Modeling Anet
We modelled photosynthesis according to Farquhar et al . (1980),
where Anet is the minimum of carboxylation and
electron transport limitations:
\(A_{\text{net}}=min\left(A_{c},\ A_{j},\ A_{t}\right)-R_{d}\)(Equation 1)
\(A_{c}=V_{c,max}\frac{C_{i}-\Gamma^{*}}{C_{i}+K_{c}\left(1+\frac{O}{K_{o}}\right)}\)(Equation 2)
\(A_{j}=J\frac{\left(C_{i}-\Gamma^{*}\right)}{\left(4C_{i}+8\Gamma^{*}\right)}\)(Equation 3)
\(\left[J-0.5\left(1-f\right)I\right]\left[J-J_{\max}\right]=0\)(Equation 4)
\(A_{t}=V_{c,max}/2\) (Equation 5)
Where Ac, Aj,, andAt are carboxylation, electron transport, and
triose phosphate utilization limited photosynthesis, respectively;Rd is respiration in the light;Vc,max is the maximum rate of Rubisco
carboxylation, Ci is leaf intercellular
[CO2]; Γ* is the
CO2 compensation point in the absence of mitochondrial
respiration; Kc and Ko are
the Michaelis-Menten constants for Rubisco carboxylation and
oxygenation, respectively; O is the O2concentration in the chloroplast (O = 210 μmol
mol-1); J is the rate of photosynthetic
electron transport; f is the fraction of light energy not
absorbed by the chloroplast (0.15); I is the incident irradiance;
and Jmax is the maximum rate of photosynthetic
electron transport.
Vc,max , Jmax ,Kc , Ko , and Γ* were
thermally scaled using an Arrhenius equation:
\(f\left(T\right)=k_{\text{ref}}\exp\left[E_{a}\frac{T-T_{\text{ref}}}{T\times T_{\text{ref}}\times R_{g}}\right]\)(Equation 6)
Where f(T) is the parameter at temperature T in K;kref is the parameter at the reference
temperature (either 25 °C or 30 °C); Tref is the
reference temperature in K (either 298 K or 303 K);Ea is the activation energy in kJ
mol-1; and Rg is the universal
gas constant (0.008314 kJ K-1mol-1). See Bernacchi et al . (2001) forEa , and kref for all
parameters except Jmax , and see Bernacchiet al . (2003) for Ea forJmax (note that kref forVc,max and Jmax were
derived from measured RACiR curves for each species).
Respiration (R ) was modelled as according to Atkin & Tjoelker
(2003):
\(f\left(T\right)=10^{\frac{{T-T}_{\text{ref}}}{10}\times\operatorname{}{Q_{10}+\operatorname{}R_{\text{ref}}}}\)(Equation 7)
Where f(T) is the parameter at temperature T in K;Q10 is the thermal sensitivity coefficient
(assumed to be 2); and Rref is respiration at the
reference temperature.
Since the photosynthetic rates depend on Ci , we
modelled CO2 diffusion into the leaf using Moss and
Rawlins (1963):
\(A_{\text{net}}=g_{s}\left(C_{a}-C_{i}\right)\) (Equation 8)
Where gs is stomatal conductance (mol
m-2 s-1), Caand Ci are the concentrations of
CO2 at the leaf surface and intercellular airspace,
respectively (μmol mol-1).
To close the system of equations, we used the stomatal conductance model
from Medlyn et al . (2011) as implemented by Lin et al .
(2015):
\(g_{s}=1.6\left(1+\frac{g_{1}}{\sqrt{D}}\right)\frac{A_{\text{net}}}{C_{a}}\)(Equation 9)
Where g1 is the model coefficient equal to 4.16,
and D is vapor pressure deficit.
Daily net leaf carbon uptake was modelled in R assuming an
ambient CO2 concentration (Ca ) of
400 μmol mol-1, and constant dark respiration
(R ) at 25 °C (unless otherwise stated) (2.27 ± 0.16 µmol
m-2 s-1 for Populus
deltoides , 0.46 ± 0.15 µmol m-2 s-1for Capsicum annuum , 3.36 µmol m-2s-1 for Malus domestica (Bunce, 1992), 2.30 ±
0.16 µmol m-2 s-1 for Populus
trichocarpa , 2.49 ± 1.00 µmol m-2s-1 for Asclepias speciosa (30 °C), 0.74 ± 0.07
µmol m-2 s-1 for Quercus
muehlenbergii (30 °C), 1.85 ± 1.08 µmol m-2s-1 for Rosa grandiflora (30 °C), 0.24 µmol
m-2 s-1 for Pinus ponderosa(10 °C; Law et al ., 2001), 0.71 ± 0.11 µmol m-2s-1 for Ginkgo biloba (30 °C), and 0.85 ± 0.22
µmol m-2 s-1 for Cedrus
deodar (30 °C)). Environmental conditions at the University of New
Mexico were taken for June 28, August 24, and October 9 in 2018 (Fig. 1)
and used to provide driving data for all species. Half-hourly time
intervals were summed for total carbon uptake for all species. Models
were run for four scenarios (1) Vcmax andJmax scaled from maximumVcmax and Jmax to account
for diurnal dynamics, (2) maximum measured Vcmaxand Jmax , (3) minimum measuredVcmax and Jmax , and (4)
average measured Vcmax andJmax . All R code is available as a supplementary
file (“Stinziano et al Modeling.Rmd”, “environmentdata.csv”). We
also tested the diurnal modeling by modeling the leaf chamber conditions
used to measure RACiR at each time point for each species, comparing
modelled Anet and gs at
400 μmol CO2 mol-1. We then tested
model performance by using the {lm} function in R (R Core Team, 2018).