DOI: 10.5061/dryad.vx0k6djz5
title: Data from: Stomatal response to VPD in C4 plants with different biochemical sub-pathways

description: C4 plants are integral to many ecosystems around the world and are
 abundantly found in grasslands and savannas in North America, Australia,
 and Africa, and deserts in Central Asia among other ecosystems in and
 around Europe (Edwards and Still 2008; Pyankov et al. 2010; Rudov et al.
 2020; Wan et al. 2001). Despite making up 20% of the global plant biomass
 (Ehleringer et al. 1997), our understanding of C4 physiology and
 biochemistry still has room for improvements. More specifically, the three
 subtypes of C4 plants (NADP-malic enzyme, NAD-malic enzyme, and PEP
 carboxykinase) should be better characterized in terms of their
 biochemistry. To do that, we require a comprehensive characterization of
 species from across C4 families, not just model C4 species. However, it is
 often labor-intensive to collect the full gamut of physiological and
 biochemical data for large numbers of species. Here, I describe a
 hierarchical Bayesian approach in parametrizing the C4 photosynthesis
 model that can estimate biochemical parameters using gas exchange data
 while accounting for plant, species, and subtype variation.
description: To enable a comparative analysis, we compared 6 closely related
 C<sub>4</sub> lineages that each contain an independent origin
 of NAD-ME and NADP-ME subtypes, for a total of 12 species. 
 We analyzed the response of net CO<sub>2</sub>
 assimilation rate (<em>A</em>) to intercellular concentration
 of CO<sub>2</sub>
 (<em>C<sub>i</sub></em>) and we measured the
 response of stomatal conductance
 (<em>g<sub>s</sub></em>) to VPD. All gas exchange
 measurements were conducted with two Li-6400 Portable Photosynthesis
 Systems (Li-Cor Biosciences, Lincoln, NE, USA) over a course of five
 months. We conducted measurements at a constant leaf temperature of 30 °C,
 PPFD of 1800 µmol m<sup>-2</sup>s<sup>-1</sup>,
 and CO<sub>2</sub> concentration at ambient level of 400 ppm,
 unless otherwise noted.  We used a hierarchical
 Bayesian approach to model C<sub>4</sub> photosynthesis to
 estimate maximum PEPC activity
 (<em>V<sub>pmax</sub></em>) and maximum Rubisco
 activity (<em>V<sub>cmax</sub></em>) from the
 <em>A/C<sub>i</sub></em> data. The hierarchical
 Bayesian approach followed methods of Patrick et al. (2009) and allowed us
 to estimate multiple parameters (namely
 <em>V<sub>pmax</sub></em> and
 <em>V<sub>cmax</sub></em>) simultaneously, as well
 as accounting for observational error in the data set while identifying
 uncertainty in the estimated parameters. We used a
 C<sub>4</sub> photosynthesis model (von Caemmerer 2000) that
 was simplified to only estimate PEPC-limited and Rubisco-limited values of
 <em>A</em>. From the model, we estimated the
 <em>C<sub>i</sub></em> where the transition from
 PEPC-limited to Rubisco-limited <em>A</em> occurred. Our
 hierarchical model had three main components: the likelihood equation of
 observing the data, the deterministic model which is the
 C<sub>4</sub> photosynthesis model (von Caemmerer 2000), and
 the prior distributions of the variables involved in the deterministic
 model. These components generated posterior distributions of
 V<sub>pmax</sub>, V<sub>cmax</sub>, and the
 transition <em>C<sub>i</sub></em> between the
 limitations. Because this was a hierarchical model, we were able to set
 parameters to vary at either the species level or the plant level.
 V<sub>pmax</sub>, V<sub>cmax</sub>, and the
 transition point were all set to vary at the plant level such that each
 plant can have its own distinct value. The Michaelis-Menten constants for
 CO<sub>2</sub> for PEPC and for O<sub>2</sub> and
 CO<sub>2</sub> for Rubisco were allowed to vary at the species
 level such that all the replicates within a species shared the same value.
 All other parameters in the model were included as constants. Because
 there were small variations in temperature during gas exchange
 measurements (28.3 – 32.1 °C) and the oxygenation and carboxylation rates
 of Rubisco and carboxylation rates of PEPC are temperature dependent, we
 used an Arrhenius function to standardize all values to 30 °C (von
 Caemmerer, 2000). The hierarchical Bayesian photosynthesis model was
 implemented using JAGS (Plummer 2003) interfaced with RStudio using the
 package “rJAGS” (Plummer et al. 2022). We ran three parallel Markov chain
 Monte Carlo (MCMC) chains for 30 000 iterations each and the chains were
 evaluated for convergence using the Gelman-Rubin diagnostic (Gelman and
 Rubin 1992). The burn-in samples (first 5000) were discarded. The model
 goodness-of-fit was evaluated by generating predicted
 <em>A</em> values and comparing these with observed
 <em>A</em> values. If the model was a good fit, then the
 predicted <em>A</em> and observed <em>A</em>
 should fall along the 1:1 line.
description: # Data from: Stomatal response to VPD in C4 plants with different
 biochemical sub-pathways
 [https://doi.org/10.5061/dryad.vx0k6djz5](https://doi.org/10.5061/dryad.vx0k6djz5) This dataset contains a file of net CO2 assimilation rate (photosynthesis rate) vs intercellular CO2 response for twelve C4 species measured using Li-Cor 6400-XT Portable Photosynthesis System. There are five replicates for each species which were grown in a growth chamber. This dataset can be used in the Bayesian model of C4 photosynthesis coded in R using the package rJAGS (included in the files). The C4 photosynthesis process model is taken from von Caemmerer's C4 photosynthesis model. The Bayesian approach allows hierarchical parametrization of key biochemical variables and can account for error in the data, thus making parametrizations more robust. This model allows the parametrization of maximum ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco the main photosynthetic enzyme) activity, maximum PEP carboxylase activity, among other important components of C4 photosynthesis with the use of experimental data of photosynthesis rate.  ## Description of the data and file structure The data file containing photosynthesis response to intercellular CO2 data (Full_ACi_1.csv) is in long format, meaning that there are several rows of entry for each replicate. The column with the title "A" is net CO2 assimilation rate (photosynthesis rate) with the units of µmol m^-2s^-1 and "Ci" is intercellular CO2 concentration in µmol m^-2s^-1. Each replicate is indicated by the "Biorep" column as well as the "Plant" column. The abbreviation of the species name is given in the first column under "Species" and is as follow: Acara = Alternanthera caracasana; Ainc = Allionia incarnata; Aretro = Amaranthus retroflexus; Aros = Atriplex rosea; Bcocc = Boerhavia coccinea; Kscop = Kochia scoparia; Pami = Portulaca amilis; Pcap = Panicum capillare; Pole = Portulaca oleracea; Svir = Setaria viridis; Tport = Trianthema portulacastrum; Zpent = Zaleya pentandra. There is a column for the C4 subtype called "Subtype". The "Pairing" column refers to species that are from the same family. For example, Acara and Aretro are both from pair a because they are both from the Amaranthaceae family. "Pressure" refers to the atmospheric pressure in kilopascal (kPa) during which the measurements were taken. "Temp" column is temperature in Celsius. "Ci_p" column is the intercellular CO2 in partial pressure (kPa). "Cm" is the mesophyll CO2 concentration in µmol m^-2s^-1 as measured by the Li-Cor 6400-XT. "Qobs" is the light level in photosynthetically active radiation (PAR) at which the measurements were taken. There are two R scripts: one in R markdown format of the interface for running the Bayesian model; one in R script format of the Bayesian model. The R markdown file (C4 model for pub.Rmd) is where the data set is loaded into the model and all the starting parameters of the model are listed. The file also contains the R code for executing the Bayesian model as well as the Gelman-Rubin test for convergence. Comments are provided within the file to aid with clarity and usage. The R script file (Vsimp C4 JAGS model 3.R) contains the code for the model itself, which includes all of the equations of the C4 photosynthesis model as well as the hierarchical Bayesian structure for parametrizing the model. The code includes output for the photosynthesis rate (A) as predicted by the model which can be compared to the experimental data of photosynthesis rate. "Aobs" are the photosynthesis rate values as measured experimentally, and "Apred" are the photosynthesis rate values predicted by the model. Both are assumed to follow a normal distribution. All the variable and parameter names are exactly as written in the original C4 photosynthesis model by von Caemmerer, 2000. Please refer to the publications for explanation of all constants and parameters. ## Code/Software The code is run using R version 4.3.2 in RStudio Version 2023.9.1.494 using JAGS and interfaced through the rJAGS package. Please be sure to set the working directory to where all the scripts and data file are.