• Quercus coccifera;
  • canopy structure;
  • chlorophyll a fluorescence;
  • Fv/Fm;
  • leaf orientation;
  • leaf area index (LAI);
  • photoinhibition;
  • photosynthetic light-response curve;
  • model development;
  • whole-plant photosynthesis model


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A canopy photosynthesis model was modified to assess the effect of photoinhibition on whole-plant carbon gain. Photoinhibitory changes in maximum quantum yield of photosystem II (Fv/Fm) could be explained solely from a parameter (Lflux) calculated from the light micro-environment of the leaves. This relationship between Fv/Fm and the intercepted cumulative light dose, integrated and equally weighted over several hours was incorporated into the model. The effect of photoinhibition on net photosynthesis was described through relationships between photoinhibition and the shaping parameters of the photosynthetic light-response curve (quantum use efficiency, convexity, and maximum capacity). This new aspect of the model was then validated by comparing measured field data (diurnal courses of Fv/Fm) with simulation results. Sensitivity analyses revealed that the extent of photoinhibitory reduction of whole-plant photosynthesis was strongly dependent on the structural parameters (LAI and leaf angle). Simulations for a Mediterranean evergreen oak, Quercus coccifera, under climatic conditions which cause mild photoinhibition revealed a daily loss of 7·5–8·5% of potential carbon gain in the upper sunlit canopy layers, a 3% loss in the bottom canopy, and an overall loss of 6·1%. Thus, this canopy photoinhibition model (CANO-PI) allows the quantitative evaluation of photoinhibition effects on primary production.




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Within the past two decades, considerable information has been collected on the occurrence of photoinhibition under natural conditions among species, environments and ecotypes. It is now well recognized that exposure of leaves to excessive light, particularly in combination with other environmental stresses, can result in enhanced photoinhibition (e.g. Powles & Critchley 1980; Long, Humphries & Falkowski 1994; Werner & Correia 1996). Furthermore, there is increasing evidence that natural light levels alone are sufficient to cause photoinhibition (Bolhár-Nordenkampf, Hofer & Lerchner 1991; Ögren & Evans 1992; Raven 1994). Despite the rather good understanding of the phenomenon of photoinhibition, little is known about its importance for photosynthetic carbon assimilation, whole-plant primary production and growth under natural field conditions (Ögren 1994). Few studies have yet attempted to quantitatively estimate the effect of photo-inhibition on plant primary production (Ögren & Sjöström 1990; Long et al. 1994).

Whereas in former studies photoinhibition was frequently considered as a damaging process (e.g. Osmond & Chow 1988), there is now increasing evidence for its importance as a protective process which mediates the controlled dissipation of excessive light energy (Krause 1988; Demmig-Adams 1990; Demmig-Adams & Adams 1992). This comprises a variety of processes at different sites in the chloroplast, as for example non-radiative dissipation of the excess excitation energy in the antenna or degradation of the D1-protein and D1-turnover (Bilger, Schreiber & Bock 1995). The development of new molecular techniques stimulated intense research on the physiological mechanisms of photoinhibition and elucidate our understanding of the related processes. However, many of these studies have been conducted in the laboratory under conditions which are barely relevant for the natural behaviour of the plants. In such experiments photoinhibition is often induced by exposing plants to conditions to which they are not adapted, for example by transferring shade plants into full sunlight (Powles 1984; Osmond & Chow 1988). Even in studies with attached leaves in a natural environment, measurements are primarily restricted to the most exposed leaves of a plant that are certainly not representative of the entire leaf population of the canopy. Thus, to truly evaluate the importance of photoinhibition for natural plant stands, the contributions of leaves from all parts of the canopy have to be considered. Since different parts of the canopy reveal different microclimatic conditions, a thorough characterization of the micro-environment of the leaves is an essential part of such an analysis.

To better understand the effects of photoinhibition on carbon gain, the three-dimensional whole-plant photosynthesis model of Ryel, Beyschlag & Caldwell (1993) was modified to incorporate photoinhibitory effects. This model was selected since it calculates microclimatic conditions within the canopy with a high degree of realism, and links these directly to physiologically based single-leaf photosynthesis calculations. In this work, only photo-inhibition induced by natural light levels was considered for the evaluation of high light stress without additional environmental stresses (as high temperature or drought).

The model was modified to account for photoinhibition and a validation of this new routine is presented. In the present paper, the effects of photoinhibition on whole-plant carbon gain were evaluated for different plant structures and for a Quercus coccifera shrub under natural conditions. This new model version CANO-PI (canopy photoinhibition model) provides a means to quantify photoinhibition effects on whole-plant carbon gain.


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Field site and climatic data

All experimental data were recorded at a field site in south-west Portugal (see Werner, Correia & Beyschlag 1999). The study site is a natural Mediterranean macchia in the Parque Natural da Serra da Arrábida (38°28′40′′ N, 8°59′34′′ W, elevation 280 m above sea level). Measurements were performed on the evergreen sclerophylls Quercus coccifera L., Arbutus unedo L., Olea europaea var.◊sylvestris Brot., Phillyrea latifolia L., Phillyrea angustifolia L., Pistacia lentiscus L., Erica arborea L. and Juniperus phoenicea L., and the drought semi-deciduous shrubs Cistus albidus L., Cistus monspeliensis L. and Rosmarinus officinalis L. Weather conditions were continuously recorded by a standardized solar-powered meteorological station (data-logger CR10, Campbell Scientific, Logan, UT, USA). Air and soil temperatures, relative humidity, wind speed, photosynthetic photon flux density (PPFD) above the plant canopy and precipitation were measured in 10 s intervals and were automatically stored as half hourly and daily means. Climate data for 12 June, 1996 were used in the simulations: air temperature at 0500 h, 12·8 °C; maximum temperature 26·3 °C (at 1400 h); maximum PPFD at noon 2027 μmol m−2 s−1; wind velocity 1·5–2·6 m s−1.

Chlorophyll a fluorescence

Photoinhibition was determined from the maximum quantum yield of photosystem (PS) II (Fv/Fm, where Fv and Fm are the variable and maximum fluorescence, respectively), one of the most reliable parameters of photoinhibition under natural conditions. All chlorophyll fluorescence measurements were conducted in situ with a portable, pulse-modulated fluorometer (PAM-2000, Walz, Effeltrich, Germany) on attached leaves in their natural position. The leaves were dark-adapted with leaf-clips for 15 min, which was determined to be sufficient to allow complete re-oxidation of the PS II reaction centres. Diurnal courses of maximum quantum yield were recorded on cloudless days on six (either naturally vertical- or horizontal-orientated) leaves per species which were marked and repeatedly measured throughout the day. Incident PPFD on the leaf blade was recorded with the PPFD-sensor of the leaf-clip holder (2030-B, Walz, Effeltrich, Germany) shortly before the Fv/Fm measurements. The optical fibre was always kept at 8 mm distance to avoid indirect shading of the leaf surface and the light sensor. Additionally nine to ten south-facing leaves with either vertical or horizontal leaf orientation were measured at predawn (complete darkness) and during maximum solar radiation (1100–1400 h true solar time). The quantum use efficiency was estimated from the initial slope of the photosynthetic light-response curve, which was measured on attached leaves after 30 min of dark adaptation. After determination of Fv/Fm the actinic light was slowly, stepwise increased in five intervals from 0 to 100 μmol m−2 s−1. Care was taken that the photosynthetic equilibrium was reached before each measurement (approx. 10 min).

Structural parameters

Leaf area index (LAI) was measured with a LAI-2000 Plant Canopy Analyzer (PCA, LiCor, Inc. Lincoln, NE, USA) under diffuse light conditions. Measurements were calibrated by destructive harvest. Structural data for Q. coccifera were derived from stratified clipping of representative portions of the canopy. Samples were separated into leaves and stems. Leaf area was measured with the LI-3000 leaf-area meter in the laboratory (LiCor, Inc.). Stem area index (SAI) was determined manually, by measuring stem length and diameter. Leaves were oven dried at 70° to constant dry weight (minimum 48 h) and at least 10–20 leaves per sample were homogenized (Retsch Schwingmühle Typ MM 2000, Haan, Germany). The C : N ratio was determined in two probes per sample (Elementaranalysis Vario El, Elementar Analysensysteme, Hanau, Germany). Leaf and stem angles were measured relative to the horizon (= 0°) using a compass-protractor similar to the one described by Norman & Campbell (1989). All statistical analyses were performed with Statistica (StatSoft, Inc. 1995, Tulsa, OK, USA).

Model development

The three-dimensional canopy model of Ryel et al. (1993) was used to simulate whole-plant daily carbon gain. As several versions of the model have been described extensively in the literature (Caldwell et al. 1986; Harley, Tenhunen & Lange 1986; Tenhunen et al. 1987, 1990; Beyschlag et al. 1990; Ryel et al. 1990, 1993; Beyschlag, Ryel & Dietsch 1994; for review see Beyschlag & Ryel 1998, 1999), only a short summary of the general model structure is presented along with a detailed description of modifications performed to incorporate photoinhibition.

The model consists of an integrated light interception and photosynthesis submodel. The photosynthesis submodel contains the equations developed by Farquhar, von Caemmerer & Berry (1980) as implemented by Harley et al. (1992) and is based on ribulose-1,5-bisphosphate-carboxylase-oxygenase (Rubisco) kinetics. Stomatal conductance is simulated by the empirical model of Ball, Woodrow & Berry (1987). Parameter estimates for describing carboxylase kinetics, electron transport, and stomatal function were derived from both single factor dependencies and diurnal time course measurements of gas exchange as described by Harley & Tenhunen (1991). This model has been parameterized for several evergreen Mediterranean species (Tenhunen et al. 1990), and particularly for Q. coccifera (Tenhunen et al. 1987). Physiological para-meters for Q. coccifera in spring were derived from Harley & Tenhunen (1991), Tenhunen et al. (1984, 1985) and Beyschlag (unpublished results). Parameters used in the simulations are shown in Table 1. Gfac is an proportionality factor expressing the relation of conductance to net photosynthesis (see Tenhunen et al. 1990). The rate of CO2 fixation is reduced by dark respiration which is a function of temperature (‘day’ respiration term of Farquhar & von Caemmerer 1982).

Table 1.  Model parameters used in the simulations. Parameters were estimated from gas-exchange data of Quercus coccifera in May (Tenhunen et al. 1985 and unpublished results) and are in part from Harley & Tenhunen (1991) and Tenhunen et al. (1990). The rage of scaling constants denotes to the upper sunlit and inner shaded subsections, respectively
Parameter ValueUnits
  1. f(t)

  2. − 3·9489

Quantum use efficiencyΦ0·06(mol CO2 mol photons−1)
Activation energyEa (Rd)55 000(J mol−1)
Scaling constantf (Rd)23·22–22·0
Electron transport capacity
Scaling constantc (Pml)15·2–14·9
Activation energyΔHa (Pml)43 500(J mol−1)
Energy of deactivationΔHd (Pml)200 000(J mol−1)
Entropy termΔS (Pml)656(J K−1 mol−1)
Carboxylase capacity
Scaling constantc (Vcmax)34·35
Activation energyΔHa (Vcmax)74 400(J mol−1)
Energy of deactivationΔHd (Vcmax)197 500(J mol−1)
Entropy termΔS (Vcmax)648(J K−1 mol−1)
Stomatal conductance
Scaling parameterGfac12·5
Carboxylase kinetics
Michaelis–Menten constant for carboxylationf(Kc)31·95
 Ea(Kc)65 000(J mol−1)
Michaelis–Menten constant for oxygenationf (Ko)19·61
 Ea(Ko)36 000(J mol−1)

The structure of the single-leaf photosynthesis submodel was modified to assess photoinhibition effects on the three shaping parameters of the light-response curve: the quantum use efficiency, the convexity and the maximum photosynthetic capacity. The following considerations of the theoretical causes and the potential effects of these changes on net photosynthesis provide the basis for the photoinhibition model.

Relationship between photoinhibition and quantum use efficiency Φ

The primary effect of photoinhibition is that of a reduced photon use efficiency at PS II (Φ) in low light, i.e. a reduction of the initial slope of the light-response curve (Powles 1984; Björkman & Demmig 1987; Krause & Weis 1991). It has been shown that changes in Fv/Fm are linearly correlated to changes in the quantum-use efficiency with nearly equal changes (1 : 1) (Björkman & Demmig 1987; Genty, Briantais & Baker 1989; Long et al. 1994). A linear correlation between Fv/Fm and the initial slope of the light-response curve was confirmed for pooled field data of 11 different Mediterranean macchia species (Fig. 1). The residual analysis shows the high scatter in the data, which were measured under different field conditions in spring and summer. A low but significant correlation of the residuals with leaf temperature during the measurement (which ranged from 18·5 to 40·4 °C, from April to September, respectively) was found (P < 0·05, R = 0·27). However, the data underline that the linear relationship found in many laboratory studies (e.g. Björkman & Demmig 1987) is also consistent for a variety of field conditions and a 1 : 1 relationship was used in the model to change Φ in response to changes in Fv/Fm.


Figure 1. Correlation between reduction in Fv/Fm and in the quantum use efficiency (Φ). Data are expressed relative to maximum values (highest values observed during the year). Data were derived from 11 Mediterranean macchia species under natural conditions from April to September 1997 (n = 67, P < 0·001). Residuals of the linear regression are shown as an insert.

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Relationship between photoinhibition and convexity θ

In the model of Farquhar et al. (1980), CO2 assimilation is limited at low light by the rate of electron transport and at high light by the maximum activity of Rubisco. The light dependency of photosynthesis is often described by a non-rectangular hyperbola which is based on these limitations (Prioul & Chartier 1977; Leverenz et al. 1990; Ögren 1993; Ögren & Evans 1993; Cannell & Thornley 1998; see also Farquhar & Wong 1984):

  • image(1)

where I is the incident PPFD, Φ is the maximum quantum use efficiency, P is the net photosynthetic rate, and Pml is the assimilation rate at saturating light and CO2 concentration, representing therefore the maximum potential rate of carbon assimilation. θ is the convexity or bending factor, which is determined by a transition between the two limitations of photosynthesis as light increases. Although Φ and Pml can be related to underlying biochemical properties of the leaf, the physiological meaning of θ is probably attributable to several factors (Ögren 1993; Leverenz 1994). The lower the capacity of Rubisco relative to that of electron transport, the earlier the transition to Pml and the higher θ. If the light activation of Rubisco proceeds over an extended light range, the transition becomes more gradual, and θ will become somewhat lower than expected, given a sharp truncation of the electron transport curve by Rubisco (Ögren & Evans 1993).

Very high θ-values (> 0·96) were found in unicellular algae (Leverenz 1994), whereas lower values of θ = 0·85 were found in optically complex systems such as leaves (Ögren & Sjöström 1990; Evans, Jakobsen & Ögren 1993). The measured light-response curves of Q. coccifera fit well using θ = 0·85 (data not shown), and this value was used in the simulations. However, θ is an input parameter of the model and can be scaled to any specific data set used for parameterization.

The effects of possible photoinhibitory reduction of maximum quantum use efficiency on the shape of the light-response curves with two different initial Φ and θ-values are illustrated in Fig. 2 (curve 2). Several authors (Ögren & Sjöström 1990; Leverenz et al. 1990) have reported that a photoinhibitory reduction in Φ was accompanied by a similar reduction in θ which is also shown (curve 3, Fig. 2). The main difference between the two parameters is that a reduction in θ will also reduce photosynthesis at intermediate light levels. Furthermore, the effect of a photoinhibitory reduction in Φ (curve 2) is dependent on the shape of the light-response curve: if the initial θ- and Φ-values are high, light saturation is still reached at intermediate light levels after a 50% reduction in Φ (Fig. 2c curve 2). A 50% reduction of lower initial Φ (Fig. 2d) and θ (Fig. 2a & b) causes light saturation to shift to higher light intensities and net photosynthesis is reduced over the whole range of naturally occurring PPFDs.


Figure 2. (ad), Theoretical photosynthetic light-response curves with two different initial quantum use efficiencies: (a,c) Φ = 0·06; (b,d) Φ = 0·04 and convexities: (a,b) θ = 0·85; (c,d) θ = 0·96 and Pml = 26·3 for all curves. The initial values of curve 1 are given in each graph. The effects of a potential reduction of quantum use efficiency, convexity and Pml are shown relative to the initial values of curve 1; curve 2: 50% reduction in Φ; curve 3: 50% reduction in Φ and θ; curve 4: 50% reduction in Φ and θ and 3% reduction in Pml.

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To explore the potential effects of each factor on daily carbon gain, model simulations were performed with two different initial values of Φ and θ (Table 2). A 50% reduction in Φ (relative to initial value) resulted in a decline of daily photosynthesis of 10% at high, and 21% at low initial Φ- and θ-values, respectively. This indicates the interdependence of both parameters: the effect of a reduction in Φ is enhanced at lower initial θ-values, and vice versa. A simultaneous 50% decrease in both parameters reduced daily carbon gain by 23–38%. Hence, the strongest effect on net photosynthesis is exerted by a concomitant reduction in Φ and θ.

Table 2.  Sensitivity analysis of the potential effect of changes in shaping parameters of the photosynthetic light-response curve on net photosynthesis. Effects of reduction of maximum quantum use efficiency (Φ) and of the convexity of the light-response curve (θ) are presented. Simulations were performed using two different initial values of Φ (0·06 and 0·04) and θ (0·96 and 0·85). Simulations were also conducted reducing these parameters by 25, 50 and 75% of initial values. Relative reduction (%) in daily net photosynthesis is given for an isolated, sunlit model plant on a sunny day in June
 Φ = 0·06Φ = 0·04
Initial values:θ = 0·96θ = 0·85θ = 0·96θ = 0·85
  1. 75%

  2. 54

  3. 53

  4. 63

  5. 61

Reduction in ΦReduction in daily net carbon gain (%)
Reduction in θ
Reduction in both Φ and θ

The model was set such that relative changes in the calculated values of Fv/Fm caused identical relative changes in Φ and θ in the photosynthesis routine.

Relationship between photoinhibition and maximum capacity Pml

While the effects of photoinhibition on the first two parameters (Φ and θ) are more or less well described (Powles 1984; Leverenz 1994), the effect on the maximum capacity of photosynthesis (Pml) is more difficult to examine. In many experiments, light saturation is not reached and the effect of a change in Φ caused by photoinhibition (Kok 1956) changes photosynthesis measurably even at the highest irradiance. Therefore, it is difficult to separate direct photoinhibitory effects on Pml from a decline of Φ or θ which will shift the maximum capacity to very high light intensities.

Significant reductions of photosynthetic capacity (in most cases measured as light but not CO2 saturated photosynthesis rate) were found in plants which were subjected to photoinhibitory conditions strongly exceeding their growth conditions (Powles & Critchley 1980; Ögren, Öquist & Hällgren 1984). A decrease in Φ and θ has been observed to precede a decrease in Pml, and may often occur without decrease in Pml (Henley et al. 1991; Long et al. 1994; Ball et al. 1997). A decline of the light-saturated photosynthesis has further been observed after photoinhibition at low or high temperatures (Powles, Berry & Björkman 1983; Schreiber, Bilger & Neubauer 1994), although other authors found no effect of low temperatures on Pml (Ball, Hodges & Laughlin 1991; Ball et al. 1997). Pml should not be affected by photoinhibition of PS II reaction centres until photosynthesis is limited by the capacity for PS II electron transport at all light levels (Leverenz et al. 1990). Since no sufficient support was found in the literature for photo-inhibition effects on Pml under natural conditions without any other stresses than high light stress, changes in Pml were not considered.

Model simulation of diurnal changes in Fv/Fm

The diurnal pattern of Fv/Fm, which often follows an inverted dome-shaped curve with the minimum reached during midday or early afternoon, was simulated solely from changes in the light micro-environment of the leaves. All PPFD-dependent parameters discussed below were calculated from recordings of incident radiation on naturally horizontally and vertically orientated leaves, which were taken immediately before the Fv/Fm measurements. Several PPFD-dependent parameters were calculated by weighting the light values on an hourly basis and integrating them over different time periods, which were then correlated with diurnal Fv/Fm measurements (Table 3).

Table 3.  Correlation between diurnal measurements of Fv/Fm and several variables calculated from the incident light on vertical and horizontal leaves. The time period used for the calculations and the correlation coefficients are shown for Q. coccifera in June under field conditions (n = 33)
VariableTime period (h)R2
  1. 6

  2. 0·96

I. Instantaneous PPFD0·55
II. Mean PPFD of 1 h preceding the measurement by:10·79
III. Light dose integrated and equally weighted (moving average) over a time period of:20·64
as III. but only horizontal leaves20·49
as III. but only vertical leaves20·65
IV. Linearly weighted light dose (see Ögren & Sjöström 1990) calculated over a time period of:20·59

Only a weak correlation was found between Fv/Fm and the instantaneous irradiance (Table 3, I). Similarly weak was the correlation with light values from single hours preceding the fluorescence measurements (Table 3, II). The correlation improved when the PPFD values were integrated over several preceding hours. The best correlation was found for PPFD values integrated and equally weighted over a time period of 6 h (i.e. a moving average over 6 h, Table 3, III), where a highly significant linear correlation was obtained (P < 0·001, Fig. 3), which explained 96% of the variance of the data. No further improvement was achieved by extending the time period for longer than 6 h. Residuals were randomly distributed and did not show any correlation with temperature, time of the day or magnitude of Fv/Fm. As the relationship was obtained from measurements of leaves which differed in their extent of light interception and photoinhibition, it covers a wide range of possible photoinhibition responses. The correlation improved, when calculated from data of horizontal leaves alone (Table 3, III). No further improvement was achieved by linearly weighting the data with weights equal to 0 and 1 for the first and the last increments, respectively, as proposed by Ögren & Sjöström (1990; Table 3, IV).


Figure 3. Correlation between Fv/Fm and integrated and equally weighted incident light values (Lflux, moving average over the preceding 6 h-period) for vertical and horizontal leaves (closed and open symbols, respectively). Diurnal measurements were conducted on Q. coccifera in June (means of three leaves per orientation, n = 24, P < 0·001). Residuals of the linear regression line are shown as an insert.

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This correlation was implemented in the model to calculate Fv/Fm using measured diurnal courses of PPFD, by:

  • image(2)

where m is the slope (as a positive number), fmax the intercept with the Fv/Fm axis (see Fig. 3), and Lflux the calculated light parameter. Lflux is calculated from the incident PPFD on the leaves which is stored in the model, integrated and equally weighted over the defined time period (6 h for Q. coccifera). A scaling factor (S) for Φ and θ was then calculated as the ratio of Fv/Fm to maximum Fv/Fm:

  • image(3)

Changes in S range from 1 (no photoinhibition) to 0 (total inhibition), and proportionate changes in Φ and θ are calculated by multiplying them by S. Fv/FmMax is the maximum quantum yield of PS II of unstressed leaves, which has been shown to be similar for C3 species (see Björkman & Demmig 1987) and literature values can be used if measurements are not available. The incorporation of Fv/FmMax also permits the consideration of chronic photoinhibition, i.e. a sustainable depression of predawn Fv/Fm which may occur during periods of prolonged environmental stress (Adams & Demmig-Adams 1995; Werner et al. 1999). It has been pointed out that predawn fluorescence values, which are also used for the computation of various quenching coefficients, frequently do not correspond to a maximal Fv/Fm, resulting in an underestimation of photoinhibition (Demmig-Adams et al. 1996). The effect of this sustainable depression in quantum yield of PS II, when Fv/Fm values do not fully recover to maximum over night, is integrated in the model by Eqn 3. Fv/FmMax, fmax, m and the time period to calculate Lflux are input parameters.

A validation of the photoinhibition routine of the model was conducted by calculating a diurnal course of Fv/Fm from an independent set of climate data from the meteorological station, and comparing to field measurements for sun-exposed naturally occurring vertical and horizontal Q. coccifera leaves (Fig. 4). Data are shown for a day in spring with only mild photoinhibition (Fig. 4a) and a day in August when the horizontal exposure led to pronounced photoinhibition (Fig. 4b). In both cases the correspondence between calculated and measured data was good: differences between measured and simulated data were 0·1–3·3% in spring (both leaf orientations) and 0·5–4·3% in vertical leaves in August. Measured data of horizontal leaves in August had higher scatter and deviation from the simulations (1–15% deviation). Residuals were randomly distributed although with a higher scatter in the afternoon due to the higher variation in the measured data. Residuals were tested for additional factors influencing the correlation by multiple regression analysis against leaf temperature, magnitude of simulated Fv/Fm, time of the day and combinations of these, but no significant correlations were found (R2 ranged between 0·0001 and 0·005).


Figure 4. (a,b). Diurnal course of Fv/Fm from field measurements on horizontal and vertical leaves of Q. coccifera (means of six to ten leaves ± SD) and respective model simulations (dotted and continuous lines for horizontal and vertical leaves, respectively) for a sunny day in (a) June (b) August. An independent set of PPFD measurements from a climate station was used for the model simulations. Residuals are shown in the inserts.

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Canopy photosynthesis model

The photoinhibition submodel was integrated into the canopy model which approximates the plant structure as being cylindrical in shape, subdivided in concentric subcylinders and horizontal layers. It is assumed that foliage density and orientation are relatively homogeneous within these subsections and foliage and stem surface areas and inclination angles represent the measured canopy structure (see Fig. 8c). Such multi-layer models allow the incorporation of within-canopy profiles of both environmental and physiological variables and avoid errors of big-leaf models (de Pury & Farquhar 1997). The microclimate submodel simulates in detail the canopy radiation environment, including penetration of the direct solar beam to different canopy layers, the behaviour of diffuse radiation from the sky as well as that reflected by and transmitted through other leaves. Long-wave radiation attenuation and leaf energy balance are integrated into this submodel. The penetration of direct beam solar radiation into the canopy is calculated following the classical gap probability function (Monsi & Saeki 1953; Warren Wilson 1960; Duncan et al. 1967) and is a function of solar position in the sky and the surface area, and inclination and dispersion patterns of foliage in each layer. This canopy submodel has been validated for Q. coccifera (Caldwell et al. 1986).


Figure 8. (a–c). Simulated reduction of daily carbon gain due to photoinhibition within the crown of a Q. coccifera shrub for a sunny day in June. Reductions are shown for different canopy layers and the three subcylinders (C1, inner – C3, outer cylinder) defined in (c). (a) Reduction due to photoinhibition expressed as percentage loss per canopy subsection. (b) Reduction in daily carbon gain expressed as percentage of loss in whole-plant carbon gain in each subsection. The width of horizontal bars is proportional to the total carbon gain in each layer. Calculation of photoinhibition was based on the correlation shown in Figs 3 & 4a. Overall reduction in daily whole-plant carbon gain was 6·1%. (c) Structural parameters (leaf area index (LAI), stem area index (SAI) and leaf orientation) of the measured Q. coccifera. The crown was divided into seven horizontal layers and three concentric subcylinders (C1 – C3). Total canopy height was 1·55 m; the diameter of the subcylinders was 1, 1·6 and 2·5 m for C1 – C3, respectively. All data were recorded during May 1996. Total LAI was 3·4 and leaf width varied from 0·9 to 1·7 cm from the top to the bottom of the canopy.

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The calculated integrated irradiance for a leaf at a given position in the canopy is stored in the model to calculate the light parameter (Lflux) in the photoinhibition subroutine (Eqn 2). Diurnal courses of photoinhibition are calculated from changes in Lflux which differ with location and orientation of the leaf. Figure 5 shows the calculated diurnal courses for sunlit leaves at four different azimuthal positions at the outer crown (Fig. 5a) or shade leaves at the same positions but deeper in the canopy (Fig. 5b). Leaves at the east side of the canopy show an early decline in Fv/Fm, followed by south and later west side leaves. Leaves on the north side are generally less photoinhibited, whereas highest photo-inhibition occurs at the top of the canopy. The patterns are similar, although less pronounced, in leaves of deeper canopy layers (Fig. 5b). With increasing canopy depth the effect decreases and differences among canopy locations disappear (not shown). Figure 5b further shows measurements and simulations (points and solid line) of south-facing leaves at 25 cm depth in the inner upper canopy. These leaves are not exposed to direct sunlight during most of the day. The model simulations and Fv/Fm measurements fit within 1–3%. The calculated Fv/Fm changes induce relative changes in Φ and θ in the photosynthesis subroutine at each specific position in the canopy as outlined above.


Figure 5. Model simulations of diurnal courses of Fv/Fm of leaves at different locations in the simulated Q. coccifera shrub (North, South, East, West) at 0·5 m height for either (a) outer sunlit leaves at the canopy periphery (N,S,E,W) and at the top (top) or (b) inner shaded leaves at the same position but 40 cm horizontally into the canopy. Measured Fv/Fm values of south-facing shade leaves (symbols) at the mid canopy (at 25 cm depth) and simulations (solid line) for this position are also shown in (b).

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Carbon fixation and transpiration are calculated separately for sunlit and shaded leaves in each canopy subsection; six azimuthal orientations are considered for sunlit leaves. Leaf temperatures of sunlit and shaded leaves in each layer are determined iteratively, considering incident radiation, energy balance, transpiration, and convective heat exchange. Rates of photosynthesis are calculated for representative foliage elements within each subsection, weighted by the size of the subsection, the fraction of sunlit and shaded foliage and summed up to obtain whole-canopy photosynthesis.

Physiological differences of the leaves due to light acclimation were considered by using different parameter sets for each subsection based on the relationship of Pml with measured leaf nitrogen content. Leaf N was converted to rubisco capacity (Pml) using a linear relationship between Pml and N, assuming that a residual leaf N content (Nb) that correspond to 0·5% of the total leaf N was not associated with photosynthesis (see Anten 1997; de Pury & Farquhar 1997):

  • image(4)

where Nc,l is the measured leaf N content in a canopy layer (l) and subcylinder (c), Nb the residual leaf N content and χ is the ratio of maximum photosynthetic capacity to leaf N. The value of χ was estimated from gas exchange measurements of sun leaves and the N content in the uppermost canopy layer. The calculated Pml gradient was comparable to measured data of Q. coccifera from Tenhunen et al. (1984; approx. 25–19 μmol m−2 s−1 for a LAI of approx. 4 versus 25–17 μmol m−2 s−1 for a LAI of 3·4). A spatial matrix of photosynthetic capacities was developed for the canopy and used in the simulations. Johnson, Parson & Ludlow (1989) showed that the values of θ and Φ are relatively unaffected by light acclimation as compared to Pml and that it is reasonable to assume that they are constant with canopy depth. Temperature dependence of dark-respiration and the light compensation point at different depths of a Q. coccifera canopy were derived from Meister (1987) and scaled relative to the Pml distribution within the canopy (Table 1).

Whole-plant simulations

Whole-plant simulations were conducted for both, measured and hypothetical plants. To assess the effects of plant structure on photoinhibition, a hypothetical plant of 100 cm height was subdivided into five homogeneous layers of 20 cm thickness with LAI varying from 0·1 to 7·0. The target plant was placed in a closed canopy with regularly spaced neighbours. Further simulations were conducted for a fixed LAI of 3·0 but for foliage orientation varying from 0 to 90° to assess the effect of foliage orientation. To evaluate the effect of photoinhibition on primary production under natural conditions, the model was parameterized with measured structural data of a Q. coccifera shrub. The leaf and stem area indexes as well as mean leaf-angle distribution for each canopy subunit (seven layers, three subcylinders) are shown in Fig. 8c. The plant was placed among neighbour plants according to the field situation to simulate the natural environment.

Model simulations were performed for an array of equally spaced points within the canopy, with a matrix of 160 000 points in the case of Q. coccifera to ensure a sufficient resolution in canopy sections with dense foliage. One-hour time steps were used and all simulations were performed for conditions of mild photoinhibition as shown in Fig. 4a. Simulations were performed both with and without photoinhibition but otherwise equal input, and the photoinhibition effect on total daily carbon gain were estimated as the difference between these simulation pairs.


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Whole-plant simulations: sensitivity analysis of the effects of leaf area index and foliage orientation

Model simulations in Fig. 6 show the effect of photo-inhibition in canopies with different densities. Highest photoinhibitory reduction in daily whole-plant carbon gain occurred at relatively low LAI because of deep light penetration into the canopy. With increasing LAI the loss of potential photosynthesis due to photoinhibition decreased from nearly 8% to approximately 6% in dense canopies. In very dense canopies the lowest leaf layer revealed a negative carbon balance, due to reduced light penetration. With low LAI all canopy layers were similarly affected by photo-inhibition, but as density increased, the photoinhibitory reduction of whole-plant carbon gain primarily occurred in the uppermost leaf layer.


Figure 6. Simulated reduction in daily photosynthetic carbon gain by photoinhibition as a function of different leaf area index (LAI 0·1–7·0). The canopy of a hypothetical plant was subdivided into five homogeneous layers of 20 cm height (layer 1 = top; layer 5 = bottom), mean leaf angle 45°; climatic data from a sunny day in June with photoinhibition as in Fig. 4a. The target plant was positioned in a canopy surrounded by equal-sized neighbouring plants.

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The loss of potential photosynthesis was slightly increased if sun/shade leaf differentiation was not considered in the simulations. In this case (only considering sun leaf physiology) the simulated photoinhibition effects were slightly higher in plants with high LAI. This was caused by a negative carbon balance in the lower canopy layers, but the overall pattern was similar to that in Fig. 6 (data not shown). The effect of canopy density on photo-inhibition was even more pronounced in isolated plants, with nearly a two-fold increase in photoinhibitory reduction from dense to open crowns (approx. 6 and 11%, respectively, data not shown).

Figure 7 illustrates that for a given LAI of 3 the photo-inhibitory reduction depends on the foliage orientation. Overall photoinhibition is lower in a canopy with vertical leaf orientation compared to horizontal leaf orientation, although the differences between these simulations with mild photoinhibition were not high (5·5 versus 6·2% total canopy reduction, respectively). Total daily light interception of the plant was reduced by vertical leaf orientation (solid line in Fig. 7). Although photoinhibition effects decreased in the upper canopy layer with steeper leaf angles, the reverse pattern was observed in the lower layers, as a consequence of increased light penetration into these layers.


Figure 7. Simulated reduction in daily photosynthetic carbon gain by photoinhibition in the crown of an isolated shrub plant with a LAI of 3 as a function of different leaf angles (0° = horizontal, 90° = vertical leaf orientation). Reductions are expressed as percentage of loss in whole-plant carbon gain in each layer (layer 1 = top; layer 5 = bottom; see Fig. 6). The continuous line represents the total integrated daily PPFD intercepted by the whole plant. All simulations were performed as in Fig. 6.

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Photoinhibitory reduction in carbon gain in Quercus coccifera

In the measured Q. coccifera shrub (Fig. 8c), mild photoinhibition resulted in an overall reduction of 6·1% of potential daily carbon gain. An analysis of the relative reduction at different canopy subsections (Fig. 8a) revealed that the highest photoinhibitory reduction occurred in the uppermost canopy layer and in the outer, sunlit crown (7·5–8·5%). Due to the dense leaf layers in the upper crown, this reduction declined rapidly with canopy depth. Shade leaves at the inner crown had only approx. 3% loss in carbon gain. Figure 8(b) shows the distribution of the photoinhibitory loss relative to total plant carbon gain. The bar width presents the contribution of the different layers to the overall plant carbon gain. The highest reduction was found in the upper, mostly sunlit layers which contributed the largest portion of carbon assimilation to total plant carbon gain, while the contribution of the shade leaves at the inner lower layers was rather small. This pattern was similar, even in simulations without consideration of different leaf physiology due to light acclimation (data not shown). Shade leaf differentiation was important to assure a positive carbon balance under low light conditions (e.g. in the inner canopy), but had little influence on whole-plant photoinhibitory reduction because these leaves were only slightly photoinhibited. Furthermore, in the case of Q. coccifera these leaves contributed little to the overall carbon gain, and 3% reduction in shade leaf assimilation (Fig. 8a) is negligible relative to their contribution to whole-plant carbon gain (Fig. 8b).


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The model CANO-PI was developed to assess photo-inhibition effects using diurnal courses of Fv/Fm which were simulated solely from a microclimatic parameter (incident light). The best predictor of Fv/Fm was the cumulative light dose, integrated and equally weighted over several preceding hours. This indicates that photoinhibition is dependent on the combined effect of light intensity and duration of exposure as proposed by Ögren & Sjöström (1990).

While Ögren & Sjöström (1990) found a curvilinear relationship between the afternoon reduction of Fv/Fm relative to morning values and the weighted light dose, we found a good linear fit for data based on field-measured diurnal courses of Fv/Fm and the corresponding light dose (Fig. 3). A linear relation between the linearly weighted light dose and inhibition in Fv/Fm was also reported by Valladares & Pearcy (1999). However, our correlation was not improved by linearly weighting the light measurements (Table 3, IV). This may be explained by the fact, that our relationship is based on diurnal light measurements and therefore an integration with equal weights over the course of the day (i.e. a moving average) results in a diurnal increase and decrease in light dose due to the course of the sun. Considering that our relationship was established from field measurements, the linear correlation (r2 = 0·96) was very good.

The effect of photoinhibition is dependent on the capacity of the leaf to utilize the incident PPFD which is described by the shape of the light-response curve. Sensitivity analysis revealed that the shaping parameters Φ and θ determined the responsiveness of a plant to photoinhibition: a relative photoinhibitory reduction in Φ had a lower effect on carbon assimilation in a plant with a high quantum use efficiency (high initial Φ), whereas it can have a pronounced effect if the quantum use efficiency is already low (see Fig. 2). Therefore, any stress effects which causes a decline in quantum use efficiency, should increase the susceptibility of plants to photoinhibition.

In the case of Q. coccifera the best linear correlation was found by integrating over a 6 h time period. Similar linear correlations were found for a variety of Mediterranean species under several environmental conditions (data not shown), but the integrated time period differed among species. The time period used in this correlation should relate to the sensitivity of a particular species to photo-inhibition and the velocity of recovery, which is dependent on photoprotective mechanisms and repair processes, and may be species specific. Additional environmental stresses (e.g. high temperature, water stress) make plants more vulnerable to photoinhibition, and might influence the extent of decline in Fv/Fm as well as the recovery time. However, our model uses a single-factorial relationship to predict changes in Fv/Fm from one microclimatic variable, where the light environment seemed to be the most appropriate parameter. Residual analysis did not indicate further correlations with additional factors. A single-factor relationship has the advantage to avoid additional complexities in model structure with the already implemented effects of temperature, humidity or plant water status on net photosynthesis.

The correlation of the weighted light dose and Fv/Fm might change whenever species show any adaptation which influences their susceptibility to photoinhibition. These changes can be either of physiological nature (changes in xanthophyll cycle, higher repair rate, changes in photosynthetic capacity, etc.) or structural regulation of light interception (e.g. changes in pubescence, reflectance or leaf orientation). However, once this empirical linear relationship is established (from diurnal courses of Fv/Fm and corresponding incident light values on the leaves), simple measurements of predawn and minimum Fv/Fm are sufficient to obtain a function which realistically describes the diurnal course of photoinhibition.

This model is not mechanistic in the sense that photo-inhibition is linked to the underlying biochemical processes, such as degradation of the D1 protein, loss of functional PS II reaction centres, or non-radiative dissipation mechanisms in the antenna. There is an ongoing controversy as to what extent a reduction in Fv/Fm represents reversible photoprotection through harmless dissipation of excess radiation energy, or a damaging process at the PS II reaction centre, repair of which involves turnover of the D1 protein (Bilger et al. 1995). Inactivation of PS II may also provide photoprotection (Krause 1988). However, all these processes result in a deflection of light energy away from photosynthetic energy conversion. The model estimates the loss in potential carbon gain resulting from this photoinhibitory decline in quantum use efficiency, independent of the underlying processes.

Osmond & Grace (1995) suggested separating dynamic (short-term) and chronic (long-term) photoinhibition. The latter is characterized by a slow reversible depression in Fv/Fm after prolonged exposure to excessive radiation, which might prevent full recovery to maximum Fv/Fm over extended time periods. Both cases are integrated in the model: the diurnal decline in Fv/Fm is expressed relative to the maximum Fv/Fm which is similar for unstressed C3 leaves (see Björkman & Demmig 1987). Species-specific values can be implemented if measurements are available. Photodamage, a process that occurs when extended exposure to excessive light leads to irreversible photooxidative damage, chlorophyll bleaching, and loss of activity is not integrated in the model. However, changes to model inputs for overall photosynthetic capacity can be made to account for this permanent loss of activity.

The reduction in carbon gain strongly depends on the momentary capability of photosynthetic light utilization. In this study, only conditions resulting in mild photoinhibition were considered. Under additional environmental stresses (e.g. water stress) photoinhibition can be enhanced and may show higher photoinhibitory reduction in whole-plant carbon gain. However, the primary limitation of carbon assimilation can also be due to a stomatal restriction of CO2 uptake due to stomatal closure rather than a photo-inhibitory restriction of efficient light utilization (e.g. Valladares & Pearcy 1997). The extent of reduction in carbon gain will always depend on the prevailing limitations for carbon fixation. Our model provides a means to assess the contributions of each factor to reductions in carbon assimilation.

Ögren & Sjöström (1990) estimated that 10% of the potential carbon gain was lost due to mild photoinhibition on clear days in leaves of a peripheral shoot of a willow canopy. We estimated a slightly smaller reduction in the upper sunlit leaf layer of 7·5–8·5% of Q. coccifera. Some degree of photoinhibition during peak light levels is probably inevitable, especially if a leaf invests in a photosynthetic apparatus that operates optimally at the average, rather than peak light conditions (Ögren 1994).

Our model simulations demonstrate the important role of canopy structure which determines the light penetration and microclimate within the plant canopy and, hence, the extent of photoinhibition. It is well known that an increase in leaf angle can considerably decrease the amount of intercepted light and photoinhibition (Ryel & Beyschlag 1995; Valladares & Pearcy 1997; Werner et al. 1999). However, at the canopy level, a steep leaf orientation also increases the light penetration into lower canopy layers, where increased photoinhibition may offset the higher carbon gain in upper layers (Fig. 7). Quercus coccifera has a rather dense leaf layer in the upper and outer crown where most of the light (approximately 80%, data not shown) is absorbed. Therefore, high photoinhibitory reduction in net photosynthesis was only found in sunlit leaves, with a rapid two-fold decline in the upper 20 cm (Fig. 8a).

Shade leaf differentiation was found to improve carbon balance and water use efficiency in dense Q. coccifera canopies (Meister et al. 1987). However, these effects were most important in dense canopies (LAI 3–8), whereas in open canopies (LAI 2) sun/shade differentiation was not beneficial. LAI at our site ranged from 2 to 4, similar to other sites (Tenhunen et al. 1984; Rambal 1993), and these plants typically developed a dense mono-layer of leaves at the outer crown with only a few shade leaves deep within the canopy (Fig. 8c).

Shade leaf differentiation becomes important in dense canopies to maintain a positive carbon balance in lower leaf layers, but has little influence on overall plant photo-inhibition because: (i) shade leaves receive little sunlight and thus exhibit little photoinhibition, and (ii) shade leaves contribute only a small portion of the overall carbon gain. More important might be the fraction of leaves which grow as sun leaves but are overtopped by new leaves during the next growing season (e.g. layer 5 in Fig. 8b). These leaves still contribute to overall canopy carbon gain, but are protected from severe photoinhibition by the outer sunlit leaves. These examples underline the importance of whole-canopy simulations, since photoinhibition effects obviously vary strongly among different parts of the canopy.

Since the simulations were performed for mild photoinhibition resulting only from high light stress, the overall reduction of 6·1% daily carbon gain for Q. coccifera may represent a lower bound which may increase with additional stress. However, plants may adapt in several ways to conditions of more severe photoinhibition. Werner et al. (1998, 1999) indicated the importance of structural regulation of light interception as well as species specific susceptibility to photoinhibition. Thus, adaptations to environmental conditions may help to compensate the effects of the prevailing limitations for carbon assimilation. However, neglecting photoinhibition in carbon gain estimates can result in a significant overestimation of CO2 uptake. This might be of special relevance for up-scaling studies and estimates of ecosystem fluxes.


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This work is part of the PhD-dissertation of C.W. and was supported by a fellowship of the DAAD to C.W. (HSPII/AUFE D/95/09180) and by NSF grant (partial funding for R.J.R., no. DEB-9807097). We are grateful to G. Oliveira, three anonymous referees and Dr G. Farquhar for constructive comments on the manuscript.


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  • Adams W.W. III & Demmig-Adams B. (1995) The xanthophyll cycle and sustained thermal energy dissipation activity in Vicia minor and Euonymus kiautschovicus in winter. Plant, Cell and Environment 18, 117127.
  • Anten N.P. (1997) Modelling canopy photosynthesis using parameters determined from simple non-destructive measurements. Ecological Research 12, 7788.
  • Ball J.T., Woodrow I.E. & Berry J.A. (1987) A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. Progress in Photosynthesis Research 4, 221224.
  • Ball M.C., Egerton J.G., Leuning R., Cunningham R.B. & Dunne P. (1997) Mircoclimate above grass adversely affects spring growth of seedling snow gum (Eucalyptus pauciflora). Plant, Cell and Environment 20, 155166.
  • Ball M.C., Hodges V.S. & Laughlin G.P. (1991) Cold-induced photoinhibition limits regeneration of snow gum at tree line. Functional Ecology 5, 663668.
  • Beyschlag W. & Ryel R.J. (1998) Leaf/canopy photosynthesis and crop productivity. In Photosynthesis a Comprehensive Treatise (ed. A.S. Raghavendra), pp. 215225. Cambridge University Press, Cambridge, New York, Melbourne.
  • Beyschlag W. & Ryel R.J. (1999) Canopy photosynthesis modelling. In Handbook of Functional Plant Ecology (eds F.I. Pugnaire & F. Valladares), pp. 771804. Marcel Dekker, Inc., New York, Basel.
  • Beyschlag W., Barnes P.W., Ryel R., Caldwell M.M. & Flint S.D. (1990) Plant competition for light analysed with a multispecies canopy model. II. Influence of photosynthetic characteristics on mixtures of wheat and wild oat. Oecologia 82, 374380.
  • Beyschlag W., Ryel R. & Dietsch C. (1994) Shedding of older needle age classes does not necessarily reduce photosynthetic primary production of Norway spruce. Analysis with 3-dimensional canopy photosynthesis model. Trees Structure and Function 9, 5159.
  • Bilger W., Schreiber U. & Bock M. (1995) Determination of the quantum efficiency of photosystem II and of non-photochemical quenching of chlorophyll fluorescence in the field. Oecologia 102, 425432.
  • Björkman O. & Demmig B. (1987) Photon yield of O2 evolution and chlorophyll fluorescence characteristics at 77 K among vascular plants of diverse origins. Planta 170, 489504.
  • Bolhár-Nordenkampf H.R., Hofer M. & Lerchner E.G. (1991) Analysis of light-induced reduction of the photochemical capacity in field-grown plants. Evidence for photoinhibition? Photosynthesis Research 27, 3139.
  • Caldwell M.M., Meister H.P., Tenhunen J.D. & Lange O.L. (1986) Canopy structure, light microclimate and leaf gas exchange of Quercus coccifera L. in a Portuguese macchia: measurements in different canopy layers and simulations with a canopy model. Trees Structure and Function 1, 2541.
  • Cannell M.G.R. & Thornley J.H.M. (1998) Temperature and CO2 responses of leaf and canopy photosynthesis: a clarification using the non-rectangular hyperbola model of photosynthesis. Annals of Botany 82, 883892.DOI: 10.1006/anbo.1998.0777
  • De Pury D.G.G. & Farquhar G.D. (1997) Simple scaling of photosynthesis from leaves to canopies without the errors of big-leaf models. Plant, Cell and Environment 20, 537557.
  • Demmig-Adams B. (1990) Carotenoids and photoprotection in plants: a role for the xanthophyll zeaxanthin. Biochimica et Biophysica Acta 1020, 124.
  • Demmig-Adams B. & Adams W.W. III (1992) Photoprotection and other responses of plants to high light stress. Annual Review of Plant Physiology and Plant Molecular Biology 43, 599626.
  • Demmig-Adams B., Adams W.W., Iiibarker D.H., Logan B.A., Bowling D.R. & Verhoeven A.S. (1996) Using chlorophyll fluorescence to assess the fraction of absorbed light allocated to thermal dissipation of excess excitation. Physiologia Plantarum 98, 253264.
  • Duncan W.G., Loomis R.S., Williams W.A. & Hanau R. (1967) A model for simulating photosynthesis in plant communities. Hilgardia 38, 181205.
  • Evans J.R., Jakobsen I. & Ögren E. (1993) Photosynthetic light-response curves. 2. Gradients of light absorption and photosynthetic capacity. Planta 189, 191200.
  • Farquhar G.D. & Von Caemmerer S. (1982) Modelling of photosynthetic response to environmental conditions. In Physiological Plant Ecology II. Water Relations and Carbon Assimilation (eds O.L. Lange, P.S. Nobel, C.B. Osmond & H. Ziegler), pp. 549587. Springer-Verlag, Berlin, Heidelberg, New York.
  • Farquhar G.D. & Wong S.C. (1984) An empirical model of stomatal conductance. Australian Journal of Plant Physiology 11, 191210.
  • Farquhar G.D., Von Caemmerer S. & Berry J.A. (1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149, 7890.
  • Genty B., Briantais J.-M. & Baker N.R. (1989) The relationship between the quantum yield of photosynthetic electron transport and quenching of chlorophyll fluorescence. Biochimica et Biophysica Acta 990, 8792.
  • Harley P.C. & Tenhunen J.D. (1991) Modelling the photosynthetic response of C3 leaves to environmental factors. In Modelling Crop Photosynthesis – from Biochemistry to Canopy (eds American Society of Agronomy & Crop Science Society of America), pp. 1738. CSSA Special Publishers, Madison, WI.
  • Harley P.C., Tenhunen J.D. & Lange O.L. (1986) Use of an analytical model to study limitations on net photosynthesis in Arbutus unedo under field conditions. Oecologia 70, 393401.
  • Harley P.C., Thomas R.B., Reynolds J.F. & Strain B.R. (1992) Modelling photosynthesis of cotton growth in elevated CO2. Plant, Cell and Environment 15, 271282.
  • Henley W.J., Levavasseur G., Franklin L.A., Osmond C.B. & Ramus J. (1991) Photoacclimation and photoinhibition in Ulva rotundata as influenced by nitrogen availability. Planta 184, 235243.
  • Johnson I.R., Parson A.J. & Ludlow M.M. (1989) Modelling photosynthesis in monocultures and mixtures. Australian Journal of Plant Physiology 16, 501516.
  • Kok B. (1956) On the inhibition of photosynthesis by intense light. Biochimica et Biophysica Acta 21, 234244.
  • Krause G.H. (1988) Photoinhibition of photosynthesis. An evaluation of damaging and protective mechanisms. Physiologia Plantarum 74, 566576.
  • Krause G.H. & Weis E. (1991) Chlorophyll fluorescence and photosynthesis: the basics. Annual Review of Plant Physiology and Plant Molecular Biology 42, 313349.
  • Leverenz J.W. (1994) Factors determining the nature of the light dosage response curve of leaves. In Photoinhibition of Photosynthesis – from Molecular Mechanisms to the Field (eds N.R. Baker & J.R. Bowyer), pp. 239254. Bios Scientific Publishing, Oxford, Amsterdam.
  • Leverenz J.W., Falk S., Pilström C.-M. & Samuelsson G. (1990) The effects of photoinhibition on the photosynthetic light-response curve of green plant cells (Chlamydomonas reinhardtii). Planta 182, 161168.
  • Long S.P., Humphries S. & Falkowski P.G. (1994) Photoinhibition of photosynthesis in nature. Annual Review of Plant Physiology and Plant Molecular Biology 45, 633662.
  • Meister H.P. (1987) Mikroklima, Photosynthese und Transpiration mediterraner Kermeseichen: Entwichklung und Anwendung eines Bestandessimulationsmodells auf der Grundlage ökologischer Messungen im portugiesischen Freiland. PhD Thesis. pp. 1162. University of Würzburg.
  • Meister H.P., Caldwell M.M., Tenhunen J.D. & Lange O.L. (1987) Ecological implications of sun/shade-leaf differentiation in sclerophyllous canopies: assessment by canopy modelling. In Plant Response to Stress. Functional Analysis in Mediterranean Ecosystems (eds J.D. Tenhunen, F.M. Catarino, O.L. Lange & W.C. Oechel), NATO ASI Series, pp. 402411. Springer-Verlag, Berlin, New York, Paris.
  • Monsi M. & Saeki T. (1953) Über den Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung für die Stoffproduktion. Japanese Journal of Botany 14, 2252.
  • Norman J.M. & Campbell G.S. (1989) Canopy structure. In Plant Physiological Ecology – Field Methods and Instrumentation (eds R.W. Pearcy, J. Ehleringer, H.A. Mooney & P.W. Rundel), pp. 301325. Chapman & Hall, London New York.
  • Ögren E. (1993) Convexity of the photosynthetic light-response curve in relation of intensity and direction of light during growth. Plant Physiology 101, 10131019.
  • Ögren E. (1994) The significance of photoinhibition for photosynthetic productivity. In Photoinhibition of Photosynthesis – from Molecular Mechanisms to the Field (eds N.R. Baker & J.R. Bowyer), pp. 433447. Bios Scientific Publishing, Oxford.
  • Ögren E. & Evans J.R. (1992) Photoinhibition of photosynthesis in situ in six species of Eucalyptus. Australian Journal of Plant Physiology 19, 223232.
  • Ögren E. & Evans J.R. (1993) Photosynthetic light-response curves. I. The influence of CO2 partial pressure and leaf inversion. Planta 189, 182190.
  • Ögren E. & Sjöström M. (1990) Estimation of the effect of photoinhibition on the carbon gain in leaves of a willow canopy. Planta 181, 560567.
  • Ögren E., Öquist G. & Hällgren J.-E. (1984) Photoinhibition of photosynthesis in Lemna gibba as induced by interaction between light and Temperature. I. Photosynthesis in vivo. Physiologia Plantarum 62, 181186.
  • Osmond C.B. & Chow W.S. (1988) Ecology of photosynthesis in the sun and shade: summary and prognostications. Australian Journal of Plant Physiology 15, 19.
  • Osmond C.B. & Grace S.C. (1995) Perspective on photoinhibition and photorespiration in the field: quintessential inefficiencies of light and dark reactions of photosynthesis? Journal of Experimental Botany 46, 13511362.
  • Powles S.B. (1984) Photoinhibition of photosynthesis induced by visible light. Annual Review Plant Physiology 35, 1544.
  • Powles S.B. & Critchley C. (1980) Effect of light intensity during growth on photoinhibition of intact attached bean leaflets. Plant Physiology 65, 11811187.
  • Powles S.B., Berry J.A. & Björkman O. (1983) Interactions between light and chilling temperature on the inhibition of photosynthesis in chilling-sensitive plants. Plant, Cell and Environment 6, 117123.
  • Prioul J.L. & Chartier P. (1977) Partitioning of transfer and carboxylation components of intracellular resistance to photosynthetic CO2 fixation: a critical analysis of the methods used. Annals of Botany 41, 789800.
  • Rambal S. (1993) The differential role of mechanisms for drought resistance in a Mediterranean evergreen shrub: a simulation approach. Plant, Cell and Environment 16, 3544.
  • Raven J.A. (1994) The cost of photoinhibition to plant communities. In Photoinhibition of Photosynthesis – from Molecular Mechanisms to the Fields (eds N.R. Baker & J.R. Bowyer), pp. 449464. Bios Scientific Publishing, Oxford.
  • Ryel R.J. & Beyschlag W. (1995) Benefits associated with steep foliage orientation in two tussock grasses of the American Intermountain West. A look at water-use-efficiency and photoinhibition. Flora 190, 251260.
  • Ryel R.J., Barnes P.W., Beyschlag W., Caldwell M.M. & Flint S.D. (1990) Plant competition for light analysed with a multispecies canopy model. I. Model development and influence of enhanced UV-B conditions on photosynthesis in mixed wheat and wild oat canopies. Oecologia 82, 304310.
  • Ryel R.J., Beyschlag W. & Caldwell M.M. (1993) Foliage orientation and carbon gain in two tussock grasses as assessed with a new whole-plant gas-exchange model. Functional Ecology 7, 115124.
  • Schreiber U., Bilger W. & Neubauer C. (1994) Chlorophyll fluorescence as a nonintrusive indicator for rapid assessment of in vivo photosynthesis. In Ecophysiology of Photosynthesis (eds E.-D. Schulze & M.M. Caldwell), pp. 4970. Springer-Verlag, Berlin, Heidelberg, New York.
  • Tenhunen J.D., Harley P.C., Beyschlag W. & Lange O.L. (1987) A model of net photosynthesis for leaves of the sclerophyll Quercus coccifera. In Plant Response to Stress (eds J.D. Tenhunen, F. Catarino, O.L. Lange & W.E. Oechel), pp. 339354. Springer-Verlag, Berlin.
  • Tenhunen J.D., Lange O.L., Harley P.C., Beyschlag W. & Meyer A. (1985) Limitations due to water stress on leaf net photosyn-thesis of Quercus coccifera in the Portuguese evergreen shrub. Oecologia 67, 2330.
  • Tenhunen J.D., Meister H.P., Caldwell M.M. & Lange O.L. (1984) Environmental constraints on productivity of the Mediterranean sclerophyll shrub Quercus coccifera. Options Méditerranéennes 1, 3353.
  • Tenhunen J.D., Sala Serra A., Harley P.C., Dougherty R.L. & Reynolds F.J. (1990) Factors influencing carbon fixation and water use by Mediterranean sclerophyll shrubs during summer drought. Oecologia 82, 381393.
  • Valladares F. & Pearcy R.W. (1997) Interactions between water stress, sun-shade acclimation, heat tolerance and photoinhibition in the sclerophyll Heteromeles arbutifolia. Plant, Cell and Environment 20, 2536.
  • Valladares F. & Pearcy R.W. (1999) The geometry of light interception by shoots of Heteromeles arbutifolia: morphological and physiological consequences for individual leaves. Oecologia 121, 171182.DOI: 10.1007/s004420050919
  • Warren Wilson J. (1960) Inclined point quadrats. New Phytologist 58, 18.
  • Werner C. & Correia O. (1996) Photoinhibition in cork-oak leaves under stress: influence of the bark-stripping on the chlorophyll fluorescence emission in Quercus suber L. Trees 10, 288292.DOI: 10.1007/s004680050035
  • Werner C., Correia O. & Beyschlag W. (1999) Two different strategies of Mediterranean macchia plants to avoid photoinhibitory damage by excessive radiation levels during summer drought. Acta Oecologica 20, 1523.
  • Werner C., Correia O.A., Ryel R.J. & Beyschlag W. (1998) Modelling whole-plant primary production of macchia species: assessing the effects of photoinhibition and foliage orientation. Revista de Biologia 16, 247257.