Calculate confidence intervals for C4 A-Ci fitting parameters — confidence_intervals_c4

Calculates confidence intervals for parameters estimated by a C4 A-Ci curve fit. It is rare for users to call this function directly, because it can be automatically applied to each curve when calling fit_c4_aci.

Usage

confidence_intervals_c4_aci(
    replicate_exdf,
    best_fit_parameters,
    lower = list(),
    upper = list(),
    fit_options = list(),
    sd_A = 1,
    relative_likelihood_threshold = 0.147,
    x_etr = 0.4,
    a_column_name = 'A',
    ao_column_name = 'ao',
    ci_column_name = 'Ci',
    gamma_star_column_name = 'gamma_star',
    gmc_norm_column_name = 'gmc_norm',
    j_norm_column_name = 'J_norm',
    kc_column_name = 'Kc',
    ko_column_name = 'Ko',
    kp_column_name = 'Kp',
    oxygen_column_name = 'oxygen',
    qin_column_name = 'Qin',
    rl_norm_column_name = 'RL_norm',
    total_pressure_column_name = 'total_pressure',
    vcmax_norm_column_name = 'Vcmax_norm',
    vpmax_norm_column_name = 'Vpmax_norm',
    hard_constraints = 0
  )

Arguments

replicate_exdf: An exdf object representing one CO2 response curve.
best_fit_parameters: An exdf object representing best-fit parameters for the CO2 response curve in replicate_exdf, as calculated by fit_c4_aci.
lower: The same value that was passed to fit_c4_aci when generating best_fit_parameters.
upper: The same value that was passed to fit_c4_aci when generating best_fit_parameters.
fit_options: The same value that was passed to fit_c4_aci when generating best_fit_parameters.
sd_A: The same value that was passed to fit_c4_aci when generating best_fit_parameters.
relative_likelihood_threshold: The threshold value of relative likelihood used to define the boundaries of the confidence intervals; see details below.
x_etr: The fraction of whole-chain electron transport occurring in the mesophyll (dimensionless). See Equation 29 from S. von Caemmerer (2021).
a_column_name: The name of the column in replicate_exdf that contains the net assimilation in micromol m^(-2) s^(-1).
ao_column_name: The name of the column in replicate_exdf that contains the dimensionless ratio of solubility and diffusivity of O2 to CO2.
ci_column_name: The name of the column in replicate_exdf that contains the intercellular CO2 concentration in micromol mol^(-1).
gamma_star_column_name: The name of the column in replicate_exdf that contains the dimensionless gamma_star values.
gmc_norm_column_name: The name of the column in replicate_exdf that contains the normalized mesophyll conductance values (with units of normalized to gmc at 25 degrees C).
j_norm_column_name: The name of the column in exdf_obj that contains the normalized Jmax values (with units of normalized to Jmax 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 microbar.
ko_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for rubisco oxygenation in mbar.
kp_column_name: The name of the column in replicate_exdf that contains the Michaelis-Menten constant for PEP carboxylase carboxylation in microbar.
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.
qin_column_name: The name of the column in exdf_obj 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 exdf_obj 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).
vpmax_norm_column_name: The name of the column in replicate_exdf that contains the normalized Vpmax values (with units of normalized to Vpmax at 25 degrees C).
hard_constraints: To be passed to calculate_c4_assimilation; see that function for more details.

Details

In maximum likelihood fitting, each set of parameter values has an associated likelihood value. If the maximum likelihood is known, then it is also possible to define a relative likelihood p according to p = L / L_max. The set of all parameter values where p exceeds a threshold value p_0 defines a region in parameter space called like a "relative likelihood region." When taking one-dimensional cuts through parameter space, the boundaries of the relative likelihood region define a relative likelihood interval.

Here we calculate the upper and lower limits of the relative likelihood intervals for each parameter. This is done by fixing the other parameters to their best-fit values, and varying a single parameter to find the interval where the relative likelihood is above the threshold value (set by the relative_likelihood_threshold input argument). If the threshold is set to 0.147, then these intervals are equivalent to 95% confidence intervals in most situations. See the Wikipedia page about relative likelihood for more information.

Internally, this function uses error_function_c4_aci to calculate the negative logarithm of the likelihood (-ln(L)). It varies each fitting parameter independendently to find values where ln(L) - ln(p_0) - ln(L_max) = 0.

If the upper limit of a confidence interval is found to exceed ten times the upper limit specified when fitting that parameter, then the upper limit of the condfidence interval is taken to be infinity.

Value

An exdf object based on best_fit_parameters that contains lower and upper bounds for each parameter; for example, if Vcmax_at_25 was fit, best_fit_parameters will contain new columns called Vcmax_at_25_lower and Vcmax_at_25_upper.

Examples

# Read an example Licor file included in the PhotoGEA package
licor_file <- read_gasex_file(
  PhotoGEA_example_file_path('c4_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 temperature-dependent values of C4 photosynthetic parameters
licor_file <- calculate_temperature_response(licor_file, c4_temperature_param_vc)

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

# Fit just one curve from the data set
one_result <- fit_c4_aci(
  licor_file[licor_file[, 'species_plot'] == 'maize - 5', , TRUE],
  Ca_atmospheric = 420
)

# Calculate confidence limits for the fit parameters
parameters_with_limits <- confidence_intervals_c4_aci(
    licor_file[licor_file[, 'species_plot'] == 'maize - 5', , TRUE],
    one_result$parameters
)

# View confidence limits and best estimate for Vcmax_at_25
parameters_with_limits[, c('Vcmax_at_25_lower', 'Vcmax_at_25', 'Vcmax_at_25_upper')]
#>   Vcmax_at_25_lower Vcmax_at_25 Vcmax_at_25_upper
#> 1          33.38873    33.90721          34.42717