total variation in European beech and 38.9% of 236 the total variation in Norway spruce data (Fig. 3). The functional traits responded significantly to PAR. 237 PAR determines the positions of individual values on the variable factor map, with individual data 238 points measured at low irradiances situated towards the bottom, negative part of the axis, whereas 239 data measured under high irradiances (1500 µmol m−2 s−1) are situated towards the opposite end of 240 the graph. Even though trait responses to PAR showed general trends that were common to both 241 species, responses for both species were positioned on a gradient ranging from those that did not 242 respond significantly (with a closer link to PC2) to those that displayed high PAR trait plasticity. The 243 analysis showed that PAR differences were a common factor in determining the distribution of ΦPSII, 244 qP, LUE, and ΔPRI on the variable factor map. High PAR values produce low photochemical quenching 245 and LUE values and extremely negative ΔPRI values. The impact of PAR on values of PRI and NPQ was 246 still significant, but the relationship among PAR, PRI, and NPQ was weaker than expected (calculated 247 from research data). PRI was the only variable with a link to PC1, which showed a strong correlation to 248 Chla+b/Carx+c belonging to PC2 with a coefficient of correlation (R) equal to 0.89 (p < 0.001) in the 249 beech data set and 0.58 (p < 0.001) in the spruce data (calculated from research data). The lower LAI 250 of the beech canopy produced deeper amplitudes of PRI (Fig. 2) and resulted in a higher correlation 251 between Chla+b/Carx+c and PRI. 10 252 Principal component 2 (PC2) explained 23.8% of the total PCA variation in European beech and 25.2% 253 of that in Norway spruce data (Fig. 3). The main factors A, Tr, and Gs were placed in the lower and 254 upper quadrants of the PCA biplots in beech and spruce, respectively staying in contrast to the position 255 of temperature vector. This difference in directionality of A, Tr and Gs vectors is likely associated with 256 species specific sensitivity of photosynthesis to temperature variations. The opposite temperature 257 effects on the regulation of photosynthesis were reflected also in the directionality of the adjacent 258 Chla+b/Carx+c and PRI vectors. 259 3.2 | Factors affecting the development of PRI and ΔPRI 260 The two principal components in the PCA plots comparing early morning (before 8:00) values of 261 selected parameters to midday values (Fig. 4) explained approximately 64% of variability in the tested 262 data. The dependencies in the graphs could be rotated according to significance of predictors, but the 263 basic relationships among the measured data were similar between the species. Key relationships 264 among midday values of PAR, ΦPSII, LUE and ΔPRI were similar to those identified among all the data in 265 Fig. 3. NPQ showed a link to midday PRI, which was itself correlated with the Chla+b/Carx+c (including 266 VAZ/Chla+b) ratio. The PRI showed a progressive decline (Fig. 7) that corresponded rather to a 267 decreasing Chla+b/Carx+c (Fig. 6). The third set of correlations in these PCA graphs was formed by 268 variable vectors of A, predawn DEPS and Fv/Fm. These connections placed Fv/Fm and predawn DEPS 269 into the role of photosynthesis predictor. 270 Chla+b/Carx+c plays an important role in determining both PRI0 and midday PRI values. However, sharp 271 differences in predawn DEPS (Fig. 6) with a significant correlation with differences in ΔPRI suggested 272 that xanthophyll cycle pigment de-epoxidation was very important in the development of ΔPRI. Among 273 those factors affecting ΔPRI development, PAR was found to be a very important factor that affects 274 the magnitude of the response (Fig. 4). Although PRI0 showed a weaker association with morning DEPS 275 (Fig. 4), the correlation between PRI0 and predawn DEPS was nevertheless significant (research data), 11 276 thus confirming the importance of xanthophyll cycle pigments in the observed trends. Shifts in the 277 PRI0–DEPS relationship might be influenced by Chla+b/Carx+c modulating PRI value. 278 3.3 | PRI dynamics that are consequential to photosynthesis 279 Differences in the regulation of photosynthesis with temperature are most apparent from comparisons 280 between photosynthesis data that are measured midday (Fig. 5). Based on the observed differences, 281 relationships were developed, as shown in Fig.4. The PRI response was to a certain extent sensitive to 282 dynamic day-to-day changes in photosynthesis induced by temperature (Fig. 7), thus indicating the 283 utility of PRI for estimating dynamics of photosynthesis in fluctuating temperatures. However, 284 sensitivity to temperature-induced changes in photosynthesis did not occur within irradiance regimes 285 IRR1 and IRR2 with progressive declines in Chla+b/Carx+c (Fig. 6). The decreasing PRI in beech during 286 cold periods (second measuring days) in the IRR regimes (Fig. 7) corresponded to declining 287 photosynthesis under high-light and low-temperature conditions (Fig. 5). The further decrease in PRI 288 on the following day that was in contrast to the rising A might be related first to the increased predawn 289 DEPS and diminished PRI0 under low-temperature conditions, consequently also resulting in a lower 290 PRI at midday (Figs. 6 and 7). The observed trend of progressively decreasing PRI with Chla+b/Carx+c 291 was also observed for the spruce data set. Based on these observations we assume that the decreasing 292 PRI with Chla+b/Carx+c and cold stress was a limiting factor in enhancing the PRI response to LUE. 293 In contrast, ΔPRI showed an increase and a lower magnitude in spruce that were consistent with the 294 rise in photosynthesis upon the reduced midday temperature on measurement day 2 for each IRR 295 regime (Fig. 7). This sensitivity was the result of the increasing PRI values in spruce (Fig. 7), whereas a 296 less pronounced increase in PRI was observed in beech that was consistent with the reduced 297 photosynthesis, as shown in Fig. 9. This opposite reaction in ΔPRI in beech and spruce observed in the 298 final two measurement days for each IRR period suggested an overall increased sensitivity of ΔPRI to 299 photosynthesis (Figs. 5 and 7). 12 300 The inconclusive results of first-day measurements for each IRR regime might indicate possible minor 301 limitations of the applicability of ΔPRI. The low ΔPRI consistent with the high Chla+b/Carx+c on the 302 initial day of IRR1 (Fig. 6) disrupted the observed ΔPRI–LUE dependency in the spruce data. The high 303 ΔPRI amplitude in beech during the first measurement days for IRR2 and IRR3 resulted from a sudden 304 PAR increase. Closer connections between photosynthesis and ΔPRI were observed towards the end 305 of the measurements as a consequence of the diminishing Chla+b/Carx+c. In addition to the observed 306 general trends, we should highlight the lowered ΔPRI in response to the higher LUE and A under later, 307 low-irradiance conditions of IRR4 that greatly strengthened the overall sensitivity of ΔPRI to LUE (Figs. 308 5 and 7). This observation thus favours ΔPRI for estimating photosynthesis responses. 309 3.4 | Role of xanthophyll cycle pigments in the sensitivity of ΔPRI to LUE 310 Predawn DEPS was increased under conditions of higher irradiance stress and coincided with the 311 decreasing Chla+b/Carx+c ratio and imposition of stress due to low night temperature (Figs. 4 and 6). 312 The dynamics of this response occurring on a day-to-day basis showed the rapid response of 313 xanthophyll cycle pigments to stress conditions. Nevertheless, DEPS value established during night 314 period is considered an important input requirement for accurately determining PRI0. Consequently 315 precisely estimated ΔPRI enables to differentiate between unstressed and stress conditions. 316 Predawn DEPS in spruce needles on the second day of the measurements within each IRR, which 317 marked the beginning of the period of dynamic temperature change, was lowered compared with the 318 values in beech and to the predawn DEPS in spruce on the first control day of the high-irradiance 319 regimes (Fig. 6). This phenomenon might be attributed to higher LAI of spruce trees, thereby providing 320 them with a greater capacity to manage excessive light in a given environment. The differences in 321 predawn DEPS were equally matched in PRI0 values (Fig. 7). A small difference between PRI and PRI0 322 thus indicated increased photosynthesis rates in cold temperatures under conditions of high light (Fig. 323 5). By contrast, cold night temperatures produced a high predawn DEPS, which in combination with a 324 high midday drop in PRI under high temperatures resulted in a large ΔPRI, which is consistent with a 13 325 drop in photosynthesis in spruce species. The reverse dynamics in pigments and PRI were observed 326 between these two days in beech (Fig. 7), concurrent with the photosynthesis dynamics (Fig. 5). 327 3.5 | Regression analyses of PRI and ΔPRI relationships to LUE 328 Among the observed relationships, and considering the stratifications between irradiance regimes 329 (IRR1–IRR4), the strongest relationships between PRI and LUE were observed in the dynamic light 330 environments IRR1, IRR2, and IRR4 with a changing light intensity from low to high (Table 1). The R2 331 values for the relationship between LUE and PRI under these conditions were often are as large as 0.8 332 (Table 1). The overall relationship between LUE and PRI was impacted by the decreasing 333 Chla+b/Carx+c, with a greater effect observed in the beech data set. By introducing ΔPRI, the overall 334 R2 for the assessment of LUE was raised from R2 = 0.26 to 0.69 in beech and from R2 = 0.61 to 0.77 in 335 spruce (Fig. 8). ΔPRI failed to improve the LUE assessment in the highest irradiance period, with 336 irradiances between 900 and 1500 µmol m−2 s−1 (IRR3, Table 1). High carotenoid levels served as a basis 337 for the effective assessment of LUE from ΔPRI in the following regime of low irradiance (IRR4) with 338 imposed low stress from irradiances in the 300–900 µmol m−2 s−1 range. The accuracy of the LUE 339 assessment using ΔPRI in this period rose by 0.1 to R2 = 0.91 and R2 = 0.77 in the beech and spruce data 340 sets, respectively. 341 4 | DISCUSSION 342 The advantage of using ΔPRI over applying simply measured PRI for the purpose of extracting LUE has 343 been examined in this study. The presented work confirmed that the de-epoxidation cycle of leaf 344 pigments involved in NPQ has a general effect of decreasing the reflectance magnitude at wavelengths 345 around 531 nm (Gamon et al., 1990) with increasing light. The dynamics of PRI in our experimental 346 regimes of heating and cooling furthermore indicated that PRI shows an ability to track photosynthesis 347 changes in environments of fluctuating temperature. According to the measured data, the PRI-LUE 348 connection may be consequential to the connection between LUE and ΦPSII, as has been previously 349 suggested (Nichol et al., 2006; Rahimzadeh-Bajgiran et al., 2012). Although the relationship of PRI to 14 350 photosynthesis beyond the ΦPSII-PRI connection may be constrained by factors related to excessive 351 energy-consuming processes that are not involved in either xanthophyll cycle or carbon assimilation, 352 such as photorespiration (altered Mehler reaction and nitrate reduction) or cyclic electron transport 353 of photosystem I (PSI) (Fréchette et al., 2015; Magney et al., 2017; Porcar-Castell et al., 2008), our 354 measurements confirm the negative interference from the slowly changing Chla+b/Carx+c ratio on 355 photosynthesis estimation using PRI. The dependency of PRI on Chla+b/Carx+c deteriorates the 356 relationship between PRI and LUE over the season, as previously shown by many authors (Fréchette 357 et al., 2016; Hmimina et al., 2014; Sims and Gamon, 2002). The R2 for the PRI–LUE relationship from 358 various plant functional types is often reported to be below 0.60, as reviewed by Garbulsky et al. 359 (2011). We were able to reach this level of connection between PRI and LUE in the spruce data set; a 360 lower R2 of 0.26 in this relationship was estimated in beech data set, which we consider to be a 361 consequence of the lower canopy LAI of the selected beech trees resulting in higher PRI amplitudes, 362 as similar changes in Chla+b/Carx+c have been estimated between species (Fig. 6). 363 There are many examples in the literature showing a negative interference from Chla+b/Carx+c in LUE 364 estimation, and several studies have suggested tactics to minimize the interfering effect of 365 Chla+b/Carx+c. The correction procedure may also be dependent on the application type. A detailed 366 analysis of measurements at changing observation angles and changing sun illumination angles at 367 grown canopy sites demonstrated the necessity to address dynamic reflectance changes in the canopy 368 structure and differences in the Chla+b/Carx+c ratio between sunlit and shaded canopy portions 369 (Hilker et al., 2008). This research addressed the necessity to create a deconvoluting algorithm to 370 estimate LUE at each unique ecosystem station by taking into account only those PRI measurements 371 taken at certain measurement geometries from unattended spectral systems (Hilker et al., 2010). In 372 the improved approach to estimate LUE that resulted from this work, the Chla+b/Carx+c ratio has 373 become regarded as an important variable indicative of canopy stress that must be accounted for – 374 and corrected – when interpreting PRI data. A group of researchers is proposing to deconvolute 375 xanthophyll-related signals by applying transformation via continuum removal of the reflectance 15 376 signature within the 500- to 600-nm range (Kováč et al., 2013, 2012; Woodgate et al., 2019) to 377 minimize the impact of Chla+b/Carx+c on the measurement outputs. Hernández-Clemente et al. (2011) 378 used the 512-nm band as a reference when estimating DEPS and basic physiology measures from 379 airborne data over boreal forests. The strong normalization effect of red-edge bands around 680 nm 380 for evaluating the variability of the “light-exposed” PRI has been reported in airborne data applications 381 (Zarco-Tejada et al., 2013) and when processing satellite images (Drolet et al., 2008). Ongoing research 382 continues to show that deconvoluting the early morning (predawn) state of pigments can be used to 383 reduce the impact of pigment changes on measurement outputs in applications designed to measure 384 plant stress and hence LUE (Hmimina et al., 2015; Liu et al., 2013; Ripullone et al., 2011). 385 A single PRI (PRI and PRI0) value taken during the day is sensitive to bulk changes in Chla+b/Carx+c 386 throughout the season (Garrity et al., 2011). Continuous lowering of Chla+b/Carx+c has been observed 387 in our data within each irradiance period IRR1–IRR4 (Fig. 6), thereby producing variability in PRI (Fig. 388 7). This drop in PRI has been partly helpful in determining the reduction in photosynthesis during 389 regimes IRR1–IRR3, as the decreasing LUE is associated with increasing irradiance stress, as also 390 reported by Peñuelas et al. (1995). We recognized a large interference from Chla+b/Carx+c when data 391 from low-irradiance IRR4 were included in the overall data analysis. This interference in LUE estimation 392 was removed with ΔPRI. Within the individual regimes, the relationship between PRI and LUE was 393 dependent on the observed change in xanthophyll cycle pigments following changes in irradiance 394 during the daytime period (Fig. 8, Table 1). The highest LUE-PRI connection has been achieved with 395 induced daily low to high PRI changes under conditions simulating irradiance increases from low to 396 high intensity. These conditions are similar to those used by Gamon and Surfus (1999) in their 397 pioneering study examining ΔPRI changes with DEPS. The observed trends suggest that Chla+b/Carx+c 398 may be unambiguous in data across longer periods if the constitutive pigment impact on PRI is 399 efficiently discarded. Estimations of pigments at different time scales may be indirectly indicative of 400 plant stress because leaf optical properties are directly impacted by the pigment composition 401 (Peñuelas and Fillela, 1998; Wong and Gamon, 2015). 16 402 Deconvolution of PRI into slow-changing and fast-changing components according to Gamon and Berry 403 (2012), assuming that the “dark” component of PRI (PRI0) is also changing between days with night 404 retention of de-epoxided xanthophyll cycle forms (Kováč et al., 2018), narrows the LUE estimation from 405 PRI. It should be noted that our PRI measurements were based on spectral sampling at nadir 406 observations and under constant light fields so that the directional effects associated with changes in 407 illumination angles (Hernandez-Clemente et al., 2016) were small. This approach helped to narrow the 408 external factors that impact PRI, but even after removing structural effects from LAI, the PRI–LUE 409 correlation was still not strong. The ΔPRI improved the sensitivity of the measured signal to LUE across 410 multiple conditions. The variations in LUE-PRI and LUE-ΔPRI relationships were evaluated upon 411 observing temporal dynamics in species, yielding contrasting sensitivity to temperature changes (Fig. 412 5). The correction procedure unravelled the effects of Chla+b/Carx+c and cold temperature on LUE 413 estimation, two main factors among three common factors impacting PRI as shown by Wong and 414 Gamon (2015). Although the spectral shift due to cold temperature was first reported as an albedo 415 shift related to changes in the physical properties of leaves in very cold temperatures (Wong and 416 Gamon, 2015), we detected low temperature interference on the LUE estimation from PRI at 12° C. 417 The shift was apparent by the decreased PRI0 at 12° C and decreased PRI measured on the days 418 following the application of cold stress (Fig. 7). In the context of our measurements, the shift appears 419 to be only partly related to the high DEPS. 420 A predictive pattern of decreasing PRI towards midday was typically observed in our testing data set 421 when the temperature increase followed the PAR increase (Fig. 2). By comparing dynamic PRI changes 422 in response to experimental temperature lowering (Fig. 9), we endeavoured to identify the change in 423 PRI in response to the increased photosynthetic efficiency in spruce and to low temperature stress in 424 beech trees. It is well known that the observed PRI dynamic changes within a matter of minutes to 425 hours result from the synergy between xanthophyll cycle pigment conversions and management of 426 the energetic carriers ATP and NADPH under changing conditions (Nichol et al., 2000), thereby 427 producing signal variation with photosynthesis efficiency. We detected an increase in PRI in spruce in 17 428 response to enhanced photosynthesis reactions (Fig. 9). As a consequence of enhancing photo 429 protection in beech, a less-pronounced increase in PRI was measured (Fig. 9), resulting in a decreased 430 PRI compared with the photosynthetically more efficient spruce. Similar PRI responses to the 431 photosynthesis changes induced in the diurnal frame have been reported by Gamon et al. (1992), who 432 examined differences in PRI between control, nutrient-stressed and water-stressed sunflower leaves. 433 In our experiment, feedback between PRI and photosynthetic reactions was detected, which greatly 434 improved the accuracy of ΔPRI in tracking dynamic photosynthetic changes with induced temperature 435 variations. 436 However, the studies of ΔPRI do not involve variations in this signal caused by the canopy structure, 437 which may render leaf traits difficult to discern (Knyazikhin et al., 2012). Magney et al. (2016) 438 postulated that ΔPRI affords limited improvements in decoupling the structural (LAI) effect from the 439 raw PRI signal, and thereby, PRI0 is primarily sensitive to variability in pigment content and should not 440 be used to correct for changes in LAI. For efficient disentangling of the desirable effect in ΔPRI to match 441 its value with photosynthesis, an accurate assessment of PRI0 that is consistent with the dynamics in 442 DEPS was required (Figs. 6 and 7). Particularly, PRI0 estimation on the second measurement days for 443 each irradiance regime is considered a crucial factor for development of the observed LUE-ΔPRI. 444 However, examining aspects of PRI0 and ΔPRI estimation on these days revealed importance of LAI in 445 the observed relationships, resulting from determinations of sapling capacity to manage the available 446 light (Ellsworth and Reich, 1993). Assessment of the PRI0 signal is based on the dependency of PRI on 447 the de-epoxidation state of xanthophyll cycle pigments (Gamon et al., 1990), and night-time levels of 448 DEPS are often influenced by temperature and induced stress (Demmig-Adams and Adams, 1996; 449 Gilmore and Björkman, 1995). The causality of the relationship between ΔPRI and LUE appears to be a 450 consequence of the differences in canopies LAI between species and levels of imposed stress. The 451 results highlight the importance of estimating PRI0 that matches DEPS and a highly complex nature of 452 the mechanisms involved in remote assessments of photosynthesis change, underscoring the need for 453 very precise data. 18 454 By concept, ΔPRI appears to be a suitable tool for observing the dynamics of changes within small areas 455 of vegetated surfaces throughout day periods to monitor short-term variations in leaf pigments. 456 Further assuming the field application of presented ΔPRI concept, difficulties may arise when isolating 457 PRI0 in early morning field reflectance measurements. The errors in estimation may originate from the 458 cosine response of the diffusers used and from the relative variation in the measured signal of the total 459 down-welling radiance flux. Variations in measured incoming radiation flux are caused by deviations 460 in the measurement of direct and diffuse components of the down-welling flux passing through the 461 diffusers (Pacheco-Labrador et al., 2019). The fraction of diffuse irradiance is usually low in remote- 462 sensing applications if the cloudy data are discarded, but the contribution of diffuse irradiance can be 463 large in the case of automated proximal sensing comparing data on a large temporal scale and 464 including measurements acquired at low and high sun elevations (Gamon et al., 2015; Pacheco- 465 Labrador and Martín, 2015). Estimating PRI0 and PRI from reflectance data may be challenging due to 466 the unknown directional distribution of the diffuse irradiance. Most applications have been set up for 467 PRI0 from measurements that have occurred in a period around 9 a.m. when the solar zenith is around 468 or greater than 40° (Liu et al., 2013; Magney et al., 2016) and the sun is potentially yielding a higher 469 intensity. This phenomenon may be considered a consequence of the observed cosine response in the 470 measured data. Improvements in instrumentation for the measurements may also be required to 471 reproduce data with higher standards. 472 The results highlight a great diversity of parameters to which PRI measurements may refer in beech 473 and spruce forests. They also show that PRI is highly comparable to indicators based on relative units 474 such as ΦPSII, LUE, or the Chla+b/Carx+c ratio, and that assessment of LUE can be improved with the 475 use of ΔPRI, which uses the balance between PRI and PRI0. The involvement of protection mechanisms 476 that are not involved in any of the NPQ mechanisms may be a reason for the weakened correlation 477 between ΔPRI and NPQ, but the weaker PRI–NPQ connection is often a result of the Chla+b/Carx+c 478 adjustments to light conditions (Stylinski et al., 2002). It can be presumed that the strong association 479 between variables is a result of applying artificial light, which minimizes fluctuations of PRI, ΦPSII, NPQ, 19 480 and LUE in the data set, as reported by Sukhov and Sukhova (2018). For the practical problem of field 481 remote sensing, the results show that the application of PRI can be effective for investigating 482 photosynthesis in dynamic irradiance and temperature regimes if the pigments are sufficiently 483 disentangled in the signal. The presented work may serve as premise for data processing if interfering 484 factors in spectral measurements in the field are efficiently reduced. However, measurements of 485 control plants that have not been affected by stressors are often necessary to establish the 486 dependency of optic parameters on observed factors (Damm et al., 2018; Sukhova and Sukhov, 2018). 487 CONCLUSION 488 The results showed that photosynthesis estimation using PRI over periods longer than days may be 489 limited by changing dynamics of the foliar Chla+b/Carx+c ratio with stress from irradiance. The extent 490 of the Chla+b/Carx+c limitation in our measurements was dependent on the leaf area index of the 491 measured trees; we recorded greater interference from Chla+b/Carx+c in beech seedlings with a lower 492 LAI. An improved assessment of dynamic changes in photosynthetic activity induced with changes in 493 irradiance and temperature was achieved using ΔPRI. The measurements also showed the importance 494 of foliage and environmental factors for the observed dynamics in PRI. The estimation of ΔPRI was 495 based on measuring PRI0 under low irradiance. Temperature was considered a factor that induces 496 changes in xanthophyll cycle pigment DEPS observed in PRI. The improved approach as proposed by 497 introducing ΔPRI may deconvolute part of the interference in the PRI signal. The limitations of the ΔPRI 498 may be related to changes in this signal with sudden increases in irradiance when evaluating canopies 499 with a lower LAI. Low foliar amounts of xanthophyll cycle pigments may render a low amplitude of 500 ΔPRI, which was a minor limiting factor when evaluating our spruce dataset. Conversely, on days 501 starting with low temperature, ΔPRI was effective in disentangling the negative effect caused by low 502 temperature on the photosynthesis estimation. Other stresses and less predictive patterns of 503 environmental changes may exist in the field; the mechanism should be further tested under various 504 conditions. 20 505 ACKNOWLEDGEMENTS 506 This work was supported by the Ministry of Education, Youth, and Sports of the Czech Republic within 507 the National Infrastructure for Carbon Observations-CzeCOS (No. LM2015061) and SustES – 508 Adaptation strategies for sustainable ecosystem services and food security under adverse 509 environmental conditions (CZ.02.1.01/0.0/0.0/16_019/0000797). JP also acknowledges funding from 510 European Research Council Synergy grant ERC-SyG-2013-610028 IMBALANCE-P. 511 REFERENCES 512 Coops, N.C., Hermosilla, T., Hilker, T., Andrew Black, T., 2017. Linking stand architecture with canopy 513 reflectance to estimate vertical patterns of light-use efficiency. Remote Sens. 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Environ. 138, 38–50. doi:10.1016/j.rse.2013.07.024 716 717 718 719 720 721 722 723 724 Fig. 1 (A) Spectral intensity emitted by white LED panels (Iref) in growth chambers under four 725 photosynthetically active radiation (PAR) intensities: 100, 600, 900, and 1500 μmol m−2 s−1; (B) 30 726 spectral intensity reflected from spruce saplings under corresponding PAR intensities (Imeas); 727 reflectance spectra of European beech (C) and Norway spruce (D) saplings under corresponding 728 irradiances in one day during the IRR2 regime. 729 730 731 732 733 734 735 736 Fig. 2 PRI dynamics on the control (normal) day of each irradiance regime (IRR1, IRR2, IRR3, IRR4) as 737 measured for beech and spruce canopies. 738 739 740 31 741 742 743 744 745 746 747 748 749 750 Fig. 3 Biplot of variables and individuals measured showing interactions among spectral information 751 (PRI and ΔPRI), environmental conditions (PAR, Temp, VPD) inside growth chambers, and gas exchange 752 (A, Gs, Tr, LUE), active fluorescence (ΦPSII, NPQ, qP), and foliar pigment (Chl, Car, Chl /Car) 753 characteristics of the examined vegetation. Individual data points are labelled to indicate the number 32 754 of measurements taken/irradiance/temperature. A group of 5 measurements represent data collected 755 on one day of measurement. A total of 60 values from 12 measurement days in leaves of spruce and 756 beech trees are shown. 757 758 759 760 761 762 763 764 Fig. 4 Biplots of variables and individuals for measurement days (n = 12) of beech and spruce trees 765 showing interactions among foliar pigments (Chl/Car, VAZ/Chl, predawn DEPS), spectral information 766 (PRI0, midday PRI, ΔPRI), environmental conditions (PAR0, midday PARm, overnight T0, and midday 33 767 temperature, Tm), and key physiology measures estimated both predawn (Fv/Fm) and during midday 768 (A, LUE, ΦPSII, NPQ). Individual data points are labelled with the measurement day number/irradiance 769 at dawn/night temperature. 770 771 772 773 774 775 34 776 777 Fig. 5 Photosynthetic capacity (A) and light use efficiency (LUE) in leaves of beech and spruce trees at 778 midday of measurement days under four irradiance regimes (IRR1–IRR4). IRR period label and midday 779 temperature indicate irradiance-and-temperature conditions during the measurements. Means and 780 standard deviations (error bars) of the measurements are presented (n = 6). Letters indicate 781 homogeneous groups (p < 0.05; Tukey’s post hoc test). Different letters above the bars indicate 782 statistically significant differences between means. 783 784 35 785 786 Fig. 6 Ratio of chlorophylls to carotenoids and de-epoxidation state of xanthophyll cycle pigments 787 (DEPS) estimated for leaves of darkness-acclimated beech and spruce trees on days of physiological 788 measurements. Means and standard deviations (error bars) of the measurements are presented (n = 789 3). Letters indicate homogeneous groups (p < 0.05; Tukey’s post hoc test). Different letters above the 790 bars indicate statistically significant differences between the means. 791 792 793 36 794 795 Fig. 7 Development of early morning PRI0, midday PRI, and differential ΔPRI in changing midday 796 temperature conditions under four irradiance regimes (IRR1–IRR4), separated by broken lines. Letters 797 indicate homogeneous groups (p < 0.05; n = 6; Tukey’s post hoc test). 798 799 800 801 37 802 803 Fig. 8 Relationships between LUE and PRI (ΔPRI) in all data measured during all four irradiance regimes 804 (IRR1–IRR4). Coefficients of determination for overall relationships between variables are displayed in 805 the figure (n = 60). 806 807 808 809 810 38 811 812 Fig. 9 PRI dynamics on a measurement day with midday cooling to 16 °C during the highest-irradiance 813 regime, IRR3. Physiology measurements and optical data to report PRI during the midday period were 814 taken at 14:00. Cooling of trees started at 12:00. 815 816 817 818 819 820 821 822 39 823 Table 1 Coefficients of determination (R2) for PRI-LUE and ΔPRI-LUE relationships in beech and spruce 824 saplings as observed in Fig. 8. Relationships estimated for data pairs estimated in four individual IRR 825 regimes (n = 15) and among all measured data (n = 60). The significance of the results was tested at 826 levels *p < 0.05, **p < 0.01, and ***p < 0.001; ns indicates a non-significant result 827 European beech Norway spruce IRR regime PRI-LUE ΔPRI-LUE PRI-LUE ΔPRI-LUE IRR1 0.30* 0.68*** 0.79*** 0.81*** IRR2 0.36* 0.54*** 0.77*** 0.74*** IRR3 0.07ns 0.20ns 0.71*** 0.53*** IRR4 0.82*** 0.91*** 0.62*** 0.77*** Total 0.27*** 0.69*** 0.61*** 0.77*** 828 829 830 Table 2 Fitting logarithmic equations for PRI-LUE and ΔPRI-LUE relationships in beech and spruce 831 saplings as observed in Fig. 8. Coefficients of determination for these relationships are shown in table 832 1. Equations were estimated for data pairs estimated in four individual IRR regimes (n = 15) and among 833 all measured data (n = 60) European beech Norway spruce IRR regime PRI-LUE ΔPRI-LUE PRI-LUE ΔPRI-LUE IRR1 y=0.0191ln(x)+0.0202 y=0.0181ln(x)+0.0701 y=0.0267ln(x)+0.0702 y=0.0221ln(x)+0.0852 IRR2 y=0.0177ln(x)+0.0128 y=0.0197ln(x)+0.0738 y=0.0229ln(x)+0.0296 y=0.0198ln(x)+0.0764 IRR3 y=0.0057ln(x)+0.1091 y=0.0087ln(x)+0.0176 y=0.0164ln(x)+0.0188 y=0.0119ln(x)+0.0362 IRR4 y=0.0230ln(x)+0.0191 y=0.0232ln(x)+0.0931 y=0.0255ln(x)+0.0344 y=0.0249ln(x)+0.0991 Total y=0.0027ln(x)+0.0259 y=0.0179ln(x)+0.0678 y=0.0339ln(x)+0.0836 y=0.0175ln(x)+0.0655 834 835 40