Estimate the relative limiting factors to C3 photosynthesis — calculate_c3_limitations

Uses the method from Warren et al. (2003) to estimate the relative limitations to C3 photosynthesis due to stomatal conductance and mesophyll conductance. This function can accomodate alternative column names for the variables taken from the data file in case they change at some point in the future. This function also checks the units of each required column and will produce an error if any units are incorrect.

Usage

calculate_c3_limitations_warren(
    exdf_obj,
    atp_use = 4.0,
    nadph_use = 8.0,
    curvature_cj = 1.0,
    curvature_cjp = 1.0,
    ca_column_name = 'Ca',
    cc_column_name = 'Cc',
    ci_column_name = 'Ci',
    j_norm_column_name = 'J_norm',
    kc_column_name = 'Kc',
    ko_column_name = 'Ko',
    oxygen_column_name = 'oxygen',
    rl_norm_column_name = 'RL_norm',
    total_pressure_column_name = 'total_pressure',
    vcmax_norm_column_name = 'Vcmax_norm',
    hard_constraints = 0
  )

Arguments

exdf_obj: An exdf object representing gas exchange data. Typically this should be an exdf object returned from fit_c3_aci; it will be expected to have columns for alpha_g, Gamma_star, J_at_25, RL_at_25, Tp, and Vcmax_at_25.
atp_use: The number of ATP molecules used per C3 cycle.
nadph_use: The number of NADPH molecules used per C3 cycle.
curvature_cj: A dimensionless quadratic curvature parameter greater than or equal to 0 and less than or equal to 1 that sets the degree of co-limitation between Wc and Wj. A value of 1 indicates no co-limitation.
curvature_cjp: A dimensionless quadratic curvature parameter greater than or equal to 0 and less than or equal to 1 that sets the degree of co-limitation between Wcj and Wp. A value of 1 indicates no co-limitation.
ca_column_name: The name of the column in exdf_obj that contains the ambient CO2 concentration in micromol mol^(-1).
cc_column_name: The name of the column in exdf_obj that contains the chloroplastic CO2 concentration in micromol mol^(-1). Typically these are calculated using apply_gm.
ci_column_name: The name of the column in exdf_obj that contains the intercellular CO2 concentration in micromol mol^(-1).
j_norm_column_name: The name of the column in exdf_obj that contains the normalized J values (with units of normalized to J at 25 degrees C). Typically these are the leaf-temperature dependent values calculated using calculate_arrhenius.
kc_column_name: The name of the column in exdf_obj that contains the Michaelis-Menten constant for rubisco carboxylation in micromol mol^(-1). Typically these are the leaf-temperature dependent values calculated using calculate_arrhenius.
ko_column_name: The name of the column in exdf_obj that contains the Michaelis-Menten constant for rubisco oxygenation in mmol mol^(-1). Typically these are the leaf-temperature dependent values calculated using calculate_arrhenius.
oxygen_column_name: The name of the column in exdf_obj that contains the concentration of O2 in the ambient air, expressed as a percentage (commonly 21% or 2%); the units must be percent.
rl_norm_column_name: The name of the column in exdf_obj that contains the normalized RL values (with units of normalized to RL at 25 degrees C).
total_pressure_column_name: The name of the column in exdf_obj that contains the total pressure in bar. Typically this is calculated using calculate_total_pressure.
vcmax_norm_column_name: The name of the column in exdf_obj that contains the normalized Vcmax values (with units of normalized to Vcmax at 25 degrees C).
hard_constraints: To be passed to calculate_c3_assimilation; see that function for more details.

Details

When analyzing or interpreting C3 gas exchange data, it is often useful to estimate the relative limitations to assimilation that are due to stomatal conductance or mesophyll conductance. This can be done using a framework first introduced by Warren et al. (2003). In this framework, the relative limitation due to stomatal conductance (ls) is

ls = (An_inf_gsc - A_modeled) / An_inf_gsc

and the relative limitation due to mesophyll conductance (lm) is

lm = (An_inf_gmc - A_modeled) / An_inf_gmc. These are equations 10 and 11 in Warren et al. (2003).

In these equations A_modeled is the net assimilation rate calculated using the Farquhar-von-Caemmerer-Berry (FvCB) model at the measured value of the chloroplast CO2 concentration (Cc). The other two assimilation rates (An_inf_gsc and An_inf_gmc) are also calculated using the FvCB model, but under different assumptions: An_inf_gsc assumes that stomatal conductance is infinite while mesophyll conductance is as measured, while An_inf_gmc assumes that mesophyll conductance is infinite while stomatal conductance is as measured.

In other words, ls expresses the observed assimilation rate as a fractional decrease relative to a hypothetical plant with infinite stomatal conductance, while lm expresses the observed assimilation rate as a fractional decrease relative to a hypothetical plant with infinite mesophyll conductance.

For example, if lm = 0.4, this means that the observed assimilation rate is 40 percet lower than a hypothetical plant with infinite mesophyll conductance. If mesophyll conductance were to increase (all else remaining the same), then lm would decrease. This is not the case with other estimations of limiting factors, such as the one used in calculate_c3_limitations_grassi. (See Leverett & Kromdijk for more details.)

To actually calculate An_inf_gsc and An_inf_gmc, it is first necessary to estimate the corresponding values of Cc that would occur with infinite stomatal or mesophyll conductance. This can be done with a 1D diffusion equation expressed using drawdown values:

Cc = Ca - drawdown_cs - drawdown_cm,

where drawdown_cs = Ca - Ci is the drawdown of CO2 across the stomata (assuming infinite boundary layer conductance) and drawdown_cm = Ci - Cc is the drawdown of CO2 across the mesophyll. If one conductance is infinite, the corresponding drawdown becomes zero. Thus, we have:

Cc_inf_gsc = Ca - 0 - (Ci - Cc) = Ca - Ci + Cc

and

Cc_inf_gmc = Ca - (Ca - Ci) - 0 = Ci,

where Cc_inf_gsc is the value of Cc that would occur with infinite stomatal conductance and the measured mesophyll conductance, and Cc_inf_gmc is the value of Cc that would occur with infinite mesophyll conductance and the measured stomatal conductance.

Once values of Cc, Cc_inf_gsc, and Cc_inf_gmc, the corresponding assimilation rates are calculated using calculate_c3_assimilation, and then the limitation factors are calculated as described above.

References:

Warren, C. R. et al. "Transfer conductance in second growth Douglas-fir (Pseudotsuga menziesii (Mirb.)Franco) canopies." Plant, Cell & Environment 26, 1215–1227 (2003) [doi:10.1046/j.1365-3040.2003.01044.x ].

Leverett, A. & Kromdijk, J. "The long and tortuous path towards improving photosynthesis by engineering elevated mesophyll conductance." [doi:10.22541/au.170016201.13513761/v1 ].

Value

This function returns an exdf object based on exdf_obj but with several new columns representing the quantities discussed above: Cc_inf_gsc, Cc_inf_gmc, An_inf_gsc, An_inf_gmc, ls_warren, and lm_warren.

Examples

# Read an example Licor file included in the PhotoGEA package
licor_file <- read_gasex_file(
  PhotoGEA_example_file_path('c3_aci_1.xlsx')
)

# Define a new column that uniquely identifies each curve
licor_file[, 'species_plot'] <-
  paste(licor_file[, 'species'], '-', licor_file[, 'plot'] )

# Organize the data
licor_file <- organize_response_curve_data(
    licor_file,
    'species_plot',
    c(9, 10, 16),
    'CO2_r_sp'
)

# Specify mesophyll conductance
licor_file <- set_variable(
  licor_file,
  'gmc', 'mol m^(-2) s^(-1) bar^(-1)', value = 0.5
)

# Calculate the total pressure in the Licor chamber
licor_file <- calculate_total_pressure(licor_file)

# Calculate additional gas properties
licor_file <- calculate_gas_properties(licor_file)

# Calculate Cc
licor_file <- apply_gm(licor_file)

# Calculate temperature-dependent values of C3 photosynthetic parameters
licor_file <- calculate_arrhenius(licor_file, c3_arrhenius_bernacchi)

# Fit all curves in the data set. Here we use a faster optimizer than the
# default one to ensure the example runs quickly.
aci_results <- consolidate(by(
  licor_file,
  licor_file[, 'species_plot'],
  fit_c3_aci,
  Ca_atmospheric = 420,
  OPTIM_FUN = optimizer_nmkb(1e-7)
))

# Get a subset of fitting results corresponding to the first measured point
# in each curve (where CO2_r_sp = 400 ppm)
aci_fit_subset <- aci_results$fits[aci_results$fits[, 'CO2_r_sp'] == 400, , TRUE]

# Calculate limiting factors
aci_fit_subset <- calculate_c3_limitations_warren(aci_fit_subset)

# View the limiting factors for each species / plot
col_to_keep <- c(
  'species', 'plot',       # identifiers
  'ls_warren', 'lm_warren' # limitation info
)

aci_fit_subset[ , col_to_keep, TRUE]
#>    species [UserDefCon] (NA) plot [UserDefCon] (NA)
#> 8                    soybean                     5a
#> 21                   tobacco                      1
#> 34                   tobacco                      2
#>    ls_warren [calculate_c3_limitations_warren] (dimensionless)
#> 8                                                           NA
#> 21                                                          NA
#> 34                                                          NA
#>    lm_warren [calculate_c3_limitations_warren] (dimensionless)
#> 8                                                           NA
#> 21                                                          NA
#> 34                                                          NA