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\begin{document}

\title{Photosynthetic capacity exhibits diurnal variation, implications for
terrestrial biosphere models and gas exchange measurements}



\author[1]{Joseph Stinziano}%
\author[1]{Marissa Harjoe}%
\author[1]{Cassaundra Roback}%
\author[1]{Nellie Toliver}%
\author[2]{Alistair Rogers}%
\author[3]{David T. Hanson}%
\affil[1]{University of New Mexico}%
\affil[2]{Brookhaven National Laboratory}%
\affil[3]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\selectlanguage{english}
\begin{abstract}
Terrestrial biosphere models (TBMs) are extremely sensitive to the
parameterization of the Farquhar, von Caemmerer \& Berry model of
photosynthesis, particularly the apparent maximum carboxylation capacity
(Vcmax) of Rubisco. New instrumentation and approaches have enabled the
rapid measurement of apparent Vcmax that paves the way for the
investigation of diurnal variation in Vcmax and improved understanding
of the potential impact on representation of photosynthesis in TBMs.
Here we show that reductions in Vcmax over the course of a photoperiod
can be as great as 50\% and, when incorporated into a model of daily CO2
assimilation, show that net carbon gain can change between -19 and 215\%
when compared to the current TBM assumption of a constant Vcmax. Given
the obvious impact on TBM representation of photosynthesis, we recommend
a renewed focus on the measurement of diurnal responses in
photosynthetic capacity across biomes to advance understanding and
enable model representation of this important phenomenon.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Uncertainty in Earth system model projections of our future climate is
largely driven by a lack of understanding and model representation of
ecosystem processes associated with CO\textsubscript{2} assimilation and
storage by the terrestrial biosphere (Friedlingstein \emph{et al} .,
2014; Lovenduski \& Bonan, 2017). Photosynthesis is the largest carbon
flux on the planet and the gatekeeper process for an uncertain
terrestrial carbon sink (Le Quere \emph{et al} ., 2016). Terrestrial
biosphere models (TBMs) are particularly sensitive to structural and
parametric representation of photosynthesis (Friend, 2010; Bonan\emph{et
al} ., 2011; LeBauer \emph{et al} ., 2013; Rogers, 2014;
Sargsyan\emph{et al} ., 2014; Rogers \emph{et al} ., 2017; Ricciuto
\emph{et al} ., 2018). Photosynthetic capacity, specifically the
apparent maximum carboxylation capacity of Rubisco at 25 \selectlanguage{ngerman}°C
(\emph{V\textsubscript{cmax,25}} ), is a key model input that drives
considerable uncertainty in TBM projections (Friend, 2010; Bonan
\emph{et al} ., 2011; LeBauer \emph{et al} ., 2013; Sargsyan \emph{et
al} ., 2014).\emph{V\textsubscript{cmax,25}} is further used to derive
the maximum rate of electron transport (\emph{J\textsubscript{max}} ),
the triose phosphate utilization rate (when implemented) and respiration
(\emph{R} ) (e.g. Sitch \emph{et al} ., 2003; Rogers \emph{et al} .,
2014; Lombardozzi\emph{et al} ., 2018). If this key parameter shows
significant diurnal variation, the implications for TBM projections of
CO\textsubscript{2}assimilation could be notable.

Terrestrial biosphere models (TBMs) typically
represent\emph{V\textsubscript{cmax}} as a fixed parameter (Rogers,
2014) but with some consideration of other factors such as day length
(Bauerle\emph{et al} ., 2012), temperature acclimation (Kattge \& Knorr,
2007; Lombardozzi \emph{et al} ., 2015; Smith \emph{et al} ., 2015), and
emerging potential for covariation with environmental drivers
(Ali\emph{et al} ., 2015; Smith et al. 2019). Only a few studies have
investigated diurnal variation in \emph{V\textsubscript{cmax}}
(Singsaas\emph{et al.} , 2000; Kets \emph{et al.} , 2010; Nascimento \&
Marenco, 2013). \emph{In vitro} , Rubisco activation state changes
rapidly with irradiance (Salvucci \& Anderson, 1987; Parry \emph{et al}
., 1997), shows diurnal variation (Sage \emph{et al.} , 1993; Pérez
\emph{et al.} , 2005), and is subject to regulation by Rubisco activase
(Portis, 2003; Sage \emph{et al} ., 2008), which could contribute
substantially to diurnal variations in \emph{V\textsubscript{cmax}} .
However, \emph{in vitro} and \emph{in vivo} data on Rubisco activation
state can vary markedly (Rogers \emph{et al} ., 2001; Sharwood \emph{et
al} ., 2017), and without an easy way to assess activation state
\emph{in vivo} , and an approach to incorporate \emph{in vitro}
measurements into TBM formulations, a gas exchange approach to measuring
Rubisco activity is desirable.

While there is a paucity of data on whether diurnal changes
in\emph{V\textsubscript{cmax}} occur (see Singsaas \emph{et al.} , 2000;
Kets \emph{et al.} , 2010; and Nascimento \& Marenco, 2013 for
examples), there are many studies investigating diurnal and circadian
patterns in gas exchange parameters. Net CO\textsubscript{2}
assimilation (\emph{A\textsubscript{net}} ) is known to vary diurnally
(Leverenz, 1981; Epron \emph{et al.} , 1992; Singsaas \emph{et al.} ,
2000; Panek, 2004; Leakey \emph{et al.} , 2004; Harrison \emph{et al.} ,
2010; Kets \emph{et al.} , 2010; Nascimento \& Marenco, 2013; Bader
\emph{et al.} , 2016), which can be driven by environmental changes.
There is a midday depression in net CO\textsubscript{2} assimilation
that has been related to vapor pressure deficit and water relations
(Tenhunen \emph{et al} ., 1984; Rodà, 1999), whereby stomatal
conductance mediates a supply-driven change in carbon assimilation
(Leverenz, 1981; Epron \emph{et al.} , 1992; Harrison\emph{et al.} ,
2010; Resco de Dios \emph{et al.} , 2016a,b) and balances the need to
fix carbon with preventing water loss (Matthews \emph{et al} ., 2017),
although circadian changes in \emph{A\textsubscript{net}}and
\emph{g\textsubscript{s}} are decoupled from one another (Dodd\emph{et
al} ., 2004; Resco de Dios, 2017). Brodribb \& Holbrook (2004) found
that leaf hydraulic conductance declines over the day, which may mediate
declines in mesophyll conductance (\emph{g\textsubscript{m}} ) (Bickford
\emph{et al} ., 2009; Flexas \emph{et al} ., 2013), reducing
chloroplastic CO\textsubscript{2} supply (and
therefore\emph{A\textsubscript{ne}} \textsubscript{t}) later in the day
and may even mediate changes in stomatal behaviour (Sack \emph{et al} .,
2016). Nardini \emph{et al} . (2005) found that leaf hydraulic
conductance (\emph{K\textsubscript{leaf}} ) was under circadian
regulation in\emph{Helianthus annuus} , which was the cause of diurnal
oscillations in\emph{K\textsubscript{leaf}} . There may be further
changes in realized quantum yield of photosynthesis that result from
delays in recovering from photoprotection or photodamage throughout the
day, limiting energy available for carbon fixation (Long \& Humphries,
1994; Gamon, 2015; Kromdijk \emph{et al} ., 2016). As well, there are
diurnal shifts in carbohydrate accumulation, and this can lead to
feedback inhibition of photosynthesis (Sun \emph{et al} ., 1999). In
this way, diurnal changes in net CO\textsubscript{2} assimilation can be
driven by both supply and demand of substrates, and these diurnal
changes in gas exchange scale up to the canopy level (Resco de Dios,
2016a). Many of the diurnal changes in \emph{A\textsubscript{net}}
outlined above are due to diurnal environmental changes which models can
mimic well. However, it is unclear whether there may be diurnal
variation in\emph{V\textsubscript{cmax}} , and if there is, diurnal
variation in\emph{V\textsubscript{cmax}} may present a simple way to
account for the effect of diurnal changes in leaf carbon exchange in
models.

Current approaches for measuring \emph{V\textsubscript{cmax} in
vivo}require measurement of the response of photosynthesis (\emph{A} )
to internal CO\textsubscript{2} concentration (\emph{C\textsubscript{i}}
) which can take over an hour for a single measurement (Bernacchi
\emph{et al} ., 2003). Recently, Stinziano \emph{et al} . (2017)
developed a method for the rapid measurement of the
\emph{A-C\textsubscript{i}} response (the RACiR technique). The dramatic
shortening of measurement time enables the collection of high-resolution
diurnal patterns in apparent\emph{V\textsubscript{cmax}} and apparent
\emph{J\textsubscript{max}}(Stinziano \emph{et al} ., 2017, 2019ab;
Coursolle \emph{et al} ., 2019; Lawrence \emph{et al} ., 2019). In
addition, this new technique provides values for parameters measured
\emph{in vivo} that are directly applicable to current TBM model
formulations and enables measurement of diurnal dynamics under
circumstances where \emph{in vitro} work cannot be done, e.g. where
sampling constraints in remote locations are logistically challenging,
or when secondary compounds limit the ability to successfully extract
and measure Rubisco activity. Studies assessing TBM performance on a
diurnal scale are limited (in some cases due to temporal resolution of
the models). in the case of ORCHIDEE, carbon fluxes are consistently
over-estimated relative to eddy covariance data later in the day across
plant functional types (Krinner \emph{et al} ., 2005), while the
Community Atmosphere Model (CAM4 and CAM5) over-estimates latent heat
fluxes later in the day at mid-latitude and boreal regions (Lindvall
\emph{et al} ., 2012) suggesting an over-estimation of transpiration,
which would imply overestimations of stomatal conductance,
\emph{C\textsubscript{i}} , and\emph{A\textsubscript{net}} . These
discrepancies may be related to endogenous rhythms in ecosystem-level
gas exchange (Resco de Dios\emph{et al} ., 2012) that are currently
unaccounted for.

Our objective was to determine whether diurnal variation
in\emph{V\textsubscript{cmax}} occurs, and if so, the extent to which
such variation affects leaf-level gas exchange modeling. Here we show
that the RACiR technique can be used to successfully measure diurnal
variation in \emph{V\textsubscript{cmax}} . We demonstrate that diurnal
variation in \emph{V\textsubscript{cmax}} is variable across 11 species
from several plant functional types, leading to a variable effect on
modelled leaf-level gas exchange, underscoring the need to consider
diurnal dynamics in \emph{V\textsubscript{cmax}} when modeling.

\textbf{Materials and Methods}

\emph{Plant Material}

Cuttings of poplar (\emph{Populus deltoides} Barr. S7c8 East Texas day
neutral clone; and \emph{Populus trichocarpa} BESC2074639) were grown at
the University of New Mexico (35.0843° N, 106.6198° W, 1587 m a.s.l.) at
18.3 to 21.1/15.6 to 21.1 °C day/night temperature in a rooftop
greenhouse, and bell pepper (\emph{Capsicum annuum} var. V6220
California Wonder Bell Pepper) were grown in an indoor greenhouse at
22/16 °C day/night temperature with 12/12 day/night photoperiod
maintained using a SPYDR 600 LED lighting system (BML Horticulture,
Austin, TX, USA) at a minimum intensity of 170 \selectlanguage{greek}μ\selectlanguage{english}mol
m\textsuperscript{-2} s\textsuperscript{-1} (maximum light intensity of
\textasciitilde{}720 \selectlanguage{greek}μ\selectlanguage{english}mol m\textsuperscript{-2}
s\textsuperscript{-1}including the natural light in the indoor
greenhouse). \emph{Populus deltoides} were grown in 28 L pots and were
\textasciitilde{}2 years old during measurements, \emph{Populus
trichocarpa} were grown in 7 L pots and were \textless{}6 months old
during measurements, and \emph{Capsicum annuum} were grown in 28 L pots.
All three greenhouse species were grown in Metro-Mix 300 potting soil
(Sun Gro Horticulture, Seba Beach, AB, Canada), and were fertilized
twice weekly with Peters 20-20-20 (Scotts Miracle-Gro, Marysville, OH,
USA) and once weekly with chelated liquid iron (Ferti-Lome, Bonham, TX,
USA). USDA-certified organic Granny Smith apple trees (\emph{Malus
domestica} Borkh.) were grown in Los Lunas, NM at the New Mexico State
University Agricultural Science Center (34.6007\selectlanguage{ngerman}° N, 103.2139° W, 1793 m
a.s.l., MAP: 241 mm, MAT: 13.9 °C, Soil: loam, Slope: 0 -- 1\%; USDA,
2018). Showy milkweed (\emph{Asclepias speciosa} ), mature Chinquapin
oak (\emph{Quercus muehlenbergii} ), and Queen Elizabeth rose
(\emph{Rosa grandiflora} ) were grown at the ABQ BioPark Botanic Garden
in Albuquerque, NM (35.0933° N 106.6813° W, 1587 m a.s.l., MAP: 203 mm,
MAT: 17.5 °C, Soil: fine sandy loam, Slope: 0 -- 1\%, USDA, 2018).
Mature ponderosa pine (\emph{Pinus ponderosa} ) were measured at Las
Huertas Upper Picnic Grounds in Cibola National Forest, Sandoval County,
NM (35.235458° N, 106.413012° W, 2316 m a.s.l., MAP: 546 mm, MAT: 6.1
°C, Soil: stony loam, Slope: 35 -- 70\%, USDA, 2018). Measurements were
made on October 26\textsuperscript{th}, 2017, and observed
sunrise/sunset was 8:30am and 5:00pm due to the location of the
measurement site in a canyon with mountains on all sides. Mature Deodar
cedar (\emph{Cedrus deodar} , sample size limited to 4 available trees)
and mature ginkgo (\emph{Ginkgo biloba} , sample size limited to 3
available trees) from the University of New Mexico Arboretum (35.0843°
N, 106.6198° W, 1587 m a.s.l., MAP: 203 mm, MAT: 17.5 °C, Soil: cut and
fill, USDA, 2018) were measured on August 24\textsuperscript{th}, 2018.
Unless stated above, sample size for each species was one leaf (or
branch for needleleaf species) from each of six individuals. Note: the
timing of measurements and sample size varied depending on access to
equipment, facilities and biological material (especially for field
measurements), however this should not affect the presence or absence of
diurnal changes in \emph{V\textsubscript{cmax}} .

\emph{Gas exchange measurements}

The RACiR technique was used according to Stinziano \emph{et al} .
(2017, 2019a). Briefly, we used a Licor 6800 portable photosynthesis
machine equipped with a fluorescence head (Licor Biosciences, Lincoln,
Nebraska, USA), and tailored chamber and RACiR parameters to each
species (Table 1). RACiR range was selected after initial analyses to
ensure that we captured part of the inflection region of
the\emph{A-C\textsubscript{i}} response as required by the curve fitting
procedure we used. Initial light responses were measured to determine
saturating light intensity for each species. Note that the overpressure
(\selectlanguage{greek}Δ\selectlanguage{english}P) controls and accounts for chamber leaks. Starting at Zeitgeiber
Time (ZT, also photoperiod time; the time since sunrise) of 1 hour (1
hour after meteorological sunrise) on October 31\textsuperscript{st},
2016, RACiR curves were run every hour until ZT10 for \emph{P}
opulus\emph{deltoides} , while for \emph{Populus trichocarpa} , RACiR
curves were run on November 30\textsuperscript{th}, 2016 every 1.5 hours
from ZT1.5 until ZT9. For \emph{Capsicum annuum} , RACiR curves were run
every two hours from ZT0 until ZT12. \emph{Malus domestica} were
measured in the field every two hours from ZT2.5 until ZT8.5 on October
9\textsuperscript{th}, 2016. \emph{Asclepias speciosa} , \emph{Quercus
muehlenbergii} , and \emph{Rosa grandiflora} were measured on June
28\textsuperscript{th}, 2018 from \textasciitilde{}ZT1.5 until
\textasciitilde{}ZT12. \emph{Pinus ponderosa} were measured on October
26\textsuperscript{th}, 2017 from observed \textasciitilde{}ZT0.5 to
\textasciitilde{}ZT8.5 (meteorological ZT1.5 to ZT9.5). Due to issues
with low g\textsubscript{s} (which can interfere with
C\textsubscript{i}calculations), sample size for each time point for
\emph{P. ponderosa}varies from 1 to 4. \emph{Cedrus deodar} and
\emph{Ginkgo biloba} were measured from ZT2.5 until ZT12 on August
24\textsuperscript{th}, 2018. All measurements were performed on the
same area of leaf tissue for broad leaf species and the same branch for
each needle leaf species. Note that due to external environmental
temperatures, \emph{Asclepias speciosa} , \emph{Quercus muehlenbergii} ,
\emph{Rosa grandiflora} ,\emph{Cedrus deodar} , and \emph{Ginkgo biloba}
were all measured at 30 \selectlanguage{ngerman}°C. Dark respiration (\emph{R} ) was measured in
each species by letting the leaf equilibrate to dark cuvette conditions
for 30 min prior to measurements (note: chamber conditions are outlined
in Table 1).

RACiR data were corrected using the R package \{racir\} (Stinziano,
2018) and were analyzed for \emph{V\textsubscript{cmax}}
and\emph{J\textsubscript{max}} using the \{plantecophys\} package
(Duursma, 2015) in R v3.5.1 (R Core Team, 2018), and default parameters
were used as in Stinziano \emph{et al} . (2017), which correspond to
Rubisco kinetics and thermal coefficients as in Bernacchi \emph{et al} .
(2001).

\emph{Clamping Experiment}

We tested the impacts of repeated clamping on leaves of \emph{Capsicum
annuum} , \emph{Populus deltoides} , and \emph{Populus trichocarpa} .
For each of five sequential clamps on each measured leaf, we allowed the
chamber to stabilize (\textless{} 2 min in all cases), and
measured\emph{A\textsubscript{net}} at 400 \selectlanguage{greek}μ\selectlanguage{english}mol
CO\textsubscript{2}mol\textsuperscript{-1} for 30 s at 0.5 Hz. Between
clamps, the leaf was given a 1 min recovery. On clamps 1 and 5, a RACiR
was run as specified above for each species. We then fit
\emph{V\textsubscript{cmax}} and\emph{J\textsubscript{max}} as above.
These measurements were performed on an individual leaf spot within 30
min to minimize diurnal effects.

\emph{Modeling A\textsubscript{net}}

We modelled photosynthesis according to Farquhar \emph{et al} . (1980),
where \emph{A\textsubscript{net}} 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 \emph{A\textsubscript{c}, A\textsubscript{j},,}
and\emph{A\textsubscript{t}} are carboxylation, electron transport, and
triose phosphate utilization limited photosynthesis,
respectively;\emph{R\textsubscript{d}} is respiration in the
light;\emph{V\textsubscript{c,max}} is the maximum rate of Rubisco
carboxylation, \emph{C\textsubscript{i}} is leaf intercellular
{[}CO\textsubscript{2}{]}; \selectlanguage{greek}\emph{Γ\textsuperscript{*}}\selectlanguage{english} is the
CO\textsubscript{2} compensation point in the absence of mitochondrial
respiration; \emph{K\textsubscript{c}} and \emph{K\textsubscript{o}} are
the Michaelis-Menten constants for Rubisco carboxylation and
oxygenation, respectively; \emph{O} is the
O\textsubscript{2}concentration in the chloroplast (\emph{O =} 210 \selectlanguage{greek}μ\selectlanguage{english}mol
mol\textsuperscript{-1}); \emph{J} is the rate of photosynthetic
electron transport; \emph{f} is the fraction of light energy not
absorbed by the chloroplast (0.15); \emph{I} is the incident irradiance;
and \emph{J\textsubscript{max}} is the maximum rate of photosynthetic
electron transport.

\emph{V\textsubscript{c,max}} , \emph{J\textsubscript{max}}
,\emph{K\textsubscript{c}} , \emph{K\textsubscript{o}} , and \selectlanguage{greek}\emph{Γ*}\selectlanguage{english}
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 \emph{f(T)} is the parameter at temperature \emph{T} in
K;\emph{k\textsubscript{ref}} is the parameter at the reference
temperature (either 25 \selectlanguage{ngerman}°C or 30 °C); \emph{T\textsubscript{ref}} is the
reference temperature in K (either 298 K or 303
K);\emph{E\textsubscript{a}} is the activation energy in kJ
mol\textsuperscript{-1}; and \emph{R\textsubscript{g}} is the universal
gas constant (0.008314 kJ K\textsuperscript{-1}mol\textsuperscript{-1}).
See Bernacchi \emph{et al} . (2001) for\emph{E\textsubscript{a}} , and
\emph{k\textsubscript{ref}} for all parameters except
\emph{J\textsubscript{max}} , and see Bernacchi\emph{et al} . (2003) for
\emph{E\textsubscript{a}} for\emph{J\textsubscript{max}} (note that
\emph{k\textsubscript{ref}} for\emph{V\textsubscript{c,max}} and
\emph{J\textsubscript{max}} were derived from measured RACiR curves for
each species).

Respiration (\emph{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 \emph{f(T)} is the parameter at temperature \emph{T} in
K;\emph{Q\textsubscript{10}} is the thermal sensitivity coefficient
(assumed to be 2); and \emph{R\textsubscript{ref}} is respiration at the
reference temperature.

Since the photosynthetic rates depend on \emph{C\textsubscript{i}} , we
modelled CO\textsubscript{2} diffusion into the leaf using Moss and
Rawlins (1963):

\(A_{\text{net}}=g_{s}\left(C_{a}-C_{i}\right)\) (Equation 8)

Where \emph{g\textsubscript{s}} is stomatal conductance (mol
m\textsuperscript{-2} s\textsuperscript{-1}),
\emph{C\textsubscript{a}}and \emph{C\textsubscript{i}} are the
concentrations of CO\textsubscript{2} at the leaf surface and
intercellular airspace, respectively (\selectlanguage{greek}μ\selectlanguage{english}mol mol\textsuperscript{-1}).

To close the system of equations, we used the stomatal conductance model
from Medlyn \emph{et al} . (2011) as implemented by Lin \emph{et al} .
(2015):

\(g_{s}=1.6\left(1+\frac{g_{1}}{\sqrt{D}}\right)\frac{A_{\text{net}}}{C_{a}}\)(Equation 9)

Where \emph{g\textsubscript{1}} is the model coefficient equal to 4.16,
and \emph{D} is vapor pressure deficit.

Daily net leaf carbon uptake was modelled in \emph{R} assuming an
ambient CO\textsubscript{2} concentration (\emph{C\textsubscript{a}} )
of 400 \selectlanguage{greek}μ\selectlanguage{english}mol mol\textsuperscript{-1}, and constant dark respiration
(\emph{R} ) at 25 \selectlanguage{ngerman}°C (unless otherwise stated) (2.27 ± 0.16 \selectlanguage{greek}µ\selectlanguage{english}mol
m\textsuperscript{-2} s\textsuperscript{-1} for \emph{Populus deltoides}
, 0.46 \selectlanguage{ngerman}± 0.15 \selectlanguage{greek}µ\selectlanguage{english}mol m\textsuperscript{-2} s\textsuperscript{-1}for
\emph{Capsicum annuum} , 3.36 \selectlanguage{greek}µ\selectlanguage{english}mol
m\textsuperscript{-2}s\textsuperscript{-1} for \emph{Malus domestica}
(Bunce, 1992), 2.30 \selectlanguage{ngerman}± 0.16 \selectlanguage{greek}µ\selectlanguage{english}mol m\textsuperscript{-2}
s\textsuperscript{-1} for \emph{Populus trichocarpa} , 2.49 \selectlanguage{ngerman}± 1.00 \selectlanguage{greek}µ\selectlanguage{english}mol
m\textsuperscript{-2}s\textsuperscript{-1} for \emph{Asclepias speciosa}
(30 \selectlanguage{ngerman}°C), 0.74 ± 0.07 \selectlanguage{greek}µ\selectlanguage{english}mol m\textsuperscript{-2} s\textsuperscript{-1}
for \emph{Quercus muehlenbergii} (30 \selectlanguage{ngerman}°C), 1.85 ± 1.08 \selectlanguage{greek}µ\selectlanguage{english}mol
m\textsuperscript{-2}s\textsuperscript{-1} for \emph{Rosa grandiflora}
(30 \selectlanguage{ngerman}°C), 0.24 \selectlanguage{greek}µ\selectlanguage{english}mol m\textsuperscript{-2} s\textsuperscript{-1} for
\emph{Pinus ponderosa}(10 \selectlanguage{ngerman}°C; Law \emph{et al} ., 2001), 0.71 ± 0.11
\selectlanguage{greek}µ\selectlanguage{english}mol m\textsuperscript{-2}s\textsuperscript{-1} for \emph{Ginkgo biloba}
(30 \selectlanguage{ngerman}°C), and 0.85 ± 0.22 \selectlanguage{greek}µ\selectlanguage{english}mol m\textsuperscript{-2}
s\textsuperscript{-1} for \emph{Cedrus deodar} (30 \selectlanguage{ngerman}°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)
\emph{V\textsubscript{cmax}} and\emph{J\textsubscript{max}} scaled from
maximum\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}} to
account for diurnal dynamics, (2) maximum measured
\emph{V\textsubscript{cmax}}and \emph{J\textsubscript{max}} , (3)
minimum measured\emph{V\textsubscript{cmax}} and
\emph{J\textsubscript{max}} , and (4) average measured
\emph{V\textsubscript{cmax}} and\emph{J\textsubscript{max}} . 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 \emph{A\textsubscript{net}}
and \emph{g\textsubscript{s}} at 400 \selectlanguage{greek}μ\selectlanguage{english}mol CO\textsubscript{2}
mol\textsuperscript{-1}. We then tested model performance by using the
\{lm\} function in R (R Core Team, 2018).

\emph{Data analysis}

Zeitgeiber Time 0 (ZT0) was calculated based on meteorological sunrise
(07:30 for \emph{Populus deltoides} and \emph{Populus trichocarpa} ;
07:00 for \emph{Malus domestica} ; 06:00 for \emph{Asclepias speciosa}
,\emph{Quercus muehlenbergii} , and \emph{Rosa grandiflora} ; 06:30
for\emph{Ginkgo biloba} and \emph{Cedrus deodar} ), observed sunrise
for\emph{Pinus ponderosa} (08:30) or the time that growth lights turned
on (08:30 for \emph{Capsicum annuum} ). Diurnal variation was tested
within each species using a repeated measures linear regression using
the \{lme\} function of the \{nlme\} package in R (Pinheiro \emph{et al}
., 2018). Relative \emph{V\textsubscript{c,max}}
and\emph{J\textsubscript{max}} were calculated for each species by
standardizing to the highest average value (i.e.
dividing\emph{V\textsubscript{c,max}} and \emph{J\textsubscript{max}} at
each time point by the peak \emph{V\textsubscript{c,max}}
and\emph{J\textsubscript{max}} ) within a species.

\textbf{Results}

\emph{Photosynthetic capacity shows diurnal variability}

Photosynthetic capacity (both \emph{V\textsubscript{cmax}}
and\emph{J\textsubscript{max}} ) at 25 \selectlanguage{ngerman}°C shows significant diurnal
change with a consistent decline of \textasciitilde{}50\% towards the
end of day, with the largest declines beginning at ZT8 in \emph{Populus
deltoides} (2\textsuperscript{nd} order polynomial
responses;\emph{V\textsubscript{cmax}} : \emph{t\textsubscript{52}} =
-6.67,\emph{P} \textless{} 0.0001; \emph{J\textsubscript{max}}
:\emph{t\textsubscript{52}} = -7.30, \emph{P} \textless{} 0.0001; Fig.
2a, d), ZT8 in \emph{Capsicum annuum} (\emph{V\textsubscript{cmax}}
:\emph{t\textsubscript{33}} = -5.24, \emph{P} \textless{}
0.0001;\emph{J\textsubscript{max}} : \emph{t\textsubscript{33}} =
-4.10,\emph{P} = 0.0003 ; Fig. 2b, e), and ZT2 in \emph{Malus
domestica}(\emph{V\textsubscript{cmax}} : \emph{t\textsubscript{17}} =
-9.25,\emph{P} \textless{} 0.0001); \emph{J\textsubscript{max}}
:\emph{t\textsubscript{17}} = -9.13, \emph{P} \textless{} 0.0001; Fig.
2b, e). \emph{Populus trichocarpa} showed slight but significant
declines in \emph{V\textsubscript{cmax}} at 25 °C
(\emph{t\textsubscript{19}} = -3.39, \emph{P} = 0.003)
and\emph{J\textsubscript{max}} (\emph{t\textsubscript{19}} =
-2.81,\emph{P} = 0.01) (Fig. 2b, e). \emph{Pinus ponderosa} did not show
any significant declines in
\emph{V\textsubscript{cmax}}(\emph{t\textsubscript{8}} = -1.50, \emph{P}
= 0.17) or\emph{J\textsubscript{max}} (\emph{t\textsubscript{8}} =
-1.71, \emph{P}= 0.13; Fig. 2c, f). Photosynthetic capacity measured at
30 °C shows significant diurnal changes in \emph{V\textsubscript{cmax}}
for\emph{Quercus muehlenbergii} (\emph{t\textsubscript{24}} =
-6.39,\emph{P} \textless{} 0.0001; Fig. 2a), \emph{Rosa
grandiflora}(\emph{t\textsubscript{24}} = -5.57, \emph{P} \textless{}
0.0001, Fig. 2b), and \emph{Ginkgo biloba} (\emph{t\textsubscript{14}} =
-5.90,\emph{P} \textless{} 0.0001; Fig. 2c) but not \emph{Asclepias
speciosa}(\emph{t\textsubscript{24}} = -1.77, \emph{P} = 0.09; Fig. 2a)
and\emph{Cedrus deodar} (\emph{t\textsubscript{20}} = 0.648, \emph{P} =
0.52; Fig. 2c). For \emph{J\textsubscript{max}} at 30 °C, there are
linear declines in \emph{Quercus
muehlenbergii}(\emph{t\textsubscript{24}} = -5.75, \emph{P} \textless{}
0.0001; Fig. 2d), \emph{Rosa grandiflora} (\emph{t\textsubscript{24}} =
-5.95,\emph{P} \textless{} 0.0001; Fig. 2e), \emph{Ginkgo
biloba}(\emph{t\textsubscript{14}} = -9.29, \emph{P} \textless{} 0.0001;
Fig. 2f) and \emph{Asclepias speciosa} (\emph{t\textsubscript{24}} =
-2.09,\emph{P} = 0.047; Fig. 2d), but not for \emph{Cedrus
deodar}(\emph{t\textsubscript{20}} = -0.10, \emph{P} = 0.92; Fig. 2f).
Across all species, apparent \emph{J\textsubscript{max}}
and\emph{V\textsubscript{cmax}} were strongly correlated as expected
(slope = 1.99, intercept = -13.54, \emph{F\textsubscript{1,293}} =
1826,\emph{R} \textsuperscript{2} = 0.86, \emph{P} \textless{} 0.0001;
Fig. 3; Wullschleger, 1993). Diurnal variation in relative
photosynthetic capacity is quite variable (Fig. 4), with convergent
responses for\emph{Capsicum annuum} , \emph{Ginkgo biloba} , \emph{Malus
domestica} , and \emph{Rosa grandiflora} , but varying patterns in the
remaining species.

\emph{Modeling diurnal A\textsubscript{net} responses}

Using the species-specific diurnal patterns (Fig. 2), we
modelled\emph{A\textsubscript{net}} for all species with diurnal changes
in\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}} (scaled
to maximum average \emph{V\textsubscript{cmax}}
and\emph{J\textsubscript{max}} ), maximum
(peak)\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}} ,
average\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}} ,
and minimum \emph{V\textsubscript{cmax}} and
\emph{J\textsubscript{max}}(Fig. 5). When integrating modelled
\emph{A\textsubscript{net}} over three separate 24-hour periods,
accumulated net carbon gain is increased under peak photosynthetic
capacity relative to the diurnal case by \textasciitilde{}8 to 215\%
(corresponding to a 5 to 67\% change in gross CO\textsubscript{2}
assimilation (\emph{A\textsubscript{gross}} ); Table 2, Fig. 5). Under
average photosynthetic capacity relative to the diurnal case,
\emph{A\textsubscript{net}} changes by -19 to 36\% (corresponding to a
-16 to 28\% change in \emph{A\textsubscript{gross}} ; Table 2, Fig. 5).
Under minimum photosynthetic capacity relative to the diurnal case,
\emph{A\textsubscript{net}} changes by -303 to -6\% (corresponding to a
-61 to -4\% change in \emph{A\textsubscript{gross}} ; Table 2, Fig. 5).

\emph{Measurement and modeling bias assessment}

To determine whether repeated clamping could bias the measurements (i.e.
through leaf damage), we ran RACiRs after 1 and 5 one-minute clamps on
the three greenhouse species (\emph{Capsicum annuum} , \emph{Populus
deltoides} , and \emph{Populus trichocarpa} ). We found no significant
decline between clamps 1 and 5 for
\emph{V\textsubscript{cmax}}(\emph{Capsicum annuum} :
\emph{t\textsubscript{2}} = -1.47, \emph{P} = 0.28; \emph{Populus
deltoides} : \emph{t\textsubscript{4}} = -1.82,\emph{P} = 0.14;
\emph{Populus trichocarpa} : \emph{t\textsubscript{5}} = -1.67, \emph{P}
= 0.16; Fig. 6a), \emph{J\textsubscript{max}}(\emph{Capsicum annuum} :
\emph{t\textsubscript{2} = -1.43, P} = 0.29;\emph{Populus deltoides} :
\emph{t\textsubscript{4}} = -2.01\emph{, P} = 0.11; \emph{Populus
trichocarpa} : \emph{t\textsubscript{5}} = -1.70\emph{, P} = 0.15; Fig.
6b), and \emph{A\textsubscript{net}}(\emph{Capsicum annuum} :
\emph{t\textsubscript{2}} = 1.39, \emph{P} = 0.40; \emph{Populus
deltoides} : \emph{t\textsubscript{4}} = -1.84,\emph{P} = 0.21;
\emph{Populus trichocarpa} : \emph{t\textsubscript{2}} = 0.48, \emph{P}
= 0.68; Fig. 6c).

To check for model biases, we compared model predictions of the
leaf-level gas exchange to measured \emph{A\textsubscript{net}}
and\emph{g\textsubscript{s}} . The model consistently
over-estimated\emph{A\textsubscript{net}} by 9.8\% (slope =
1.098,\emph{R\textsuperscript{2}} = 0.96, \emph{F\textsubscript{1,63}} =
1356,\emph{P} \textless{} 0.0001) while
underestimating\emph{g\textsubscript{s}} by \textasciitilde{}18\% (slope
= 0.82,\emph{R\textsuperscript{2}} = 0.85, \emph{F\textsubscript{1,63}}
= 345,\emph{P} \textless{} 0.0001) (Fig. 7).

\textbf{Discussion}

\emph{Apparent photosynthetic capacity exhibits substantial diurnal
variation}

There is substantial diurnal variation in apparent photosynthetic
capacity (apparent \emph{V\textsubscript{cmax}} \textsubscript{}
and\emph{J\textsubscript{max}} ) (ranging from 0\% change to over 50\%
decline). This variation has been ignored by TBMs, which typically use
fixed estimates of apparent \emph{V\textsubscript{cmax}} and by leaf
level physiologists who previously lacked an approach to collect high
temporal resolution data \emph{in vivo} . While we found interspecific
differences in the diurnal response, the decline in
apparent\emph{V\textsubscript{cmax}} and apparent
\emph{J\textsubscript{max}}has important implications for modelling
photosynthetic carbon uptake and should not be ignored.

\emph{Possible mechanisms for diurnal variation in photosynthetic
capacity}

We were able to rule out that repeated clamping could cause the
substantial diurnal declines in photosynthetic capacity in the three
species we tested (Fig. 6). Regarding biological mechanisms, the decline
in apparent \emph{V\textsubscript{cmax}} could be driven by declines in
Rubisco activation (Pérez \emph{et al.} , 2005), diurnal changes in
mesophyll conductance (Bickford \emph{et al} ., 2010), diurnal changes
in\emph{K\textsubscript{leaf}} (Brodribb \& Holbrook, 2004), or possibly
from the movement of chloroplasts (e.g. Tholen \emph{et al} ., 2008).
Rubisco activase is regulated by light through ATP:ADP (Streusand \&
Portis, 1987) and redox potential (Zhang \emph{et al} ., 2002), and is
responsible for removing the inhibitor 2-carboxyarabinitol 1-phosphate
(CA1P) from Rubisco (Robinson \& Portis, 1988); therefore diurnal
changes in irradiance may be regulating
apparent\emph{V\textsubscript{cmax}} through changes in Rubisco activase
activity. CA1P could be further implicated in diurnal regulation of
apparent \emph{V\textsubscript{cmax}} , as it is exhibits diurnal
changes associated with changes in \emph{in vitro} Rubisco activity in
several species -- though not all species have CA1P (Kobza \& Seemann,
1989). Mesophyll conductance ultimately determines the supply of
CO\textsubscript{2} from the intercellular airspace to the chloroplast,
and diurnal changes in mesophyll conductance may cause changes in the
slope of the \emph{A-C\textsubscript{i}} response, leading to a false
interpretation that there are diurnal changes in
apparent\emph{V\textsubscript{cmax}} . Mesophyll conductance is tightly
linked to\emph{K\textsubscript{leaf}} (leaf hydraulic conductance),
which exhibits diurnal dynamics (Brodribb \& Holbrook, 2004) which could
then mediate diurnal changes in apparent \emph{V\textsubscript{cmax}}
via mesophyll conductance (Flexas \emph{et al} ., 2013). If we assume
that the diurnal patterns observed in \emph{K\textsubscript{leaf}} are
general, then declines in \emph{K\textsubscript{leaf}} would reduce
g\textsubscript{m} (Flexas \emph{et al} ., 2013), reducing
apparent\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}} .
However, these effects appear nonlinear, and we would have expected
nonlinear diurnal dynamics, which we only observed in \emph{P.
deltoides} . Meanwhile, chloroplast movements (Tholen \emph{et al} .,
2008) could also mediate changes in mesophyll conductance. We note that
applying the model of Farquhar \emph{et al} . (1980) in full, accounting
for both mesophyll conductance and Rubisco activation state, could allow
for\emph{V\textsubscript{cmax}} to remain constant while
apparent\emph{V\textsubscript{cmax}} could vary diurnally. Whether such
mechanisms explain diurnal dynamics in
apparent\emph{V\textsubscript{cmax}} remains to be seen.

\emph{Model biases}

The model tended to over-estimate \emph{A\textsubscript{net}} and
under-estimate \emph{g\textsubscript{s}} , although the correlations
between the measured and modelled data were quite strong
(\emph{R}\textgreater{} 0.9 for both) suggesting that our modeling
correctly captured the behaviour of \emph{A\textsubscript{net}}
and\emph{g\textsubscript{s}} . These biases have several possible
sources: 1) the RACiR measurements were obtained as soon as the leaf
chamber stabilized, which means that while the RACiR data may reflect
the underlying biochemistry, the stomata will not have adjusted to the
irradiance and the vapor pressure deficit in the leaf chamber that
drives the Medlyn \emph{et al} . (2011) stomatal conductance model.
Since the modeling assumes a steady state, this could contribute to the
biases. 2) RACiR is known to introduce metabolic mismatches that do not
affect \emph{V\textsubscript{cmax}} and
\emph{J\textsubscript{max}}estimates, but may affect
\emph{A\textsubscript{net}} values (Stinziano\emph{et al} ., 2019ab).
These metabolic mismatches might thus contribute to some of the bias,
although it should be minimal at the RACiR rates used (i.e. 100 \selectlanguage{greek}μ\selectlanguage{english}mol
CO\textsubscript{2} mol\textsuperscript{-1}min\textsuperscript{-1}). 3)
It is possible that respiration in the light is greater than respiration
in the dark for some of these species. In this case, modelled
\emph{A\textsubscript{net}} would necessarily over-estimate measurements
of \emph{A\textsubscript{net}} . 4) We used the general slope from Lin
\emph{et al} . (2015) for the Medlyn \emph{et al} . (2011) model. It is
also possible that there is variation in the stomatal slope parameter
(g\textsubscript{1}) between species (Wolz et al 2017; Miner et al 2017;
Franks et al. 2018).

\emph{Implications for measuring V\textsubscript{cmax}}

In terms of measuring \emph{V\textsubscript{cmax}} , the required timing
of \emph{V\textsubscript{cmax}} measurements depends on the aims of the
measurements. For comparing maximum apparent\emph{V\textsubscript{cmax}}
, our data suggest that for most species, photosynthetic
CO\textsubscript{2} responses should be measured in the morning, prior
to midday. If the aim is to obtain data useful for model
parameterization, there are two avenues: daily average or diurnal
photosynthetic CO\textsubscript{2} response measurements. For daily
average measurements, care is needed to make sure that the measurements
occur across the entire light period of the photoperiod, with the
recognition that there may be biases in conclusions based on
average\emph{V\textsubscript{cmax}} . For diurnal measurements, there
are again two approaches: RACiR, and the one-point method to
estimating\emph{V\textsubscript{cmax}} . We have demonstrated this
diurnal application of RACiR, however RACiR may not be feasible in all
cases due to equipment or instrument precision. However, De Kauwe
\emph{et al} . (2016) showed that the one-point method for estimating
apparent\emph{V\textsubscript{cmax}} can produce similar estimates to
those from full photosynthetic CO\textsubscript{2} responses, providing
sufficient time is allowed for leaf gas exchange to reach steady state
in the chamber (Burnett et al. 2019). Given that diurnal dynamics
in\emph{V\textsubscript{cmax}} can incur large changes on timescales of
\textless{} 2 hrs, diurnal dynamics would affect temperature response
measurements of \emph{V\textsubscript{cmax}} , with the effect dependent
on which temperatures are measured earlier or later. It may be possible
to circumvent these effects using RACiR-based approaches to temperature
responses, although the timescales for chamber equilibration times may
limit such an approach. We call for more diurnal measurements
of\emph{V\textsubscript{cmax}} as current measurement approaches may be
introducing biases into conclusions based on the assumption
the\emph{V\textsubscript{cmax}} is diurnally static.

\emph{Implications for TBMs}

Accounting for diurnal dynamics of apparent
\emph{V\textsubscript{cmax}}and \emph{J\textsubscript{max}} means that
gross carbon assimilation could be mis-estimated \textasciitilde{}-4 to
40\% (standard deviation based on the average and peak
\emph{V\textsubscript{cmax}} scenarios relative to the diurnal
scenario). If extrapolated to global gross primary production
(\textasciitilde{}123 Pg C yr\textsuperscript{-1}; Beer \emph{et al} .,
2010), diurnal variation in photosynthetic parameters could create a
revised estimate range of 101 \selectlanguage{ngerman}± 27 Pg C yr\textsuperscript{-1} (mean ±
standard deviation) in global GPP. This uncertainty introduced here is
similar to the uncertainty in unconstrained CMIP5 estimates of GPP
(standard deviation: 27.5 Pg C yr\textsuperscript{-1}; Mystakidis
\emph{et al} ., 2016), implying that understanding diurnal processes
regulating \emph{V\textsubscript{cmax}}may warrant more attention.
Although limited in scope, this study clearly shows that diurnal
variation in apparent\emph{V\textsubscript{cmax}} and
\emph{J\textsubscript{max}} exists across multiple species under
greenhouse and field conditions. While there are factors such as
mesophyll conductance,\emph{K\textsubscript{leaf}} , and Rubisco
activation state that could cause these diurnal dynamics in apparent
\emph{V\textsubscript{cmax}}such that there is no effect on the amount
of Rubisco in the leaf, it is important to note that TBMs currently use
apparent\emph{V\textsubscript{cmax}} to model carbon assimilation
(Rogers\emph{et al} ., 2017). TBMs are also not ready for incorporation
of\emph{g\textsubscript{m}} , Rubisco activation state,
and\emph{K\textsubscript{leaf}} due to a paucity of data for these
parameters. Therefore, if multiple processes are producing diurnal
changes in apparent \emph{V\textsubscript{cmax}} , then including
diurnal dynamics in apparent \emph{V\textsubscript{cmax}} may present a
relatively simple way to include these important dynamics in TBMs.
However, this requires broad diurnal RACiR surveys, paired with
measurements such as \emph{g\textsubscript{m}} , Rubisco activation
state, and \emph{K\textsubscript{leaf}} , to confirm the underlying
mechanisms behind diurnal \emph{V\textsubscript{cmax}} .

Implementing diurnal changes in \emph{V\textsubscript{cmax}} into TBMs
requires more physiological understanding of this phenomenon. Our data
provide preliminary evidence that diurnal variation
in\emph{V\textsubscript{cmax}} may depend on the evolutionary history of
the organism as well (the two species from \emph{Pinaceae} did not show
a diurnal pattern), however this could be related to different diurnal
dynamics (or lack thereof) in \emph{g\textsubscript{m}} , Rubisco
activation state, and \emph{K\textsubscript{leaf}} . These areas still
require a marked advance in process knowledge
of\emph{g\textsubscript{m}} (Rogers \emph{et al} ., 2017), Rubisco
activation state, and \emph{K\textsubscript{leaf}} before they could be
implemented into TBMs. However, ignoring these diurnal dynamics could
lead to a mis-estimation of CO\textsubscript{2} assimilation by TBMs,
especially since diurnal variation could be as significant as other
sources of variation (e.g. leaf age, Wu \emph{et al} ., 2016; species,
Wullschleger, 1993; model structure, Mystakidis \emph{et al} ., 2016).
Greater mechanistic understanding of diurnal variation
in\emph{V\textsubscript{cmax}} and quantification of the phenomenon in
key biomes is required to so that improved model formulations of
photosynthesis can be considered for inclusion in future TBMs.

\textbf{Acknowledgments}

We would like to thank Jeremiah Anderson, Kaitlyn Read, and Jun Tominaga
for their help in the field, Mark Marsalis of the New Mexico State
University Agricultural Center for allowing us to conduct research on
their land, Todd Rosenstiel (Portland State University) for
providing\emph{P. deltoides} , David Weston (Oak Ridge National Lab) for
providing\emph{P. trichocarpa} , and Maria J. Thomas (ABQ BioPark
Botanic Gardens) for allowing us to conduct research at the botanical
gardens. This research was partially supported by a Fulbright Canada
scholarship to JRS. JRS would also like to acknowledge scholarship
support from the Natural Sciences and Engineering Research Council of
Canada (NSERC). This work was also supported by funding to DTH through
the NSF EPSCoR Program under Award \# IIA-1301346 at the University of
New Mexico. Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the authors and do not
necessarily reflect the views of the National Science Foundation. AR was
supported by the Next-Generation Ecosystem Experiments (NGEE Arctic and
NGEE Tropics) projects that are supported by the Office of Biological
and Environmental Research in the Department of Energy, Office of
Science, and through the United States Department of Energy contract No.
DE-SC00112704 to Brookhaven National Laboratory.

\textbf{Author Contributions}

JRS, MJH, CR, and NLT carried out the research. JRS and DTH designed the
study. All authors contributed ideas and provided written input. JRS
wrote the manuscript with input from all authors.

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\textbf{Tables}

Table 1. Leaf chamber conditions for each species for RACiR
measurements.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
Species & \emph{I\textsubscript{sat}} & \emph{VPD\textsubscript{leaf}} &
\emph{T\textsubscript{leaf}} & \emph{FS} & \emph{FR} & \selectlanguage{greek}\emph{ΔP}\selectlanguage{english} & Rate
& Range & Date\tabularnewline
\midrule
\endhead
\emph{Ascelpias speciosa} & 1800 & 2.5 & 30 & 10000 & 600 & 0.2 & 100 &
300 - 900 & 28/06/2018\tabularnewline
\emph{Capsicum annuum} & 1000 & 1.8 & 25 & 10000 & 600 & 0.2 & 100 & 600
- 100 & 30/11/2016\tabularnewline
\emph{Cedrus deodar} & 1750 & 2.5 & 30 & 14000 & 600 & 0.05 & 60 & 300 -
900 & 24/08/2018\tabularnewline
\emph{Ginkgo biloba} & 1500 & 2.5 & 30 & 10000 & 600 & 0.2 & 100 & 300 -
1000 & 24/08/2018\tabularnewline
\emph{Malus domestica} & 1800 & 1.5 & 25 & 10000 & 600 & 0.2 & 100 & 600
- 100 & 09/10/2016\tabularnewline
\emph{Pinus ponderosa} & 2000 & 1.5 & 25 & 10000 & 600 & 0.2 & 70 & 300
- 1000 & 26/10/2017\tabularnewline
\emph{Populus deltoides} & 1000 & 1.5 & 25 & 10000 & 600 & 0.2 & 100 &
600 - 100 & 31/10/2016\tabularnewline
\emph{Populus trichocarpa} & 1000 & 1.5 & 25 & 10000 & 600 & 0.2 & 100 &
600 - 100 & 31/10/2016\tabularnewline
\emph{Quercus muehlenbergii} & 1500 & 2.5 & 30 & 10000 & 600 & 0.2 & 100
& 300 - 900 & 28/06/2018\tabularnewline
\emph{Rosa grandiflora} & 1000 & 2.5 & 30 & 10000 & 600 & 0.2 & 100 &
300 - 900 & 28/06/2018\tabularnewline
\bottomrule
\end{longtable}

RACiR: the rapid \emph{A/C\textsubscript{i}}
response;\emph{I\textsubscript{sat}} : saturating light intensity (\selectlanguage{greek}μ\selectlanguage{english}mol
m\textsuperscript{-2}
s\textsuperscript{-1});\emph{VPD\textsubscript{leaf}} : leaf to air
vapor pressure deficit (kPa); \emph{T\textsubscript{leaf}} : leaf
temperature (\selectlanguage{ngerman}°C); \emph{FS} : fan speed (rpm); \emph{FR} : flow rate
(\selectlanguage{greek}μ\selectlanguage{english}mol s\textsuperscript{-1});\selectlanguage{greek}\emph{ΔP}\selectlanguage{english} : chamber overpressure (kPa);
Rate: rate of RACiR (\selectlanguage{greek}μ\selectlanguage{english}mol CO\textsubscript{2} mol\textsuperscript{-1}
min\textsuperscript{-1}); Range: range of RACiR (\selectlanguage{greek}μ\selectlanguage{english}mol
CO\textsubscript{2}mol\textsuperscript{-1}).

Table 2. Modelled net daily carbon (C) gain under scenarios of diurnally
changing, peak, average, or minimum \emph{V\textsubscript{cmax}}
and\emph{J\textsubscript{max}} , Percentage changes are expressed as
change relative to the diurnal scenario. Bold values indicate cases
where diurnal changes in photosynthetic capacity
(both\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}} ) were
significant.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllllll@{}}
\toprule
& Daily C Gain (g C m\textsuperscript{-2} day\textsuperscript{-1}) &
Daily C Gain (g C m\textsuperscript{-2} day\textsuperscript{-1}) & Daily
C Gain (g C m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C
Gain (g C m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain
(g C m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1}) & Daily C Gain (g C
m\textsuperscript{-2} day\textsuperscript{-1})\tabularnewline
\midrule
\endhead
& June 28 & June 28 & June 28 & June 28 & August 24 & August 24 & August
24 & August 24 & October 9 & October 9 & October 9 & October
9\tabularnewline
Species & Diurnal & Peak & Average & Minimum & Diurnal & Peak & Average
& Minimum & Diurnal & Peak & Average & Minimum\tabularnewline
\emph{Asclepias speciosa} & \textbf{3.98} & \textbf{4.53} &
\textbf{3.98} & \textbf{2.97} & \textbf{4.58} & \textbf{5.18} &
\textbf{4.6} & \textbf{3.54} & \textbf{4.39} & \textbf{4.84} &
\textbf{4.41} & \textbf{3.6}\tabularnewline
& & \textbf{14\%} & \textbf{0.3\%} & \textbf{-25\%} & & \textbf{13\%} &
\textbf{1\%} & \textbf{-22\%} & & \textbf{10\%} & \textbf{0.3\%} &
\textbf{-18\%}\tabularnewline
\emph{Capsicum annuum} & \textbf{4.49} & \textbf{6.34} & \textbf{4.7} &
\textbf{2.14} & \textbf{4.79} & \textbf{6.59} & \textbf{4.85} &
\textbf{2.32} & \textbf{3.43} & \textbf{5.01} & \textbf{3.51} &
\textbf{1.68}\tabularnewline
& & \textbf{41\%} & \textbf{5\%} & \textbf{-52\%} & & \textbf{38\%} &
\textbf{1\%} & \textbf{-51\%} & & \textbf{46\%} & \textbf{2\%} &
\textbf{-51\%}\tabularnewline
\emph{Cedrus deodar} & 4.36 & 7.61 & 5.91 & 1.64 & 4.74 & 8.03 & 3.25 &
1.93 & 3.72 & 6.21 & 4.86 & 1.59\tabularnewline
& & 75\% & 36\% & 0.62\% & & 70\% & 32\% & -59\% & & 67\% & 31\% &
-57\%\tabularnewline
\emph{Ginkgo biloba} & \textbf{3.1} & \textbf{3.8} & \textbf{2.77} &
\textbf{0.8} & \textbf{3.45} & \textbf{1.01} & \textbf{3.04} &
\textbf{4.09} & \textbf{2.67} & \textbf{3.17} & \textbf{2.37} &
\textbf{0.87}\tabularnewline
& & \textbf{23\%} & \textbf{-10\%} & \textbf{-74\%} & & \textbf{18\%} &
\textbf{-12\%} & \textbf{-71\%} & & \textbf{19\%} & \textbf{-11\%} &
\textbf{-67\%}\tabularnewline
\emph{Malus domestica} & \textbf{0.86} & \textbf{2.7} & \textbf{1.15} &
\textbf{-1.74} & \textbf{2.7} & \textbf{4.72} & \textbf{3.14} &
\textbf{-0.07} & \textbf{3.81} & \textbf{5.22} & \textbf{4.02} &
\textbf{2.86}\tabularnewline
& & \textbf{215\%} & \textbf{34\%} & \textbf{-303\%} & & \textbf{75\%} &
\textbf{17\%} & \textbf{-103\%} & & \textbf{37\%} & \textbf{6\%} &
\textbf{-25\%}\tabularnewline
\emph{Pinus ponderosa} & 6.79 & 11.52 & 8.08 & 5.14 & 7.41 & 12.02 &
8.54 & 5.5 & 5.48 & 9.06 & 6.65 & 4.34\tabularnewline
& & 70\% & 19\% & -24\% & & 62\% & 15\% & -26\% & & 65\% & 21\% &
-21\%\tabularnewline
\emph{Populus deltoides} & \textbf{3.86} & \textbf{6.14} & \textbf{3.33}
& \textbf{-0.43} & \textbf{5.3} & \textbf{7.1} & \textbf{4.27} &
\textbf{0.59} & \textbf{5.5} & \textbf{6.56} & \textbf{4.44} &
\textbf{2.47}\tabularnewline
& & \textbf{59\%} & \textbf{-14\%} & \textbf{-111\%} & & \textbf{34\%} &
\textbf{-19\%} & \textbf{-89\%} & & \textbf{19\%} & \textbf{-19\%} &
\textbf{-55\%}\tabularnewline
\emph{Populus trichocarpa} & \textbf{3.51} & \textbf{3.95} &
\textbf{3.58} & \textbf{3.17} & \textbf{4.41} & \textbf{4.94} &
\textbf{4.53} & \textbf{4.11} & \textbf{4.59} & \textbf{4.97} &
\textbf{4.66} & \textbf{4.34}\tabularnewline
& & \textbf{13\%} & \textbf{2\%} & \textbf{-10\%} & & \textbf{12\%} &
\textbf{3\%} & \textbf{-7\%} & & \textbf{8\%} & \textbf{1\%} &
\textbf{-6\%}\tabularnewline
\emph{Quercus muehlenbergii} & \textbf{1.72} & \textbf{3.55} &
\textbf{1.74} & \textbf{0.19} & \textbf{1.94} & \textbf{3.85} &
\textbf{1.99} & \textbf{0.31} & \textbf{1.71} & \textbf{3.01} &
\textbf{1.58} & \textbf{0.59}\tabularnewline
& & \textbf{106\%} & \textbf{1.00\%} & \textbf{-89\%} & & \textbf{98\%}
& \textbf{2\%} & \textbf{-84\%} & & \textbf{76\%} & \textbf{-8\%} &
\textbf{-66\%}\tabularnewline
\emph{Rosa grandiflora} & \textbf{1.25} & \textbf{2.57} & \textbf{1.4} &
\textbf{-1.08} & \textbf{1.86} & \textbf{3.13} & \textbf{1.96} &
\textbf{-0.57} & \textbf{2.06} & \textbf{3.02} & \textbf{2.14} &
\textbf{0.52}\tabularnewline
& & \textbf{105\%} & \textbf{11\%} & \textbf{186\%} & & \textbf{68\%} &
\textbf{5\%} & \textbf{-131\%} & & \textbf{47\%} & \textbf{4\%} &
\textbf{-75\%}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Figure Captions}

Figure 1 -- Diurnal air temperature (T), photosynthetically active
radiation (Q), and relative humidity (RH) used for
modelling\emph{A\textsubscript{net}} in all species. Dates indicate the
environmental conditions at the University of New Mexico in 2018. Grey
regions indicate night.

Figure 2 -- Diurnal variation of apparent
\emph{V\textsubscript{cmax}}(a, b, c) and \emph{J\textsubscript{max}}
(d, e, f) show consistent declines by the end of day at 25 \selectlanguage{ngerman}°C in
\emph{Populus deltoides} (a, d;\emph{N} = 6), \emph{Capsicum annuum} (b,
e; \emph{N} = 6), \emph{Malus domestica} (b, e; \emph{N} = 6),
\emph{Populus trichocarpa} (b, e;\emph{N} = 4) but not \emph{Pinus
ponderosa} (c, f; \emph{N} = 3). At 30 °C there are diurnal declines in
photosynthetic capacity in\emph{Asclepias speciosa}
(\emph{J\textsubscript{max}} only; d; \emph{N}= 6), \emph{Quercus
muehlenbergii} (a, d; \emph{N} = 5), \emph{Rosa grandiflora} (b, e;
\emph{N} = 6), and \emph{Ginkgo biloba} (c, f;\emph{N} = 3) but not in
\emph{Cedrus deodar} (c, f; \emph{N} = 4). Data presented as means ±
s.e.m.

Figure 3 -- Apparent \emph{J\textsubscript{max}} is strongly correlated
with apparent \emph{V\textsubscript{cmax}} across all species. Data
presented as means for each timepoint for each species; s.e.m. was not
included for clarity.

Figure 4 -- Relative \emph{V\textsubscript{cmax}} (a-c)
and\emph{J\textsubscript{max}} (d-f) for all species shown in Fig. 1.
Data presented as means ± s.e.m.

Figure 5 -- Modelled diurnal \emph{A\textsubscript{net}}
for\emph{Asclepias speciosa} (a), \emph{Capsicum annuum} (b),
\emph{Malus domestica} (c), \emph{Quercus muehlenbergii} (d),
\emph{Populus deltoides} (e), \emph{Populus trichocarpa} (f), \emph{Rosa
grandiflora}(g), \emph{Ginkgo biloba} (h), \emph{Pinus ponderosa} (i),
and\emph{Cedrus deodar} (j) under conditions of constant
maximum\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}}
(Peak), and diurnally changing \emph{V\textsubscript{cmax}}
and\emph{J\textsubscript{max}} (Changing), constant
mean\emph{V\textsubscript{cmax}} and \emph{J\textsubscript{max}}
(Average), and constant minimum \emph{V\textsubscript{cmax}}
and\emph{J\textsubscript{max}} .

Figure 6 -- Apparent \emph{V\textsubscript{cmax}}
(a),\emph{J\textsubscript{max}} (b), and \emph{A\textsubscript{net}} (c)
did not decline significantly after 5 one-minute clamps on the same leaf
spot of individuals of \emph{Populus deltoides} , \emph{Capsicum annuum}
, and \emph{Populus trichocarpa.} \emph{N} = 6, data presented as means
± s.e.m.

Figure 7 -- Modelled versus measured net CO\textsubscript{2}assimilation
(\emph{A\textsubscript{net}} ) (a) and stomatal conductance
(\emph{g\textsubscript{s}} ). Solid line indicates 1:1 relationship. See
text for statistics.

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