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Photon Flux Density
Related terms:
Wavelength
Irradiance
Photosynthetically Active Radiation
Photon
Biomass
Chlorophyll
Photosynthesis
Transpiration
Vapour Pressure
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CO2 Elevation and Canopy Development in Stands of Herbaceous Plants
T. Hirose, ... F.A. Bazzaz, in Carbon Dioxide, Populations, and Communities, 1996
II. Light Interception in Mixed Species Stands
Natural plant communities are composed of a variety of species with a broad range of plant heights and abundances. The variation in plant height, and in the placement of leaf area, has important implications for the capture of light (photosynthetic photon flux density, PPFD), the most important energy source for plant growth. Leaves in the upper layer of the canopy overshade the leaves in the lower layer and thus a gradient of light climate develops within a canopy (Monsi and Saeki, 1953). When a plant community is composed of a range of species with different plant heights, a hierarchy of individuals and species can be established in the canopy with respect to the availability of PPFD (Weaver and Clements, 1929; Keddy and Shipley, 1989; Weiner, 1990). Species that are able to grow tall can place their leaves in upper layers of the canopy. Such species intercept greater fractions of available PPFD and dominate in the stand. Shorter, subordinate species occupy lower layers in the canopy and receive smaller fractions of the available PPFD, nevertheless coexisting with taller species. Thus dominant and subordinate species in a plant community can be differentiated along this light gradient (Grime, 1987). What mechanisms are involved in the coexistence of these species in a plant community? Hirose and Werger (1995) presented a model, based on leaf area distribution and the cost and efficiency of light capture, to analyze canopy structure in multispecies communities and applied it to an herbaceous plant community on a floating fen.
A. The Model
Attenuation of PPFD through the canopy is assumed to follow Beer's law (Monsi and Saeki, 1953):
(1)I=I0exp(−KF),
where F is the cumulative leaf area index (LAI) from the top of the canopy, I0 and I are PPFD on a horizontal level above the canopy and within the canopy at depth F, respectively, and K is the coefficient of light extinction. PPFD intercepted by the leaves of species i in the jth layer in the canopy (ϕij) is given by
(2)φij=−ΔIj·(Δfij/ΣiΔfij),
where –ΔIj is the amount of PPFD absorbed in layer j and Δfij is the leaf area of species i in layer j. Since ΔIj/ΣiΔfij = ΔIj/ΔFj and from Eq. (1), ΔIj/ΔFj = − KI0 exp(–KFj), Eq. (2) is rewritten as
(3)φij=KI0exp(−KFj)·Δfij,
where Fj is the cumulative LAI at layer j. Thus ϕij can be determined from K and the distribution of leaf area of each species in the canopy. Total PPFD absorbed by species i (Φ) is given by
(4)Φ=Σjφij.
Because photons are intercepted by leaves, a positive correlation is expected between photon absorption and leaf area. A power equation is fitted to the relationship between total photon absorption (Φ) and leaf area (A):
(5)Φ=aAb,
where Φ and A are defined for each species in a stand and a and b are positive constants. To achieve high photon absorption (Φ), plants need not only to develop a large leaf area, but also have to place their leaves at relatively higher positions in the canopy, or in more open locations to avoid direct shading from above; such plants may invest a large fraction of biomass in supporting tissues such as stems, petioles, or heavier leaf venation. Then we expect a positive correlation between Φ and the aboveground biomass (M) as well:
(6)Φ=cMd,
where c and d are positive constants. Dividing both sides of Eq. (5) by A gives
(7)Φarea=Φ/A=αAb−1.
Φarea is the photon flux absorbed per unit leaf area which is defined for each species. Likewise, dividing both sides of Eq. (6) by M gives
(8)Φmass=Φ/M=cMd−1.
Φmass is the photon flux absorbed per unit aboveground biomass and defined for each species. If M is considered as the investment cost to absorb photons, Φ is the benefit gained for that investment. Then Φmass as a ratio of the benefit to the cost indicates an efficiency of aboveground biomass use to absorb photons. The following relationship holds between Φmass and Φarea:
(9)Φmass=ALAR·Φarea,
where ALAR (aboveground leaf area ratio) is the ratio of leaf area per unit amount of aboveground dry mass (not total dry mass as in conventional growth analysis). ALAR is further analyzed as:
(10)ALAR=ALAR·SLA,
where ALMR (aboveground leaf mass ratio) is the ratio of leaf dry mass to the aboveground dry mass and SLA (specific leaf area) is the leaf area per unit leaf dry mass.
Hirose and Werger (1995) hypothesized that tall dominant species have higher Φarea than shorter subordinate species because the former develops their foliage in the upper layers of the canopy. They further hypothesized that Φmass of the tall dominant species is not necessarily higher than that of short subordinate species because the former should invest more biomass to supporting tissues.
B. Partitioning of Photons among Species in a Plant Community
The above hypothesis was tested in a tall herbaceous plant community (Thelypterido-Phragmitetum) on a floating fen at the time of peak standing crop (Hirose and Werger, 1995). There were 11 species coexisting in an area of 0.5 × 1 m. Total aboveground standing dry mass was 407 g/m2. Three taller dominant species, Phragmites australis, Calamagrostis canescens, and Carex acutiformis, accounted for 94.6% in dry mass and 8 subordinate species for the rest of 5.4%. The green LAI was 3.42, of which the 3 tall dominant species accounted for 93.4% and 8 subordinate species for the rest of 6.6%. Of incident PPFD, 77.5% was intercepted by the photosynthetic tissue of the canopy and 8.0% by the dead leaves. The rest (14.5%) reached ground level. The 3 dominant species intercepted 75% of the incident PPFD and the 8 subordinate together 2.5%.
Power equations fitted to the relationships between photon absorption (Φ) and leaf area (A) over 11 species and between photon absorption (Φ) and total aboveground biomass (M) were: Φ = 0.40 A1.19 (r2 = 0.988) and Φ = 0.74 M0.94 (r2 = 0.968). Photon absorption increased more than proportionately with increasing leaf area (b > 1) and less than proportionately with increasing biomass (d < 1, though not significant). Dividing both sides of these two equations by A and M, respectively, gave:
Φarea=0.40 A0.19Φarea=0.74 M0.06.
Φarea increased significantly with increasing A (P < 0.01; Fig. la), while Φarea tended to decrease with M (not significant; P > 0.1; Fig. lb). The amount of PPFD absorbed per unit leaf area (Φarea) was large in tall, dominant species high in the canopy, whereas the amount of photons absorbed per unit aboveground mass (Φmass) was not higher in those species. Φmass is a product of ALAR and Φarea (Eq. 9). There was a trade-off relationship between ALAR and Φarea, leading to relatively constant values of Φmass. Similar tradeoffs were reported by Givnish (1982), who showed that taller species, which invest more resources in supporting tissues to remain mechanically stable, display lower proportional allocation to foliage. To obtain a high photon flux per unit leaf area, plants should place their leaves at higher positions in the canopy. Such plants have to invest a large fraction of biomass in supporting tissues. Tall species appeared to have an advantage over subordinate species in receiving a large fraction of incident PPFD, whereas subordinate species have an advantage in efficiently using their biomass to capture PPFD. Both ALMR and SLA contributed to larger ALAR (see Eq. 10) of subordinate species, though the contribution of SLA was much larger. Light use efficiency (photosynthetic return per unit amount of absorbed PPFD) depends both on species and on the level of PPFD absorbed (Björkman, 1982). If higher light use efficiencies at lower levels of PPFD are taken into account, the efficiency of biomass use for dry mass production is even higher in subordinate species. However, we may hypothesize that species maintaining a certain level of Φmass is a necessary condition for their coexistence in a plant community.
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Figure 1. Relationship (a) between photon absorption per unit leaf area (ordinate) and leaf area (abscissa) and (b) between photon absorption per unit aboveground dry mass (ordinate) and aboveground dry mass (abscissa) for 11 species in the canopy of the Thelypterido-Phragmitetum, Both axes are in relative values (total lead area, 100; total aboveground dry mass, 100, and total photon absorption, 100).
(Redrawn from Hirose and Werger, 1995, with permission).
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Physiological Ecology of Forest Production
Joe Landsberg, Peter Sands, in Terrestrial Ecology, 2011
3.2.1 Stomatal Response to Irradiance
Stomatal responses to irradiance (photon flux density) are driven by photochemical processes, interacting with leaf–air vapour pressure difference, temperature and leaf water status. Many of the earlier studies on stomatal conductance, particularly those based on field measurements with porometers (e.g. Jarvis 1976; Watts et al. 1976) showed considerable scatter because of these interactions, but the relationship with irradiance was unequivocally established by many laboratory studies (see, for example Warrit et al. 1980) to be hyperbolic. Warrit et al. fitted the equation
(3.18)gS=gmax(1+β/φP),
where gmax is conductance under high light levels, φP (μmol m− 2 s− 1) denotes photon flux density incident on the leaf and β (μmol m− 2 s− 1) indicates the sensitivity of gS to φP and is the value of φP at which gS = gmax/2. Values of β for apple leaves varied through the growing season and were in the range 50–90 μmol m− 2 s− 1, while gS generally reached the gmax values reported in the experiments at φP ≈ 400 μmol m− 2 s− 1.
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Measurement of light penetration in relation to seagrass
Timothy J.B. Carruthers, ... Keiko Aioi, in Global Seagrass Research Methods, 2001
19.5.7 Discussion
Measuring instantaneous light with a PPFD sensor has a moderate hardware cost but with some care will provide excellent measures of either direct or diffuse attenuation coefficient. This method is widely used for monitoring as well as direct comparison between sites. Instantaneous light meters can be used in a 5-10 second integration mode so that sun flecks within the water column are integrated. The only limitation of this method is that at low solar angles (high latitude or early and late in the day) attenuation coefficients will be overestimated as the light passes on an oblique angle to the sensor, so for accurate results use this method within 2 hrs of solar noon.
Attenuation coefficient will continue to be a useful and informative parameter of water quality in relation to seagrass occurrence and survival. Therefore, there will continue to be an important role for instantaneous light meters in monitoring, surveys, as well as broad scale ecological questions related to seagrass meadows.
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Cultivation of Algae in Photobioreactors for Biodiesel Production
J. Pruvost, in Biofuels, 2011
2.2 Characterization of the Incident PFD
The light energy received by the cultivation system is represented by the hemispherical incident light flux density q, or photon flux density (PFD) as it is commonly termed in microalgae studies. For any light source, the PFD has to be expressed in the range of PAR, in most cases in the 0.4-0.7 μm bandwidth. For example, the whole solar spectrum at ground level covers the range 0.26-3 μm. The PAR range thus corresponds to almost 43% of the full solar energy spectrum.
As light is converted inside the culture volume, it is also necessary to add to PFD determination a rigorous treatment of radiative transfer inside the culture. This enables us, for example, to couple the resulting irradiance field with photosynthetic conversion of the algal suspension to simulate light-limited growth. However, this determination requires certain information. In addition to the PFD value, light source positioning with respect to the optical transparent surface of the cultivation system is important, as light penetration inside a turbid medium is affected by the incident polar angle θ of the radiation on the illuminated surface (Figure 2). Ideally, beam and diffuse components of radiation should be considered separately. By definition, the direction of a beam of radiation, which represents direct radiation received from the light source, will define the incident polar angle θ with the illuminated surface. By contrast, diffuse radiation cannot be defined by a single incident angle, but has an angular distribution over the illuminated surface (on a 2π solid angle for a plane). We note that isotropic angular distribution is usually assumed, although an anisotropic distribution should ideally be considered because of the dependency of radiative transfer inside the culture volume on the angular nature of incident diffuse PFD. Both the incident angle and the degree of collimation of the light flux can be difficult to characterize. However, in most artificial light cultivation systems, normal incidence is usually chosen as the most effective way to transfer light into the culture volume (less reflection on optical surfaces and better light penetration in the culture bulk). The PFD can also in most cases be assumed to be quasicollimated (so we can consider the PFD as beam radiation only). However, these characteristics cannot be assumed in solar technology. The sun's displacement makes the incident angle time dependent and so non-normal incidence conditions will be encountered. Sunlight can also present a large proportion of diffuse radiation due to scattering through the atmosphere or by reflection from various surfaces, such as the ground. A detailed description of the respective consequences of neglecting incidence angle and direct/diffuse distribution effects in solar cultivation systems was recently published (Pruvost et al., in press). It was shown that each assumption led to an overestimation of 10-20% in biomass productivity. When the two assumptions were combined (the simplest case of radiative transfer representation), an overestimation of up to 50% was obtained, emphasizing the relevance of an accurate consideration of the incident angle and direct/diffuse distribution in the radiative transfer modeling when applied to the solar case.
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Figure 2. Solar radiation on a microalgal cultivation system: incident angle and diffuse-beam radiations (left), evolution of solar sky path during the year in France (right).
The PFD can be measured using a cosine quantum sensor (LI-190-SA, LI-COR, Lincoln, NE) with multipoint measurements to obtain an average over the illuminated surface (Janssen et al., 2000b; Pottier et al., 2005; Sanchez Miron et al., 2003). The accuracy will closely depend on the average procedure, especially if the PFD is unevenly distributed. Actinometry could also be used for accurate characterization, as this is sensitive to all photons absorbed in the reaction volume. A detailed example of the experimental procedure in artificial light can be found in Pottier et al. (2005). In the case of sunlight, measurement is obviously also possible, but mathematical relations are also available to determine radiation conditions on a collecting surface as a function of the Earth's location, year period, and surface geometry (Duffie and Beckman, 2006). An example was recently given by Sierra et al. (2008) for a solar photobioreactor. Some commercial software packages integrating solar models are also available (METEONORM 6.0 software; www.meteonorm.com). These allow easy determination of irradiation conditions on a given surface. Such an approach is thus of particular interest in the case of solar production and was applied in Pruvost et al. (in press).
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Mass Production of Marine Macroalgae
R. Pereira, C. Yarish, in Encyclopedia of Ecology, 2008
Control of conchospore formation and release
Conchospore formation and release usually requires a particular combination of conditions such as nutrient availability, temperature, photoperiod and photon flux density, depending on the species. Conchospore release is promoted by stirring, using compressed air bubbling, or by treating cultures with lower temperature seawater (18 °C from 20–22 °C). For the latter treatment, conchocelis-bearing shells are transferred to lower temperature seawater tanks 5–7 days before seeding. Replacing the seawater in conchocelis culture tanks and adding vitamin B-12 can also promote conchospore release. To inhibit conchospore release, conchocelis tanks may be covered by black vinyl sheets and the culture seawater maintained calm with little, if any, aeration.
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Effects of Light
Walter Hill, in Algal Ecology, 1996
D. Saturation
Despite the varied light regimes of benthic algae, most P–I studies indicate that photosaturation occurs in a relatively narrow range of PFDs, from 100 to 400 (μmol m−2 s−1 Saturation irradiances are often well beyond the typical irradiances found in situ, implying that in situ photosynthesis is very strongly light-limited. For example, photosynthesis by attached algae in heavily shaded forest streams saturates between 100 and 200 (μmol m−2 s−1, yet maximum irradiances during summer (when shade is greatest) rarely exceed 30 μmol m−2 s−1 (Hill et al., 1995). The relatively high saturation intensities are somewhat puzzling, given the phylogenetic and/or ontogenetic flexibility other microalgae exhibit in adapting to dark habitats. Microalgae living under the ice in the Arctic and Antarctic exhibit saturation at less than 10 μmol m−2 s−1 (Cota, 1985; Palmisano et al., 1985). The photosynthetic machinery of the freshwater species studied to date may be geared to harness higher irradiances that occur infrequently (e.g., sunflecks) or seasonally (e.g., winter and spring maxima for streams shaded by deciduous trees). Further work in consistently dark freshwater habitats such as lake benthos may reveal saturation values under 50 μmol m−2 s−1.
Saturation is not apparent in the results of all freshwater benthic P–I studies. Kelly et al. (1974) reported that photosynthesis in an open stream was a linear function of light intensity, even at very high intensities. They suggest that nonlinear P–I curves result from nutrient depletion or other container effects. However, other open-stream P–I responses show typical nonlinear curves (Erich Marzolf, unpublished data). It is difficult to give much credence to linear P–I relationships, given the tremendous volume of literature reporting photosaturation in C3 plants and algae, but two other benthic algal P–I studies also reported linear relationships between light and photosynthesis (Dodds, 1992; Wootton and Power, 1993). However, the data in both of these studies were variable enough that nonlinear functions could also be fit to the data.
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Mass Cultivation of Freshwater Microalgae
J. Masojídek, G. Torzillo, in Encyclopedia of Ecology, 2008
Light
Light is the most important factor for microalgal growth. The amount of photon energy received by each cell is a combination of several factors: photon flux density, cell density, length of optical path (thickness of culture layer), and rate of mixing. The light capture by photosynthetic pigments is roughly 10 times higher under full sunlight (2000 μmol photons m−2s−1) than that required to saturate growth. In other words, up to 90% of the photons captured in full sunlight by chlorophyll and other pigments are not being used for photosynthesis and instead must be dissipated as heat and fluorescence. Consequently, the efficiency of light utilization usually drops from a theoretical value of 20% (based on photosynthetically active irradiance) to lower than 4%, roughly corresponding to an annual biomass yield of about 40 t ha−1.
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Mass Cultivation of Freshwater Microalgae☆
J. Masojídek, G. Torzillo, in Reference Module in Earth Systems and Environmental Sciences, 2014
Light
Light is the most important factor for microalgal growth. The amount of photon energy received by each cell is a combination of several factors: photon flux density, cell density, length of optical path (thickness of culture layer), and rate of mixing. The ambient light maxima available for photosynthetic antennae represents an intensity roughly ten times higher (about 2000 μmol photons m− 2 s− 1) than that required to saturate growth. In other words, we have to adjust the optimum culture density for an optimal light regime and growth – otherwise as much as 90% of the photons captured by the photosynthetic antennae may be dissipated as heat. Therefore, the efficiency of light utilization usually drops from a theoretical value of about 20% (based on photosynthetically active irradiance, PAR) to 2–3%, roughly corresponding to an annual biomass yield of about 40–60 metric tons per hectare at the latitude of Central Europe and assuming a mean solar irradiance of 18 MJ m− 2 days− 1 for about 210 days of cultivation. Different ways for reducing the light saturation effect has been proposed to: (i) increase the population density and mixing rate of the cultures; (ii) use special designs of photobioreactors; and (iii) select suitable strains. One way to reduce the 'saturation effect' of photosynthesis is to achieve 'light dilution'. This situation can be accomplished by increasing the cross-section of the photobioreactor, i.e. increasing the illuminated surface of the reactor with respect to the ground area it occupies (see Figure 3(e) and 3(f)). Another important aspect is that the light–dark cycles of cells facilitated by culture turbulence must be fast, i.e. close to the turnover of the photosynthetic apparatus, in order to secure a 'flashing light effect' in the range of tens to hundreds of milliseconds (Zarmi et al., 2013). Various sophisticated photobioreactors for maintaining cells in an ordered light–dark cycle have been designed (Zittelli et al., 2013).
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Carbon Balance of Forests
J.J. Landsberg, S.T. Gower, in Applications of Physiological Ecology to Forest Management, 1997
I Leaf Photosynthesis
Photosynthesis comprises light and dark reactions that involve the removal of electrons from water—resulting in the release of O2—and donation of these electrons to CO2, leading to reduced carbon compounds (CH2O) with a gain in free energy. The process takes place in the chloroplasts. The overall process may be written
H2O+CO2+energy→O2+(CH2O).
The primary photochemical processes take place when light energy is absorbed by the photosynthetic pigments, which raises the energy level of the light-harvesting chlorophyll molecules to an excited state. A specialized chlorophyll molecule donates electrons to electron carriers. The electrons flow down the transport chain and their energy is used to generate adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADPH2). The photophysical and photochemical light reactions proceed at a rate that depends only on the wavelength and light intensity. These reactions are not affected by temperature or CO2 concentration. In contrast, electron transport is strongly dependent on temperature because it occurs through the chemical reactions of molecules bound to the chloroplast membranes.
The dark reactions use the energy (ATP) and reducing power (NADPH2) produced by the light reactions to reduce CO2 to carbohydrate (CH2O). The acceptor of CO2 is ribulose-1,5-bisphosphate (RuBP), the reaction being catalyzed by the enzyme RuBP carboxylase-oxygenase (Rubisco). The first carbon reduction product in most trees is a 3-carbon (C3) compound, 3-phosphoglyceric acid, reduced by ATP and NADPH2, which further metabolizes to form sugars. The RuBP is regenerated in the Calvin-Benson cycle. [There is a large and important group of plants—including some trees—in which the first carbon reduction product is a C4 compound. However, these will not be considered in this book; readers interested in this alternative biochemical pathway of CO2 assimilation are referred to Salisbury and Ross (1992).] RuBP carboxy lase constitutes a major fraction of leaf protein, but because it has a relatively low affinity for CO2 and is competitively inhibited by oxygen, it has been implicated as a factor that limits the rate of photosynthesis.
The relationship between photosynthesis (equated with CO2 assimilation rate A) and the intercellular concentrations of CO2 (ci) takes the form of an asymptotic curve (Fig. 5.2) that has been designated the "demand function," whereas the line connecting the ambient CO2 concentration ca to A is the "supply function." The slope of the supply function line is —gs [Eq. (5.8)] and the downward projection from the point of intersection of the demand and supply functions to the ci axis gives the value of ci. The regeneration of RuBP appears to be dependent on the partial pressure of CO2 at the carboxylation sites (p(CO2)). If p(CO2) is low, CO2 assimilation is not limited by the amount of the enzyme (Ru-bisco). As p(CO2) increases, electron transport reactions, and therefore the capacity to regenerate RuBP, become limiting. The linear portion of the curve has been designated RuBP saturated (Farquhar and Sharkey, 1982); in this part of the curve there is ample RuBP and Rubisco and any increase in ci results in activation of more enzyme, which increases the rate at which CO2 is fixed. Flowever, if the rate of RuBP carboxylation is increased sufficiently, the capacity to regenerate the substrate becomes limiting, and any further increase in ci does not lead to concomitant increase in A. This suggests that there is some optimum value of gs that will lead to maximum photosynthesis for a particular leaf condition (e.g., nitrogen status).
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Figure 5.2. Hypothetical A-ci curves showing the photosynthetic demand function [Eq. (5.2)] for two photon flux density values (φp = 1500 and 450 pmol m- 2 sec−1) - Supply is constrained by stomatal conductance. The dotted curves are supply constraint functions, determined by vapor pressure deficit at the leaf surface (D); their points of intersection with the demand functions give the equilibrium assimilation rates, where demand for CO2 and supply are in balance. Vertical projection from the intersection points gives the equilibrium value of ci, and the slope of the dark lines connecting these points to the ambient CO2 concentration on the ci axis gives – gs. (see Leuning, 1990, 1995; We are grateful to Dr. Ray Leuning for the diagram).
In recent years, the Farquhar and von Caemmerer (1982) model has become the most widely used as a basis for the analysis of photosynthesis by C3 plants (see, for example, Leuning, 1990, 1995; McMurtrie et al., 1992a; McMurtrie and Wang, 1993; Wullschleger, 1993; Wang and Polglase, 1995). This model gives the net rate of leaf photosynthesis as
(5.1)A=Vc(1−Γ/ci)−Rd
(μmol m −2 sec −1). Γ is the CO2 compensation point in the absence of day respiration, ci is the intercellular concentration of CO2, and Rd is the rate of day respiration. Vc is given by
(5.2)Vc=min(Wj,Wc,Wp),
where Wj, Wc, and Wp are the rates of carboxylation limited by RuBP regeneration, by Rubisco activity, and by triose phosphate utilization, respectively. Limitation by triose phosphate utilization occurs when the utilization of triose phosphates for the production of starch and sucrose does not keep pace with the rate of production of triose phosphates in the Calvin cycle. It appears, from Wullschleger's (1993) data, that this may occur in only a few plants, none of which are trees. Most treatments ignore Wp and we will do so here: There are many uncertainties in the calculation of leaf and canopy photosynthesis that can lead to errors far greater than those caused by neglecting this term.
The RuBP regeneration-limited rate of carboxylation is
(5.3)Wj=J/(4+8Γ/ci),
where J is the potential electron transport rate (μmol m−2 sec −1), calculated from a nonrectangular hyperbola given by
(5.4)ΘJ2−(αPφp+Jmax)J+αpφpJmax=0,
where Θ is a shape coefficient, which takes values between 0 and 1, and αp is the quantum requirement for electron transport; Eq. (5.4) tends to a rectangular hyperbola, as Θ tends to zero, and to a Blackman curve— with a clear transition point at which J = J max—when Θ = 1. The rate of electron transport is calculated as the smaller and positive solution of Eq. (5.4).
The Rubisco-limited rate is
(5.5)Wc=Vcmaxci/(ci+Kc(1+Oi/K∘)),
where Kc and Ko are Michaelis coefficients for CO2 and O2, respectively, and Oi is intercellular O2 concentration. Wullschleger (1993) analyzed A/ci curves in the literature and derived Vcmax and J max values for 109 C3 plant species. He found that the two parameters are strongly (linearly) related, indicating that C3 species preserve a close relationship between the carboxylation and electron transport processes. The values for broad-leaved forest trees were statistically significantly higher than for conifers (see Table 5.1). The parameters αp and Γ are specific to the Rubisco enzyme and can be taken as the same for all C3 species. Values are given in Table 5.1, together with reference values of the Michaelis constants, J max and Vcmax. Г and Rd vary with temperature: Leuning (1990), McMurtrie et al. (1992a), McMurtrie and Wang (1993), and Wang and Polglase (1995) give functional relationships for the temperature dependencies.
Table 5.1. Average Values (± 1 Standard Error, SE) for the Parameters of the Leaf Photosynthesis Equationsa
ParameterMean ± SEUnit of MeasureJmax: broad-leaved temperate104 ± 64μmol mol−1Jmax:evergreen conifers40 ± 32μmol mol−1Vcmax: broad-leaved temperate47 ± 33μmol mol−1Vcmax: evergreen conifers25 ± 12μmol mol−1Kc300μmol mol−1Ko250mmol mol−1Γ42μmol mol−1α0.385μmol mol−1
aThe Jmax and Vcmax values, and estimates of their standard errors, are from Wullschleger (1993). The values of the Michaelis constants, Γ, Oi and α are representative of the values used in a number of publications (see text).
To use Eq. (5.1), (5.3), and (5.5), we need values for ci. The rate of CO2 supply to leaves can be described as a process of diffusion across the boundary layer and stomatal resistances. It can be written
(5.6)A=gs(ca−ci)/P,
where ca is the partial pressure of ambient CO2 concentration (currently about 350 μbar) and P is atmospheric pressure. If ra and rs are the boundary layer and stomatal resistances for water vapor, respectively, then
(5.7)gs=1/(1.37ra+1.6rs).
(The molecular diffusivities for water vapor and CO2 in air are different; therefore, the ra and rs values used to calculate gs for CO2 must be corrected by the ratios of the diffusivities, i.e., by 1.6. The ratio for boundary layer resistances is 1.37 because of the influence of turbulence.) If we assume that ra > > rs (see Chapter 3), then CO2 concentration at the leaf surface (cs) can be equated to ca, and Eqs. (5.6) and (5.7) simplify to
(5.8)A=gs(ca−ci),
There have been many models of stomatal conductance and the factors affecting it; some comment is provided in the following section. The current most complete, and apparently accurate, model is the modified version, developed by Leuning (1990; 1995), of the Ball et al. (1987) equation. Eliminating a constant, and a correction for Γ, which accounts for behavior at low CO2, it can be written
(5.9)gs=a1A/(1+Ds/D∘)cs,
where D1 is the vapor pressure deficit at the leaf surface and a1 and Do are empirical parameters for which Leuning gives a range of values for E. grandis from 20 to 43 for a1 when Do = 350 Pa. Substituting for gs from Eq. (5.8) leads to
(5.10)ci/cs=1−(1+Ds/Do)/a1,
which indicates that the ratio of internal to ambient (leaf surface) CO2 concentrations varies with Ds. The conservative nature of this ratio is consistent with the idea that stomata respond to the environment in such a way that ci is maintained more or less constant (Wong et al., 1979). By the same argument used to equate cs and ca, we can take Ds ≈ D, where D is the atmospheric vapor pressure deficit in the region of the leaf. It follows that, given values for Do and a1—and we note Leuning's warning that there is considerable variation in these—we can estimate ci/cs (≈ ci/ca),and hence ci, for insertion into the photosynthesis equations. We should also note here that this model makes no allowance for the effects of leaf water status and soil water content on stomatal conductance. These are discussed in Chapter 4.
A Stomatal Conductance
Although the model outlined previously [Eqs. (5.9) and (5.10)] provides an (apparently) sound mechanistic description of variations in stomatal conductance in relation to photon flux density, vapor pressure deficit, and ambient CO2 concentrations, it has the disadvantage that an estimate of A is required before estimates of gs can be calculated. It is therefore worth briefly reviewing some more empirical models of stomatal conductance.
Jarvis (1976) presented a model to describe the responses of stomata to environmental variables and applied it to temperate conifers. He used results from controlled environment studies to choose the empirical function that best described the response of stomata to each variable and combined them in a multiplicative model of the form
(5.11)gs=f1(D)⋅f2(φp)⋅f3(ψf)⋅f4(T).
The general forms of the functions used by Jarvis (1976) have been found to be suitable for use with a number of plants other than temperate conifers (see, for example, Whitehead et al., 1981), although the values of the coefficients may vary. The model has been widely used. A similar model was developed by Thorpe et al. (1980). This omits the foliage water potential term (ψf)—because water stress does not become a factor until ψf falls quite low (Landsberg et al., 1976; Beadle et al., 1978)—and the effects of varying CO2 concentrations, which need not be included in empirical models for plants well coupled to the environment. Thorpe et al. expressed their model as a single equation:
(5.12)gs=gref(1−aD)/(1+b/φp),
where a and b are empirical "constants" and gref is a reference conductance. The parameter values may be determined from measurements of stomatal response to φ p at low values of D (e.g., from 0.5 to 1.0 kPa) and responses to D when φ p is not a limiting variable. In both cases, the analysis uses values of gs normalized to the highest observed value, i.e., that value is taken as unity. This greatly reduces the scatter in data. The reference value (gref) is then the value of gs expected when both D and φ p are nonlimiting, i.e., it is the maximum value of gs. Körner et al. (1979) list maximum leaf conductance values for 294 species. For woody species, the values range from 1 to 5 mm sec −1. If we take a = 0.3 kPa−1 and b = 70 μmol m−2 sec−1, then gs = 0 when D = 3 kPa and gs = 0.5 gref when φp = 70 μmol m−2 sec−1. Schulze et al. (1994) summarized stomatal conductance values for major vegetation biomes and demonstrated several useful scaling algorithms, and their theoretical background, for stomatal conductance and water vapor and carbon dioxide fluxes at the canopy level. They reported a strong positive linear correlation between stomatal conductance and leaf nitrogen concentration for 15 major vegetation cover types in the world, although they concluded that the relationship within a vegetation type was relatively conservative. Reich et al. (1992) reported a negative exponential relationship between gs and leaf longevity.
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Plant Ecology
J.C. Hull, in Encyclopedia of Ecology, 2008
Light
Light is the energy resource of plants captured through the process of photosynthesis, but it also affects plants in myriad other ways. The light affecting photosynthesis is expressed as photosynthetic photon flux density (PPFD) as μmol photons m−2 s−1. PPFD at sea level on a bright summer day is approximately 2000μmolm−2s−1. Alternatively, beneath a forest canopy the PPFD may be 5–50μmolm−2s−1. Most plants demonstrate maximum photosynthetic rates with PPFD between 150 and 500μmolm−2s−1. At lower irradiances, light is limiting to photosynthesis and plant growth. Plant species with high irradiance requirements are called sun plants, while those with lower light requirements are shade plants. Sun plants can photosynthesize at greater rates, but are often unable to maintain themselves under low-light environments. Because light is largely directional, competition for light is caused by differences in vertical plant size and horizontal distribution of leaves.
Plants also differ with respect to their tolerance to the periodicity of light. In virtually any canopy environment, some light passes through the canopy relatively unaffected by leaves and branches. This creates a light fleck (or sunfleck) on the surface below it. These light flecks differ considerably in their duration and energy content. In a forest understory the proportion of light received in these light flecks approaches 50% of the total daily irradiance received, but each light fleck lasts only a few seconds. The photosynthetic apparatus of plants requires the prior presence of light to react quickly to a light fleck, a phenomenon called photosynthetic induction. Understory plants have a low irradiance requirement to remain induced, while sun plants require higher light to maintain induction. These differences contribute to the ability of plants to survive in the understory.
Another response to periodicity reflects changes in day length accompanying seasonal changes in temperate regions. For many plants the length of the photoperiod controls flowering. Short-day plants will initiate flowering when day length gets shorter than some critical period. Alternatively, long-day plants will flower when day length exceeds a critical period. This ability to time flowering enables plants to complete the reproductive cycle before some adverse environmental change would limit their activity. In the prairies of North America grasses must initiate flowering early enough to complete their reproductive cycle before the first killing frost. For the same species in the north, flower initiation will occur in June, while in the south flowers are initiated in October. The two populations are ecotypes, and their differences in flowering time are maintained when they are grown together in the same environment. Light period provides a cue to how long the remaining growing season will be.