Photosynthesis is pivotal for plant growth as the source of primary production by which plants use light energy to synthesize organic compounds. The net CO₂ assimilation rat is determined by the characteristics of the photosynthetic machinery (including photosynthetic capacity), the rate of CO₂ diffusion to intercellular leaf spaces and the concentration of intercellular CO₂. These are, in turn, influenced by weather and soil conditions (e.g., solar irradiation, temperature and soil water content). As irradiance and temperature reach a maximum at mid-day and humidity declines towards a daily minimum, many plants exhibit the well-documented mid-day depression in photosynthesis. This decrease in photosynthesis can significantly limit plant growth.

Causes of mid-day depression are generally ascribed to either stomatal limitations or non-stomatal limitations (decreased photosynthetic capacity).Guo et al.(1994) also reported that the mid-day depression of photosynthesis in cotton leaves coincided with photoinhibition and increased photorespiration, consistent with the finding of Xu (1988) and Ogren (1988). Guo et al.(1996) later found that photorespiration could alleviate photoinhibition in cotton. Finally, Muraoka et al.(2000) argued that the mid-day depression of photosynthesis in Arisaema heterophyllumwasthe combined effects of diffusional (stomatal) limitation, photoinhibition and enhanced photorespiration.

Stomatal limitation results from stomatal closure, which can be induced by a large leaf-to-air water vapour pressure deficit or low leaf water potential (Hsiao, 1973; Maier-Maercker, 1983; Mott et al., 1991), thus decreasing the CO₂ concentration in the intercellular spaces (Lange et al., 1985; Raschke et al., 1986; Wise et al., 1990). Non-stomatal limitation (e.g., photoinhibition) is often assumed implicitly as a metabolic constraint (Ishida et al., 1999; Ishida et al., 1996) due to the inactivation of photosynthetic reactions associated with photo-system (PS) II (Demmig-Adams et al., 1992; Long et al., 1994; Powles, 1984).

In field environments, limitation of one process of photosynthetic CO₂ assimilation can enhance the limitations of additional processes (Cheeseman et al., 1996; Foyer et al., 1990). Thus, decreased CO₂ concentration in the intercellular spaces induced by stomatal closure at high temperature and high irradiance can enhance the sensitivity of the photosynthetic apparatus to high-light stress and damage the PSII photochemistry (Cornic et al., 1996; Peterson et al., 1988). Water availability is considered the environmental factor that most strongly limits plant CO₂ assimilation world-wide (Nemani et al., 2003), particularly during water stress (Lawlor, 1995). Thus, mid-day depression of photosynthesis during drought is more severe (Ben et al., 1987; Cornic et al., 1989; Quick et al., 1992) than in the absence of drought. It is generally assumed that water stress affects photosynthesis primarily through stomatal closure, rather than a direct effect on the capacity of the photosynthetic apparatus (Cornic, 1994; Jones, 1998; SÁnchez et al., 1999; Tourneux et al., 1995). However, Tezara et al.(1995) found that stomatal control of photosynthesis becomes progressively less effective as water stress intensifies, consistent with the results of Grassi et al.(2005), who found that about half of the decline in light saturated CO₂ assimilation may be attributable to non-stomatal limitations under severe drought conditions. It therefore remains debatable as to whether stomatal closure is more important than non-stomatal limitations in causing mid-day depression in photosynthesis during the progression of water stress (Flexas et al., 2002; Lawlor, 2002; Tezara et al., 1999).

Models of vegetation function are widely used to predict the effects of climate change on carbon, water and nutrient cycles of terrestrial ecosystems (Arnell et al., 2006; Ciais et al., 2007; Ostle et al., 2009; Sitch et al., 2008). Stomatal conductance, the process that governs plant water use and carbon uptake, is fundamental to such models (Lin et al., 2015). Stomatal conductance is linearly correlated with net carbon assimilation rate under steady state conditions (Wong et al., 1979), but when atmospheric CO₂ concentration or relative humidity are varied, this relationship breaks down. Stomatal conductance declines with increasing atmospheric CO₂ concentration, but net carbon assimilation rate increases. When relative humidity decreases, stomatal conductance declines non-linearly but net carbon assimilation rate changes little (Farquhar et al., 1984; Grantz, 1990; Mott et al., 1991). An empirical model was developed by Ball et al.(1987) (hereafter referred to as BWB model) to describe stomatal conductance as a function of biotic and abiotic factors. However stomata respond to evaporative demand or transpiration (Monteith, 1995) rather than to relative humidity perse (Sheriff, 1984) and consequently Leuning (1990) found that using C_s-Г, where C_s is the atmospheric CO₂ concentration, and Гis CO₂ compensation concentration, instead of C_s in the Ball-Berry model give a better fit and Leuning (1995) revised the Ball-Berry model using leaf-to-air water vapour pressure deficit as evaporative demand instead of relative humidity (hereafter referred to as the Leuning model). These two stomatal models are widely used as they are simple to parameterize from leaf-scale data, are easy to implement at large scales and appear to capture the fundamentals of stomatal behaviour. However, there are several important criticisms that can be made of both models (Aphalo et al., 1991; Eamus et al., 2008; Medlyn et al., 2005; Mott et al., 1991). The two major criticisms are that first, they are both empirical (i.e., derived from a large amount of experimental data), which makes them difficult to extrapolate to environmental regimes beyond their original parameterisation and second they have no theoretical basis for predicting or interpreting differences among species and environments (Krinner et al., 2005).

In contrast to these empirical models, there is along-standing theory of optimal stomatal behaviour (Cowan et al., 1977), which postulates that stomata should act to maximize carbon gain (photosynthesis, A_n) while at the same time minimizing water lost (transpiration, E). Based on this theory, Hari et al.(1986) produced the optimal stomatal conductance model. Although several implementations of this optimal model have been attempted (Arneth et al., 2002; Katul et al., 2009; Lloyd, 1991), none has been widely used, principally because the marginal water cost of carbon gain is difficult to estimate but also because previous implementations do not correctly capture stomatal responses to atmospheric CO₂ concentration.Medlyn et al.(2011) reconciled the optimal and empirical models of stomatal conductance and derived a unified model (hereafter referred to as Medlyn model). The benefits of this unified model are that it:1) included a biological interpretation of the model parameters that were previously regarded as empirical constants and 2) provided a powerful quantitative framework for research into the long-term acclimation and adaptation of stomatal function under conditions of global environmental change.

All of the three stomatal conductance models, BWB model, Leuning model, Medlyn model, successfully summarized the observations of stomatal behaviour in well-watered plants. However, soil water is frequently limiting to plant growth. Stomatal models can incorporate the effects of soil moisture on stomatal conductance using an electrical resistance analogy for the transport of water from soil to roots to correctly simulate the patterns in conductance and CO₂ as simulation during drought (Berninger et al., 1996; Op de Beeck et al., 2010; Sala et al., 1996b). Field and laboratory studies of gas exchange show a marked daytime asymmetry, with higher fluxes of water and CO₂ in the morning than in the afternoon after mid-day depression of photosynthesis (Derek et al., 2001; Grant et al., 1999), especially during conditions of low soil water content (Olioso et al., 1996; Prior et al., 1997). That accounts for the effects of supply and demand for CO₂ by photosynthesis and respiration, which affects stomatal conductance through variations in intercellular CO₂ concentration (Assmann, 1999). Whether the models are able to capture the effects of supply and demand for CO₂ is also debateable. Tardieu et al.(1993) and Tuzet et al.(2003) found the stomatal models were not able to capture the observed asymmetry for fluxes of water and CO₂ in the morning and afternoon during periods of water stress.

P.tabulaeformis, an endemic evergreen coniferous species in China, is a key species of coniferous forests in arid, semi-arid and semi-humid regions of China. It is widely used as an afforestation and reforestation tree species in ecological restoration and soil conservation programs (Liu, 2002; Zheng et al., 1978). These P.tabulaeformisforests spread naturally from northeast to north and from central to western regions of China, between east longitude 103°20′ to 124°45′, north latitude 31°00′ to 43°33′, and 100 to 2 600 m, a.s.l, (Ma, 1989; Zheng et al., 1978).The distribution area is up to 1 620 000 hm² (Ma, 1989). Across this range climatic conditions are very different, with average annual rainfall ranging from 400 mm to 1 000 mm, average annual temperature ranging from 1 to 16 ℃ and altitude ranging from 100 to 2 600 m. The principle aim of the work described here is to examine how P. tabulaeformisphotosynthesis responds to variation in soil moisture content.

In this paper, we examined diurnal changes in CO₂ exchange in needles of P. tabulaeformisseedlings grown under different soil water conditions. We hypothesised: 1) in different soil water conditions, the midday depression of photosynthesis in P. tabulaeformisseedlings was consistent; 2) the relative importance of stomatal and non-stomatal limitations on the midday depression of photosynthesis was variable in different soil water conditions; and 3) the different soil water conditions would not impacts the supply and demand for CO₂ on the relationships of CO₂ assimilation and stomatal conductance simulated by three alternative stomatal models.

1 Materials and methods 1.1 Plant materials and experimental treatments

All experiments were conducted at the Xiaotangshan Experiment Station (40°15′N, 116°13′E, and altitude 101 m) of Beijing Forestry University, located in the northern suburbs of Beijing, China. In mid-March 2012, before new leaf emergence, two-year-old P. tabulaeformis seedlings (an average of approximately 18 cm tall, obtained from the Container Tree Seedling Nursery in Luanping County, Heibei Province) were transplanted into plastic cylindrical pots (25 cm diameter×30 cm depth) filled with field soil, with one seedling per pot. Field soil was collected from the Xiaotangshan Experimental Station, and was a mixture of sand and peat (1:1 volume) with medium fertility (pH 8.8, N 19.6 mg·kg^-1, P 4.6 mg·kg^-1, K 135 mg·kg^-1). The soil was air dried and 8 kg of the mixed soil was added to each pot. The potted seedlings were held in the greenhouse and watered every two days to avoid water stress, and were exposed to ambient sunlight, temperature and relative humidity throughout the day.

In late May 2012, 80 healthy and similarly sized P. tabulaeformis seedlings were selected and randomly divided into 4 groups, with 20 seedlings per group. Each group was subjected to one of the four soil water content regimes: 1) soil water content is 8% (W₀), 2) soil water content is 12% (W₁), 3) soil water content is 16% (W₂), and 4) soil water content is 20% (W₃). An additional 20 seedlings were used to determine the average initial dry mass. Soil water treatments began on 15 June 2012, and ended on 25 October 2012. Seedlings grew under each treatment for 130 days. During those days, soil water was monitored by weighting, and watered to supplement water as needed (W₀, 8%; W₁, 12%; W₂, 16%; W₃, 20% soil water content) at 6:00 PM every day. After watered, a thick layer of straw was placed on the pot soil to ensure that the soil moisture content was similar over the course of the day. The experimental layout was surrounded with a single row of border plants to protect the experimental seedlings from external influences, and all subplots and main pots were rotated weekly to provide for random distribution. There were 4 sampling days (sunny day) following treatment initiation.

1.2 Leaf gas exchange and environment measurements (A, g_s, C_i, PPFD, T_leaf and VPD)

Leaf gas exchange was measured in the field on the clear days of 2 July, 23 July, 17 August and 21 September 2012. Three seedlings of P. tabulaeformisfor each soil water treatment were used and three needles measured per tree. For each measurement day, the same seedlings for every soil water treatment were used. All the leaf gas exchange and environmental measurements were conducted every 2 h from 7:00 to 17:00 on each sampling day. Each needle was allowed 5-10 min to equilibrate to chamber conditions, when readings were stable and the coefficient of variation was < 1%.

Leaf gas exchange was measured using a portable open gas exchange system (LI-6400;Li-Cor Inc., Lincoln, Nebraska, USA) equipped with a needle leaf chamber. The clamp-on leaf chamber allowed natural illumination of the upper and lower leaf surface during measurements. Net CO₂ assimilation rate (A), stomatal conductance (g_s), intercellular CO₂ concentration (C_i) and leaf to air vapour pressure deficit (VPD) were determined using simultaneous measurements of CO₂ and H₂O vapour flux, air temperature (T_air) and leaf temperature (T_leaf). The CO₂concentration of the air entering the leaf chamber (C_a) was controlled at 400 mmol·mol^-1. Air temperature in the chamber was adjusted manually to the air temperature outside the system, and relative humidity in the chamber was adjusted to be similar to the ambient humidity. Incident photosynthetic photon flux density (PPFD) on the leaf surface and T_leaf were measured using a chamber-in quantum sensor and a thermocouple, respectively. With C_i and C_a stomatal limitation (L) was calculated according to (Berry et al., 1982).

For each plant, total leaf area was calculated as mean leaf area per leaf × the number of leaves per plant, the number of leaves per plant were counted and the mean leaf area per leaf was calculated as follow(Li et al., 2007):

${\rm{LARL}} = \sum\limits_{i = 1}^n {\left[ {\frac{{(2h + d)}}{4} + d} \right]} l.$

(1)

Where LARL represent mean leaf area per leaf, d(mm) was the mean width of leaf, h(mm) was the mean thickness of leaf, lwas the leaf length (measured by steel tape), nwas the number of leaf samples (in this study, nwas 40 and included 20 old leaves and 20 new leaves). dand hwere the mean values measured by digital vernier caliper (accuracy 0.01 mm) at 1/4, 1/2 and 3/4 length of leaf.

The A/PPFD curves under the four soil water conditions were measured also using the LI-6400, equipped with red and blue light sources. All measurements were conducted under ambient CO₂ concentration, temperature and relative humidity.The PPFD chosen were 1 600, 1 300, 1 000, 800, 500, 300, 150, 100, 50 and 20 μmol·m^-2s^-1. There were three replicate seedlings per treatment and three needles per seedling measured.

1.3 Assessment methods

The limitations imposed by stomatal or non-stomatal factors in the mid-day depression of photosynthesis in P. tabulaeformis was investigated by: 1) comparing the changes of Ain air with the changes of g_s, 2) comparing the direction of changes in A, g_s and C_i during the diurnal course of photosynthesis, 3) comparing the co-regulations of Aand g_s, g_s and C_i, and 4) comparing the direction of changes in C_i and the stomatal limitation index (L, L=1-C_i /C_a) (Farquhar et al., 1982).

C_i is an important factor in the regulation of A, as the variations in C_i were used as a first indicator of stomatal limitations to A(Xu, 1997). So the stomatal limitation (stomatal closure) reduced C_i, but the non-stomatal limitation reduced photosynthetic activity thereby raising C_i (Xu, 1997). When the two limitation factors exist simultaneously, the direction of C_i changes depends on the direction of the dominant factor changes. So, during the diurnal courses, if the midday depression in photosynthesis (Aand g_s) is in accordance with decreases in C_i, it is the stomatal limitations that controls the midday depression of photosynthesis mainly, while if the midday depression in photosynthesis (Aand g_s) is in accordance with increases in C_i, it is mainly the non-stomatal limitations that controls the midday depression of photosynthesis. In addition, the comparison of the magnitude of midday depression in Aand g_s is also evidence to clarify whether the stomatal or non-stomatal limitations control the midday depression of photosynthesis predominantly (Quick et al., 1992). If the changes of g_s are larger than the midday depressions in A, indicates that the midday depression of photosynthesis is mainly due to stomatal limitations. However, if the changes of g_s are smaller instead, the midday depression of photosynthesis is mainly controlled by the non-stomatal limitation. Simultaneously, the co-regulation of A, C_i and g_s, is also able to demonstrate which limitations, stomatal or non-stomatal, control the midday depression of photosynthesis (Escalona et al., 2000). In the diurnal courses, when the midday depression of photosynthesis occurs, if C_i reduces but Lincreases, the stomatal limitation predominantly controls the midday depression of photosynthesis, however, if C_i increases but Lreduces, the non-stomatal limitation plays the dominant role (Farquhar et al., 1982).

1.4 The models

Wonget al.(1979) found that under steady state conditions, g_s is strongly linear correlated with A.However, when C_s or relative humidity (h_s) varied, the relationship of g_s to Awas less straight forward but presented several patterns. And in all of those patterns, g_s tended to decline with increasing C_s while Aincreased; when h_s decreased, g_s tended to decline, while there was relatively little change in A.Based on a series of leaf gas exchange experiments, (Ball et al., 1987) developed the following empirical expression for g_s:

${g_s} = a\frac{{A{h_s}}}{{{C_s}}} + {g_0}.$

(2)

Where aand g₀ are fitted parameters, Ais the net assimilation rate (μmol·m^-2 s^-1), h_s is the relative humidity and C_s is the CO₂ concentration of air at the leaf surface, g_s is the stomatal conductance.

Seeing that Eq. (2) is not applicable to low CO₂ concentration, Leuning (1990) found that using C_s-Г, where Гis the CO₂ compensation concentration, instead of C_s gives a better fit. And (Aphalo et al., 1991) found g_s responded to humidity deficit rather than to surface h_s which was widely accepted. In the same year, Mott et al.(1991) demonstrated g_s responded to atmospheric humidity through evaporation from the leaf, rather than to the humidity deficit itself, because there is a close link between the transpiration rate (E_t) and humidity deficit (E_t= g_s·VPDs). By adopting these modifications, Leuning(1995) proposed a revised form of the Ball-Berry model:

${g_s} = a\frac{A}{{({C_s} - \Gamma )(1 + VPD/VP{D_0})}} + {g_0}.$

(3)

Where a, g₀, Aand C_s are equivalent to that in Eq. (2), Г is the CO₂ compensation concentration, VPD₀ is a parameter reflecting characteristics of response of stomata to atmospheric VPD. Here, the value of VPD₀ is specified as 1.5, and VPD in air is used instead of VPDs, because VPD is a meteorological variable and can be easily obtained.

These models[Eq. (2) and (3)] are widely used because: they are straightforward to parameterize from leaf-scale data, are easy to implement at large scales, and nonetheless appear to capture the fundamentals of stomatal behaviour. However, there are several important criticisms that can be made of both models (Aphalo et al., 1991; Eamus et al., 2008; Medlyn et al., 2005; Mott et al., 1991). The major criticism of both models is that they are empirical in nature, having no theoretical basis for predicting or interpreting differences in parameter values among species and vegetation types, lacking confidence in applying them to novel situations (such as under increasing atmospheric CO₂ concentration), and the parameters are simply assumed constant for all C3 vegetation in many regional and global models (Krinner et al., 2005). In 1977, Cowan et al.(1977) developed a theory of optimal stomatal behaviour, which postulates that stomata should act to maximize carbon gain (photosynthesis, A) while at the same time minimizing water lost (transpiration, E). Based on this theory, Hari et al. (1986) obtained the optimal stomatal conductance model. Medlyn et al.(2011) reconcile the optimal and empirical models of g_s as:

${g_s} = 1.6(1 + \frac{a}{{\sqrt {{\rm{VPD}}} }})\frac{A}{{({C_s} + {g_0})}}.$

(4)

Wherea, g₀, Aand C_s are equivalent to that in Eq. (3), VPD is leaf to air vapour pressure deficit.

1.5 Statistical analyses

The experiment followed a completely randomized design.To assess the response of P. tabulaeformisseedlings to different soil water content, we further focused our analysis on the relationship between measured and simulated g_s using BWB model, Leuning model, and Medlyn model. models under the four soil water treatments. Moreover, we also fitted the three alternative models to the four soil water condition datasets separated into morning and afternoon to quantify the stomatal and non-stomatal limitation effects. The effects of soil water content and stomatal and non-stomatal limitations on the simulation of g_s in P. tabulaeformisseedlings were evaluated with R² and S_p. Here R² is coefficient for the determination of the regression formula for the models; S_p is slope of the linear regression. Because Leuning model has one additional parameter, the Akaike Information Criterion (AIC) was calculated to allow an unbiased comparison of the goodness-of-fit of the models (Hilborn et al., 1997).

2 Results 2.1 Diurnal changes of environmental conditions

The values for environmental conditions are averaged over the 4 d of measurement as the conditions were similar. At 7:00 local time, the incident PPFD was about 300 μmol·m^-2s^-1, and increased rapidly (Fig. 1a), peaking at 1 200 μmol·m^-2s^-1 at 11:00. The incident PPFD decreased thereafter, by 17:00, it was only about 200 μmol·m^-2s^-1.The leaf temperature (T_leaf) increased along with the increase of PPFD and air temperature (not shown) from about 32 ℃ at 7.00 to about 42 ℃ at 11:00. By 15:00, the T_leaf was similar to 11:00, but dropped to 40 ℃ in the late afternoon (Fig. 1b). Leaf-to-air vapour pressure deficit (VPD) was about 2.0 kPa in the early morning, increasing to about 5.0 kPa at 11:00 and by 15:00 it decreased below 4.5 kPa, further decreasing to 4.0 kPa by 17:00 (Fig. 1c).

2.2 Diurnal patterns of leaf gas exchange under natural PPFD conditions

Significant diurnal changes in A, g_s, C_i and Lwere observed in P. tabulaeformisleaves for the 4 day average values of measurements in the different soil water treatments. Aincreased rapidly from about 2.0 μmol·m^-2s^-1 at 7:00 to a maximum at 9:00 across the four soil water treatments (Fig. 2), followed by a decline during the day under W₀ and W₁ soil water treatments (Fig. 2). However, under W₂ and W₃ soil water treatments, adecreased after midday, but recovered slightly at 15:00. The decrease was larger in the W₂ soil water treatment compared to the W₃ treatment (Fig. 2). The maximum values of Awere about 3.0, 3.5, 5.5 and 5.0 μmol·m^-2s^-1 in the four soil water treatments (W₀, W₁, W₂ and W₃), respectively.

The diurnal course of g_s changes paralleled those of A(Fig. 2). Thus g_s increased in the morning and reached a maximum at 9:00 across the four soil water treatments. For the two driest treatments, g_s decreased during the day but for the two wettest soil water treatments, g_s decreased after midmorning, but recovered at 15:00. This change was slight in the W₃ soil water treatment, but more noticeable in the W₂ soil water treatment. Under the four soil water treatments, the maximum values of g_s were about 0.04, 0.05, 0.07 and 0.45 mol·m^-2s^-1 in the four soil water treatments (W₀, W₁, W₂ and W₃), respectively.

The diurnal patterns of C_i differed significantly across the four soil water treatments (Fig. 2).Under W₀ and W₁ soil water treatments, C_i responded similarly to g_s in the morning: increasing rapidly in the early morning and reaching a maximum at 9.00 h, then decreasing for the remainder of the morning. In the afternoon, C_i increased in the W₀ and W₁ treatments but then increased slightly for the rest of the day, in contrast to the pattern observed for g_s.Under the W₂ soil water treatment, the C_i responded contrarily to g_s in the morning: high in the early morning, reaching a minimum at about midday; but in the afternoon, C_i responded similarly to g_s: increasing after midday and reaching its second peak, then decreasing in the late afternoon. Under W₃ soil water treatment, the C_i responded contrarily to g_s both in the morning and afternoon: high in the early morning, reaching a minimum at about 9:00, but then increasing to its second peak at the late afternoon.

The diurnal patterns in variation of stomatal limitation index, L, were opposite to those observed in C_i in the four soil water treatments (Fig. 2). Under W₀ and W₁ soil water treatments, Lwere high in the early morning, and then declined to a minimum at 9:00, after that Lincreased at midday, but in the afternoon Ldecreased again, while in late afternoon Lsignificant further declined in W₀ but had no significant changes in W₁. Under W₂ soil water treatments, Lincreased in the early morning, reaching a maximum at 11:00, decreasing during the early and mid-afternoon, but increasing slightly in the late afternoon. In the W₃ soil water treatment, Lincreased in the early morning, reaching a maximum at 9:00, there after significant declined by afternoon and had no significant changes yet during late afternoon.

2.3 Regulation of Aby g_s and C_i by g_s in different soil water treatments

The CO₂ assimilation rate Awas a linear function of g_s across all four water treatments across both morning and afternoon dates, as the goodness-of-fit R² W₁ and W₂ soil water treatments, that linear relationship performed significantly better than the others at P < 0.05 level. Meanwhile, the sensitivity of Ato g_s decreased with the increasing of soil water content from W₀ to W₂, as the slope S_P increased from 50.072 to 65.781 and to 81.433. But when the soil water content continues to rise from W₂ to W₃, the sensitivity of Ato g_s will increase.

From Fig. 3, it was also found for low values of g_s (g_s < 0.02 mol·m^-2s^-1) there was a linear correlation between g_s and C_i for all four treatments (Fig. 3). However, as g_s increased C_i increased curvilinearly and asymptotically so that C_i approached C_a for large values of g_s.

2.4 Model comparisons

We fitted the BWB model, Leuning model, and Medlyn model to the four datasets (Fig. 4), obtained from diurnal courses of stomatal conductance measured on the four soil water treatments, using SIGMAPLOT (v. 10.0, Systat Software Inc.). Tab. 2 gives the regression equations and the goodness-of-fit R², Table 4 shows the statistics of the model fits. The Medlyn model gives the best fit for W₀, W₁ and W₂ soil water treatments datasets, when AIC statistics are compared (Tab. 4). The Leuning model was the best fit for W₃ soil water treatment datasets, but have a relatively poor fit for other soil water treatment datasets, as R² was higher than that of the other two models. The BWB model give the worst fit for all of the four treatments W₀, W₁, W₂ and W₃, particularly the W₃ soil water treatment datasets, where R² was just 0.275 3.Overall, the Medlyn model performed best, giving high R² values for all treatment datasets.

We also fitted the BWB model, Leuning model, and Medlyn model to the four soil water treatments datasets separated into morning and afternoon (before and after 12.00) (Fig. 4). The corresponding regression equations and the goodness-of-fit R² of the six datasets contained in Tab. 3, and the statistics of the model fits in Tab. 5. The Medlyn model give the best fit for W₀, W₁ and W₂ soil water treatments datasets, but the Leuning model was the best fit for W₃ soil water treatment datasets, whether in the morning or afternoon. While the BWB model give the worst fit for all of the four treatments W₀, W₁, W₂ and W₃ whether in the morning or afternoon, particularly in the W₃ afternoon soil water treatment datasets, where R² was just 0.113 9.

We visualize fits of the Medlyn et al.(2011) model to our four soil water treatment datasets in Fig. 5and morning and afternoon separated datasets in Fig. 6. The key point demonstrated by Fig. 5 is that the slope of the relationship (and therefore S_P) clearly differs among soil water treatments W₀, W₁, W₂ and W₃. And it varies in a consistent manner from W₀ to W₂, with values lowest in W₀ and highest in W₂. When morning and afternoon separated, the difference of the relationship slope is obvious yet either in the morning or in the afternoon.

3 Discussion 3.1 Diurnal variations in CO₂ exchange in different soil water conditions

Regression of Aand PPFD in the morning and afternoon shows that P. tabulaeformis leaves behaved differently in the morning and afternoon. The results of P. tabulaeformis leaves gas exchange diurnal variations suggest that midday depression of Aoccurred under our experiment conditions across the four soil water treatments. The midday depression in Acould be due to several factors, for example, large PPPF flux causing photoinhibition, high temperatures inhibiting metabolism, or large VPD causing stomatal closure and decreasing or restricting the flux of CO₂ into the leaf, all of which could be summarized in stomatal limitation and non-stomatal limitation.

3.2 Stomatal and non-stomatal effects on the midday depression of Aresponse to different soil water conditions

The relative importance of stomatal and non-stomatal effects as mechanisms controlling the leaf CO₂ assimilation under water stress has been a matter of controversy (Chaves, 1991; Cornic, 1994; Flexas et al., 2002). However the response of plant CO₂ assimilation to water stress may depend on the rapidity of the stress and the susceptibility of the individual species (Flexas et al., 2002). The present data shows that in different soil water status, the controlling effects of stomatal and non-stomatal on the midday leaf photosynthesis decline for P. tabulaeformisseedlings were different.

The results shown in Fig. 2 indicates that in the low and medium soil water status treatments, the midday depression in Acould be attributed to the closure of stomata (decrease in g_s), and consequently caused the parallel decline in intercellular CO₂ concentration C_i, rather than the decreased photosynthetic capacity of mesophyll cells. This result was constant with that observed in Norway spruce trees (Cornic, 1994; Genty et al., 1987; Medrano et al., 1997; Špunda et al., 2005). However, in the high soil water status treatments (W₃), the decrease in Aat midday were accompanied by a decrease in g_s but an increase in C_i, which suggest the midday depression in Awas more controlled by the decreased photosynthetic capacity of mesophyll cells, which consequently caused the increase in C_i, and that stomatal effects are of little or no importance. This was in full agreement with early studies by Kaiser (1987), Cornic et al.(1989) and Huang et al.(2006), who found that stomatal limitation is not responsible for the decreased CO₂ assimilation before the relative water content decreased below 70%.

In addition, during the diurnal rhythms, in W₀, W₁ and W₂ soil water treatments, the changes of g_s were larger than the inhibition of A; but in W₃ soil water treatment, the changes of g_s was of a little smaller magnitude than the inhibition of A(Fig. 2). These also supported the conclusion that in the low and medium soil water treatments (W₀, W₁and W₂), the midday depression in Awas more controlled by the decrease in g_s due to stomatal closure, but in the high soil water treatment (W₃), it was more controlled by the decrease in photosynthetic activity of mesophyll cells.

Moreover, that conclusion could also be the result of aco-regulation of A, g_s and C_i. It is expected that, for long-term experiments, Aadjustment to g_s will lead to a high Avs g_s positive correlation, even though non-stomatal effects are important. Medrano et al.(1997) and Escalona et al.(2000) previously reported, for long-term water stress, a high Avs g_s correlation took place in accordance with parallel decreases of Aand g_s, but simultaneously with important reductions in photosynthetic capacity. This further indicated that a high Avs g_s positive correlationcould not prove the depression in Awas a result of stomatal limitation. So many reports agreed with Xu (1997), that the reliable proof of stomatal limitation is not the Avs g_s positive correlation, but the parallel decreases of A, g_s and C_i, while the proof of non-stomatal limitation is the parallel decreases of Aand g_s accordance with increase of C_i. The present data shows that in low and medium soil water treatments (W₀, W₁ and W₂), there is a parallel decrease of A, g_s and C_i when all data of the diurnal courses for the four sampling days are pooled (Fig. 3). Nevertheless, in the higher soil water treatment (W₃), Aand g_s decreased parallel, but accordance with constant C_i at high g_s and with some increasing C_i and some decreasing C_i at low g_s (Fig. 3). This indicated that in low and medium soil water treatments (W₀, W₁ and W₂), the midday depression in Awere predominantly controlled by stomatal limitation, but in the higher soil water treatment (W₃), it was mainly attributed to non-stomatal limitation, though stomatal limitation also existed. In fact, Giménez et al.(1992) and Gunasekera et al.(1993) have shown by different approaches that the first g_s reduction (highest values) is not matched by a fall in C_i, indicating the presence of non-stomatal effects.

3.3 Model comparisons

Models of vegetation function have a major role to play in advancing our understanding of terrestrial ecosystem responses to global change(Ciais et al., 2007; Gedney et al., 2006; Ostle et al., 2009; Sitch et al., 2008). Whereas, stomatal conductance, the process that governs plant water use and carbon uptake, is fundamental to such models, as stomatal conductance plays a fundamental role in determining vegetation carbon and water balances. In this paper, we compared the three stomatal conductance models: BWB model, Leuning model, and Medlyn model, in P. tabulaeformisseedlings grown under four soil water treatments and found the correlations between Aand g_s give a considerably higher R² than the stomatal model of BWB, but give a considerably lower R² than the stomatal model of Leuning and Medlyn in all of the four soil water treatments. These actually indicated that the correlation between Aand g_s was improved by inclusion of a VPD (leaf-to-air vapour pressure deficit) term instead of the simple RH (relative humidity) term. This conclusion proved the criticism of Aphalo et al.(1991), Mott et al.(1991) and Eamus et al.(2008) to the BWB model that stomata sense transpiration and/or peristomatal water fluxes rather than relative humidity. So when introduced into Leuning and Medlyn model, which incorporating an empirical dependence on leaf-to-air vapour pressure deficit (VPD, kPa), a proxy for transpiration, replacing of relative humidity (RH), the regression coefficient R² was obviously increased. Meanwhile, the Medlyn model performed better than Leuning model, as the Leuning model was just the best fit for W₃ treatment datasets but had a relatively poor fit for other soil water treatment datasets. We note that the major difference between the Leuning model and the Medlyn model was the form of VPD response lying in the behaviour of g_s when VPD approaching to zero, as the Leuning model used the hyperbolic VPD response but the Medlyn model used the square root form of VPD. According to the conclusion of Medlyn et al.(2011), stomata conductance at low VPD is bounded in Leuning model but unbounded in Medlyn model. In fact, Wang et al., (2009) had suggested that stomatal conductance was unbounded as VPD approached zero from eddy covariance studies, supporting the conclusion of Medlyn et al.(2011). Meanwhile, from the viewpoints of both model correctness and model stability, Medlyn et al.(2011) also proved that an unbounded value of g_s was acceptable, as although g_s may be unbounded, transpiration (E) is not; E≈ g_s·VPD, so that Egoes to zero as VPD goes to zero. So the Medlyn model gives the best fit. Lloyd(1991) had found the square root form of VPD (VPD^-1/2) give the best fit to data from Macadamia integrifolia.

For the best fit, the Medlyn model was selected to test the effects of the soil water treatments on the regression relation between simulated g_s and observed g_s in P. tabulaeformis seedlings. The result indicated that the relationship between simulated g_s and observed g_s was significantly affected by soil water content, as the slope of the relationship (and therefore S_P) clearly differs among soil water treatments. Meanwhile, the significance of the correlation was also changed with the changing of soil water content, in the moderate soil water conditions R² was high, but in the low soil water conditions R² declined (Tab. 2). This confirms the assuming ofMedlyn et al.(2011) that the relationship given by the Medlyn model will be changed as soil moisture potential is reduced. According to the study of Medlyn et al.(2011), the key model parameter S_P was proportional to both the CO₂ compensation point and the marginal water cost of plant carbon gain, λ (mol H₂O·mol^-1C), while the value of λ could be thought of as representing the amount of water that a plant was prepared to spend to gain carbon. As early as in 1986, the theoretical studies of λ suggested that λ was likely to be related to whole-plant carbon-water economy (Givnish, 1986). Later, evidence is accumulating that photosynthetic capacity and maximal stomatal conductance are related to plant hydraulic architecture (Bucci et al., 2005; Clearwater et al., 2001; Hubbard et al., 2001; Katul et al., 2003; Taylor et al., 2008). Thus, Medlyn et al.(2011) consider the values of λ obtained under well-watered conditions are likely to be a useful quantitative way of characterizing whole-plant level water-use strategies. But under drought conditions, theoretical analysis of the optimal stomatal conductance by Makela et al.(1996) indicates that the expected value of carbon assimilation is maximized if the value of λ declines as drought progresses. So some models using the empirical approach incorporate an equivalent assumption, reducing the parameter S_P as a function of soil moisture content (Kirschbaum, 1999; Sala et al., 1996a), and some recent implementations decrease the S_P parameter as a function of leaf water potential rather than soil moisture content (Tuzet et al., 2003). Although such assumptions have been found to improve the simulations whether of forest water use during drought (Sala et al., 1996b), or of leaf-level photosynthesis and transpiration over a growing season (Berninger et al., 1996; Op de Beeck et al., 2010). However, very few studies have directly examined how the relationship between photosynthesis and stomatal conductance is affected by drought, except one study on Pinus ponderosa, which directly examined that question but found the model intercept, rather than the slope, was related to soil moisture potential (Misson et al., 2004).So Medlyn et al.(2011) considered may be the relationship given by Medlyn model would break down as soil moisture potential was reduced. All the same, Medlyn model still offers a quantitative framework within which it would be possible to critically examine how soil moisture stress affects stomatal behaviour. On this basis, we suggest that the Medlyn model should incorporate a function which can reflect the influence of soil moisture on the stomatal behaviour to improve the simulation. Like this, the Medlyn model will be able to directly exam how the relationship between photosynthesis and stomatal conductance is affected by soil moisture.

Moreover, we also compared the three stomatal conductance models in P.tabulaeformisseedlings grown under the four soil water conditions separated in morning and afternoon. The results showed that the Medlyn model performed best yet either in the morning or afternoon, and it performed different between in the morning and in the afternoon especially under water stress conditions (W₀ and W₃). There is a major assumption of the Medlyn model that stomatal conductance acts as if it was optimizing for RuBP regeneration-limited photosynthesis rather than Rubisco-limited photosynthesis, but this is not the same as assuming that photosynthesis is always limited by RuBP regeneration. Based on this assumption, the Medlyn model correctly captures the response of stomatal conductance to atmospheric CO₂ concentration (C_a), which differs considerably according to which limitation is considered. If Rubisco-limited photosynthesis is considered, stomatal conductance is predicted to increase with increased C_a, but if RuBP regeneration-limited photosynthesis is considered, stomatal conductance is predicted to decline nonlinearly with C_a, which agrees closely with observations of (Morison, 1987). However, in this research the midday depression of photosynthesis Aoccurred across the four soil water conditions especially under water stress conditions (W₀ and W₃), and the reason for themidday depression were Rubisco-limitedand RuBP regeneration-limited (stomatal and non-stomatal limited). So, when both stomatal and non-stomatal limitations exist, the simulation of the relationships between photosynthesis and stomatal conductance should be separated, or incorporated a function to the model which assumes that stomatal conductance is regulated by rates of electron translation and by rates of Rubisco activity, or by the balance between the two processes to improve the simulation.

4 Conclusion

P.tabulaeformissuffered midday depression in photosynthesis Aacross the four soil water treatments. But the depression was restored slightly in the afternoon in the medium and high soil water conditions, but was not restored under low soil water conditions. The cause of the midday depression differs across the four soil water treatments. In the low and medium soil water conditions (W₀, W₁ and W₂), midday depression in Awas caused by the closure of stomata (stomatal limitation), but in high soil water conditions (W₃) midday depression occurred because of a decreased photosynthetic capacity of mesophyll cells (non-stomatal limitation). In addition, in this experiment the Medlyn model performed best in simulating the relationship between photosynthesis and stomatal conductance and that relationship was significantly affected by soil water stress (low or high) and the relative importance of stomatal and non-stomatal limitations of photosynthesis. We propose that the Medlyn model should incorporate a function which can reflect the influence of soil moisture on the stomatal behaviour to improve the simulation of the relationship between photosynthesis and stomatal conductance under different soil water conditions. We also propose when both stomatal and non-stomatal limitations exist, the simulation of the relationships between photosynthesis and stomatal conductance should be separated, or incorporated a function to the model which assumes that stomatal conductance is regulated by rates of electron translation and by rates of Rubisco activity, or by the balance between the two processes to improve the simulation.