Optimal Control of Gas Exchange during Drought: Empirical Evidence

Transcription

1 Annals of Botany 77: , 1996 Optimal Control of Gas Exchange during Drought: Empirical Evidence FRANK BERNINGER, ANNIKKI MA KELA and PERTTI HARI Department of Forest Ecology, PL 24 (Unioninkatu 4), FIN-14 Uniersity of Helsinki, Finland Received: 13 February 1995 Accepted: 17 November 1995 The optimal regulation model by Ma kela, Berninger and Hari (Annals of Botany 77: , 1996) was applied to data for photosynthesis and transpiration of Scots pine during a 22-d drought period. There was a clear decrease in photosynthesis and transpiration during that period. The agreement between model and photosynthesis data was good. The residuals of photosynthesis were not systematic with respect to temperature, irradiance or water vapour deficit. However, the model initially overestimated transpiration by 5%, although there was a clear linear relationship between measured and estimated values. The results suggest that there was no decrease in photosynthetic capacity during the period, but a decrease in stomatal conductance was responsible for the changes in photosynthesis and transpiration. The observations are similar to results in the literature Annals of Botany Company Key words: Transpiration, photosynthesis, stomatal conductance, drought, Pinus sylestris. INTRODUCTION It has long been recognized that the inter-connection of transpiration and photosynthesis through stomatal conductance may impose a strong selective pressure in evolution. If this is the case, natural selection has favoured plant forms that have developed efficient acclimation mechanisms to drought in order to reduce transpiration relative to their carbon gain (for a summary, see Hall, 1982). The best known acclimation is undoubtedly the decrease in stomatal conductance (Hari and Luukkanen, 1973, 1974; Schulze et al., 1975; Higgins et al., 1987; Dolman, Stewart and Cooper, 1988; Korpilahti, 1988; Rambal, 1993; Granier and Lousteau, 1994). While the physiological mechanisms of the response of stomata to drought are being investigated (e.g. Gollan, Passioura and Munns, 1986; Zhang and Davies, 1989; Davies and Zhang, 1991; Trejo and Davies, 1991; Tardieu and Davies, 1992), a more readily available method for quantifying plant reactions has been provided by an approach, sometimes called teleonomic (Thornley, 1991), which determines the response of the plant by maximizing its chances of survival (Cowan, 1977; Guehl and Aussenac, 1986; Hari et al., 1986; Lloyd, 1991; Berninger and Hari, 1993). This approach is based on the idea that natural selection has favoured forms that are close to optimal behaviour. For stomatal regulation during drought, at least four models incorporating the soil water status have been proposed in this framework (Cowan, 1982; Givnish, 1986; Friend, 1995; Ma kela et al., 1996). A test of the models derived with the optimization method is difficult. This is especially the case if one attempts to devise a test for the underlying assumptions of the optimization method, concerning plant functioning under natural selection. The rationale is that if the assumptions could be tested it would, by deduction, provide a test for the $18. model of optimal regulation also. However, a stringent test of these assumptions appears difficult if not impossible (Parker and Smith, 199). There is another perspective to testing the teleonomic model; to treat the model as a hypothesis arrived at with an intelligent guess, and test this hypothesis against empirical data. Even this method has sometimes turned out to be difficult, as the optimization models have often included non-physical, conceptual variables, such as the cost of water in units of carbon (Cowan, 1977; Hari et al., 1986). As for any model, the prerequisite for testing a teleonomic model is that the variables and parameters are measurable, at least in principle. However, as a result of this test, one only obtains information about whether the actual hypothesis has passed the test, while the underlying assumptions and the justification of the optimization method remain open. In a previous paper, we derived a model of optimal stomatal regulation, during drought, for plants growing under humid temperate or boreal conditions (Ma kela et al., 1996). The model was based on the idea that stomatal regulation functions so as to maximize the expected accumulated photosynthetic production over the drought period. The model assumed that the plant is adapted to its environment with respect to drought, and may have physiological information about the availability of water in the soil. The depletion of soil water through transpiration was included in the model. The results of the model agree with our understanding of stomatal regulation during drought, but a comparison of the model with empirical data was not provided. The objective of this paper is to test this model against empirical measurements. In the following sections, predictions of transpiration and photosynthesis in shoots of Scots pine trees growing in southern Finland are produced in an application of the model by Ma kela et al. (1996). The parameter values for the model are estimated from measured data on photosynthesis and transpiration, 1996 Annals of Botany Company

2 Berninger et al. Empirical Eidence of Gas Exchange during Drought and from climatic information. Model predictions are compared with measured values of transpiration and photosynthesis during a prolonged drought period. MATERIAL AND METHODS The model The model by Ma kela et al. (1996) describes the rates of photosynthesis, A (mol m s ), and transpiration, E (mol m s ), per unit leaf area as functions of irradiance, I (mol m s ), and water vapour mole fraction difference between the leaf and the air, respectively. The latter is obtained as the difference between the water mole fraction, (w i w a ) (mol mol ) between the ambient air and inside the leaf. Additionally, both processes depend on stomatal conductance, g (mol m s ): A(t) g(t) c a (t) f [I(t)] (1) g(t)f[i(t)] E(t) ag(t)[w i (t)w a (t)] (2) Above, c a (mol mol ) is the ambient carbon dioxide concentration and a (mol H O mol CO ) is a physical constant converting the stomatal conductivity of CO to that of water: a has a value of about 16. The function f [I(t)] is a rectangular hyperbola: f [I(t)] αi(t) I(t)γ where α (mol m s ) and γ (mol m s ) are parameters. The stomatal conductance is determined by maximizing the expected photosynthetic production over the dry period, when the probability per unit time of the occurrence of rain is k (d ), and the initially available soil water (normalized per unit leaf area) is W so [mol H O(m foliage area) ]. The consumption of soil water is analysed explicitly as the accumulated transpiration. The resulting stomatal conductance is a function of irradiance, water vapour deficit, and the time elapsed since the last rainfall. It is assumed that there is a maximum stomatal conductance, g (mol m s ), determined by the morphological properties of the leaf, and that physically, stomatal conductance cannot be negative. The following equations describe the optimal stomatal conductance under these constraints: g(t) 2 3 if g (t) g g (t) if g (t) g otherwise where g (t) is defined as: c g (t) a (t) (t)a[w i (t)w a (t)] 1 f [I(t)] (5) and (3) (4) p ekt (6) The coefficient p is a constant of integration determined from the constraint that all water in the soil will be transpired if the dry period lasts until infinity, and it depends, among other factors, on the initial soil water content, W s, and the probability of rain, k. In the solution, the term can be identified with the cost of water of an earlier model which does not include the depletion of soil water explicitly (Hari et al., 1986). Since is dependent on the initial soil water content and time, information about the depletion of the soil water is embedded in it. However, as the actual soil water content is not explicit in, the interpretation of this open strategy, is that the plant is able to measure soil water content and has adapted to the prevailing environment by adjusting close to the value suggested by the optimum solution. An alternative strategy could be that the plant functions according to on-line information about the soil water content. An approximate feedback strategy of this type was worked out (Ma kela et al., 1996), resulting in the following expression for : p W so W s ek(w so W s )/E max (7) where E max is the daily transpiration when W s equals W so [mol (m foliage) d ]. In model testing, both the open and the feedback strategy for will be considered. Field measurements Photosynthesis, transpiration, temperature, irradiance and air water content were measured in the field from one shoot of a 25-year-old tree growing in a stand at the Hyytia la field measuring station in central Finland (61 51 N, E, 15 m above sea level). The dominant height of the stand was approx. 1 m, and the total (all-sided) surface area of the needles was 8 m m. The measurements started in Jun The root system of the tree was covered with a plastic sheet reaching over a total area of 13 m, in order to produce drought. A dry period occurred between 3 and 26 Jul., disturbed by a few small rainfalls only. Prior to the measuring period, the weather was dry, but there was a major rainfall directly before the period (34 mm on 2 Jul.). It was assumed that the plastic sheeting acted as a buffer for the small precipitation, and therefore, this period was chosen for the analysis. It is likely that the sheeting had somewhat reduced the available soil water for the tree analysed even prior to this period. During the period of analysis, however, soil water content was probably heterogenous because the plastic sheeting did not totally exclude stemflow, surface flow and deep seepage. The cuvette was a trap type cuvette, pointing to the zenith (in order to minimize effects of sun angle on light interception). Measurements were done on 1-year-old foliage. The buds were removed prior to measurement, in order to avoid disturbance of the measurements due to new foliage formation. Previous research (Korpilahti, 1988) showed that the photosynthetic properties of 1-year old foliage are constant throughout the growing season. The all-sided total surface area of the foliage of the shoot was 11 m and the cuvette volume 4 m. The photosynthesis, transpiration and stomatal conductance values were calculated from changes in the gas concentration over a 2 s period.

3 Berninger et al. Empirical Eidence of Gas Exchange during Drought 471 Gas exchange was measured with an open gas exchange system: CO and H O were measured with Hartman and Braun gas analysers and converted to mole fractions using standard formulas. Incident irradiation was measured with eight small cosine corrected sensors located among the needles in the cuvette. Air temperature was measured using shielded copper constantane thermocouples. Ventilated trap type cuvettes were used which kept the environmental factors close to the ambient. The air was transported to the gas analysers by heated copper pipes. There was a constant flow of air through the pipes in order to avoid condensation of water. The measurements were done about times per day (a total of 284 readings over 22 d) and the results were automatically recorded. The system is described by Hari et al. (199). After the measurement period the total surface area of the foliage, as well as shoot and foliage mass were measured from the shoot. Leaf area was determined by measuring the length and diameter of a subsample of needles and assuming that all needles were half cylinders. Deried ariables The water vapour mole fraction in the substomatal cavity, w i (t), was calculated from air temperature, assuming saturation of the air in the substomatal cavity and that air temperature equals needle temperature. w a (t) and c a (t) were measured. The photosynthesis measurements yield the net rate of photosynthesis, while the model concerns gross photosynthesis. In order to correct for this, the respiration of the shoot, R (mol CO m) was modelled for all measurements with an irradiance of less then 5 µmol m s as follows: R[L(t)] b 2L(t)/ (8) where L(t) is the air temperature at time t (C) and b (mol m s ) is an empirical parameter. The photosynthesis measurements were then compared with the following quantity, P n (t): P n (t)p(t)r(t) (9) where P(t) is the model prediction for gross photosynthesis at time t [eqns (1) and (5)]. The approximate version of the model [eqn (6)] includes the soil water content (per unit leaf area) as a variable. Since the soil water content was not measured, the values of this variable had to be estimated from the measurements. For soil water content per unit leaf area in the model, W s (t), the following surrogate variable was used: W s (t) W so t T(τ) dτ (1) where T(t) is transpiration rate at the moment t and the initial soil water content, W so, is treated as a parameter. Using this approximation assumes that the share of water available to a shoot is proportional to the leaf area of the shoot. Model testing The hypothesis tested in this study is that the model provides a qualitatively adequate description of transpiration and photosynthesis during the dry period. More specifically, it is required that there exist a set of parameter values of the model, such that model prediction is satisfactorily close to measurement. Furthermore, if a reasonable range of the parameter values can be obtained in an independent assessment, the values providing the best fit should fall within this range. When the model is once fitted to photosynthesis it should be able to describe transpiration, and vice versa, because there are no parameters that are unique for the photosynthesis or transpiration model. The open solution of the model has five parameters: α, γ, p, k, and a. In the feedback version [eqn (7)], W so and E max are added. E max and k were pooled to one parameter (k E ). All parameters were estimated using nonlinear max regression techniques [method DUD in the SAS statistical package (SAS Institute, 1985)]. The measured net rate of photosynthesis and the net rate of transpiration were used as independent variables. The nonlinear model for the net photosynthesis was written in the following form for the exact (or time-dependent) solution [from substitution of eqns (3), (5) and (6) into (1) and the result of this into eqn (9)]: P n (t) c a (t) c a (t)ap ekt[w i (t)w a (t)] αi(t) I(t)γ R(t) (11a) When eqn (7) was used for and the soil water content was estimated as in eqn (12), the following expression was obtained for the feedback solution: P n (t) c a (t) c a (t)ap [w i (t)w a (t)] e k T cum αi(t) I(t)γ R(t) where T cum (t) t T(τ) dτ. E max W so W so T cum (11b) The model was fit to the transpiration model using only the feedback solution: c T(t) a (t)w S p a (W so T cum ) et cum ke max [w i (t)w a (t)] 1 α I(t) I(t)g a[w i (t)w a (t)] (11c) Above, eqn (1) was used for the respiration term, R(t), with the parameter b estimated independently. The parameters α, γ, k, and p were estimated simultaneously for the open solution of the model. In the feedback version, the parameters α, γ, W so, p, and product ke were estimated, max respectively. The value of a was fixed to 16. During the estimations of transpiration the term ke tended to go to max. This seems contradictory to the initial meaning of the parameters. We therefore fixed the value of ke to the max estimate we obtained from the photosynthesis measurements. The proportion of explained varianced decreased only by 2% due to this change.

4 472 Berninger et al. Empirical Eidence of Gas Exchange during Drought Probability Length of the rainless period FIG. 1. The estimated probability ( relative frequency) of dry periods of length greater than or equal to n, as a function of n (d). ( ) Observed values, ( ) best-fit exponential function, e kn, with k 133 (r 998). The threshold value of rainfall required to end the dry period was 5 mm. Finally, for comparisons, an independent estimate for the probability of rain per unit time, k, was calculated from rainfall data during the growing season (1 May 1 Oct.) for 2 years ( ) at Jyva skyla (about 7 km from the field station at a similar altitude and climate). The estimation was based on the definition of the parameter k as the probability of rainfall per unit time, and the assumption that this is independent of time. It follows from this that the probability that a dry period has length greater than or equal to t is e kt (Ma kela et al., 1996). The frequency of dry periods of length greater than or equal to n days is therefore proportional to e kn. An estimate of k can be obtained by computing this distribution from data and fitting it to an exponential curve. Because rainfall is not really an on off 5 TABLE 1. Parameter alues and statistics of the three different model fits for photosynthesis and transpiration. In all cases, the respiration parameter is fixed at b mol m s. n 284. The proportion of explained ariance was defined as 1-SS ERROR SS TOTAL Stomatal conductance Cumulative transpiration FIG. 2. The daily average measured stomatal conductance (mol m s ) as a function of cumulative transpiration. phenomenon, with totally dry periods interrupted by heavy rainfalls sufficient to wet the soil to full capacity, an operational definition of the length of a dry period is required. In this study, precipitation of consecutive days was summed up, and when this reached a threshold value considered sufficient to wet the soil, the dry period was regarded as finished. The value of k depends on the threshold chosen, therefore, three different values were used: 1, 5 and 1 mm. The fitting was done using non-linear regression analysis applying the least squares method (Method DUD, SAS Institute, 1985). RESULTS The Poisson process seemed to be well suited to describe the distribution of rainfall: the value of k was 446 for a threshold of 1 mm (556 mol m ), 133 for a rainfall of at least 5 mm (2778 mol m ) and 31 for a rain of more than 1 mm (5566 mol m ) (Fig. 1). The proportion of 5 Parameter Soil water content dependent model Time dependent model Model fitted to Transpiration data α (mol m s ) γ (µmol m s ) W s [mol (m foliage) ] p (dimensionless) ke max (mol m) (fixed) k (d ) 46 1 RMSE (mol m s ) SS TOTAL Proportion of explained variance

5 Berninger et al. Empirical Eidence of Gas Exchange during Drought 473 explained variance (1SS ERROR SS TOTAL ) was 99 in each case. The estimated value of the respiration parameter, b, [eqn (8)] was 35 1 mol m s. It explained 93% of the variance in the measurements with less than 5 µmol m s irradiance (relative mean error 28%, n 68). There was a clear decrease in the stomatal conductance during the measurement period (Fig. 2). A summary of the fit of the photosynthesis model to the data is presented in Table 1. Judging by the proportion of explained variance (1SS ERROR SS TOTAL ), the fit was good with both methods for determining the cost of water,, although the model based on the soil water content [eqn (11b)] had a slightly smaller root mean square error (RMSE) than the model based on time [eqn (11a)]. The proportion of explained variance was 94 for both models. Fitting the model to transpiration resulted in a slightly lower proportion of explained variance than fitting the model to photosynthesis (91 s. 94 for photosynthesis). The parameter values differed between the models of photosynthesis, but the differences were small (Table 1). However some values of the model fit to the transpiration data differed from the values of the models fit to photosynthesis: µ and p were much smaller than for the models fit to photosynthesis (Table 1). However the model was rather insensitive to changes in a single parameter if the other parameters were allowed to adjust freely. For example for the soil water dependent model all correlation coefficients between ke max, p, and α were above 95 and the asymptotic correlation, between p and W so was above 8. All other correlations in this model were below 7. Because the two models turned out to be equally good in explaining the variance of photosynthesis in the present data set, and since empirical studies attribute the regulation of stomatal conductance to the soil water content or soil water potential rather than the time elapsed since the last rain (Schulze and Hall, 1982), the model dependent on the soil water content was subsequently used in this study. In spite of a good fit to photosynthesis, the estimated transpiration of the model was about twice the measured value. Subsequent analysis showed however, that the measured and estimated values of transpiration and stomatal conductance were closely correlated. If the parameter a was estimated using linear regression without intercept we found that the value of a of 78 explained 93% of the variance of transpiration (RMSE ). The new value of a is, however, outside the physical range (e.g. Lushnikov et al., 1994). Figure 3 depicts the measured and predicted time course of the daily averages of photosynthesis and transpiration over the measurement period, and Fig. 4 shows the respective instantaneous values during sample days at the beginning and at the end of the measurement period. The figures use the adjusted value of a (78) and transpiration estimated from the values of g estimated from the photosynthesis measurements. An analysis of the residuals indicates that the photosynthesis model is not biased with respect to temperature, irradiance, water vapour deficit or irradiance. Slightly systematic trends were observable for the residuals Photosynthesis Transpiration A B Date FIG. 3. The time course of measured ( ) and simulated ( ) daily averages of net photosynthesis (µmol m s ) (A), and transpiration (mmol m s ) (B). Transpiration values are shown after the change of the parameter a. Transpiration values were estimated from the photosynthesis measurements. of transpiration even after the change in a. The daily average residuals were not systematic with respect to time (Fig. 5). The value of increased from 3 to 9 during the time interval. The model indicates a more or less linear decrease of average stomatal conductance with the soil water content (or an increase of the cumulative transpiration, respectively) (Fig. 2). DISCUSSION Unlike empirical models, optimal regulation models encompass different aspects to be tested: the appropriateness of the assumptions made (Parker and Smith, 199), and the 3 3

6 474 Berninger et al. Empirical Eidence of Gas Exchange during Drought 3 A 1.6 B Photosynthesis Transpiration C Date Photosynthesis D Date FIG. 4. The daily course of measured ( ) and simulated ( ) net photosynthesis (µmol m s ) (A, B) and transpiration (mmol m s ) (C, D) during sample days at the beginning (A, C) and at the end (B, D) of the drought period. Values are values after the change of the parameter a. Transpiration values are estimated from the photosynthesis measurements. Transpiration explanatory power of the model. Ma kela et al. (1996) discussed the validity of some of the assumptions of the present model, while this paper focusses on its explanatory power. One should bear in mind, however, that the adequacy of an optimal regulation model is largely based on the validity of the underlying assumptions (Parker and Smith, 199). The validity of these is bound to a specific environment. The model was able to explain most of the variation in photosynthesis. No systematic trend was detected in the residuals of photosynthesis, suggesting that the variation was probably random. However the model overestimated transpiration by a factor of 5. Nevertheless linear regression analysis without intercept revealed close correlations between measured and estimated values of stomatal conductance and transpiration. The model of Ma kela et al., (1996) contains the assumption that photosynthesis is linearly related to substomatal carbon dioxide concentration. The assumption seems necessary in order to be able to formulate the optimal regulation problem in analytical form, whereas nonlinear formulations would lead to a set of numerical equations (e.g. Cowan, 1986). However, it is clear that the assumption of a linear relationship between c i and P is a simplification. For example Caemmerer and Farquhar (1982) showed a saturating relationship between the mesophyl carbon dioxide concentration and photosynthesis. These simplifications are possible causes for the divergence between estimated and measured transpiration. Another

7 Residuals of photosynthesis Berninger et al. Empirical Eidence of Gas Exchange during Drought Date FIG. 5. The time development of the daily average residuals of photosynthesis (µmol m s ) ( ) and transpiration (mmol m s ) ( ). Transpiration values are estimated from the photosynthesis measurements. The values are values after adjustment of the parameter a. possibility is that adsorption of H O in the cuvette or the copper pipes lead to biased measurements of transpiration. Also the estimation of the parameters was rather difficult due to autocorrelation and a large number of local minima of SS ERROR. It is therefore possible that a parameter combination, satisfying both transpiration and photosynthesis measurements can be found. However, such a combination did not occur in the present analysis despite a wide range of initial estimate combinations covered. Another test for the validity of the model is the realism of the estimated parameter values. The value of k in the time dependent model was close to estimated values for a precepitation threshold between 5 and 1 mm. As regards p, there are estimates for different tree species. Lloyd and Farquhar (1994) used a similar stomatal conductance model (Lloyd, 1991) and found a average value of p of 4 1 for temperate conifers, which is reasonably close to the values of 3 1 for Scots pine here. However it is possible that the plant was subject to drought stress already at the beginning of the measurements. The value of W so corresponds to an initial water storage of about 83 mm water, which seems realisitic for an already dry shallow soil. The maximal transpiration E max would be 22 mol m d. This is higher than the values measured which correspond to 43 mol m d, however the weather was rather cold at the beginning of the measurement period and transpiration was therefore low. Korpilahti (1988) who investigated the gas exchange of the same Scots pine stand gave average transpiration values from 269 mol m d to 43 mol m d, which are closer to the estimated value of E max. The model does not account for a possible decrease in the photosynthetic capacity of drought-stressed plants. If this decrease is important, major changes in model structure will be required. Such a decrease should materialize in a residual analysis of the data, because a decrease in the photosynthetic capacity of the foliage should result in a change of the Residuals of transpiration photosynthetic response at certain stomatal conductance: plants with a decreased photosynthetic capacity should either have lower photosynthesis, or higher transpiration than predicted by the model. As a consequence, the residuals of either photosynthesis or transpiration should behave systematically with time. This was not the case in the present data (Fig. 4), suggesting that there is no decrease in photosynthetic capacity or mesophyll conductance. The relationships in the present model are similar to those in other models describing photosynthesis and transpiration in Scots pine (Beadle et al., 1985; Ku ppers and Schulze, 1985; Korpilahti, 1988), other conifers (e.g. Meizsner, 1982; Sandford and Jarvis, 1986) and many other tree and plant species (see Schulze and Hall, 1982 and Shuttleworth, 1989 for summaries). However, a temperature-dependent trend in stomatal conductance has often been incorporated (Shuttleworth, 1989; Aphalo and Jarvis, 1994). In this study, the residuals were not systematic with respect to temperature. A temperature dependence independent of water vapour deficit could not be detected. This is perhaps because the temperature dependence of gross photosynthesis is rather weak in Scots pine (Korpilahti, 1988). Most previous models of stomatal conductance during drought are multiplicative (Dolman et al., 1988; Steward 1988; Shuttleworth, 1989; Granier and Lousteau, 1994). The stomatal behaviour predicted by these models is similar to the present results, in spite of some important conceptual differences. The empirical models are built upon the concept of modifying a maximum stomatal conductance by a number of environmental factors, whereas the optimal regulation model starts off concepts how plants have adapted to their environment. In conclusion, the present study demonstrates that the teleonomic approach provides a feasible tool for analysing the regulation of gas exchange during drought. The model provided a good fit to data, with no detectable trends in the residuals of photosynthesis. However there were problems in predicting transpiration and photosynthesis simultaneously, indicating that there was either a systematic error in the measurements, or a discrepancy in the model structure. The assumption of a linear relationship between the substomatal carbon dioxide concentration and photosynthesis, which is necessary for an analytical solution for the optimization problem, might be this oversimplifying assumption. However, after changing the value of one parameter the model was able to predict transpiration as well. Uncertainty also remains on single parameter estimates because of autocorrelation between parameters. As this result is in accordance with a number of other empirical studies, as well as with the present data, it would seem that the regulation strategies proposed by Ma kela et al. (1996) and tested in this paper might be more widely applicable. ACKNOWLEDGMENTS The authors would like to acknowledge Toivo Pohja whose technical genius made the photosynthesis measurements possible, and Eija Juurola whose ruthless effort kept the measurement system functioning when none of the authors

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