Tables 1 and 2 give results and all parameters of non-linear statistical estimation from field transpiration measurements of 11 plant species and three functional types, and Fig. 1 plots predicted transpirations by the present stomatal conductance and transpiration model against those observed in the field for the 11 species. The model described the transpiration rates and hence stomata behaviour well with R2 > 70% for all species and functional types. Table 2 indicates that the differences in regression analyses within each functional type are not significant, as the three F statistics are all less than the corresponding critical values at 0·05 confidence level. In other words, species within one functional type can functionally be regarded as one single species. The tests crossing functional types shows that all functional types are significantly different from each other at the 0·05 confidence level, as the F statistics of crossing functional types are larger than their corresponding table values. The observed and predicted transpiration rates (a, b, c) and calculated hourly transpiration rates in a common typical day (d, e, f) for the three functional types were plotted inFig. 2. The difference in magnitudes of transpiration rates between upper three panels (a, b, c) and lower three panels (d, e, f) is because site-specific weather data were used for the non-linear regression fitting (a, b, c), whereas transpiration rates in the bottom three panels were calculated based on a common set of hourly observations on PAR and vapour pressure deficit for a typical day in the wet season in Heshan Meteorological Station. Broken lines were calculated by setting kβg = 0, in order to see the effect of vapour pressure deficit on stomatal conductance. Figure 2 shows that vapour pressure deficit did not affect stomatal conductance of broad-leaf trees and shrubs, but significantly decreased the stomatal conductance of pines so that transpiration were suppressed by approximately five-fold.
Table 1. Result of non-linear regression of transpiration data for 11 species using the present model of stomatal conductance. Units of the parameters are: g0 (mmol m−2 s−1), kαβ(mmol µmol−1), kβg (dimensionless), SS, sum of residual squares (mmol2 m−4 s−2); R2 (%)
|Pinus massoniana||20||175·00||101·70||0·3242||275·45|| 1·5688||82·3|
|Pinus elliottii||20|| 92·73|| 86·04||0. 1861||194·46|| 0·8565||81·9|
|Pinus caribaea||20||426·30||221·10||0·5449||667·29|| 1·2531||79·1|
|Schima wallichii||20||354·14|| 14·11||0. 1798|| 0·00||21·652||92·9|
|Schima superba||20||144·91|| 0·00||0·2480|| 0·00|| 9·6061||97·6|
|Cinnamomum burmani||20||148·18|| 0·00||0·2471|| 0·00|| 6·5948||96·7|
|Cinnamomum camphora||20||290·96||152·17||0. 1943|| 0·00||27·532||89·0|
|Castonopsis hickellii||20||197·63|| 10·92||0·2380|| 0·00||13·842||93·9|
|Evodia lepta||16||115·16|| 32·69||0·2391|| 1·73|| 1·0250||81·5|
|Clerodendron fortunatumm||16||136·61|| 7·33||0·5416|| 2·97|| 2·8483||71·4|
|Dianella ensifolia||16|| 97·65|| 28·78||0·5255|| 22·53|| 1·3436||78·0|
Table 2. Results of non-linear regression of transpiration data for each of the three functional types and for every two functional types. Units of the parameters are the same as Table 1 . The F-statistics to test the significance of differences among species within each functional type and the differences between two functional types, and the corresponding critical value (Fc) values, are provided
|Functional type/ functional type pair||g0-wet||g0-dry||kαβ||kβg||SS||d.f.||R2||F||Fc (5%)|
|Pines||203·04||126·30||0·3338||352·48|| 4·46|| 68||77·7||F6068 = 1.07||1·52|
|Broad-leaf||224·07||26·68||0·2244||0·000||114·6||116||90·4||F100116 = 1.25||1·38|
|Shrubs||110·59||21·34||0·3828||0·378|| 7·82|| 56||71·9||F4856 = 1.28||1·59|
|Pines–broad-leaf|| || || || ||397·9||188||70·3||F1844 = 107.7||2·42|
|Pines–shrubs|| || || || || 29·10||128||46·8||F1244 = 42.46||2·44|
|Shrubs–broad-leaf|| || || || ||135·2||176||89·4||F1724 = 4.489||2·42|
Figure 1. Application of the present model of stomatal conductance and transpiration to 11 plant species in subtropical southern China.
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Figure 2. Application of the present model of stomatal conductance and transpiration to three functional types in subtropical southern China. (a) (b) and (c) show predicted versus observed transpiration rates by fitting the data of three functional types with the model. (d) (e) and (f) show the calculated transpiration rates plotted against time in hours. The differences in transpiration magnitudes between upper and lower panels were because site-specific climate data were used for non-linear regression analysis (upper three panels), whereas weather data for a typical day in the wet season from Heshan Meteorological Station were used to drive the model for three functional types. Broken lines were transpiration rates calculated by setting kβg = 0. Therefore the difference between broken lines and solid lines are the effects of vapour pressure deficit on stomatal conductance expressed as differences in water transpiration.
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The 11 species can be classified into two classes in the light of the dependence of their stomatal conductance and transpiration on vapour pressure deficit. Pines had kβg > 100, whereas kβg values for broad-leaf trees and shrubs were less than 25. A larger kβg means a stronger dependence of stomatal conductance and transpiration on vapour pressure deficit, and an exceedingly large vapour pressure deficit may causes excessive water loss in guard cells and decreases in xylem potential and stomata aperture. Field studies have reported that pine trees showed mid-day depression in transpiration and photosynthesis activities in summer (Yu & Peng 1996; Zhao, Yu & Zeng 1996). Our model attributed this depression to the combination of a possible large vapour pressure deficit and large kβg parameter values. As kβg = 1/(βgz), a large kβg can be the result of either a softer guard cell structure (smaller guard cell elastic modulus), or a smaller soil-to-leaf conductance, or both. In contrast, broad-leaf trees and shrubs did not show the dependence of stomata conductance on vapour pressure deficit (Cai et al. 1995; Zeng et al. 1999a). The possible explanations are because of their larger soil-to-leaf conductance compared with pine trees, or stiffer guard cell structure, or both (see discussion later).
Table 2 shows that broad-leaf trees had smaller kαβ values than other functional types. Note that kαβ = α/β, the parameter is directly proportional to the sensitivity of osmotic potential and inversely proportional to the stiffness of guard cell structure. Thus broad-leaf trees can either have stiffer guard cell walls, or lower osmotic sensitivity to PAR, than other functional types.
Plant capability to resist and to tolerate drought can be visualized by comparing parameters in Table 3, in which the parameters g0m, π0, α, β, and 1/gz for the three functional types, estimated in the light of the average soil water contents/potentials for dry and wet seasons, are given. Although g0m is the possible maximum stomatal conductance at dark with saturated soil water (zero photosynthesis and transpiration), kψ describes the slope of decline of stomatal conductance with soil water stress (negative soil water potential), and partially represents the capability of a functional type to resist incremental drought (or increases in water stress). Pine trees were the most, and broad-leaf trees the least, resistant to increases in soil water stress, leaving shrubs in between.
Table 3. Estimated parameters for three functional types using the present stomatal conductance model
|Functional type||g0m(mmol m−2 s−1)||kψ = 1/β (mmol m−2 s−1 kPa−1)||π0(kPa)||α(kPa µmol−1 m2 s)||1/gz(µmol−1 m2 s kPa)|
Dark osmotic potential π0 was calculated in light of π0 = –g0m/kψ. Parameter π0 is equivalent to the soil water potential at which stomata closure occurs. The parameter should thus reflect the capability of plants to tolerate drought. The actual wilting water potential in daytime may be much lower than this value, since stomatal conductance is strongly affected by photosynthetic activity, the relationship between stomatal conductance and soil water potential is likely to be exponential, especially for the long and narrow-shaped stomata structure of monocotyledon gramineal grasses (Kemp et al. 1997). Nevertheless, we can still use this parameter as an index to compare the drought tolerance of plants (Table 3). Again pine trees showed the highest, but broad-leaf trees the lowest, tolerance to drought, with shrubs in the middle. The great drought tolerance of pine trees and shrubs made them well-known pioneer plants for subtropical ecosystems in southern China (Yu & Peng 1996).
The estimated α and gz in Table 3 indicate that the insensitivity of broad-leaf trees to vapour pressure deficit was largely because of their greater soil-to-leaf conductance (the infinite gz for these species was because of the limited capability of statistical regression to obtain an accurate small value of kβg from field data), since they had the smallest guard cell elastic modulus compared with other functional types. On the other hand, the sensitivity of pines to vapour pressure deficit could be a result of their small soil-to-leaf conductance, as they had the largest guard cell elastic modulus. The lower sensitivity of broad-leaf stomatal conductance to photosynthetic radiation was because of their low sensitivity of osmotic potential to PAR (α), since broad-leaf trees had the lowest guard cell elastic modulus. The lowest sensitivity of guard cell osmotic potential to PAR explains the heiophyte features of these trees (Yu & Peng 1996).
Pertinent observational and anatomical evidence
Parameters α, β, and gz reflect the sensitivity of osmotic potential to variations in PAR, the sensitivity of stomata aperture to changes in guard cell turgor pressure, and the sensitivity of guard cell water potential to variations in soil water stresses. Although we cannot provide direct experimental measurements on these parameters to validate our hypothetic conclusions, the following observational and anatomic evidences are provided here to substantiate the discussion in the previous section.
Parameter β is the overall elastic modulus of guard cell structure, and is determined by the geometric shape of the guard cell structure, the elastic properties of guard cell walls, and the connection with subsidiary cells. Gao, Pitt & Bartsch (1989) measured the bulk modulus of apple and potato parenchyma cells (defined as the amount of turgor pressure per unit volumetric strain) to be 5·3 and 4·2 MPa, respectively. Dong & Zhang (2001) found that the bulk modulus of leaf cells of three desert shrubs in northern China was approximately 20 MPa, a much larger value than those for parenchyma of apple and potato. The bulk modulus reflects the mechanical properties of the cell walls. However, the finite element analysis by Cooke et al. (1976) indicated that a typical stomata opening width increases from 7 to 15 µm when turgor pressure inside guard cells increases from 0 to 700 kPa. If we assume that stomatal conductance is directly proportional to stomata opening, and that stomata openings of 7 and 15 µm approximately correspond to typical stomatal conductance values of 250 and 500 mmol m−2 s−1, respectively, a rough estimate of β can be obtained as 700/(500–250) = 2·8 kPa mmol−1 m2 s, which corresponds to guard cell compliance kψ = 0·357 mmol m−2 s−1 kPa−1. This value is of the same order as those we obtained with our stomatal conductance model. The light sensitivity coefficient α describes the sensitivity of the osmotic potential of guard cells to PAR. Nobel (1983) stated that molar concentration of K+ can increase by more than 0·3 mol L−1 under full sunlight (typical value of 1500 µmol m−2 s−1), which is equivalent to more than 0·3 × 2·437 = 0·731 MPa decrease in osmotic potential. This gives a rough estimate of α > 731/1500 = 0·487 kPa µmol−1 m2 s, again, in the same order of the smallest value in Table 3.
Anatomy of seed plants ( Esau 1977) shows that there were three types of guard cell structure, elliptic-shaped guard cells for dicotyledons, long, narrow-shaped guard cell structure for monocotyledon plants (gramineal grasses), and elliptic-shaped, sunken and suspended guard cell structure with partially lignified cell walls for gymnosperms (conifers). The sunken and suspended guard cell structure of conifer trees make the cells less sensitive to the variation in turgor pressure of subsidiary cells than broad-leaf trees, and lignified cell walls implies that the guard cells deform less with a given increase in turgor pressure. Both of these features imply that the guard cell structure of pines is stiffer than that of broad-leaf trees. Consequently, the only explanation of the large kβg is the smaller soil-to-leaf conductance of pines than broad-leaf trees. If we view soil-to-leaf conductance as xylem conductance and soil-root conductance in series, soil-to-leaf conductance can be small if one of these two (or both) conductance values is small. The anatomy of plant xylem systems ( Esau 1977) also revealed that there are two kinds of tracheid elements in xylem systems of seed plants, imperforated tracheids and end-perforated vessel members. Vessel members conduct water by means of their large perforated holes in the two ends and sometimes side walls, and thus are much more efficient than tracheids which only have small pits in their side walls to provide passages for water. Conifer trees have only tracheids in their xylem systems, thus in general should have much smaller xylem conductance (a major part of soil-to-leaf conductance) than broad-leaf trees which have both vessel members and tracheids in their xylems.