Calculate confidence intervals for C3 A-Ci fitting parameters — confidence_intervals_c3

Calculates confidence intervals for parameters estimated by a C3 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_c3_aci.

Usage

confidence_intervals_c3_aci(
    replicate_exdf,
    best_fit_parameters,
    lower = list(),
    upper = list(),
    fit_options = list(),
    sd_A = 1,
    relative_likelihood_threshold = 0.147,
    Wj_coef_C = 4.0,
    Wj_coef_Gamma_star = 8.0,
    a_column_name = 'A',
    ci_column_name = 'Ci',
    gamma_star_norm_column_name = 'Gamma_star_norm',
    gmc_norm_column_name = 'gmc_norm',
    j_norm_column_name = 'J_norm',
    kc_norm_column_name = 'Kc_norm',
    ko_norm_column_name = 'Ko_norm',
    oxygen_column_name = 'Oxygen',
    rl_norm_column_name = 'RL_norm',
    total_pressure_column_name = 'total_pressure',
    tp_norm_column_name = 'Tp_norm',
    vcmax_norm_column_name = 'Vcmax_norm',
    cj_crossover_min = NA,
    cj_crossover_max = NA,
    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_c3_aci.
lower: The same value that was passed to fit_c3_aci when generating best_fit_parameters.
upper: The same value that was passed to fit_c3_aci when generating best_fit_parameters.
fit_options: The same value that was passed to fit_c3_aci when generating best_fit_parameters.
sd_A: The same value that was passed to fit_c3_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.
Wj_coef_C: A coefficient in the equation for RuBP-regeneration-limited carboxylation, whose value depends on assumptions about the NADPH and ATP requirements of RuBP regeneration; see calculate_c3_assimilation for more information.
Wj_coef_Gamma_star: A coefficient in the equation for RuBP-regeneration-limited carboxylation, whose value depends on assumptions about the NADPH and ATP requirements of RuBP regeneration; see calculate_c3_assimilation for more information.
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).
gamma_star_norm_column_name: The name of the column in replicate_exdf that contains the normalized Gamma_star values (with units of normalized to Gamma_star at 25 degrees C).
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 replicate_exdf that contains the normalized J values (with units of normalized to J at 25 degrees C).
kc_norm_column_name: The name of the column in replicate_exdf that contains the normalized Kc values (with units of normalized to Kc at 25 degrees C).
ko_norm_column_name: The name of the column in replicate_exdf that contains the normalized Ko values (with units of normalized to Ko at 25 degrees C).
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 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.
tp_norm_column_name: The name of the column in replicate_exdf that contains the normalized Tp values (with units of normalized to Tp at 25 degrees C).
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; see that function for more details.
...: Additional arguments to be passed to calculate_c3_assimilation.

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_c3_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('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_temperature_response(licor_file, c3_temperature_param_bernacchi)

# Fit just one curve from the data set
one_result <- fit_c3_aci(
  licor_file[licor_file[, 'species_plot'] == 'tobacco - 1', , TRUE],
  calculate_confidence_intervals = FALSE
)

# Calculate confidence limits for the fit parameters
parameters_with_limits <- confidence_intervals_c3_aci(
    licor_file[licor_file[, 'species_plot'] == 'tobacco - 1', , 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          140.9971    145.3333          149.6696