Calculate RL and Ci_star using the Laisk method

Uses the Laisk method to estimate Ci_star and RL. This function can accomodate alternative colum names for the variables taken from log files 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

fit_laisk(
    replicate_exdf,
    ci_lower = 40,  # ppm
    ci_upper = 120, # ppm
    a_column_name = 'A',
    ci_column_name = 'Ci',
    ppfd_column_name = 'PPFD'
  )

Arguments

replicate_exdf: An exdf object containing multiple A-Ci curves measured at different levels of incident photosynthetically active photon flux density (PPFD).
ci_lower: Lower end of Ci range used for linear fits of An vs. Ci.
ci_upper: Upper end of Ci range used for linear fits of An vs. Ci.
a_column_name: The name of the column in replicate_exdf that contains the net CO2 assimilation rate An in micromol m^(-2) s^(-1).
ci_column_name: The name of the column in replicate_exdf that contains the intercellular CO2 concentration Ci in micromol mol^(-1).
ppfd_column_name: The name of the column in replicate_exdf that can be used to split it into individual response curves. Typically the individial curves are measured at different values of incident light, but the log entries for 'Qin' are not all exactly the same. It is advised to create a new column called 'PPFD' with rounded values. For example, licor_data[, 'PPFD'] <- round(licor_data[, 'Qin']).

Details

The Laisk method is a way to estimate RL and Ci_star for a C3 plant. Definitions of these quantities and a description of the theory underpinning this method is given below.

For a C3 plant, the net CO2 assimilation rate An is given by

An = Vc - Rp - RL,

where Vc is the rate of RuBP carboxylation, Rp is the rate of carbon loss due to photorespiration, and RL is the rate of carbon loss due to non-photorespiratory respiration (also known as the rate of day respiration, the rate of mitochondrial respiration, or the rate of respiration in the light). Because RuBP carboxylation and photorespiration both occur due to Rubisco activity, these rates are actually proportional to each other:

Rp = Vc * Gamma_star / Cc,

where Cc is the CO2 concentration in the chloroplast (where Rubisco is located) and Gamma_star will be discussed below. Using this expression, the net CO2 assimilation rate can be written as

An = Vc * (1 - Gamma_star / Cc) - RL.

When Cc is equal to Gamma_star, the net assimilation rate is equal to -RL. For this reason, Gamma_star is usually referred to as the CO2 compensation point in the absence of mitochondrial respiration.

In general, Cc is related to the intercellular CO2 concentration Ci according to

Ci = Cc + An / gmc,

where gmc is the mesophyll conductance to CO2 diffusion. When Cc is equal to Gamma_star, we therefore have Ci = Gamma_star - RL / gmc. This special value of Ci is referred to as Ci_star, and can be understood as the value of Ci where Cc = Gamma_star and An = -RL. Note that the values of Gamma_star and Ci_star depend on Rubisco properties, mesophyll conductance, and the ambient O2 concentration, but not on the incident light intensity.

These observations suggest a method for estimating RL from a leaf: Measure An vs. Ci curves at several light intensities, and find the value of Ci where the curves intersect with each other. This will be Ci_star, and the corresponding value of An will be equal to -RL.

In practice, it is unlikely that the measured curves will all exactly intersect at a single point. A method for dealing with this issue was developed in Walker & Ort (2015) and described in more detail in Busch et al. (2024). Briefly, a linear fit is first made to each A-Ci curve, enabling the calculation of an intercept-slope curve. Then another linear fit is made to the intercept-slope curve. The intercept of this fit is equal to -RL and its slope is equal to -Ci_star.

Note: it is possible that RL depends on incident light intensity, an issue which complicates the application of the Laisk method. See the references for more details.

References:

Yin, X., Sun, Z., Struik, P. C. & Gu, J. "Evaluating a new method to estimate the rate of leaf respiration in the light by analysis of combined gas exchange and chlorophyll fluorescence measurements." Journal of Experimental Botany 62, 3489–3499 (2011) [doi:10.1093/jxb/err038 ].
Walker, B. J. & Ort, D. R. "Improved method for measuring the apparent CO2 photocompensation point resolves the impact of multiple internal conductances to CO2 to net gas exchange." Plant, Cell & Environment 38, 2462–2474 (2015) [doi:10.1111/pce.12562 ].
Busch, F. A. et al. "A guide to photosynthetic gas exchang measurements: Fundamental principles, best practice and potential pitfalls." Plant, Cell & Environment 47, 3344–3364 (2024) [doi:10.1111/pce.14815 ].

Value

This function returns a list with the following named elements:

first_fit_parameters: An exdf object with the slope (and its standard error), intercept (and its standard error), R-squared value, and p-value for each linear fit of A vs. Ci. These are included as the laisk_slope, laisk_slope_err, laisk_intercept, laisk_intercept_err, r_squared, and p_value columns.
first_fits: An exdf object based on replicate_exdf that also includes the fitted values of An in a new column whose name is a_column_name followed by _fit (for example, A_fit). The fits are extrapolated to Ci = 0 so they can be visually checked for a common intersection point.
second_fit_parameters: An exdf object with RL (and its standard error), Ci_Star (and its standard error) as estimated from a linear fit of laisk_intercept vs. laisk_slope. Also includes the R-squared and p-value of the fit.
second_fit_parameters: An exdf object based on first_fit_parameters that also includes fitted values of laisk_intercept in the laisk_intercept_fit column.

As noted above, the estimated values of RL and Ci_star are included in the second_fit_parameters element of the returned list.

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'
)

# Apply the Laisk method. Note: this is a bad example because these curves were
# measured at the same light intensity, but from different species. Because of
# this, the results are not meaningful.
laisk_results <- fit_laisk(
  licor_file, 20, 150,
  ppfd_column_name = 'species_plot'
)

# Get estimated values
print(laisk_results$second_fit_parameters[, 'RL'])
#> [1] -1.617453
print(laisk_results$second_fit_parameters[, 'Ci_star'])
#> [1] 69.37657

# Plot the linear fits of A vs. Ci
plot_laisk_fit(laisk_results, 'instrument', 'first', ppfd_column_name = 'species_plot')
#> Error in plot_laisk_fit(laisk_results, "instrument", "first", ppfd_column_name = "species_plot"): object 'laisk_results' not found

# Plot the linear fits of Laisk intercept vs. Laisk slope
plot_laisk_fit(laisk_results, 'instrument', 'second', ppfd_column_name = 'species_plot')
#> Error in plot_laisk_fit(laisk_results, "instrument", "second", ppfd_column_name = "species_plot"): object 'laisk_results' not found