Plantecophys--An R Package for Analysing and Modelling Leaf Gas Exchange Data

Abstract

Here I present the R package 'plantecophys', a toolkit to analyse and model leaf gas exchange data. Measurements of leaf photosynthesis and transpiration are routinely collected with portable gas exchange instruments, and analysed with a few key models. These models include the Farquhar-von Caemmerer-Berry (FvCB) model of leaf photosynthesis, the Ball-Berry models of stomatal conductance, and the coupled leaf gas exchange model which combines the supply and demand functions for CO2 in the leaf. The 'plantecophys' R package includes functions for fitting these models to measurements, as well as simulating from the fitted models to aid in interpreting experimental data. Here I describe the functionality and implementation of the new package, and give some examples of its use. I briefly describe functions for fitting the FvCB model of photosynthesis to measurements of photosynthesis-CO2 response curves ('A-Ci curves'), fitting Ball-Berry type models, modelling C3 photosynthesis with the coupled photosynthesis-stomatal conductance model, modelling C4 photosynthesis, numerical solution of optimal stomatal behaviour, and energy balance calculations using the Penman-Monteith equation. This open-source package makes technically challenging calculations easily accessible for many users and is freely available on CRAN.

Fig 1. Supply and demand functions for leaf photosynthesis.

(a) Leaf photosynthesis—CO₂ response curve as modelled with the FvCB model. (b) The intersection of the supply and demand curves of photosynthesis. The Photosyn function solves for C_i if g_s, V_cmax, J_max and R_d (and other parameters to the FvCB model) are known.

Fig 2. Standard output from the fitaci function.

A_n is the net photosynthetic rate, C_i the intercellular CO₂ concentration. Symbols are measurements, the black line the fitted FvCB model of photosynthesis. Colored lines indicate the two photosynthesis rates in the FvCB model. In the default mode, the fitaci function estimates V_cmax, J_max and R_d from the fitted curve. Optionally, R_d is provided as an input, for example when it was measured separately. In this example, V_cmax was estimated as 46.8 (SE 1.47), J_max was 105.2 (SE 1.36) and R_d was 1.3 (SE 0.24). Assumed parameters were K_m = 1460 and Γ* = 64.8 (all in units of μmol m^-2 s^-1). The R² of a regression of measured vs. fitted was 0.99.

Fig 3. Response of A_n and C_i to combined changes in T_leaf and D.

(A) Lines are A-C_i curves simulated at a range of values for T_leaf. Symbols are the solutions of the coupled leaf gas exchange model, while also taking into account the correlation between D and T_leaf (based on an empirical relationship [35]: D = 0.000605*T_air ^2.39). Note that as T_leaf and D increase, C_i decreases. (B) The corresponding temperature optimum of A_n. Symbols are the same as in panel (A) but plotted against T_leaf.

Fig 4. Visualization of the optimal model of stomatal conductance.

Provided we have an estimate of the 'cost of water' (λ, mol C mol H₂O^-1), stomata act to maximize photosynthesis minus transpiration. In (A), individual curves at a range of values for the vapour pressure deficit (D) are plots of A−λE as a function of C_i, demonstrating that an optimum C_i exists. The FARAO function finds this optimum numerically and calculates corresponding A_n and g_s. The corresponding response of g_s to D is shown in panel (B).

Fig 5. Example application of the plantecophys package to A-C_i curves and spot gas exchange measurements on Eucalyptus delegatensis.

(A) Fitted A-C_i curves with one curve highlighted (B) Estimates of J_max plotted against V_cmax, obtained from the fitted curves in panel (A). Solid line is a regression line (J_max = 107.71 + 0.7 V_cmax, R² = 0.36) with a 95% confidence interval for the mean. (C) Modelled (with the model of Medlyn et al. 2011) versus measured g_s (p < 0.0001, R² = 0.69). Measurements included a wide range of environmental conditions (PAR, T_leaf, D). In this example, only g₁ was fit (estimate = 3.31, 95% CI = 3.15–3.47). (D) The predicted response of ITE (A_n / E) as a function of D from the fitted model in panel (C) (solid line), and the measurements from panel (C) when PAR > 1000.