A stomatal optimization theory to describe the effects of atmospheric CO2 on leaf photosynthesis and transpiration

Abstract

Background and aims: Global climate models predict decreases in leaf stomatal conductance and transpiration due to increases in atmospheric CO2. The consequences of these reductions are increases in soil moisture availability and continental scale run-off at decadal time-scales. Thus, a theory explaining the differential sensitivity of stomata to changing atmospheric CO2 and other environmental conditions must be identified. Here, these responses are investigated using optimality theory applied to stomatal conductance.

Methods: An analytical model for stomatal conductance is proposed based on: (a) Fickian mass transfer of CO2 and H2O through stomata; (b) a biochemical photosynthesis model that relates intercellular CO2 to net photosynthesis; and (c) a stomatal model based on optimization for maximizing carbon gains when water losses represent a cost. Comparisons between the optimization-based model and empirical relationships widely used in climate models were made using an extensive gas exchange dataset collected in a maturing pine (Pinus taeda) forest under ambient and enriched atmospheric CO2. Key Results and Conclusion In this interpretation, it is proposed that an individual leaf optimally and autonomously regulates stomatal opening on short-term (approx. 10-min time-scale) rather than on daily or longer time-scales. The derived equations are analytical with explicit expressions for conductance, photosynthesis and intercellular CO2, thereby making the approach useful for climate models. Using a gas exchange dataset collected in a pine forest, it is shown that (a) the cost of unit water loss lambda (a measure of marginal water-use efficiency) increases with atmospheric CO2; (b) the new formulation correctly predicts the condition under which CO2-enriched atmosphere will cause increasing assimilation and decreasing stomatal conductance.

Fig. 1.

Left panels: estimation of the effective parameters via regression analysis for the stomatal conductance models in eqns (5a) and (5b), the Ball–Berry model g₁ = m₁ f_cRH/c_a + b₁ (A) and the Leuning model g₂ = m₂ f_c[(1 + D/D₀)c_a]⁻¹ + b₂ (C) using gas exchange data collected under ambient (light circles) and elevated (heavy circles) c_a. The parameters m₁, m₂, b₁ and b₂, determined from linear regression analysis (lines), are shown in Table 1. Right panels: the distributions of m₁ and m₂ (B and D, respectively), computed with fixed b₁, b₂ and D_o, are shown for ambient and elevated c_a.

Fig. 2.

Estimated maximum carboxylation capacity (or a₁ for Rubisco-limited photosynthesis) from 193 gas exchange measurements as a function of leaf temperature (eqn 17) for needles exposed to ambient and elevated atmospheric CO₂ (sampled from 1996 to 1999). The standard temperature sensitivity function (from Campbell and Norman, 1998) with V_cmax,25 = 59 is also shown for reference (continuous line). For formulation, see Table 1.

Fig. 3.

Left panels: linear regression-based estimates of the parameter λ from eqn (18) for the non-linear (A) and the linear optimization models (C), using gas exchange measurements collected under ambient (light circles) and elevated (heavy circles) c_a (see Table 2). Right panels: frequency distribution of λ (B) and λ_LI (D) for needles exposed to ambient and elevated c_a. Note the increase in the mean (not mode) and standard deviations in λ and λ_LI with increasing c_a.

Fig. 4.

Comparison between λ (non-linear model, denoted by NL; eqn 19) and λ_LI (linearized model, LI; eqn 20) for needles exposed to ambient and elevated c_a. To estimate λ, a₁ was estimated from data points in Fig. 2. The regression model λ = 0·8λ_LI + 1·5 (continuous line) describes the data with a coefficient of determination R² = 0·92. The dot–dashed line is the one-to-one line.

Fig. 5.

The effects of elevated c_a on conductance g (top), photosynthesis A_n (middle) and c_i/c_a (bottom): a comparison between the non-linear (NL) and linearized (LI) optimality results for a constant (set at ambient) and variable λ forced by ensemble-averaged leaf temperature and relative humidity. For reference, the ensemble-averaged gas exchange observations (in terms of mean elevated to mean ambient) for 1996–1998 are also shown (symbols).

Fig. 6.

The effects of elevated c_a on conductance g (top), photosynthesis A_n (middle) and c_i/c_a (bottom) as modelled by the non-linear approach with variable λ, the Ball–Berry model and the Leuning model. For reference, the ensemble-averaged gas exchange data (i.e. the ratio of time- or treatment-average elevated to average ambient values) from a number of experiments conducted on loblolly pine are also shown (symbols).