Generate an error function for C3 Variable J curve fitting — error_function_c3_variable

Creates a function that returns an error value (the sum of squared residuals) representing the amount of agreement between modeled and measured An values.

Usage

error_function_c3_variable_j(
    replicate_exdf,
    fit_options = list(),
    sd_A = 1,
    atp_use = 4.0,
    nadph_use = 8.0,
    curvature_cj = 1.0,
    curvature_cjp = 1.0,
    a_column_name = 'A',
    ci_column_name = 'Ci',
    j_norm_column_name = 'J_norm',
    kc_column_name = 'Kc',
    ko_column_name = 'Ko',
    oxygen_column_name = 'oxygen',
    phips2_column_name = 'PhiPS2',
    qin_column_name = 'Qin',
    rl_norm_column_name = 'RL_norm',
    total_pressure_column_name = 'total_pressure',
    vcmax_norm_column_name = 'Vcmax_norm',
    cj_crossover_min = NA,
    cj_crossover_max = NA,
    hard_constraints = 0,
    require_positive_gmc = 'positive_a',
    gmc_max = Inf
  )

Arguments

replicate_exdf: An exdf object representing one CO2 response curve.
fit_options: A list of named elements representing fit options to use for each parameter. Values supplied here override the default values (see details below). Each element must be 'fit', 'column', or a numeric value. A value of 'fit' means that the parameter will be fit; a value of 'column' means that the value of the parameter will be taken from a column in replicate_exdf of the same name; and a numeric value means that the parameter will be set to that value. For example, fit_options = list(alpha_g = 0, Vcmax_at_25 = 'fit', Tp = 'column') means that alpha_g will be set to 0, Vcmax_at_25 will be fit, and Tp will be set to the values in the Tp column of replicate_exdf.
sd_A: The standard deviation of the measured values of the net CO2 assimilation rate, expressed in units of micromol m^(-2) s^(-1). If sd_A is not a number, then there must be a column in exdf_obj called sd_A with appropriate units. A numeric value supplied here will overwrite the values in the sd_A column of exdf_obj if it exists.
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.
a_column_name: The name of the column in replicate_exdf that contains the net assimilation in micromol m^(-2) s^(-1).
ci_column_name: The name of the column in replicate_exdf that contains the intercellular CO2 concentration in micromol mol^(-1).
j_norm_column_name: The name of the column in replicate_exdf that contains the normalized J values (with units of normalized to J at 25 degrees C).
kc_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for rubisco carboxylation in micromol mol^(-1).
ko_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for rubisco oxygenation in mmol mol^(-1).
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.
phips2_column_name: The name of the column in replicate_exdf that contains values of the operating efficiency of photosystem II (dimensionless).
qin_column_name: The name of the column in replicate_exdf that contains values of the incident photosynthetically active flux density in micromol m^(-2) s^(-1).
rl_norm_column_name: The name of the column in replicate_exdf 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 replicate_exdf that contains the total pressure in bar.
vcmax_norm_column_name: The name of the column in replicate_exdf that contains the normalized Vcmax values (with units of normalized to Vcmax at 25 degrees C).
cj_crossover_min: The minimum value of Cc (in ppm) where Aj is allowed to become the overall rate-limiting factor. If cj_crossover_min is set to NA, this restriction will not be applied.
cj_crossover_max: The maximim value of Cc (in ppm) where Wj is allowed to be smaller than Wc. If cj_crossover_max is set to NA, this restriction will not be applied.
hard_constraints: To be passed to calculate_c3_assimilation and calculate_c3_variable_j; see those functions for more details.
require_positive_gmc: A character string specifying the method to be used for requiring positive values of mesophyll conductance. Can be 'none', 'all', or 'positive_a'. See below for more details.
gmc_max: The maximum value of mesophyll conductance that should be considered to be acceptable. See below for more details.

Details

When fitting A-Ci + chlorophyll fluorescence curves using the Variable J method, it is necessary to define a function that calculates the likelihood of a given set of alpha_g, Gamma_star, J_at_25, RL_at_25, tau, Tp, and Vcmax_at_25 values by comparing a model prediction to a measured curve. This function will be passed to an optimization algorithm which will determine the values that produce the smallest error.

The error_function_c3_variable_j returns such a function, which is based on a particular replicate and a set of fitting options. It is possible to just fit a subset of the available fitting parameters; by default, the fitting parameters are J_at_25, RL_at_25, Tp, tau, and Vcmax_at_25. This behavior can be changed via the fit_options argument.

For practical reasons, the function actually returns values of -ln(L), where L is the likelihood. The logarithm of L is simpler to calculate than L itself, and the minus sign converts the problem from a maximization to a minimization, which is important because most optimizers are designed to minimize a value.

Sometimes an optimizer will choose biologically unreasonable parameter values that nevertheless produce good fits to the supplied assimilation values. There are several options for preventing an optimizer from choosing such parameter values:

Enforcing Rubisco limitations: A common problem is that the fit result may not indicate Rubisc-limited assimilation at low CO2 values, which should be the case for any A-Ci curves measured at saturating light. In this case, the optional cj_crossover_min and cj_crossover_max can be used to constrain the range of Cc values (in ppm) where Wj is allowed to be the overall rate limiting factor. If the crossover from Rubisco-limited to RuBP-regeneration limited carboxylation occurs outside these bounds (when they are supplied), a heavy penalty will be added to the error function, preventing the optimizer from choosing those parameter values.
Requiring positive gmc: The Variable J method sometimes predicts negative values of the mesophyll conductance (gmc). Such values are probably not realistic, especially when Cc is above the CO2 compensation point. The require_positive_gmc input argument can be used to penalize negative values of gmc. When require_positive_gmc is 'all', a heavy penalty will be added to the error function if there are any negative gmc values. When require_positive_gmc is 'positive_a', a heavy penalty will be added to the error function if there are any negative gmc values when A is positive; negative gmc for negative A will be allowed. When require_positive_gmc is 'none', these restrictions are disabled and no penalties are added for negative gmc.
Preventing large values of gmc: The Variable J method sometimes produces unreasonably high values of gmc. The gmc_max argument can be used to address this. If any predicted gmc values exceed gmc_max when A is positive, a heavy penalty will be added to the error function.

A penalty is also added for any parameter combination where An is not a number, or where calculate_c3_variable_j or calculate_c3_assimilation produce an error.

Value

A function with one input argument guess, which should be a numeric vector representing values of the parameters to be fitted (which are specified by the fit_options input argument.) Each element of guess is the value of one parameter (arranged in alphabetical order.) For example, with the default settings, guess should contain values of J_at_25, RL_at_25, tau, Tp, and Vcmax_at_25 (in that order).

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'
)

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

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

# Define an error function for one curve from the set
error_fcn <- error_function_c3_variable_j(
  licor_file[licor_file[, 'species_plot'] == 'tobacco - 1', , TRUE]
)

# Evaluate the error for J_at_25 = 200, RL_at_25 = 1, tau = 0.5, Tp = 15,
# Vcmax_at_25 = 100
error_fcn(c(200, 1, 0.5, 15, 100))
#> Warning: number of items to replace is not a multiple of replacement length
#> [1] 10580.61

# Make a plot of error vs. Tp when the other parameters are fixed to the values
# above. As Tp increases, it eventually stops limiting the assimilation rate
# and its value stops influencing the error.
tpu_error_fcn <- function(Tp) {error_fcn(c(200, 1, 0.5, Tp, 100))}
tpu_seq <- seq(5, 25)

lattice::xyplot(
  sapply(tpu_seq, tpu_error_fcn) ~ tpu_seq,
  type = 'b',
  xlab = 'Tp (micromol / m^2 / s)',
  ylab = 'Negative log likelihood (dimensionless)'
)
#> Warning: number of items to replace is not a multiple of replacement length
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