eq6 {photosynthesisLRC}R Documentation

Calculate Photosynthetic Rates Using a Nonlinear Model EQ6

Description

Uses the nonlinear least squares non-rectangular hyperbola model equation 6 from Lobo et. al (2013) to transform measured photosynthetic data into a smoothed function-valued trait with the following function: A~((((PARi)(phi_I0)+Pgmax)-((((phi_I0)(PARi)+Pgmax)^2)- (4(phi_I0)(Pgmax)(theta)(PARi))^0.5))/(2*theta))-exp(Rd) The function will return predicted values, calculated quantities, or both.

Usage

eq6(pars = c(Pgmax = 15.5,phi_I0 = .0493,theta = .433,Rd = .9),
    data,
    PARi = c(0, 50, 100, 250, 500, 1000, 1500, 2000, 2500),
    return = c("predict","calc","all")[1])

Arguments

pars

A named vector of parameters. Default values are Pgmax= 15.5, phi_I0= 0.0493, theta= 0.433, and Rd= 0.9. These serve as initial starting parameters for the function to rapidly assess your data through an iterative process. The empirical coefficient theta falls between 0 and 1, and represents the various resistances faced by CO2 as it diffuses through the leaf mesophyll and is eventually bound by carboxylation enzymes. All of these values may be changed to fall within the minimum and maximum parameter values of your study system.

data

A data frame containing the experimental data with at least two columns: 'PARi' for the incident light and 'A' for the photosynthetic rate.

PARi

A numeric vector of incident light values. Defaults to a sequence from 0 to 2500.

return

Character string indicating what the function should return. Options are "predict" for predicted values, "calc" for calculated quantities, and "all" for both. Defaults to "predict".

Details

The function uses the provided data to estimate the parameters Pgmax, phi_I0, and Rd by minimizing the squared differences between observed and predicted photosynthetic rates. The model is then used to calculate a range of derived functional trait quantities such as the dark respiration rate (Rd), light compensation point (Icomp), maximum photosynthetic rate (Pmax), and curve derived parameters (Ix) among other calculated quantities.

Value

Depending on the 'return' argument, the function returns:

References

Lobo, F. de A., M. P. de Barros, H. J. Dalmagro,  .C. Dalmolin, W. E. Pereira, É.C. de Souza, G. L. Vourlitis and C. E. Rodriguez Ortiz 2013 Fitting net photosynthetic light-response curves with Microsoft Excel – a critical look at the models. Photosynthetica 51 (3): 445-456.

Prioul, J. L., P. Chartier 1977 Partitioning of transfer and carboxylation components of intracellular resistance to photosynthetic CO2 fixation: A critical analysis of the methods used. Ann. Bot. 41: 789-800.

Davis, R.E., C. M. Mason, E. W. Goolsby 2024 Comparative evolution of photosynthetic light response curve: approaches and pitfalls in phylogenetic modeling of a function-valued trait. IJPS, in review

Examples

    # Example dataset
    example_data <- data.frame(
      PARi = c(0, 50, 100, 250, 500, 1000, 1500, 2000, 2500),
      A = c(1.8, 4.2, 7.5, 12.8, 16.2, 18.5, 19.3, 19.4, 19.5)
    )

    # Predict photosynthetic rates given the parameters
    predicted_values <- eq6(pars = c(Pgmax = 15.5, phi_I0 = .0493,
      theta = .433,Rd = .9),PARi = c(0, 100, 200, 400, 800),
      return= "predict")
    print(predicted_values)

    # Use experimental data to predict photosynthetic rates and estimate linear parameters
    result <- eq6(data = example_data, return = "all")
    print(result$calc)  # View calculated quantities
    print(result$fit)   # View fit statistics and optimized parameters

    # Get calculated quantities directly
    calculated_quantities <- eq6(data = example_data, return = "calc")
    print(calculated_quantities)


[Package photosynthesisLRC version 1.0.6 Index]