Package 'photosynthesis'

CO2 supply and demand function (mol / m^2 s)

Description

This function is not intended to be called by users directly.

Usage

A_supply(C_chl, pars, unitless = FALSE, use_legacy_version = FALSE)

A_demand(C_chl, pars, unitless = FALSE)

Arguments

C_chl	Chloroplastic CO2 concentration in Pa of class units
pars	Concatenated parameters (leaf_par, enviro_par, and constants)
unitless	Logical. Should units be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.
use_legacy_version	Logical. Should legacy model (<2.1.0) be used? See NEWS for further information. Default is FALSE.

Details

Supply function:

$A = g_\mathrm{tc} (C_\mathrm{air} - C_\mathrm{chl})$

Demand function:

$A = (1 - \Gamma* / C_\mathrm{chl}) \mathrm{min}(W_\mathrm{carbox}, W_\mathrm{regen}, W_\mathrm{tpu}) - R_\mathrm{d}$

Symbol	R	Description	Units	Default
$A$	A	photosynthetic rate	$\mu$mol CO2 / (m^2 s)	calculated
$g_\mathrm{tc}$	g_tc	total conductance to CO2	$\mu$mol CO2 / (m$^2$ s Pa)	calculated
$C_\mathrm{air}$	C_air	atmospheric CO2 concentration	Pa	41
$C_\mathrm{chl}$	C_chl	chloroplastic CO2 concentration	Pa	calculated
$R_\mathrm{d}$	R_d	nonphotorespiratory CO2 release	$\mu$mol CO2 / (m$^2$ s)	2
$\Gamma*$	gamma_star	chloroplastic CO2 compensation point	Pa	3.743

Value

Value in mol / (m^2 s) of class units

Examples

bake_par = make_bakepar()
constants = make_constants(use_tealeaves = FALSE)
enviro_par = make_enviropar(use_tealeaves = FALSE)
leaf_par = make_leafpar(use_tealeaves = FALSE)
leaf_par = bake(leaf_par, enviro_par, bake_par, constants)
# Or bake with piping (need library(magrittr))
# leaf_par %<>% bake(enviro_par, bake_par, constants)
enviro_par$T_air = leaf_par$T_leaf

pars = c(leaf_par, enviro_par, constants)
C_chl = set_units(350, umol/mol)

A_supply(C_chl, pars)

A_demand(C_chl, pars)

---

Running 2-parameter sensitivity analyses

Description

Running 2-parameter sensitivity analyses

Usage

analyze_sensitivity(
  data,
  funct,
  test1 = NA,
  values1,
  test2 = NA,
  values2,
  element_out = 1,
  ...
)

Arguments

data	Dataframe
funct	Function to use - do not use parentheses
test1	Input parameter to vary and test
values1	Values of test1 to use
test2	Input parameter to vary and test
values2	Values of test2 to use
element_out	List element to compile
...	Additional arguments required for the function

Value

analyze_sensitivity runs a 2-parameter sensitivity analysis. Note that any parameter value combinations that break the input function WILL break this function. For 1-parameter sensitivity analysis, use test1 only.

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data <- read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Define a grouping factor based on light intensity to split the ACi
# curves
data$Q_2 <- as.factor((round(data$Qin, digits = 0)))

# Convert leaf temperature to K
data$T_leaf <- data$Tleaf + 273.15

# Run a sensitivity analysis on gamma_star and mesophyll conductance
# at 25 Celsius for one individual curve
# pars <- analyze_sensitivity(
#   data = data[data$Q_2 == 1500, ],
#   funct = fit_aci_response,
#   varnames = list(
#     A_net = "A",
#     T_leaf = "T_leaf",
#     C_i = "Ci",
#     PPFD = "Qin"
#   ),
#   useg_mct = TRUE,
#   test1 = "gamma_star25",
#   element_out = 1,
#   test2 = "g_mc25",
#   fitTPU = TRUE,
#   Ea_gamma_star = 0,
#   Ea_g_mc = 0,
#   values1 = seq(
#     from = 20,
#     to = 40,
#     by = 2
#   ),
#   values2 = seq(
#     from = 0.5,
#     to = 2,
#     by = 0.1
#   )
# )

# Graph V_cmax
# ggplot(pars, aes(x = gamma_star25, y = g_mc25, z = V_cmax)) +
#   geom_tile(aes(fill = V_cmax)) +
#   labs(
#     x = expression(Gamma * "*"[25] ~ "(" * mu * mol ~ mol^
#       {
#         -1
#       } * ")"),
#     y = expression(g[m][25] ~ "(" * mu * mol ~ m^{
#       -2
#     } ~ s^{
#       -1
#     } ~ Pa^
#       {
#         -1
#       } * ")")
#   ) +
#   scale_fill_distiller(palette = "Greys") +
#   geom_contour(colour = "Black", size = 1) +
#   theme_bw()
#

---

Non-rectangular hyperbolic model of light responses

Description

Please use marshall_biscoe_1980().

Usage

aq_response(k_sat, phi_J, Q_abs, theta_J)

Arguments

k_sat	Light saturated rate of process k
phi_J	Quantum efficiency of process k
Q_abs	Absorbed light intensity (umol m-2 s-1)
theta_J	Curvature of the light response

Value

aq_response is used to describe the response of a process to absorbed light intensity. Assumes that input is absorbed light. Note that if absorbed light is not used, then the meaning of phi_J becomes unclear. This function is designed to be used with fit_aq_response, however it could easily be fed into a different fitting approach (e.g. Bayesian approaches). Originally from Marshall et al. 1980.

References

Marshall B, Biscoe P. 1980. A model for C3 leaves describing the dependence of net photosynthesis on irradiance. J Ex Bot 31:29-39

---

Leaf parameter temperature responses

Description

'bake' leaf parameters using temperature response functions

Usage

bake(leaf_par, enviro_par, bake_par, constants, assert_units = TRUE)

temp_resp1(par25, E_a, R, T_leaf, T_ref, unitless)

temp_resp2(par25, D_s, E_a, E_d, R, T_leaf, T_ref, unitless)

Arguments

leaf_par	A list of leaf parameters inheriting class leaf_par. This can be generated using the make_leafpar function.
enviro_par	A list of environmental parameters inheriting class enviro_par. This can be generated using the make_enviropar function.
bake_par	A list of temperature response parameters inheriting class bake_par. This can be generated using the make_bakepar function.
constants	A list of physical constants inheriting class constants. This can be generated using the make_constants function.
assert_units	Logical. Should parameter units be checked? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.
par25	Parameter value at 25 °C of class units.
E_a	Empirical temperature response value in J/mol of class units.
R	Ideal gas constant in J / (mol K) of class units. See make_constants().
T_leaf	Leaf temperature in K of class units. Will be converted to °C.
T_ref	Reference temperature in K of class units.
unitless	Logical. Should units be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.
D_s	Empirical temperature response value in J / (mol K) of class units.
E_d	Empirical temperature response value in J/mol of class units.

Details

Several leaf parameters (leaf_par()) are temperature sensitive. Temperature-sensitive parameters are input at a reference temperature of 25 °C. These parameters are provided as par_name25 and then "baked" using the appropriate temperature response function and parameters in bake_par(). The "baked" parameter will have the name without "25" appended (par_name). E.g. V_cmax25 becomes V_cmax.

Temperature response functions following Buckley and Diaz-Espejo (2015)

Temperature response function 1 (temp_response1):

$\mathrm{par}(T_\mathrm{leaf}) = \mathrm{par25}~\mathrm{exp}(E_\mathrm{a} / (R T_\mathrm{ref}) (T_\mathrm{leaf} - 25) / (T_\mathrm{leaf} + 273.15))$

$T_\mathrm{ref}$ is the reference temperature in K
$T_\mathrm{leaf}$ is the leaf temperature in °C

Temperature response function 2 (temp_response2) is the above equation multiplied by:

$(1 + \mathrm{exp}((D_\mathrm{s} / R - E_\mathrm{d} / (R T_\mathrm{ref})))) / (1 + \mathrm{exp}((D_\mathrm{s} / R) - (E_\mathrm{d} / (R (T_\mathrm{leaf} + 273.15)))))$

Function 1 increases exponentially with temperature; Function 2 peaks a particular temperature.

Value

Constructor function for baked class. This will also inherit class leaf_par() and list(). This function ensures that temperature is "baked in" to leaf parameter calculations T_leaf using temperature response functions detailed below.

References

Buckley TN, Diaz-Espejo A. 2015. Partitioning changes in photosynthetic rate into contributions from different variables. Plant, Cell and Environment 38: 1200-1211.

Examples

bake_par = make_bakepar()
constants = make_constants(use_tealeaves = FALSE)
enviro_par = make_enviropar(use_tealeaves = FALSE)
leaf_par = make_leafpar(
  replace = list(T_leaf = set_units(293.15, K)),
  use_tealeaves = FALSE
)
baked_leafpar = bake(leaf_par, enviro_par, bake_par, constants)

baked_leafpar$V_cmax25
baked_leafpar$V_cmax

---

S3 class bake_par

Description

S3 class bake_par

Usage

bake_par(.x)

Arguments

.x	A list to be constructed into bake_par.

Value

Constructor function for bake_par class. This function ensures that leaf temperature gets properly "baked" into leaf parameters.

---

S3 class baked

Description

See bake()

---

Inverse non-rectangular hyperbola for J_max calculation

Description

Inverse non-rectangular hyperbola for J_max calculation

Usage

calculate_jmax(PPFD, alpha, J, theta_J)

calculate_j(PPFD, alpha, J_max, theta_J)

Arguments

PPFD	light intensity in umol m-2 s-1
alpha	initial slope of the light response
J	electron transport rate in umol m-2 s-1
theta_J	curvature of the light response
J_max	maximum rate of electron transport in umol m-2 s-1

Value

calculate_jmax calculates J_max given PPFD and J. It is necessary for the electron transport component of the fit_aci_response function.

calculate_j provides a model of the light response of J. It is necessary for fitting the electron transport component of the photosynthetic CO2 response curves in fit_aci_response.

---

Get default functions for calculated parameters in photosynthesis

Description

Get default functions for calculated parameters in photosynthesis

Usage

get_f_parameter(.f_name)

Arguments

.f_name

character string of function

---

Conductance to CO2 (mol / m^2 / s)

Description

Conductance to CO2 (mol / m^2 / s)

• g_tc: total conductance to CO2

• g_uc: cuticular conductance to CO2

• g_bc: boundary layer conductance to CO2

• g_mc: mesophyll conductance to CO2

• g_sc: stomatal conductance to CO2

Usage

.get_gtc(pars, unitless, use_legacy_version)

.get_guc(pars, surface, unitless)

.get_gbc(pars, surface, unitless, use_legacy_version)

.get_gmc(pars, surface, unitless)

.get_gsc(pars, surface, unitless)

Arguments

pars	Concatenated parameters (leaf_par, enviro_par, and constants)
unitless	Logical. Should units be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.
use_legacy_version	Logical. Should legacy model (<2.1.0) be used? See NEWS for further information. Default is FALSE.
surface	Leaf surface (lower or upper)

Details

Default conductance model

The conductance model described in this section is used by default unless additional anatomical parameters described in the next section are provided.

Total conductance to CO2 is the sum of parallel conductances on the lower ($g_\mathrm{c,lower}$) and upper ($g_\mathrm{c,upper}$) leaf portions:

$g_\mathrm{c,total} = g_\mathrm{c,lower} + g_\mathrm{c,upper}$

Each partial conductance consists of two parallel conductances, the cuticular conductance ($g_\mathrm{u,c}$) and the in-series conductances through mesophyll ($g_\mathrm{m,c}$), stomata ($g_\mathrm{s,c}$), and boundary layer ($g_\mathrm{b,c}$). To simplify the formula, I use substitute resistance where $r_x = 1 / g_x$. For surface $i$:

$g_{\mathrm{c},i} = g_{\mathrm{u},i} + (1 / (r_{\mathrm{m},i} + r_{\mathrm{s},i} + r_{\mathrm{b},i}))$

The cuticular, stomatal, and mesophyll conductances can be the same or different for upper and lower. The partitioning factors ($k_x$) divide the conductance between surfaces while keeping the total conductance constant:

$g_{x,\mathrm{lower}} = g_x (1 / (1 + k_x))$

$g_{x,\mathrm{upper}} = g_x (k_x / (1 + k_x))$

$g_x = g_{x,\mathrm{lower}} + g_{x,\mathrm{upper}}$

How the partitioning factors work:

$k_x$	description
0	all conductance on lower surface/portion
0.5	2/3 conductance on lower surface
1	conductance evenly divided between surfaces/portions
2	2/3 conductance on upper surface
Inf	all conductance on upper surface/portion

The boundary layer conductances for each are calculated on the basis of mass and heat transfer (see .get_gbc()).

Symbol	R	Description	Units	Default
$g_\mathrm{mc}$	g_mc	mesophyll conductance to CO2 (T_leaf)	mol / m$^2$ / s	calculated
$g_\mathrm{sc}$	g_sc	stomatal conductance to CO2	mol / m$^2$ / s	0.4
$g_\mathrm{uc}$	g_uc	cuticular conductance to CO2	mol / m$^2$ / s	0.01
$k_\mathrm{mc}$	k_mc	partition of $g_\mathrm{mc}$ to lower mesophyll	none	1
$k_\mathrm{sc}$	k_sc	partition of $g_\mathrm{sc}$ to lower surface	none	1
$k_\mathrm{uc}$	k_uc	partition of $g_\mathrm{uc}$ to lower surface	none	1

New conductance model

The conductance model described in this section is implemented in photosynthesis (>= 2.1.0) if parameters to calculate the internal airspace and liquid-phase conductances (A_mes_A, g_liqc) are provided. These parameters are 1) the effective path lengths through the lower and upper leaf internal airspaces (delta_ias_lower, delta_ias_upper) and 2) the mesophyll area per leaf area (A_mes_A) and liquid-phase conductance per mesophyll cell area (g_liqc).

Two parallel diffusion pathways, one from each leaf surface, converge to a single CO2 concentration at the mesophyll cell boundary. We use a single liquid-phase resistance to represent the combined cell wall, plasmalemma, and chloroplast resistances. The gas-phase resistance through boundary layer, cuticle/stomata, and internal airspace is $r_\mathrm{gas,c}$; the liquid-phase intracellular resistance is $r_\mathrm{i,c}$.

$r_\mathrm{total,c} = r_\mathrm{gas,c} + r_\mathrm{i,c}$

The gas-phase resistance occurs through two parallel pathways, which we refer to as the 'lower' and 'upper' pathways because horizontally oriented leaves often have different anatomical properties on each surface. The gas-phase resistance through pathway $i \in \{\textrm{lower,upper\}}$ is:

$r_{\mathrm{gas,c},i} = r_{\mathrm{b,c},i} + r_{\mathrm{u+s,c},i} + r_{\mathrm{ias,c},i}$

The subscripts $_\mathrm{b}$, $_\mathrm{u+s}$, and $_\mathrm{ias}$ denote boundary layer, cuticular + stomatal, and internal airspace, respectively. The subscript $_\mathrm{c}$ indicates we are considering the conductance to CO2 rather than another molecular species.

Cuticular and stomatal conductances (1 / resistance) are parallel, so:

$1 / r_{\mathrm{u+s,c},i} = g_{\mathrm{u+s,c},i} = g_{\mathrm{u,c},i} + g_{\mathrm{s,c},i}$

Substituting the above expression into the equation for $r_{\mathrm{gas,c},i}$:

$r_{\mathrm{gas,c},i} = r_{\mathrm{b,c},i} + 1 / (g_{\mathrm{u,c},i} = g_{\mathrm{s,c},i}) + r_{\mathrm{ias,c},i}$

The total gas-phase resistance is the inverse of the sum of the parallel lower and upper conductances:

$1 / r_{\mathrm{gas,c}} = g_\mathrm{gas,c,lower} + g_\mathrm{gas,c,upper}$

The cuticular, stomatal, and mesophyll conductances can be the same or different for upper and lower. The partitioning factors $k_u$ and $k_s$ divide the total cuticular and stomatal conductances, respectively, between surfaces while keeping the total conductance constant:

$g_{x,\mathrm{lower}} = g_x (1 / (1 + k_x))$

$g_{x,\mathrm{upper}} = g_x (k_x / (1 + k_x))$

$g_x = g_{x,\mathrm{lower}} + g_{x,\mathrm{upper}}$

How the partitioning factors work:

$k_x$	description
0	all conductance on lower surface/portion
0.5	2/3 conductance on lower surface
1	conductance evenly divided between surfaces/portions
2	2/3 conductance on upper surface
Inf	all conductance on upper surface/portion

The internal airspace conductance is the diffusivity of CO2 at a given temperature and pressure divided by the effective path length:

$g_\mathrm{ias,c,lower} = D_\mathrm{c} / \delta_\mathrm{ias,lower}$

$g_\mathrm{ias,c,upper} = D_\mathrm{c} / \delta_\mathrm{ias,upper}$

g_iasc_lower and g_iasc_upper are calculated in the bake function. See tealeaves::.get_Dx() for calculating D_c.

The liquid-phase intracellular resistance is given by:

$1 / r_\mathrm{i,c} = g_\mathrm{i,c} = g_\mathrm{liq,c} A_\mathrm{mes} / A$

$g_\mathrm{liq,c}$ is temperature sensitive. See bake().

The boundary layer conductances for each are calculated on the basis of mass and heat transfer (see .get_gbc()).

---

Compiling outputs from lists

Description

Compiling outputs from lists

Usage

compile_data(data, output_type = "list", list_element)

Arguments

data	List of elements
output_type	Type of desired output. For graphs or models, use "list", for parameters, use "dataframe".
list_element	Which elements of the sublists do you wish to compile?

Value

compile_data converts the outputs of fit_many into a form more readily usable for analysis. Can be used to create dataframe of all fitted parameters, a list of model outputs, a list of graphs for plotting. This function is NOT restricted to compiling outputs from plantecophystools but could be used to compile elements from ANY list of lists.

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data <- read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Define a grouping factor based on light intensity to split the ACi
# curves
data$Q_2 <- as.factor((round(data$Qin, digits = 0)))

# Convert leaf temperature to K
data$T_leaf <- data$Tleaf + 273.15

# Fit many curves
fits <- fit_many(
  data = data,
  varnames = list(
    A_net = "A",
    T_leaf = "T_leaf",
    C_i = "Ci",
    PPFD = "Qin"
  ),
  funct = fit_aci_response,
  group = "Q_2"
)

# Compile graphs into a list for plotting
fits_graphs <- compile_data(fits,
  list_element = 2
)

# Plot one graph from the compiled list
plot(fits_graphs[[1]])

---

Computing measures of sensitivity

Description

Computing measures of sensitivity

Usage

compute_sensitivity(
  data,
  varnames = list(Par = "Par", test1 = "test1", test2 = "test2"),
  test1_ref,
  test2_ref
)

Arguments

data	Dataframe with output from sensitivity_analysis()
varnames	Variable names
test1_ref	Reference value for parameter
test2_ref	Reference value for parameter

Value

compute_sensitivity calculates two sets of sensitivity measures: parameter effect (Bauerle et al., 2014), and control coefficient (Capaldo & Pandis, 1997). This function is useful in determining how much a given input (assumed or otherwise) can affect the model output and conclusions. Particularly useful if a given parameter is unknown during a fitting or modeling process.

References

Bauerle WL, Daniels AB, Barnard DM. 2014. Carbon and water flux responses to physiology by environment interactions: a sensitivity analysis of variation in climate on photosynthetic and stomatal parameters. Climate Dynamics 42: 2539-2554.

Capaldo KP, Pandis SN 1997. Dimethylsulfide chemistry in the remote marine atmosphere: evaluation and sensitivity analysis of available mechanisms. J Geophys Res 102:23251-23267

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data <- read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Define a grouping factor based on light intensity to split the ACi
# curves
data$Q_2 <- as.factor((round(data$Qin, digits = 0)))

# Convert leaf temperature to K
data$T_leaf <- data$Tleaf + 273.15

# Run a sensitivity analysis on gamma_star and mesophyll conductance
# at 25 Celsius for one individual curve
# pars <- analyze_sensitivity(
#   data = data[data$Q_2 == 1500, ],
#   funct = fit_aci_response,
#   varnames = list(
#     A_net = "A",
#     T_leaf = "T_leaf",
#     C_i = "Ci",
#     PPFD = "Qin"
#   ),
#   useg_mct = TRUE,
#   test1 = "gamma_star25",
#   element_out = 1,
#   test2 = "g_mc25",
#   fitTPU = TRUE,
#   Ea_gamma_star = 0,
#   Ea_g_mc = 0,
#   values1 = seq(
#     from = 20,
#     to = 60,
#     by = 2
#   ),
#   values2 = seq(
#     from = 0.2,
#     to = 2,
#     by = 0.1
#   )
# )
# Compute measures of sensitivity
# par2 <- compute_sensitivity(
#   data = pars,
#   varnames = list(
#     Par = "V_cmax",
#     test1 = "gamma_star25",
#     test2 = "g_mc25"
#   ),
#   test1_ref = 42,
#   test2_ref = 1
# )
# # Plot control coefficients
# ggplot(par2, aes(y = CE_gamma_star25, x = CE_g_mc25, colour = V_cmax)) +
#   geom_point() +
#   theme_bw()
# # Note that in this case a missing point appears due to an infinity

---

S3 class constants

Description

S3 class constants

Usage

constants(.x, use_tealeaves)

Arguments

.x	A list to be constructed into constants.
use_tealeaves	Logical. Should leaf energy balance be used to calculate leaf temperature (T_leaf)? If TRUE, tleaf() calculates T_leaf. If FALSE, user-defined T_leaf is used. Additional parameters and constants are required, see make_parameters().

Value

Constructor function for constants class. This function ensures that physical constant inputs are properly formatted.

---

S3 class enviro_par

Description

S3 class enviro_par

Usage

enviro_par(.x, use_tealeaves)

Arguments

.x	A list to be constructed into enviro_par.
use_tealeaves	Logical. Should leaf energy balance be used to calculate leaf temperature (T_leaf)? If TRUE, tleaf() calculates T_leaf. If FALSE, user-defined T_leaf is used. Additional parameters and constants are required, see make_parameters().

Value

Constructor function for enviro_par class. This function ensures that environmental parameter inputs are properly formatted.

---

Fitting ACi curves

Description

Fitting ACi curves

Usage

fit_aci_response(
  data,
  varnames = list(A_net = "A_net", T_leaf = "T_leaf", C_i = "C_i", PPFD = "PPFD", g_mc =
    "g_mc"),
  P = 100,
  fitTPU = TRUE,
  alpha_g = 0,
  R_d_meas = NULL,
  useR_d = FALSE,
  useg_mc = FALSE,
  useg_mct = FALSE,
  usegamma_star = FALSE,
  useK_M = FALSE,
  useK_C_K_O = FALSE,
  alpha = 0.24,
  theta_J = 0.85,
  gamma_star25 = 42.75,
  Ea_gamma_star = 37830,
  K_M25 = 718.4,
  Ea_K_M = 65508.28,
  g_mc25 = 0.08701,
  Ea_g_mc = 0,
  K_C25 = NULL,
  Ea_K_C = NULL,
  K_O25 = NULL,
  Ea_K_O = NULL,
  Oconc = 21,
  gamma_star_set = NULL,
  K_M_set = NULL,
  ...
)

Arguments

data	Dataframe for A-Ci curve fitting
varnames	List of variable names. varnames = list(A_net = "A_net", T_leaf = "T_leaf", C_i = "C_i", PPFD = "PPFD", g_mc = "g_mc"), where A_net is net CO2 assimilation, T_leaf is leaf temperature in Kelvin, C_i is intercellular CO2 concentration in umol/mol, PPFD is incident irradiance in umol m-2 s-1 (note that it is ASSUMED to be absorbed irradiance, so be sure to adjust according to light absorbance and PSI/PSII partitioning accordingly OR interpret the resultant values of J and J_max with caution), g_mc is mesophyll conductance to CO2 in mol m-2 s-1 Pa-1.
P	Atmospheric pressure in kPa
fitTPU	Should triose phosphate utilization (V_TPU) be fit?
alpha_g	Fraction of respiratory glycolate carbon that is not returned to the chloroplast (von Caemmerer, 2000). If ACi curves show high-CO2 decline, then this value should be > 0.
R_d_meas	Measured value of respiratory CO2 efflux in umol m-2 s-1. Input value should be positive to work as expected with the equations.
useR_d	Use a measured value of R_d? Set to TRUE if using R_d_meas.
useg_mc	Use mesophyll conductance? Set to TRUE if specifying g_mc in varnames above.
useg_mct	Use mesophyll conductance temperature response? Set to TRUE if using a temperature response of mesophyll conductance.
usegamma_star	Specify gamma_star value? If FALSE, uses a temperature response function with Nicotiana tabacum defaults from Bernacchi et al. 2001.
useK_M	Specify K_M? If FALSE, uses an Arrhenius temperature response function with Nicotiana tabacum defaults from Bernacchi et al. 2001.
useK_C_K_O	Use individual carboxylation/oxygenation constants for rubisco? If TRUE, need to specify values at 25C and activation energy for the Arrhenius temperature response function.
alpha	Quantum yield of CO2 assimilation
theta_J	Curvature of the photosynthetic light response curve
gamma_star25	gamma_star at 25C in umol mol-1
Ea_gamma_star	Activation energy of gamma_star in J mol-1
K_M25	Michaelis-Menten constant for rubisco at 25C
Ea_K_M	Activation energy for K_M in J mol-1
g_mc25	Mesophyll conductance at 25C in mol m-2 s-1
Ea_g_mc	Activation energy of g_mc in J mol-1
K_C25	Michaelis-Menten constant for rubisco carboxylation at 25C
Ea_K_C	Activation energy for K_C in J mol-1
K_O25	Michaelis-Menten constant for rubisco oxygenation at 25C
Ea_K_O	Activation energy for K_O in J mol-2
Oconc	O2 concentration in %. Used with P to calculate intracellular O2 when using K_C_K_O
gamma_star_set	Value of gamma_star to use (in ppm) if usegamma_star = TRUE
K_M_set	Value of K_M to use if useK_M = TRUE
...	Other arguments to pass on

Value

fit_aci_response fits ACi curves using an approach similar to Gu et al. 2010. Iterates all possible C_i transition points and checks for inadmissible curve fits. If no curves are admissible (either due to poor data or poor assumed parameters), the output will include a dataframe of NA values. Default parameters are all from Bernacchi et al. 2001, 2002.

References

Bernacchi CJ, Singsaas EL, Pimentel C, Portis AR, Long SP. 2001. Improved temperature response functions for models of rubisco-limited photosynthesis. Plant Cell Environment 24:253-259.

Bernacchi CJ, Portis AR, Nakano H, von Caemmerer S, Long SP. 2002. Temperature response of mesophyll conductance. Implications for the determination of rubisco enzyme kinetics and for limitations to photosynthesis in vivo. Plant Physiology 130:1992-1998.

Gu L, Pallardy SG, Tu K, Law BE, Wullschleger SD. 2010. Reliable estimation of biochemical parameters from C3 leaf photosynthesis-intercellular carbon dioxide response curves. Plant Cell Environment 33:1852-1874.

von Caemmerer S. 2000. Biochemical models of leaf photosynthesis. CSIRO Publishing, Collingwood.

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data <- read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Define a grouping factor based on light intensity to split the ACi
# curves
data$Q_2 <- as.factor((round(data$Qin, digits = 0)))

# Convert leaf temperature to K
data$T_leaf <- data$Tleaf + 273.15

# Fit ACi curve. Note that we are subsetting the dataframe
# here to fit for a single value of Q_2
fit <- fit_aci_response(data[data$Q_2 == 1500, ],
  varnames = list(
    A_net = "A",
    T_leaf = "T_leaf",
    C_i = "Ci",
    PPFD = "Qin"
  )
)

# View fitted parameters
fit[[1]]

# View graph
fit[[2]]

# View data with modelled parameters attached
fit[[3]]

# Fit many curves
fits <- fit_many(
  data = data,
  varnames = list(
    A_net = "A",
    T_leaf = "T_leaf",
    C_i = "Ci",
    PPFD = "Qin"
  ),
  funct = fit_aci_response,
  group = "Q_2"
)

# Print the parameters
# First set of double parentheses selects an individual group value
# Second set selects an element of the sublist
fits[[3]][[1]]

# Print the graph
fits[[3]][[2]]

# Compile graphs into a list for plotting
fits_graphs <- compile_data(fits,
  list_element = 2
)

# Compile parameters into dataframe for analysis
fits_pars <- compile_data(fits,
  output_type = "dataframe",
  list_element = 1
)

---

Fitting light responses of net CO2 assimilation

Description

Please use fit_aq_response2().

Usage

fit_aq_response(
  data,
  varnames = list(A_net = "A_net", PPFD = "PPFD"),
  usealpha_Q = FALSE,
  alpha_Q = 0.84,
  title = NULL
)

Arguments

data	Dataframe containing CO2 assimilation light response
varnames	Variable names where varnames = list(A_net = "A_net", PPFD = "PPFD"). A_net is net CO2 assimilation in umol m-2 s-1, PPFD is incident irradiance. PPFD can be corrected for light absorbance by using useapha_Q and setting alpha_Q.
usealpha_Q	Correct light intensity for absorbance? Default is FALSE.
alpha_Q	Absorbance of incident light. Default value is 0.84.
title	Title for graph

Value

fit_aq_response fits the light response of net CO2 assimilation. Output is a dataframe containing light saturated net CO2 assimilation, quantum yield of CO2 assimilation (phi_J), curvature of the light response (theta_J), respiration (Rd), light compensation point (LCP), and residual sum of squares (resid_SS). Note that Rd fitted in this way is essentially the same as the Kok method, and represents a respiration value in the light that may not be accurate. Rd output should thus be interpreted more as a residual parameter to ensure an accurate fit of the light response parameters. Model originally from Marshall & Biscoe 1980.

References

Marshall B, Biscoe P. 1980. A model for C3 leaves describing the dependence of net photosynthesis on irradiance. J Ex Bot 31:29-39

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data = read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Fit many AQ curves
# Set your grouping variable
# Here we are grouping by CO2_s and individual
data$C_s = (round(data$CO2_s, digits = 0))

# For this example we need to round sequentially due to CO2_s setpoints
data$C_s = as.factor(round(data$C_s, digits = -1))

# To fit one AQ curve
fit = fit_aq_response(data[data$C_s == 600, ],
  varnames = list(
    A_net = "A",
    PPFD = "Qin"
  )
)

# Print model summary
summary(fit[[1]])

# Print fitted parameters
fit[[2]]

# Print graph
fit[[3]]

# Fit many curves
fits = fit_many(
  data = data,
  varnames = list(
    A_net = "A",
    PPFD = "Qin",
    group = "C_s"
  ),
  funct = fit_aq_response,
  group = "C_s"
)

# Look at model summary for a given fit
# First set of double parentheses selects an individual group value
# Second set selects an element of the sublist
summary(fits[[3]][[1]])

# Print the parameters
fits[[3]][[2]]

# Print the graph
fits[[3]][[3]]

# Compile graphs into a list for plotting
fits_graphs = compile_data(fits,
  list_element = 3
)

# Compile parameters into dataframe for analysis
fits_pars = compile_data(fits,
  output_type = "dataframe",
  list_element = 2
)

---

Fit photosynthetic light-response curves

Description

We recommend using fit_photosynthesis() with argument .photo_fun = "aq_response" rather than calling this function directly.

Usage

fit_aq_response2(
  .data,
  .model = "default",
  .method = "ls",
  usealpha_Q = FALSE,
  alpha_Q = 0.84,
  quiet = FALSE,
  brm_options = NULL
)

Arguments

.data	A data frame containing plant ecophysiological data. See required_variables() for the variables required for each model.
.model	A character string of model name to use. See get_all_models().
.method	A character string of the statistical method to use: 'ls' for least-squares and 'brms' for Bayesian model using brms::brm(). Default is 'ls'.
usealpha_Q	Flag. Should light intensity be multiplied by alpha_Q before fitting? Default is FALSE (i.e. assume that '.Q' is absorbed light).
alpha_Q	Number. Absorbance of incident light. Default value is 0.84. Ignored if usealpha_Q = FALSE.
quiet	Flag. Should messages be suppressed? Default is FALSE.
brm_options	A list of options passed to brms::brm() if .method = "brms". Default is NULL.

Value

• If .method = 'ls': an stats::nls() object.

• If .method = 'brms': a brms::brmsfit() object.

Note

Rd fitted in this way is essentially the same as the Kok (1956) method, and represents a respiration value in the light that may not be accurate. Rd output should thus be interpreted more as a residual parameter to ensure an accurate fit of the light response parameters. Model originally from Marshall & Biscoe (1980).

References

Marshall B, Biscoe P. 1980. A model for C3 leaves describing the dependence of net photosynthesis on irradiance. J Ex Bot 31:29-39

Examples

library(broom)
library(dplyr)
library(photosynthesis)

# Read in your data
dat = system.file("extdata", "A_Ci_Q_data_1.csv", package = "photosynthesis") |>
  read.csv() |>
  # Set grouping variable
  mutate(group = round(CO2_s, digits = 0)) |>
  # For this example, round sequentially due to CO2_s set points
  mutate(group = as.factor(round(group, digits = -1)))

# Fit one light-response curve
fit = fit_photosynthesis(
  .data = filter(dat, group == 600),
  .photo_fun = "aq_response",
  .vars = list(.A = A, .Q = Qabs),
)

# The 'fit' object inherits class 'nls' and many methods can be used

## Model summary:
summary(fit)

## Estimated parameters:
coef(fit)

## 95% confidence intervals:
confint(fit)

## Tidy summary table using 'broom::tidy()'
tidy(fit, conf.int = TRUE, conf.level = 0.95)

# Fit multiple curves with **photosynthesis** and **purrr**

library(purrr)

fits = dat |>
  split(~ group) |>
  map(fit_photosynthesis, .photo_fun = "aq_response", .vars = list(.A = A, .Q = Qabs))

---

Fitting mesophyll conductance with the variable J method

Description

Fitting mesophyll conductance with the variable J method

Usage

fit_g_mc_variableJ(
  data,
  varnames = list(A_net = "A_net", J_etr = "J_etr", C_i = "C_i", PPFD = "PPFD", phi_PSII
    = "phi_PSII"),
  usealpha_Q = FALSE,
  alpha_Q = 0.84,
  beta_Q = 0.5,
  gamma_star,
  R_d,
  P = 100
)

Arguments

data	Dataframe
varnames	Variable names to fit g_mc. varnames = list(A_net = "A_net", J_etr = "J_etr", C_i = "C_i", PPFD = "PPFD", phi_PSII = "phi_PSII"), where A_net is net CO2 assimilation in umol m-2 s-1, J_etr is linear electron transport flux in umol m-2 s-1, C_i is intercellular CO2 concentration in umol mol-1, PPFD is incident irradiance in umol m-2 s-1, phi_PSII is the operating efficiency of photosystem II.
usealpha_Q	Recalculate electron transport with new absorbance value?
alpha_Q	Absorbance of photosynthetically active radiation
beta_Q	Partitioning of absorbed light energy between PSI and PSII
gamma_star	Photorespiratory CO2 compensation point in umol mol-1
R_d	Respiration rate in umol m-2 s-1
P	Atmospheric pressure in kPa

Value

fit_g_mc_variableJ fits mesophyll conductance according to Harley et al. 1992. It also tests the reliability of the calculation and calculates a mean with only reliable values. Note that the output is in units of umol m-2 s-1 Pa-1.

References

Harley PC, Loreto F, Di Marco G, Sharkey TD. 1992. Theoretical considerations when estimating mesophyll conductance to CO2 flux by analysis of the response of photosynthesis to CO2. Plant Physiol 98:1429 - 1436.

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data <- read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Note: there will be issues here if the alpha value used
# for calculating ETR is off, if gamma_star is incorrect,
# if R_d is incorrect.
data <- fit_g_mc_variableJ(data,
  varnames = list(
    A_net = "A",
    J_etr = "ETR",
    C_i = "Ci",
    PPFD = "Qin",
    phi_PSII = "PhiPS2"
  ),
  gamma_star = 46,
  R_d = 0.153,
  usealpha_Q = TRUE,
  alpha_Q = 0.84,
  beta_Q = 0.5,
  P = 84
)

# Note that many g_mc values from this method can be unreliable
ggplot(data, aes(x = CO2_s, y = g_mc, colour = reliable)) +
  labs(
    x = expression(CO[2] ~ "(" * mu * mol ~ mol^
      {
        -1
      } * ")"),
    y = expression(g[m] ~ "(mol" ~ m^{
      -2
    } ~ s^{
      -1
    } ~ Pa^
      {
        -1
      } * ")")
  ) +
  geom_point(size = 2) +
  theme_bw() +
  theme(legend.position = "bottom")

# Plot QAQC graph according to Harley et al. 1992
ggplot(data, aes(x = CO2_s, y = dCcdA, colour = reliable)) +
  labs(
    x = expression(CO[2] ~ "(" * mu * mol ~ mol^
      {
        -1
      } * ")"),
    y = expression(delta * C[chl] * "/" * delta * A)
  ) +
  geom_hline(yintercept = 10) +
  geom_point(size = 2) +
  theme_bw() +
  theme(legend.position = "bottom")

---

Fitting stomatal conductance models

Description

Fitting stomatal conductance models

Usage

fit_gs_model(
  data,
  varnames = list(A_net = "A_net", C_air = "C_air", g_sw = "g_sw", RH = "RH", VPD =
    "VPD"),
  model = c("BallBerry", "Leuning", "Medlyn_partial", "Medlyn_full"),
  D0 = 3,
  ...
)

Arguments

data	Dataframe
varnames	Variable names For the Ball-Berry model: varnames = list(A_net = "A_net", C_air = "C_air", g_sw = "g_sw", RH = "RH") where A_net is net CO2 assimilation, C_air is CO2 concentration at the leaf surface in umol mol-1, g_sw is stomatal conductance to H2O, and RH is relative humidity as a proportion. For the Leuning model: varnames = list(A_net = "A_net", C_air = "C_air", g_sw = "g_sw", VPD = "VPD") where A_net is net CO2 assimilation, C_air is CO2 concentration at the leaf surface in umol mol-1, g_sw is stomatal conductance to H2O, and VPD is leaf to air vapor pressure deficit in kPa. For the Medlyn et al. 2011 models: varnames = list(A_net = "A_net", C_air = "C_air", g_sw = "g_sw", VPD = "VPD") where A_net is net CO2 assimilation, C_air is CO2 concentration at the leaf surface in umol mol-1, g_sw is stomatal conductance to H2O, and VPD is leaf to air vapor pressure deficit in kPa.
model	Which model(s) to fit? Defaults to all models. Available options are "BallBerry", "Leuning", "Medlyn_partial", and "Medlyn_full", from Ball et al. (1987), Leuning (1995), and Medlyn et al. (2011).
D0	Vapor pressure sensitivity of stomata (Leuning 1995)
...	Arguments to pass on to the nlsLM() function for the Medlyn models.

Value

fit_gs_model fits one or more stomatal conductance models to the data. The top level of the output list is named after the fitted model, while the second level contains the Model, Parameters, and Graph, in that order.

References

Ball JT, Woodrow IE, Berry JA. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions, in Progress in Photosynthesis Research, Proceedings of the VII International Congress on Photosynthesis, vol. 4, edited by I. Biggins, pp. 221–224, Martinus Nijhoff, Dordrecht, Netherlands.

Leuning R. 1995. A critical appraisal of a coupled stomatal- photosynthesis model for C3 plants. Plant Cell Environ 18:339-357

Medlyn BE, Duursma RA, Eamus D, Ellsworth DS, Prentice IC, Barton CVM, Crous KY, Angelis PD, Freeman M, Wingate L. 2011. Reconciling the optimal and empirical approaches to modeling stomatal conductance. Glob Chang Biol 17:2134-2144

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data <- read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Convert RH to a proportion
data$RH <- data$RHcham / 100

# Fit stomatal conductance models
# Can specify a single model, or all as below
fits <- fit_gs_model(
  data = data,
  varnames = list(
    A_net = "A",
    C_air = "Ca",
    g_sw = "gsw",
    RH = "RH",
    VPD = "VPDleaf"
  ),
  model = c(
    "BallBerry",
    "Leuning",
    "Medlyn_partial",
    "Medlyn_full"
  ),
  D0 = 3
)

# Look at BallBerry model summary:
summary(fits[["BallBerry"]][["Model"]])

# Look at BallBerry parameters
fits[["BallBerry"]][["Parameters"]]

# Look at BallBerry plot
fits[["BallBerry"]][["Graph"]]

# Fit many g_sw models
# Set your grouping variable
# Here we are grouping by Qin and individual
data$Q_2 <- as.factor((round(data$Qin, digits = 0)))

fits <- fit_many(data,
  varnames = list(
    A_net = "A",
    C_air = "Ca",
    g_sw = "gsw",
    RH = "RH",
    VPD = "VPDleaf"
  ),
  funct = fit_gs_model,
  group = "Q_2"
)

# Look at the Medlyn_partial outputs at 750 PAR
# Model summary
summary(fits[["750"]][["Medlyn_partial"]][["Model"]])

# Model parameters
fits[["750"]][["Medlyn_partial"]][["Parameters"]]

# Graph
fits[["750"]][["Medlyn_partial"]][["Graph"]]

# Compile parameter outputs for BallBerry model
# Note that it's the first element for each PAR value
# First compile list of BallBerry fits
bbmods <- compile_data(
  data = fits,
  output_type = "list",
  list_element = 1
)
# Now compile the parameters (2nd element) into a dataframe
bbpars <- compile_data(
  data = bbmods,
  output_type = "dataframe",
  list_element = 2
)

# Convert group variable back to numeric
bbpars$ID <- as.numeric(bbpars$ID)

# Take quick look at light response of intercept parameters
plot(g0 ~ ID, bbpars)

# Compile graphs
graphs <- compile_data(
  data = bbmods,
  output_type = "list",
  list_element = 3
)

# Look at 3rd graph
graphs[[3]]

---

Fitting hydraulic vulnerability curves

Description

Fitting hydraulic vulnerability curves

Usage

fit_hydra_vuln_curve(
  data,
  varnames = list(psi = "psi", PLC = "PLC"),
  start_weibull = list(a = 2, b = 2),
  title = NULL
)

Arguments

data	Dataframe
varnames	List of variable names. varnames = list(psi = "psi", PLC = "PLC") where psi is water potential in MPa, and PLC is percent loss conductivity.
start_weibull	starting values for the nls fitting routine for the Weibull curve
title	Title for the output graph

Value

fit_hydra_vuln_curve fits a sigmoidal function (Pammenter & Van der Willigen, 1998) linearized according to Ogle et al. (2009). Output is a list containing the sigmoidal model in element 1 and Weibull model in element 4, the fit parameters with 95% confidence interval for both models are in element 2, and hydraulic parameters in element 3 (including P25, P50, P88, P95, S50, Pe, Pmax, DSI). Px (25 to 95): water potential at which x% of conductivity is lost. S50: slope at 50% loss of conductivity. Pe: air entry point. Pmax: hydraulic failure threshold. DSI: drought stress interval. Element 5 is a graph showing the fit, P50, Pe, and Pmax.

References

Ogle K, Barber JJ, Willson C, Thompson B. 2009. Hierarchical statistical modeling of xylem vulnerability to cavitation. New Phytologist 182:541-554

Pammenter NW, Van der Willigen CV. 1998. A mathematical and statistical analysis of the curves illustrating vulnerability of xylem to cavitation. Tree Physiology 18:589-593

Examples

# Read in data
data <- read.csv(system.file("extdata", "hydraulic_vulnerability.csv",
  package = "photosynthesis"
))

# Fit hydraulic vulnerability curve
fit <- fit_hydra_vuln_curve(data[data$Tree == 4 & data$Plot == "Control", ],
  varnames = list(
    psi = "P",
    PLC = "PLC"
  ),
  title = "Control 4"
)

# Return Sigmoidal model summary
summary(fit[[1]])

# Return Weibull model summary
summary(fit[[4]])

# Return model parameters with 95\% confidence intervals
fit[[2]]

# Return hydraulic parameters
fit[[3]]

# Return graph
fit[[5]]

# Fit many curves
fits <- fit_many(
  data = data,
  varnames = list(
    psi = "P",
    PLC = "PLC"
  ),
  group = "Tree",
  funct = fit_hydra_vuln_curve
)

# To select individuals from the many fits
# Return model summary
summary(fits[[1]][[1]]) # Returns model summary

# Return sigmoidal model output
fits[[1]][[2]]

# Return hydraulic parameters
fits[[1]][[3]]

# Return graph
fits[[1]][[5]]

# Compile parameter outputs
pars <- compile_data(
  data = fits,
  output_type = "dataframe",
  list_element = 3
)

# Compile graphs
graphs <- compile_data(
  data = fits,
  output_type = "list",
  list_element = 5
)

---

Fitting many functions across groups

Description

We are no longer updating this function. Please use generic methods like map instead. See vignette("light-response") for an example.

Usage

fit_many(data, funct, group, progress = TRUE, ...)

Arguments

data	Dataframe
funct	Function to fit
group	Grouping variables
progress	Flag. Show progress bar?
...	Arguments for the function to fit. Use ?functionname to read the help file on available arguments for a given function.

Value

fit_many fits a function across every instance of a grouping variable.

Examples

# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data = read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Define a grouping factor based on light intensity to split the ACi
# curves
data$Q_2 = as.factor((round(data$Qin, digits = 0)))

# Convert leaf temperature to K
data$T_leaf = data$Tleaf + 273.15

# Fit many curves
fits = fit_many(
  data = data,
  varnames = list(
    A_net = "A",
    T_leaf = "T_leaf",
    C_i = "Ci",
    PPFD = "Qin"
  ),
  funct = fit_aci_response,
  group = "Q_2"
)

# Print the parameters
# First set of double parentheses selects an individual group value
# Second set selects an element of the sublist
fits[[3]][[1]]

# Print the graph
fits[[3]][[2]]

# Compile graphs into a list for plotting
fits_graphs = compile_data(fits,
  list_element = 2
)


# Compile parameters into dataframe for analysis
fits_pars = compile_data(fits,
  output_type = "dataframe",
  list_element = 1
)

---

Fit photosynthetic models with gas-exchange data

Description

Fit photosynthetic models with gas-exchange data

Usage

fit_photosynthesis(
  .data,
  .photo_fun,
  .model = "default",
  .vars = NULL,
  .method = "ls",
  ...,
  quiet = FALSE,
  brm_options = NULL
)

Arguments

.data	A data frame containing plant ecophysiological data. See required_variables() for the variables required for each model.
.photo_fun	A character string of photosynthesis function to call. One of: ⁠aq_response, r_light⁠.
.model	A character string of model name to use. See get_all_models().
.vars	A list to rename variables in .data. See required_variables() for the accepted variable names.
.method	A character string of the statistical method to use: 'ls' for least-squares and 'brms' for Bayesian model using brms::brm(). Default is 'ls'.
...	Additional arguments passed to specific models. See specific help pages for each type of photosynthetic model: Light-response curves fit_aq_response2() Light respiration fit_r_light2()
quiet	Flag. Should messages be suppressed? Default is FALSE.
brm_options	A list of options passed to brms::brm() if .method = "brms". Default is NULL.

Value

A fitted model object

• class 'lm' or 'nls' if method = 'ls'

• class 'brmsfit' if method = 'brms'

Note

This function will fit models to data but several methods require post-processing to extract meaningful parameter estimates and confidence intervals. See vignettes for further explanation and examples.

• Light-response curves: vignette("light-response", package = "photosynthesis")

• Light respiration: vignette("light-respiration", package = "photosynthesis")

---

Fitting pressure-volume curves

Description

Fitting pressure-volume curves

Usage

fit_PV_curve(
  data,
  varnames = list(psi = "psi", mass = "mass", leaf_mass = "leaf_mass", bag_mass =
    "bag_mass", leaf_area = "leaf_area"),
  title = NULL
)

Arguments

data	Dataframe
varnames	Variable names. varnames = list(psi = "psi", mass = "mass", leaf_mass = "leaf_mass", bag_mass = "bag_mass", leaf_area = "leaf_area") where psi is leaf water potential in MPa, mass is the weighed mass of the bag and leaf in g, leaf_mass is the mass of the leaf in g, bag_mass is the mass of the bag in g, and leaf_area is the area of the leaf in cm2.
title	Graph title

Value

fit_PV_curve fits pressure-volume curve data to determine: SWC: saturated water content per leaf mass (g H2O g leaf dry mass ^ -1), PI_o: osmotic potential at full turgor (MPa), psi_TLP: leaf water potential at turgor loss point (TLP) (MPa), RWC_TLP: relative water content at TLP (%), eps: modulus of elasticity at full turgor (MPa), C_FT: relative capacitance at full turgor (MPa ^ -1), C_TLP: relative capacitance at TLP (MPa ^ -1), and C_FTStar: absolute capacitance per leaf area (g m ^ -2 MPa ^ -1). Element 1 of the output list contains the fitted parameters, element 2 contains the water-psi graph, and element 3 contains the 1/psi-100-RWC graph.

References

Koide RT, Robichaux RH, Morse SR, Smith CM. 2000. Plant water status, hydraulic resistance and capacitance. In: Plant Physiological Ecology: Field Methods and Instrumentation (eds RW Pearcy, JR Ehleringer, HA Mooney, PW Rundel), pp. 161-183. Kluwer, Dordrecht, the Netherlands

Sack L, Cowan PD, Jaikumar N, Holbrook NM. 2003. The 'hydrology' of leaves: co-ordination of structure and function in temperate woody species. Plant, Cell and Environment, 26, 1343-1356

Tyree MT, Hammel HT. 1972. Measurement of turgor pressure and water relations of plants by pressure bomb technique. Journal of Experimental Botany, 23, 267

Examples

# Read in data
data <- read.csv(system.file("extdata", "PV_curve.csv",
  package = "photosynthesis"
))

# Fit one PV curve
fit <- fit_PV_curve(data[data$ID == "L2", ],
  varnames = list(
    psi = "psi",
    mass = "mass",
    leaf_mass = "leaf_mass",
    bag_mass = "bag_mass",
    leaf_area = "leaf_area"
  )
)

# See fitted parameters
fit[[1]]

# Plot water mass graph
fit[[2]]

# Plot PV Curve
fit[[3]]

# Fit all PV curves in a file
fits <- fit_many(data,
  group = "ID",
  funct = fit_PV_curve,
  varnames = list(
    psi = "psi",
    mass = "mass",
    leaf_mass = "leaf_mass",
    bag_mass = "bag_mass",
    leaf_area = "leaf_area"
  )
)

# See parameters
fits[[1]][[1]]

# See water mass - water potential graph
fits[[1]][[2]]

# See PV curve
fits[[1]][[3]]

# Compile parameter outputs
pars <- compile_data(
  data = fits,
  output_type = "dataframe",
  list_element = 1
)

# Compile the water mass - water potential graphs
graphs1 <- compile_data(
  data = fits,
  output_type = "list",
  list_element = 2
)

# Compile the PV graphs
graphs2 <- compile_data(
  data = fits,
  output_type = "list",
  list_element = 3
)

---

Estimating light respiration

Description

Please use fit_r_light2().

Usage

fit_r_light_kok(
  data,
  varnames = list(A_net = "A_net", PPFD = "PPFD"),
  PPFD_lower = 40,
  PPFD_upper = 100
)

fit_r_light_WalkerOrt(
  data,
  varnames = list(A_net = "A_net", C_i = "C_i", PPFD = "PPFD"),
  P = 100,
  C_i_threshold = 300
)

fit_r_light_yin(
  data,
  varnames = list(A_net = "A_net", PPFD = "PPFD", phi_PSII = "phi_PSII"),
  PPFD_lower = 40,
  PPFD_upper = 100
)

Arguments

data	Dataframe
varnames	List of variable names
PPFD_lower	Lower light intensity limit for estimating Rlight (Kok & Yin)
PPFD_upper	Upper light intensity limit for estimating Rlight (Kok & Yin)
P	Atmospheric pressure in kPa (Walker & Ort, 2015)
C_i_threshold	Threshold C_i (in umol / mol) to cut data to linear region for fitting light respiration and gamma_star (Walker & Ort, 2015)

Value

fit_r_light_kok estimates light respiration using the Kok method (Kok, 1956). The Kok method involves looking for a breakpoint in the light response of net CO2 assimilation at very low light intensities and extrapolating from data above the breakpoint to estimate light respiration as the y-intercept. r_light value should be negative, denoting an efflux of CO2.

fit_r_light_WalkerOrt estimates light respiration and GammaStar according to Walk & Ort (2015) using a slope- intercept regression method to find the intercept of multiple ACi curves run at multiple light intensities. Output GammaStar and respiration should be negative If output respiration is positive this could indicate issues (i.e. leaks) in the gas exchange measurements. GammaStar is output in umol mol-1, and respiration is output in umol m-2 s-1 of respiratory flux. Output is a list containing the slope intercept regression model, a graph of the fit, and estimates of the coefficients. NOTE: if using C_i, the output value is technically C_istar. You need to use Cc to get GammaStar. Also note, however, that the convention in the field is to completely ignore this note.

fit_r_light_yin estimates light respiration according to the Yin et al. (2009, 2011) modifications of the Kok method. The modification uses fluorescence data to get a better estimate of light respiration. Note that respiration output should be negative here to denote an efflux of CO2.

References

Kok B. 1956. On the inhibition of photosynthesis by intense light. Biochimica et Biophysica Acta 21: 234–244

Walker BJ, Ort DR. 2015. Improved method for measuring the apparent CO2 photocompensation point resolves the impact of multiple internal conductances to CO2 to net gas exchange. Plant Cell Environ 38:2462- 2474

Yin X, Struik PC, Romero P, Harbinson J, Evers JB, van der Putten PEL, Vos J. 2009. Using combined measurements of gas exchange and chlorophyll fluorescence to estimate parameters of a biochemical C3 photosynthesis model: a critical appraisal and a new integrated approach applied to leaves in a wheat (Triticum aestivum) canopy. Plant Cell Environ 32:448-464

Yin X, Sun Z, Struik PC, Gu J. 2011. 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

Examples

# FITTING KOK METHOD
# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data = read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Fit light respiration with Kok method
r_light = fit_r_light_kok(
  data = data,
  varnames = list(
    A_net = "A",
    PPFD = "Qin"
  ),
  PPFD_lower = 20,
  PPFD_upper = 150
)
# Return r_light
r_light

# FITTING WALKER-ORT METHOD
# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data = read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Fit the Walker-Ort method for GammaStar and light respiration
walker_ort = fit_r_light_WalkerOrt(data,
  varnames = list(
    A_net = "A",
    C_i = "Ci",
    PPFD = "Qin"
  )
)
# Extract model
summary(walker_ort[[1]])

# View graph
walker_ort[[2]]

# View coefficients
walker_ort[[3]]

# FITTING THE YIN METHOD
# Read in your data
# Note that this data is coming from data supplied by the package
# hence the complicated argument in read.csv()
# This dataset is a CO2 by light response curve for a single sunflower
data = read.csv(system.file("extdata", "A_Ci_Q_data_1.csv",
  package = "photosynthesis"
))

# Fit light respiration with Yin method
r_light = fit_r_light_yin(
  data = data,
  varnames = list(
    A_net = "A",
    PPFD = "Qin",
    phi_PSII = "PhiPS2"
  ),
  PPFD_lower = 20,
  PPFD_upper = 250
)

---

Fit models to estimate light respiration ($R_\mathrm{d}$)

Description

We recommend using fit_photosynthesis() with argument .photo_fun = "r_light" rather than calling this function directly.

Usage

fit_r_light2(
  .data,
  .model = "default",
  .method = "ls",
  Q_lower = NA,
  Q_upper = NA,
  Q_levels = NULL,
  C_upper = NA,
  quiet = FALSE,
  brm_options = NULL
)

Arguments

.data	A data frame containing plant ecophysiological data. See required_variables() for the variables required for each model.
.model	A character string of model name to use. See get_all_models().
.method	A character string of the statistical method to use: 'ls' for least-squares and 'brms' for Bayesian model using brms::brm(). Default is 'ls'.
Q_lower	Lower light intensity limit for estimating Rd using kok_1956 and yin_etal_2011 models.
Q_upper	Upper light intensity limit for estimating Rd using kok_1956 and yin_etal_2011 models
Q_levels	A numeric vector of light intensity levels ($\mu$mol / mol) for estimating $R_\mathrm{d}$ from the linear region of the A-C curve using the walker_ort_2015 model.
C_upper	Upper C ($\mu$mol / mol) limit for estimating $R_\mathrm{d}$ from the linear region of the A-C curve using the walker_ort_2015 model.
quiet	Flag. Should messages be suppressed? Default is FALSE.
brm_options	A list of options passed to brms::brm() if .method = "brms". Default is NULL.

Value

• If .method = 'ls': an stats::nls() or stats::lm() object.

• If .method = 'brms': a brms::brmsfit() object.

Note

Confusingly, $R_\mathrm{d}$ typically denotes respiration in the light, but you might see $R_\mathrm{day}$ or $R_\mathrm{light}$.

Models

Kok (1956)

The kok_1956 model estimates light respiration using the Kok method (Kok, 1956). The Kok method involves looking for a breakpoint in the light response of net CO2 assimilation at very low light intensities and extrapolating from data above the breakpoint to estimate light respiration as the y-intercept. Rd value should be negative, denoting an efflux of CO2.

Yin et al. (2011)

The yin_etal_2011 model estimates light respiration according to the Yin et al. (2009, 2011) modifications of the Kok method. The modification uses fluorescence data to get a better estimate of light respiration. Rd values should be negative here to denote an efflux of CO2.

Walker & Ort (2015)

The walker_ort_2015 model estimates light respiration and $\Gamma*$ according to Walker & Ort (2015) using a slope- intercept regression method to find the intercept of multiple A-C curves run at multiple light intensities. The method estimates $\Gamma*$ and $R_\mathrm{d}$. If estimated $R_\mathrm{d}$ is positive this could indicate issues (i.e. leaks) in the gas exchange measurements. $\Gamma*$ is in units of umol / mol and $R_\mathrm{d}$ is in units of $\mu$mol m$^{-2}$ s$^{-1}$ of respiratory flux. If using $C_\mathrm{i}$, the estimated value is technically $C_\mathrm{i}$*. You need to use $C_\mathrm{c}$ to get $\Gamma*$ Also note, however, that the convention in the field is to completely ignore this note.

References

Kok B. 1956. On the inhibition of photosynthesis by intense light. Biochimica et Biophysica Acta 21: 234–244

Walker BJ, Ort DR. 2015. Improved method for measuring the apparent CO2 photocompensation point resolves the impact of multiple internal conductances to CO2 to net gas exchange. Plant Cell Environ 38:2462- 2474

Yin X, Struik PC, Romero P, Harbinson J, Evers JB, van der Putten PEL, Vos J. 2009. Using combined measurements of gas exchange and chlorophyll fluorescence to estimate parameters of a biochemical C3 photosynthesis model: a critical appraisal and a new integrated approach applied to leaves in a wheat (Triticum aestivum) canopy. Plant Cell Environ 32:448-464

Yin X, Sun Z, Struik PC, Gu J. 2011. 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

Examples

# Walker & Ort (2015) model

library(broom)
library(dplyr)
library(photosynthesis)

acq_data = system.file("extdata", "A_Ci_Q_data_1.csv", package = "photosynthesis") |> 
  read.csv()

fit = fit_photosynthesis(
  .data = acq_data,
  .photo_fun = "r_light",
  .model = "walker_ort_2015",
  .vars = list(.A = A, .Q = Qin, .C = Ci),
  C_upper = 300,
  # Irradiance levels used in experiment
  Q_levels =  c(1500, 750, 375, 125, 100, 75, 50, 25),
)

# The 'fit' object inherits class 'lm' and many methods can be used

## Model summary:
summary(fit)

## Estimated parameters:
coef(fit)

## 95% confidence intervals:
## n.b. these confidence intervals are not correct because the regression is fit 
## sequentially. It ignores the underlying data and uncertainty in estimates of 
## slopes and intercepts with each A-C curve. Use '.method = "brms"' to properly 
## calculate uncertainty. 
confint(fit)

## Tidy summary table using 'broom::tidy()'
tidy(fit, conf.int = TRUE, conf.level = 0.95)

## Calculate residual sum-of-squares
sum(resid(fit)^2)

# Yin et al. (2011) model

fit = fit_photosynthesis(
  .data = acq_data,
  .photo_fun = "r_light",
  .model = "yin_etal_2011",
  .vars = list(.A = A, .phiPSII = PhiPS2, .Q = Qin),
  Q_lower = 20,
  Q_upper = 250
)

# The 'fit' object inherits class 'lm' and many methods can be used

## Model summary:
summary(fit)

## Estimated parameters:
coef(fit)

## 95% confidence intervals:
confint(fit)

## Tidy summary table using 'broom::tidy()'
tidy(fit, conf.int = TRUE, conf.level = 0.95)

## Calculate residual sum-of-squares
sum(resid(fit)^2)

# Kok (1956) model

fit = fit_photosynthesis(
  .data = acq_data,
  .photo_fun = "r_light",
  .model = "kok_1956",
  .vars = list(.A = A, .Q = Qin),
  Q_lower = 20,
  Q_upper = 150
)

# The 'fit' object inherits class 'lm' and many methods can be used

## Model summary:
summary(fit)

## Estimated parameters:
coef(fit)

## 95% confidence intervals:
confint(fit)

## Tidy summary table using 'broom::tidy()'
tidy(fit, conf.int = TRUE, conf.level = 0.95)

## Calculate residual sum-of-squares
sum(resid(fit)^2)

---

Fitting temperature responses

Description

Fitting temperature responses

Usage

fit_t_response(
  data,
  varnames = list(Par = "Par", T_leaf = "T_leaf"),
  model = c("Arrhenius", "Kruse", "Heskel", "Medlyn", "MMRT", "Quadratic", "Topt"),
  start = list(a = 1, b = 1, c = 1, dEa = 1, Ea_ref = 1, Par_ref = 1, Ea = 40000, Par25 =
    50, Hd = 2e+05, dS = 650, dCp = 1, dG = 1, dH = 1),
  setvar = "none",
  hdset = 2e+05,
  dSset = 650,
  title = NULL,
  ...
)

Arguments

data	Dataframe with temperature response variables
varnames	Variable names, where Par is the parameter of interest, and T_leaf is the leaf temperature in K.
model	Which temperature response model do you want to use? Defaults to all: Arrhenius, Heskel, Kruse, Medlyn, MMRT, Quadratic, and Topt.
start	List of starting parameters for the nls model fits. a, b, and c are needed for the Heskel model, dEa, Ea_ref, and Par_ref are needed for the Kruse model, Ea, Par25, and Hd are all needed for the Medlyn and Topt models while the Medlyn model also requires dS, and dCP, dG, and dH are all for the MMRT model.
setvar	Which variable to set as constant for the Medlyn model? Defaults to "none", while "Hd" and "dS" options are available.
hdset	Which value should Hd be set to when setvar = "Hd"? Specify in J/mol.
dSset	Which value should dS be set to when setvar = "dS"? Specify in J/mol/K.
title	Title of output graphs
...	Further arguments to pass on to the nlsLM() function

Value

fit_t_response fits one or more temperature response models to a dataset, returning a list of lists. The parent list contains the models, while the child list for each model contains the fitted model in element 1, the coefficients in element 2, and a graph in element 3.

References

Arrhenius S. 1915. Quantitative laws in biological chemistry. Bell.

Heskel MA, O'Sullivan OS, Reich PB, Tjoelker MG, Weerasinghe LK, Penillard A, Egerton JJG, Creek D, Bloomfield KJ, Xiang J, Sinca F, Stangl ZR, la Torre AM, Griffin KL, Huntingford C, Hurry V, Meir P, Turnbull MH, Atkin OK. 2016. Convergence in the temperature response of leaf respiration across biomes and plant functional types. PNAS 113:3832-3837

Hobbs JK, Jiao W, Easter AD, Parker EJ, Schipper LA, Arcus VL. 2013. Change in heat capacity for enzyme catalysis determines temperature dependence of enzyme catalyzed rates. ACS Chemical Biology 8:2388-2393.

Kruse J, Adams MA. 2008. Three parameters comprehensively describe the temperature response of respiratory oxygen reduction. Plant Cell Environ 31:954-967

Liang LL, Arcus VL, Heskel MA, O'Sullivan OS, Weerasinghe LK, Creek D, Egerton JJG, Tjoelker MG, Atkin OK, Schipper LA. 2018. Macromolecular rate theory (MMRT) provides a thermodynamics rationale to underpin the convergent temperature response in plant leaf respiration. Glob Chang Biol 24:1538-1547

Medlyn BE, Dreyer E, Ellsworth D, Forstreuter M, Harley PC, Kirschbaum MUF, Le Roux X, Montpied P, Strassemeyer J, Walcroft A, Wang K, Loutstau D. 2002. Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data. Plant Cell Environ 25:1167-1179

Examples

# Read in data
data <- read.csv(system.file("extdata", "A_Ci_T_data.csv",
  package = "photosynthesis"
),
stringsAsFactors = FALSE
)

library(tidyr)

# Round temperatures to group them appropriately
# Use sequential rounding
data$T2 <- round(data$Tleaf, 1)
data$T2 <- round(data$Tleaf, 0)

# Look at unique values to detect rounding issues
unique(data$T2)

# Some still did not round correctly,
# manually correct
for (i in 1:nrow(data)) {
  if (data$T2[i] == 18) {
    data$T2[i] <- 17
  }
  if (data$T2[i] == 23) {
    data$T2[i] <- 22
  }
  if (data$T2[i] == 28) {
    data$T2[i] <- 27
  }
  if (data$T2[i] == 33) {
    data$T2[i] <- 32
  }
  if (data$T2[i] == 38) {
    data$T2[i] <- 37
  }
}

# Make sure it is a character string for grouping
data$T2 <- as.character(data$T2)

# Create grouping variable by ID and measurement temperature
data <- unite(data,
  col = "ID2", c("ID", "T2"),
  sep = "_"
)

# Split by temperature group
data <- split(data, data$ID2)

# Obtain mean temperature for group so temperature
# response fitting is acceptable later, round to
# 2 decimal places
for (i in 1:length(data)) {
  data[[i]]$Curve_Tleaf <- round(mean(data[[i]]$Tleaf), 2)
}

# Convert from list back to dataframe
data <- do.call("rbind", data)

# Parse grouping variable by ID and measurement temperature
data <- separate(data,
  col = "ID2", into = c("ID", "T2"),
  sep = "_"
)

# Make sure number of values matches number of measurement
# temperatures. May vary slightly if plants had slightly
# different leaf temperatures during the measurements
unique(data$Curve_Tleaf)

# Create ID column to curve fit by ID and temperature
data <- unite(data,
  col = "ID2", c("ID", "Curve_Tleaf"),
  sep = "_"
)

# Convert leaf temperature to K
data$T_leaf <- data$Tleaf + 273.15

# Fit many CO2 response curves
fits2 <- fit_many(
  data = data,
  group = "ID2",
  varnames = list(
    A_net = "A",
    C_i = "Ci",
    T_leaf = "T_leaf",
    PPFD = "Qin",
    g_mc = "g_mc"
  ),
  funct = fit_aci_response,
  alphag = 0
)

# Extract ACi parameters
pars <- compile_data(fits2,
  output_type = "dataframe",
  list_element = 1
)

# Extract ACi graphs
graphs <- compile_data(fits2,
  output_type = "list",
  list_element = 2
)

# Parse the ID variable
pars <- separate(pars, col = "ID", into = c("ID", "Curve_Tleaf"), sep = "_")

# Make sure curve leaf temperature is numeric
pars$Curve_Tleaf <- as.numeric(pars$Curve_Tleaf)
pars$T_leaf <- pars$Curve_Tleaf + 273.15

# Fit all models, set Hd to constant in Medlyn model
out <- fit_t_response(
  data = pars[pars$ID == "S2", ],
  varnames = list(
    Par = "V_cmax",
    T_leaf = "T_leaf"
  ),
  setvar = "Hd",
  hdset = 200000
)

out[["Arrhenius"]][["Graph"]]
out[["Heskel"]][["Graph"]]
out[["Kruse"]][["Graph"]]
out[["Medlyn"]][["Graph"]]
out[["MMRT"]][["Graph"]]
out[["Quadratic"]][["Graph"]]
out[["Topt"]][["Graph"]]

---

Farquhar-von Caemmerer-Berry (FvCB) C3 photosynthesis model

Description

Farquhar-von Caemmerer-Berry (FvCB) C3 photosynthesis model

Rubisco-limited assimilation rate

RuBP regeneration-limited assimilation rate

TPU-limited assimilation rate

Usage

FvCB(C_chl, pars, unitless = FALSE)

W_carbox(C_chl, pars, unitless = FALSE)

W_regen(C_chl, pars, unitless = FALSE)

W_tpu(C_chl, pars, unitless = FALSE)

Arguments

C_chl	Chloroplastic CO2 concentration in Pa of class units
pars	Concatenated parameters (leaf_par, enviro_par, and constants)
unitless	Logical. Should units be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

Equations following Buckley and Diaz-Espejo (2015):

Rubisco-limited assimilation rate:

$W_\mathrm{carbox} = V_\mathrm{c,max} C_\mathrm{chl} / (C_\mathrm{chl} + K_\mathrm{m})$

where:

$K_\mathrm{m} = K_\mathrm{C} (1 + O / K_\mathrm{O})$

RuBP regeneration-limited assimilation rate:

$W_\mathrm{regen} = J C_\mathrm{chl} / (4 C_\mathrm{chl} + 8 \Gamma*)$

where $J$ is a function of PPFD, obtained by solving the equation:

$0 = \theta_J J ^ 2 - J (J_\mathrm{max} + \phi_J PPFD) + J_\mathrm{max} \phi_J PPFD$

TPU-limited assimilation rate:

$W_\mathrm{tpu} = 3 V_\mathrm{tpu} C_\mathrm{chl} / (C_\mathrm{chl} - \Gamma*)$

Symbol	R	Description	Units	Default
$C_\mathrm{chl}$	C_chl	chloroplastic CO2 concentration	Pa	input
$\Gamma*$	gamma_star	chloroplastic CO2 compensation point (T_leaf)	Pa	calculated
$J_\mathrm{max}$	J_max	potential electron transport (T_leaf)	$\mu$mol CO2 / (m$^2$ s)	calculated
$K_\mathrm{C}$	K_C	Michaelis constant for carboxylation (T_leaf)	$\mu$mol / mol	calculated
$K_\mathrm{O}$	K_O	Michaelis constant for oxygenation (T_leaf)	$\mu$mol / mol	calculated
$O$	O	atmospheric O2 concentration	kPa	21.27565
$\phi_J$	phi_J	initial slope of the response of J to PPFD	none	0.331
PPFD	PPFD	photosynthetic photon flux density	umol quanta / (m^2 s)	1500
$R_\mathrm{d}$	R_d	nonphotorespiratory CO2 release (T_leaf)	$\mu$mol CO2 / (m$^2$ s)	calculated
$\theta_J$	theta_J	curvature factor for light-response curve	none	0.825
$V_\mathrm{c,max}$	V_cmax	maximum rate of carboxylation (T_leaf)	$\mu$mol CO2 / (m$^2$ s)	calculated
$V_\mathrm{tpu}$	V_tpu	rate of triose phosphate utilization (T_leaf)	$\mu$mol CO2 / (m$^2$ s)	calculated

Value

A list of four values with units umol CO2 / (m^2 s) of class units:

• W_carbox: Rubisco-limited assimilation rate
  

• W_regen: RuBP regeneration-limited assimilation rate
  

• W_tpu: TPU-limited assimilation rate
  

• A: minimum of W_carbox, W_regen, and W_tpu

References

Buckley TN and Diaz-Espejo A. 2015. Partitioning changes in photosynthetic rate into contributions from different variables. Plant, Cell & Environment 38: 1200-11.

Farquhar GD, Caemmerer S, Berry JA. 1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149: 78–90.

Examples

bake_par = make_bakepar()
constants = make_constants(use_tealeaves = FALSE)
enviro_par = make_enviropar(use_tealeaves = FALSE)
leaf_par = make_leafpar(use_tealeaves = FALSE)
leaf_par = bake(leaf_par, enviro_par, bake_par, constants)

pars = c(leaf_par, enviro_par, constants)
C_chl = set_units(246.0161, umol / mol)
FvCB(C_chl, pars)

---

Get default model

Description

Get the name of the default model used for different plant ecophysiological data analysis methods implemented in photosynthesis. Currently only used for fit_aq_response2() and fit_r_light2().

Light response models:

• marshall_biscoe_1980(): Non-rectangular hyperbolic model of light responses

• photoinhibition(): Non-rectangular hyperbolic model of light responses with photoinhibition of k_sat at increasing Q_abs

Usage

get_default_model(.photo_fun)

get_all_models(method)

marshall_biscoe_1980(Q_abs, k_sat, phi_J, theta_J)

photoinhibition(Q_abs, k_sat, phi_J, theta_J, b_inh)

Arguments

.photo_fun	A character string of photosynthesis function to call. One of: ⁠aq_response, r_light⁠.
method	A character string of the statistical method to use: 'ls' for least-squares and 'brms' for Bayesian model using brms::brm(). Default is 'ls'.
Q_abs	Absorbed light intensity ($\mu$mol m$^{-2}$ s$^{-1}$)
k_sat	Light saturated rate of process k
phi_J	Quantum efficiency of process k
theta_J	Curvature of the light response
b_inh	Inhibition parameter

Value

A character string with name of model.

Examples

get_default_model("aq_response")
get_default_model("r_light")

---

Stomatal conductance models

Description

Stomatal conductance models

Usage

gs_mod_ballberry(A_net, C_air, RH)

gs_mod_leuning(A_net, C_air, D0, VPD)

gs_mod_opti(g0, g1, VPD, A_net, C_air)

gs_mod_optifull(g0, g1, gk, VPD, A_net, C_air)

Arguments

A_net	Net CO2 assimilation in umol m-2 s-1
C_air	CO2 concentration at the leaf surface in umol mol-1
RH	Relative humidity as a proportion
D0	Vapor pressure sensitivity of stomata (Leuning 1995)
VPD	Vapor pressure deficit (kPa)
g0	Optimization model intercept term (Medlyn et al. 2011)
g1	Optimization model slope term (Medlyn et al. 2011)
gk	Optimization model root term (Medlyn et al. 2011)

Value

gs_mod_ballberry is used for fitting the Ball et al. (1987) model of stomatal conductance

gs_mod_leuning is used for fitting the Leuning (1995) model of stomatal conductance

gs_mod_opti fits the optimal stomatal conductance model according to Medlyn et al. 2011

gs_mod_optifull fits the full optimal stomatal conductance model according to Medlyn et al. 2011

References

Ball JT, Woodrow IE, Berry JA. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions, in Progress in Photosynthesis Research, Proceedings of the VII International Congress on Photosynthesis, vol. 4, edited by I. Biggins, pp. 221–224, Martinus Nijhoff, Dordrecht, Netherlands.

Leuning R. 1995. A critical appraisal of a coupled stomatal- photosynthesis model for C3 plants. Plant Cell Environ 18:339-357

Medlyn BE, Duursma RA, Eamus D, Ellsworth DS, Prentice IC, Barton CVM, Crous KY, Angelis PD, Freeman M, Wingate L. 2011. Reconciling the optimal and empirical approaches to modeling stomatal conductance. Glob Chang Biol 17:2134-2144

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J: Rate of electron transport (umol/m^2/s)

Description

Calculate the rate of electron transport as a function of photosynthetic photon flux density (PPFD).

Usage

J(pars, unitless = FALSE)

Arguments

pars	Concatenated parameters (leaf_par, enviro_par, and constants)
unitless	Logical. Should units be set? The function is faster when FALSE, but input must be in correct units or else results will be incorrect without any warning.

Details

$J$ as a function of PPFD is the solution to the quadratic expression:

$0 = \theta_J J ^ 2 - J (J_\mathrm{max} + \phi_J PPFD) + J_\mathrm{max} \phi_J PPFD$

Symbol	R	Description	Units	Default
$J_\mathrm{max}$	J_max	potential electron transport (T_leaf)	$\mu$mol CO2 / (m$^2$ s)	calculated
$\phi_J$	phi_J	initial slope of the response of J to PPFD	none	0.331
PPFD	PPFD	photosynthetic photon flux density	$\mu$mol quanta / (m^2 s)	1500
$\theta_J$	theta_J	curvature factor for light-response curve	none	0.825

Value

Value in $\mu$mol/ (m^2 s) of class units

Examples

library(magrittr)
library(photosynthesis)

bake_par = make_bakepar()
constants = make_constants(use_tealeaves = FALSE)
enviro_par = make_enviropar(use_tealeaves = FALSE)
leaf_par = make_leafpar(use_tealeaves = FALSE)
enviro_par$T_air = leaf_par$T_leaf
leaf_par %<>% bake(enviro_par, bake_par, constants)

pars = c(leaf_par, enviro_par, constants)
J(pars, FALSE)

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S3 class leaf_par

Description

S3 class leaf_par

Usage

leaf_par(.x, use_tealeaves)

Arguments

.x	A list to be constructed into leaf_par.
use_tealeaves	Logical. Should leaf energy balance be used to calculate leaf temperature (T_leaf)? If TRUE, tleaf() calculates T_leaf. If FALSE, user-defined T_leaf is used. Additional parameters and constants are required, see make_parameters().

Value

Constructor function for leaf_par class. This function ensures that leaf parameter inputs are properly formatted.

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Make lists of parameters for photosynthesis

Description

Make lists of parameters for photosynthesis

make_leafpar

make_enviropar

make_bakepar

make_constants

Usage

make_leafpar(replace = NULL, use_tealeaves)

make_enviropar(replace = NULL, use_tealeaves)

make_bakepar(replace = NULL)

make_constants(replace = NULL, use_tealeaves)

Arguments

replace	A named list of parameters to replace defaults. If NULL, defaults will be used.
use_tealeaves	Logical. Should leaf energy balance be used to calculate leaf temperature (T_leaf)? If TRUE, tleaf() calculates T_leaf. If FALSE, user-defined T_leaf is used. Additional parameters and constants are required, see make_parameters().

Details

Constants:

Symbol	R	Description	Units	Default
$D_{\mathrm{c},0}$	D_c0	diffusion coefficient for CO2 in air at 0 °C	m$^2$ / s	$1.29\times 10^{-5}$
$D_{\mathrm{h},0}$	D_h0	diffusion coefficient for heat in air at 0 °C	m$^2$ / s	$1.90\times 10^{-5}$
$D_{\mathrm{m},0}$	D_m0	diffusion coefficient for momentum in air at 0 °C	m$^2$ / s	$1.33\times 10^{-5}$
$D_{\mathrm{w},0}$	D_w0	diffusion coefficient for water vapor in air at 0 °C	m$^2$ / s	$2.12\times 10^{-5}$
$\epsilon$	epsilon	ratio of water to air molar masses	none	0.622
$G$	G	gravitational acceleration	m / s$^2$	9.8
$eT$	eT	exponent for temperature dependence of diffusion	none	1.75
$R$	R	ideal gas constant	J / mol / K	8.31
$\sigma$	sigma	Stephan-Boltzmann constant	W / m$^2$ / K$^4$	$5.67\times 10^{-8}$
$f_\mathrm{Sh}$	f_sh	function to calculate constant(s) for Sherwood number	none	NA
$f_\mathrm{Nu}$	f_nu	function to calculate constant(s) for Nusselt number	none	NA

Baking (i.e. temperature response) parameters:

Symbol	R	Description	Units	Default
$D_\mathrm{s,gmc}$	Ds_gmc	empirical temperature response parameter	J / mol / K	487
$D_\mathrm{s,Jmax}$	Ds_Jmax	empirical temperature response parameter	J / mol / K	388
$E_\mathrm{a,\Gamma *}$	Ea_gammastar	empirical temperature response parameter	J / mol	24500
$E_\mathrm{a,gmc}$	Ea_gmc	empirical temperature response parameter	J / mol	68900
$E_\mathrm{a,Jmax}$	Ea_Jmax	empirical temperature response parameter	J / mol	56100
$E_\mathrm{a,KC}$	Ea_KC	empirical temperature response parameter	J / mol	81000
$E_\mathrm{a,KO}$	Ea_KO	empirical temperature response parameter	J / mol	23700
$E_\mathrm{a,Rd}$	Ea_Rd	empirical temperature response parameter	J / mol	40400
$E_\mathrm{a,Vcmax}$	Ea_Vcmax	empirical temperature response parameter	J / mol	52200
$E_\mathrm{a,Vtpu}$	Ea_Vtpu	empirical temperature response parameter	J / mol	52200
$E_\mathrm{d,gmc}$	Ed_gmc	empirical temperature response parameter	J / mol	149000
$E_\mathrm{d,Jmax}$	Ed_Jmax	empirical temperature response parameter	J / mol	121000

Environment parameters:

Symbol	R	Description	Units	Default
$C_\mathrm{air}$	C_air	atmospheric CO2 concentration	umol/mol	420
$O$	O	atmospheric O2 concentration	mol/mol	0.21
$P$	P	atmospheric pressure	kPa	101
$\mathrm{PPFD}$	PPFD	photosynthetic photon flux density	umol / m$^2$ / s	1500
$\mathrm{RH}$	RH	relative humidity	none	0.5
$u$	wind	windspeed	m / s	2

Leaf parameters:

Symbol	R	Description	Units	Default
$d$	leafsize	leaf characteristic dimension	m	0.1
$\Gamma*$	gamma_star	chloroplastic CO2 compensation point (T_leaf)	umol/mol	NA
$\Gamma*_{25}$	gamma_star25	chloroplastic CO2 compensation point (25 °C)	umol/mol	37.9
$g_\mathrm{mc}$	g_mc	mesophyll conductance to CO2 (T_leaf)	mol / m$^2$ / s	NA
$g_\mathrm{mc,25}$	g_mc25	mesophyll conductance to CO2 (25 °C)	mol / m$^2$ / s	0.4
$g_\mathrm{sc}$	g_sc	stomatal conductance to CO2	mol / m$^2$ / s	0.4
$g_\mathrm{uc}$	g_uc	cuticular conductance to CO2	mol / m$^2$ / s	0.01
$J_\mathrm{max,25}$	J_max25	potential electron transport (25 °C)	umol / m$^2$ / s	200
$J_\mathrm{max}$	J_max	potential electron transport (T_leaf)	umol / m$^2$ / s	NA
$k_\mathrm{mc}$	k_mc	partition of g_mc to lower mesophyll	none	1
$k_\mathrm{sc}$	k_sc	partition of g_sc to lower surface	none	1
$k_\mathrm{uc}$	k_uc	partition of g_uc to lower surface	none	1
$K_\mathrm{C,25}$	K_C25	Michaelis constant for carboxylation (25 °C)	umol / mol	268
$K_\mathrm{C}$	K_C	Michaelis constant for carboxylation (T_leaf)	umol / mol	NA
$K_\mathrm{O,25}$	K_O25	Michaelis constant for oxygenation (25 °C)	umol / mol	165000
$K_\mathrm{O}$	K_O	Michaelis constant for oxygenation (T_leaf)	umol / mol	NA
$\phi_J$	phi_J	initial slope of the response of J to PPFD	none	0.331
$R_\mathrm{d,25}$	R_d25	nonphotorespiratory CO2 release (25 °C)	umol / m$^2$ / s	2
$R_\mathrm{d}$	R_d	nonphotorespiratory CO2 release (T_leaf)	umol / m$^2$ / s	NA
$\theta_J$	theta_J	curvature factor for light-response curve	none	0.825
$T_\mathrm{leaf}$	T_leaf	leaf temperature	K	298
$V_\mathrm{c,max,25}$	V_cmax25	maximum rate of carboxylation (25 °C)	umol / m$^2$ / s	150
$V_\mathrm{c,max}$	V_cmax	maximum rate of carboxylation (T_leaf)	umol / m$^2$ / s	NA
$V_\mathrm{tpu,25}$	V_tpu25	rate of triose phosphate utilization (25 °C)	umol / m$^2$ / s	200
$V_\mathrm{tpu}$	V_tpu	rate of triose phosphate utilisation (T_leaf)	umol / m$^2$ / s	NA

If use_tealeaves = TRUE, additional parameters are:

Constants:

Symbol	R	Description	Units	Default
$c_p$	c_p	heat capacity of air	J / g / K	1.01
$R_\mathrm{air}$	R_air	specific gas constant for dry air	J / kg / K	287

Baking (i.e. temperature response) parameters:

Symbol	R	Description	Units	Default

Environment parameters:

Symbol	R	Description	Units	Default
$E_q$	E_q	energy per mole quanta	kJ / mol	220
$f_\mathrm{PAR}$	f_par	fraction of incoming shortwave radiation that is photosynthetically active radiation (PAR)	none	0.5
$r$	r	reflectance for shortwave irradiance (albedo)	none	0.2
$T_\mathrm{air}$	T_air	air temperature	K	298
$T_\mathrm{sky}$	T_sky	sky temperature	K	NA

Leaf parameters:

Symbol	R	Description	Units	Default
$\alpha_\mathrm{l}$	abs_l	absorbtivity of longwave radiation (4 - 80 um)	none	0.97
$\alpha_\mathrm{s}$	abs_s	absorbtivity of shortwave radiation (0.3 - 4 um)	none	0.5
$g_\mathrm{sw}$	g_sw	stomatal conductance to H2O	mol / m$^2$ / s	NA
$g_\mathrm{uw}$	g_uw	cuticular conductance to H2O	mol / m$^2$ / s	NA
$\mathrm{logit}(sr)$	logit_sr	stomatal ratio (logit transformed)	none	NA

Optional leaf parameters:

Symbol	R	Description	Units	Default
$\delta_\mathrm{ias,lower}$	delta_ias_lower	effective distance through lower internal airspace	um	NA
$\delta_\mathrm{ias,upper}$	delta_ias_upper	effective distance through upper internal airspace	um	NA
$A_\mathrm{mes} / A$	A_mes_A	mesophyll surface area per unit leaf area	none	NA
$g_\mathrm{liq,c,25}$	g_liqc25	liquid-phase conductance to CO2 (25 °C)	mol / m$^2$ / s	NA
$g_\mathrm{liq,c}$	g_liqc	liquid-phase conductance to CO2 (T_leaf)	mol / m$^2$ / s	NA
$g_\mathrm{ias,c,lower}$	g_iasc_lower	internal airspace conductance to CO2 in lower part of leaf (T_leaf)	mol / m$^2$ / s	NA
$g_\mathrm{ias,c,upper}$	g_iasc_upper	internal airspace conductance to CO2 in upper part of leaf (T_leaf)	mol / m$^2$ / s	NA

Value

make_leafpar: An object inheriting from class leaf_par()
make_enviropar: An object inheriting from class enviro_par()
make_bakepar: An object inheriting from class bake_par()
make_constants: An object inheriting from class constants()

References

Buckley TN and Diaz-Espejo A. 2015. Partitioning changes in photosynthetic rate into contributions from different variables. Plant, Cell & Environment 38: 1200-11.

Examples

bake_par = make_bakepar()
constants = make_constants(use_tealeaves = FALSE)
enviro_par = make_enviropar(use_tealeaves = FALSE)
leaf_par = make_leafpar(use_tealeaves = FALSE)

leaf_par = make_leafpar(
  replace = list(
    g_sc = set_units(0.3, mol / m^2 / s),
    V_cmax25 = set_units(100, umol / m^2 / s)
  ), use_tealeaves = FALSE
)

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