# Introduction to the photosynthesis package

#### Chris Muir

#### 2023-05-11

The photosynthesis package simulates photosynthetic rate given a set of leaf traits and environmental conditions by solving the Farquhar-von Caemmerer-Berry C3 biochemical model. There are two main steps to using photosynthesis:

1. define leaf parameters, environmental parameters, temperature response parameters, and physical constants; and
2. solve for the chloroplastic CO2 concentration that balances CO2 supply and demand (`photo` and `photosynthesis` for single and multiple parameter sets, respectively).

In this vignette, I’ll show you how to:

- run a minimum worked example using default parameters
- replace default parameters
- simulate photosynthetic rate along a gradient of CO\(_2\) concentrations (\(A-C_\mathrm{c}\) curve)

## Minimum worked example

You can use the default parameter settings and simulate photosynthetic rate in a single leaf using the `make_*()` functions and `photo()`.

    library(dplyr)
    library(magrittr)
    library(photosynthesis)

    # Leaving the make_* functions empty will automatically default to defaults
    # parameters.
    bake_par   = make_bakepar()                       # temperature response parameters
    constants  = make_constants(use_tealeaves = FALSE) # physical constants
    leaf_par   = make_leafpar(use_tealeaves = FALSE)   # leaf parameters
    enviro_par = make_enviropar(use_tealeaves = FALSE) # environmental parameters

    photo(leaf_par, enviro_par, bake_par, constants, quiet = TRUE,
          use_tealeaves = FALSE)
    #>                 C_chl         value convergence                  g_tc
    #> 1 258.1218 [umol/mol] -1.363227e-06           0 0.1726157 [mol/m^2/s]
    #>                       A            J_max          J_max25              K_C
    #> 1 27.94273 [umol/m^2/s] 200 [umol/m^2/s] 200 [umol/m^2/s] 268.3 [umol/mol]
    #>              K_C25                 K_O               K_O25            R_d
    #> 1 268.3 [umol/mol] 165084.2 [umol/mol] 165084.2 [umol/mol] 2 [umol/m^2/s]
    #>            R_d25     T_leaf           V_cmax         V_cmax25            V_tpu
    #> 1 2 [umol/m^2/s] 298.15 [K] 150 [umol/m^2/s] 150 [umol/m^2/s] 200 [umol/m^2/s]
    #>            V_tpu25            g_mc          g_mc25            g_sc
    #> 1 200 [umol/m^2/s] 0.4 [mol/m^2/s] 0.4 [mol/m^2/s] 0.4 [mol/m^2/s]
    #>               g_uc         gamma_star       gamma_star25  k_mc  k_sc  k_uc
    #> 1 0.01 [mol/m^2/s] 37.9258 [umol/mol] 37.9258 [umol/mol] 1 [1] 1 [1] 1 [1]
    #>   leafsize     phi_J   theta_J          C_air              O              P
    #> 1  0.1 [m] 0.331 [1] 0.825 [1] 420 [umol/mol] 0.21 [mol/mol] 101.3246 [kPa]
    #>                PPFD      RH    wind          Ds_Jmax           Ds_gmc
    #> 1 1500 [umol/m^2/s] 0.5 [1] 2 [m/s] 388.04 [J/K/mol] 487.29 [J/K/mol]
    #>            Ea_Jmax            Ea_KC            Ea_KO            Ea_Rd
    #> 1 56095.18 [J/mol] 80989.78 [J/mol] 23719.97 [J/mol] 40446.75 [J/mol]
    #>           Ea_Vcmax          Ea_Vtpu     Ea_gammastar           Ea_gmc
    #> 1 52245.78 [J/mol] 52245.78 [J/mol] 24459.97 [J/mol] 68901.56 [J/mol]
    #>            Ed_Jmax           Ed_gmc             D_c0            D_h0
    #> 1 121244.8 [J/mol] 148788.6 [J/mol] 1.29e-05 [m^2/s] 1.9e-05 [m^2/s]
    #>               D_m0             D_w0           G                 R       eT
    #> 1 1.33e-05 [m^2/s] 2.12e-05 [m^2/s] 9.8 [m/s^2] 8.31446 [J/K/mol] 1.75 [1]
    #>     epsilon                sigma                 C_i
    #> 1 0.622 [1] 5.67e-08 [W/K^4/m^2] 350.1432 [umol/mol]

## Replace default parameters

You can look at default parameters settings in the manual (run `?make_parameters`). These defaults are reasonable, but of course you will probably want to use different choices and allow some parameters to vary. Here, I’ll demonstrate how to replace a default. In the next section, I’ll show you how to set up a gradient of parameter values over which to solve for leaf temperature.

    # Use the `replace` argument to replace defaults. This must be a named list, and
    # each named element must have the proper units specified. See `?make_parameters`
    # for all parameter names and proper units.

    # Temperature response parameters can be updated (but we won't do that here)
    bake_par = make_bakepar()

    # Physical constants probably do not need to be replaced in most cases,
    # that's why we call them 'constants'!
    constants  = make_constants(use_tealeaves = FALSE)

    # First, we'll change photosynthetic photon flux density to 1000 umol / (m^2 s)
    enviro_par = make_enviropar(
      replace = list(
        PPFD = set_units(1000, "umol/m^2/s")
        ), use_tealeaves = FALSE
      )

    # Next, we'll change stomatal conductance to 0.3 mol / m^2 / s.
    leaf_par = make_leafpar(
      replace = list(
        g_sc = set_units(0.3, mol / m^2 / s)
        ), use_tealeaves = FALSE
      )

    photo <- photo(leaf_par, enviro_par, bake_par, constants, quiet = TRUE,
                   use_tealeaves = FALSE)

    photo |>
      select(PPFD, C_chl, A) |>
      knitr::kable()

PPFD | C_chl | A
--- | --- | ---
1000 [umol/m^2/s] | 252.6879 [umol/mol] | 25.63373 [umol/m^2/s]

## Environmental gradients

In the previous two examples, I used the `photo` function to solve for a single parameter set. In most cases, you’ll want to solve for many parameter sets. The function `photosynthesis` generalizes `photo` and makes it easy to solve for multiple parameter sets using the same argument structure. All you need to do is specify multiple values for one or more leaf or environmental parameters and `photosynthesis` uses the `purrr::cross` function to fit all combinations1.

    # As before, use the `replace` argument to replace defaults, but this time we
    # enter multiple values

    bake_par = make_bakepar()
    constants = make_constants(use_tealeaves = FALSE)

    # First, we'll change the PPFD to 1000 and 1500 umol / (m^2 s)
    enviro_par = make_enviropar(
      replace = list(
        PPFD = set_units(c(1000, 1500), umol / m^2 / s)
        ), use_tealeaves = FALSE
      )

    # Next, we'll change stomatal conductance to to 0.2 and 0.4 mol / m^2 / s
    leaf_par  = make_leafpar(
      replace = list(
        g_sc = set_units(c(0.2, 0.4), mol / m^2 / s)
        ), use_tealeaves = FALSE
      )

    # Now there should be 4 combinations (high and low g_sc crossed with high and low PPFD)
    ph = photosynthesis(leaf_par, enviro_par, bake_par, constants,
                         use_tealeaves = FALSE, progress = FALSE, quiet = TRUE)

    ph |>
      select(g_sc, PPFD, A) |>
      knitr::kable()

g_sc | PPFD | A
--- | --- | ---
0.2 [mol/m^2/s] | 1000 [umol/m^2/s] | 24.34817 [umol/m^2/s]
0.4 [mol/m^2/s] | 1000 [umol/m^2/s] | 26.27649 [umol/m^2/s]
0.2 [mol/m^2/s] | 1500 [umol/m^2/s] | 25.68222 [umol/m^2/s]
0.4 [mol/m^2/s] | 1500 [umol/m^2/s] | 27.94273 [umol/m^2/s]

## Parallel processing

It can take a little while to simulate many different parameter sets. If you have multiple processors available, you can speed things up by running simulations in parallel. In the `photosynthesis` function, simply use the `parallel = TRUE` argument to simulate in parallel. You’ll need to set up a future `plan()`. See `?future::plan` for more detail. Here I’ll provide an example simulating an \(A-C_c\) curve.

    # NOTE: parallel example is not evaluated because it was causing an issue with CRAN, but you can copy-and-paste the code to run on your own machine.

    library(future)
    plan("multisession") # Set up plan

    # We'll use the `replace` argument to enter multiple atmospheric CO2 concentrations

    bake_par = make_bakepar()
    constants  = make_constants(use_tealeaves = FALSE)

    enviro_par = make_enviropar(
      replace = list(
        C_air = set_units(seq(10, 2000, length.out = 20), umol / mol)
        ), use_tealeaves = FALSE
      )

    leaf_par  = make_leafpar(use_tealeaves = FALSE)

    ph = photosynthesis(leaf_par, enviro_par, bake_par, constants,
                         use_tealeaves = FALSE, progress = FALSE,
                         quiet = TRUE, parallel = TRUE)

    # Plot C_c versus A
    library(ggplot2)

    ## Drop units for plotting
    ph %<>% mutate_if(~ is(.x, "units"), drop_units)
    ggplot(ph, aes(C_chl, A)) +
      geom_line(size = 2) +
      xlab(expression(paste(C[chl], " [ppm]"))) +
      ylab(expression(paste("A [", mu, "mol ", m^-2~s^-1, "]"))) +
      theme_bw() +
      NULL

## Incorporating leaf temperature using tealeaves

In experiments, leaf temperature can be kept close to air temperature, but in nature, leaf temperature can be quite a bit different than air temperature in the shade depending on environmental and leaf parameters. If `use_tealeaves = TRUE`, `photo()` and `photosynthesis()` will call on the tealeaves package to calculate leaf temperature using an energy balance model.

    # NOTE: parallel example is not evaluated because it was causing an issue with CRAN, but you can copy-and-paste the code to run on your own machine.

    # You will need to set use_tealeaves = TRUE when making parameters because additional parameters are needed for tealeaves.

    bake_par = make_bakepar()
    constants  = make_constants(use_tealeaves = TRUE)

    enviro_par = make_enviropar(
      replace = list(
        T_air = set_units(seq(288.15, 313.15, 1), K)
        ), use_tealeaves = TRUE
      )

    leaf_par = make_leafpar(replace = list(
        g_sc = set_units(c(0.2, 0.4), mol / m^2 / s)
        ), use_tealeaves = TRUE
      )

    ph = photosynthesis(leaf_par, enviro_par, bake_par, constants,
                         use_tealeaves = TRUE, progress = FALSE,
                       quiet = TRUE, parallel = TRUE)

    # Plot temperature and photosynthesis
    library(ggplot2)

    ## Drop units for plotting
    ph %<>%
      mutate_if(~ is(.x, "units"), drop_units) %>%
      mutate(`g[s]` = ifelse(g_sc == 0.2, "low", "high"))

    ggplot(ph, aes(T_air, T_leaf, color = `g[s]`)) +
      geom_line(size = 2, lineend = "round") +
      geom_abline(slope = 1, intercept = 0, linetype = "dotted") +
      scale_color_discrete(name = expression(g[s])) +
      xlab(expression(paste(T[air], " [K]"))) +
      ylab(expression(paste(T[leaf], " [K]"))) +
      theme_bw() +
      NULL

    ggplot(ph, aes(T_air, A, color = `g[s]`)) +
      geom_line(size = 2, lineend = "round") +
      scale_color_discrete(name = expression(g[s])) +
      xlab(expression(paste(T[leaf], " [K]"))) +
      ylab(expression(paste("A [", mu, "mol ", m^-2~s^-1, "]"))) +
      theme_bw() +
      NULL

1. Since optimization is somewhat time-consuming, be careful about crossing too many combinations. Use `progress = TRUE` to show progress bar with estimated time remaining.↩︎