Modeling
The large data set used for the g1 estimates
required careful evaluation and screening for erroneous data points.
Thus, we used a methodical approach to screen, evaluate, test and if
necessary, remove outlier and/or high leverage points as outlined below.
We started screening of the data set for any potentially erroneous data
points based on physiological and environmental constraints that were
considered either physiologically unlikely (e.g., data points with
extremely negative Ci while positiveAnet , etc.) or measured at unfavorable chamber
conditions (e.g., extremely high Tleaf, very low RH,
etc.) or any points that were indicated by the operator of the
instrument during measurement as potentially erroneous, all those points
were removed. For additional details outlining methodology of initial
evaluation of the carbon assimilation measurements used in the further
modeling work see supplemental materials.
We used the subsequent data set to
fit the USO model (see equation 1 in supplement and for its derivation
details see Medlyn et al., (2011)) and to estimate and
effectively define g1 for each species in
accordance with their respective growing conditions (i.e., respective
treatments and replication, see below). We used estimatedg1 values to analyze and quantify the size of the
warming and rainfall reduction effects across spatial and temporal
scales (i.e., site, canopy, and growing season). Theg0 parameter was set to zero as suggested
(Duursma et al., 2019, B Medlyn, pers comm), given its otherwise
high correlation to g1 and lack of precision. We
used the “plantecophys” package (Duursma, 2015) in R (R Development
Core Team, 2019) to fit the USO model (Medlyn et al., 2011). In
some cases, the final data set at the finest levels of factorial
combinations (i.e., species × warming × rainfall reduction × treatment
replicate (i.e., individual research plot) × block × canopy × site ×
year × measurement campaign) did not have a sufficient number of
replicates (i.e., at least 3 replicates are needed) to fit the USO model
and/or available replicates were not enough to produce a fit with good
confidence. Thus, the 17,727 collected observations were binned by
experimental treatment, effectively pooling measurements across the same
treatment combination by combining plot replicates of the same treatment
together to achieve the following factorial combination by canopy:
closed canopy: species × warming × site × year × measurement campaign,
open canopy: species × warming × rainfall reduction × site × year ×
measurement campaign.
This yielded a total of 2,732 estimates of g1 by
fitting the USO model. The mean number of data points used to fit the
USO model was six (±2 SD) with less than 2.5% of the model fits
constructed based on the minimum of three data points and
>75% based on six or more, with the maximum of 18 points.
A data point was a unique instance where the four metrics needed to fit
the USO model (Anet , gs , D
and Ca) were sampled on a single leaf.
Overall, estimates of g1 values for our species
(Table S2 and Figures 1-3) are within the range of those found by others
(e.g., Franks et al., 2017; Medlyn et al., 2011; Zhouet al., 2013). However, to further evaluate the quality of theg1 estimates we implemented a two-step process.
First, we compared values of observed stomatal conductance used in the
USO model to estimate g1 values, to the values ofgs predicted by the A-gscoupled model (as described by Duursma, 2015). UsedA-gs coupled model predictAnet and gs based on the
environmental conditions that a given leaf experienced during
measurement (i.e., leaf temperature, VPD, Ca, PAR),
estimated g1 values (based on USO model), and
estimated photosynthetic capacity (i.e., rate of Rubisco carboxylation
and photosynthetic electron transport, estimated based on one-point
method (De Kauwe et al., 2015)) (for more details on theA-gs coupled model used here see Duursma, 2015).
The overall linear fit for the entire data set minus outliers (n= 17,040) produced R 2 = 0.71 with nearly 1:1
slope adding confidence to the fits of the model. Second, we used a
multivariate jackknife analysis of the g1estimates, performed in JMP statistical software (JMP 14.2, SAS
Institute), that detected 146 (~5%) out of 2732 totalg1 estimates as potential outliers. Out of those
146 g1 estimates ~75% of them
were above the maximum values reported elsewhere in the literature
(e.g., Medlyn et al., 2011; Gimeno et al., 2016; Héroultet al., 2013; Franks et al., 2017). Thus, we removed all
146 points indicated as outliers. We note that, in an analysis (not
shown here) that excluded only the 12 most extreme values
(g1 ≥ 500; orders of magnitude higher than
average g1 values reported here and elsewhere)
the overall effects detected did not change.
To separate thermal effects from the indirect effect of warming on soil
VWC we examined g1 parameters for observations
grouped by different VWC classes. To do this we used the 24h averages of
the soil VWC on the day when theAne t measurements were made. The
categorical values of VWC were created by binning 24h soil VWC averages
into three categories as follows: i) low VWC < 12.99%, ii)
medium VWC 13 – 17.99%, and high VWC
≥ 18% (for details on soil VWC
measurements see Rich et al., 2015).