Earth system scientists working with radiocarbon in
organic samples use a stable carbon isotope (δ13C) correction
to account for mass-dependent fractionation, but it has not been evaluated
for the soil gas environment, wherein both diffusive gas transport and
diffusive mixing are important. Using theory and an analytical soil gas
transport model, we demonstrate that the conventional correction is
inappropriate for interpreting the radioisotopic composition of CO2
from biological production because it does not account for important gas
transport mechanisms. Based on theory used to interpret δ13C of
soil production from soil CO2, we propose a new
solution for radiocarbon applications in the soil gas environment that fully
accounts for both mass-dependent diffusion and mass-independent diffusive
mixing.
Introduction
Radiocarbon allows us to measure the age of soil-respired CO2 (CO2 diffusing from
the soil surface to the atmosphere, also called soil flux as in Cerling
et al., 1991), but the traditional reporting convention for radiocarbon was
not established for soil gas-phase sampling; rather, it was established for solid (organic
matter) sample analysis. The validity of this convention has never been
explicitly tested for soil-respired CO2.
The traditional radiocarbon reporting convention, Δ14C
(Stuiver and Polach, 1977), uses a mass-dependent correction based
on the isotopic composition of wood. Its purpose is to correct for
biochemical fractionation against the radiocarbon isotopologue
(14CO2) abundance during photosynthesis, which is assumed to be
twice as strong as for 13CO2 based on their respective departures
in molecular mass from 12CO2. The classical reference describing
these conventional calculations is Stuiver and Polach (1977).
In the soil gas environment, researchers have different implicit
expectations for fractionation processes. They generally assume that
14C of CO2 is not biochemically fractionated in the gas phase
between the points of CO2 production (biological production of CO2 by soil
organisms and roots) and measurement (subsurface or flux chamber samples).
This assumption is reasonable based on the short residence time of CO2 (minutes to days) in the soil profile before emission to the atmosphere.
However, soil gas isotopic signatures depart in predictable ways from the
signature of production because of physical fractionation. It has been
recognized for decades that δ13C of CO2 at any point in
the soil profile will never equal the isotopic signature of production
because of transport fractionations that alter produced CO2 before it
is measured (Cerling et al., 1991). This theory readily extends
to 14C.
We argue here that in the case of soil pore space 14C in which mixing of
air masses occurs, the assumption that mass-dependent fractionation is
twice as large for 14C as δ13C by biochemical and physical
processes no longer holds. Using theory and the physical modeling of soil gas
transport to illustrate the issue with the current reporting convention
correction, we propose an alternative approach for specific use cases.
Theory
To understand why the mass-dependent correction used in the Stuiver and
Polach (1977) radiocarbon reporting convention may be a poor fit for soil
gas studies, we can look at our current understanding of the stable isotopic
composition, δ13C, of soil CO2 (pore space CO2, mole
fraction with respect to dry air). We use delta notation to present the
stable isotopic composition of CO2:
δ13C=RsRVPDB-11000,
where δ13C is the isotopic composition in per mill (see Table 1 for a full list of abbreviations),
Rs is the 13C/12C ratio of the sample, and RVPDB is the
13C/12C ratio of the international standard, Vienna Pee Dee
Belemnite.
List of symbols used. Note that the isotope composition ratios are also
unitless but traditionally expressed using per mill (‰)
notation.
SymbolDescriptionUnitAssample activityunitlessASNnormalized sample activity, relative to δ13C of terrestrial woodunitlessAabsage-corrected absolute international standard for activityunitlessConcCO2 concentrationµmol m-3ConcatmCO2 concentration in air just above the soilµmol m-3CaCO2 mole fraction in air just above the soilµmol mol-1CO2CO2 mole fraction relative to dry airµmol mol-1CsCO2 mole fraction in soil pore spaceµmol mol-1Dsoil gas diffusivitym2 s-1D(z,t)soil gas diffusivity at depth z and time tm3 s-1δ13Cstable (13C/12C) isotope composition (relative to VPDB)‰δ14Cradiocarbon (14C/12C) isotope composition (relative to Aabs)‰Δ14Coldradiocarbon (14C/12C) isotope composition with δ13C correction‰Δ14Cnewradiocarbon (14C/12C) isotope composition with δJ13 correction‰δa13δ13C of CO2 in air above the soil‰δa14δ14C of CO2 in air above the soil‰ΔaΔ14C of CO2 in air above the soil‰δJ13δ13C of CO2 from soil production, calculated using Eq. ()‰δJ14δ14C of CO2 from soil production, calculated using Eq. ()‰ΔJ14Δ14C of CO2 from soil production, calculated using Eq. ()‰δs13δ13C of CO2 in soil pore space‰δs14δ14C of CO2 in soil pore space‰ΔsΔ14C of CO2 in soil pore space‰Llower model depth boundarymP(z,t)biological production rate at depth z and time tµmolCO2 m-3 s-1Pbiological production rateµmolCO2 m-3 s-1Rsisotopic ratio (heavy / light) of CO2 sampleunitlessRVPDBisotopic ratio (heavy / light) of Vienna Pee Dee Belemnite standardunitlessttimesθair-filled porosity of soilunitlesszdepthm
From foundational work done by Cerling et al. (1991) we know that the isotopic
composition of soil CO2 is different from that of soil-respired
CO2. Any change in δ13C of soil CO2 with depth is
influenced by (1) mixing of atmospheric and biological (or biogeochemical)
sources of isotopically distinct CO2, which may occur via diffusion (no
bulk gas flow; referred to as diffusive mixing for the remainder of the
paper) or advection (bulk gas flow), and (2) kinetic fractionation by
diffusion. The effect of these is illustrated in Fig. 1 using a simulated
soil gas profile. In panel (a) two depth profiles of δ13C of
CO2 that were modeled in a steady-state environment are shown (the
model will be described in Sect. 3). The profiles differ only in soil
diffusivity; all other characteristics were held constant, including rates
of production, δ13C of CO2 in the atmosphere (-8 ‰; circle), and biological production (-25 ‰; square with dashed line). In the resultant depth
profile with higher soil diffusivity in panel (a), the δ13C of soil CO2 ranges from -8 ‰ to -15.1 ‰. In the depth profile representing a soil with lower
diffusivity, the δ13C of soil CO2 ranges from -8 ‰ to
-20.6 ‰. We stress again that these two isotopic depth
profiles differ only due to differences in transport as a result of their
varying soil diffusivities. In the depth profile with lower soil
diffusivity, atmospheric CO2 does not penetrate downwards as readily,
so the profile shape is much steeper near the soil–atmosphere boundary and
is more reflective of the production source composition, -25 ‰, at depth. In the depth profile with higher soil
diffusivity, atmospheric air of -8 ‰ more readily mixes
from the surface downward by diffusion, so the near-surface isotopic
composition will be more reflective of the atmosphere due to diffusive
mixing of these end-members near the soil surface.
Modeled steady-state diffusive vertical depth profiles for
δ13C and δ14C of soil CO2. In panel (a) the δ13C of atmospheric CO2 (circle) is -8 ‰ and CO2 from biological production (square with
dashed line; δJ) is -25 ‰. In panel (b) the δ14C of atmospheric CO2 (circle) is 45.5 ‰ and CO2 from biological production (square with
dashed line) is -50 ‰. Both profiles
have the same biological production rates and isotopic composition of
biological production, but each profile has a different soil diffusivity as
indicated.
Importantly, the soil CO2 never equals the δ13C of
production (-25 ‰) at any depth in either profile in
Fig. 1a. It is not possible to directly measure δ13C of
production in situ because diffusion and diffusive mixing alter the character of
CO2 immediately after its production. From the site of production in
the soil, 12CO2 diffuses somewhat faster through the soil than
13CO2 because the former has a lower mass. This diffusive
difference leads to isotopic fractionation and results in depth profiles of
δ13C of soil CO2 that are isotopically enriched (less
negative) compared to the source of production. Work by Cerling (1984)
and later by Cerling et al. (1991) demonstrated that the mass differences
between the two isotopologues led to a difference in the diffusion rate of each
in air, amounting to a fractionation of 4.4 ‰ (note that
this applies only to binary diffusion of CO2 in air and will differ if
CO2 diffuses in other gases). As a result, the δ13C of
soil CO2 measured at any depth will be enriched by a minimum of 4.4 ‰ relative to the biological production CO2 source.
However, the δ13C of soil-respired CO2 can be
considerably more enriched than 4.4 ‰ relative to
production due to diffusive mixing with the atmosphere as shown in Fig. 1a.
A convenient theoretical formulation for correcting δ13C for
both diffusion fractionation and diffusive mixing was introduced by Davidson (1995), following on the work of Cerling (1984) and
Cerling et al. (1991). This approach allows one to combine
measurements of CO2 and its isotopic composition within the soil and
the air above it to infer the isotopic composition of CO2 produced in
the soil. This only applies when transport within the soil is purely by
diffusion (no bulk air movement). The Davidson (Davidson, 1995)
solution uses the difference between the diffusion coefficients for 12C
and 13C as follows:
δJ13=Csδs13-4.4-Ca(δa13-4.4)1.0044(Cs-Ca),
where δJ13 is the δ13C composition of
CO2 from soil production (biological respiration within the soil),
Cs and δs13 are the mole fraction and isotopic
composition of soil CO2, and Ca and δa13
are the mole fraction and isotopic composition of CO2 in the air just
above the soil. In Fig. 2a the mole fraction and isotopic composition of
soil CO2 at a 40 cm depth and of the air just above the soil were
“sampled” from model-generated soil depth profiles and the (unrounded)
values were used to calculate the isotopic composition of production using
Davidson's equation (Cs= 14 780 ppm, δs13=-20.3832 ‰, Ca=380 ppm, and δa13=-8 ‰). The resulting δJ13 (e.g., Eq. ) at this depth equals the true isotopic
composition of production (see inset box, Fig. 2a). However, because the
Davidson approach accounts for diffusion and diffusive mixing, at any given
soil depth, not just 40 cm, the modeled values of Cs and
δs13 in Figs. 1a and 2a will always yield (via Eq. ) the true isotopic composition of production, δJ13=-25 ‰ (dashed line). If δ13C of soil CO2 were (erroneously) interpreted to represent the
δ13C of soil-respired CO2, the error could be as large as
the absolute value of (δa-δJ13)-4.4 ‰. This Davidson (1995) δJ13 approach has been shown to be robust when applied to field data from natural soils (Breecker et al., 2012; Bowling
et al., 2015; Liang et al., 2016).
Modeled steady-state diffusive vertical depth profiles for
δ13C(a), δ14C(b), and
Δ14Cold(c) of soil CO2. The three
soil profiles were generated using the same soil production and diffusivity
rates (2 µmol m-3 s-1 and 1×10-6 m2 s-1,
respectively). Panels (a) and (b) were prepared using δ13C
and δ14C as noted. Panel (c) shows an approach consistent with
present day, whereby the Δ14C profile generated by the model
incorporates the traditional Stuiver and Polach (1974) correction for
biochemical fractionation. Inset “Calculated” panels show how, using input
data read directly from each depth profile, a user would arrive at either
the correct or incorrect isotopic value of production using a Davidson
approach to adjust for in-soil gas transport. The atmospheric source (Ca)
composition is presented as a white circle, the soil CO2 composition
(Cs) is a black circle, and the isotopic composition of production is a
black square. Note that values for the isotopic composition of soil in the
three panels are rounded for ease of reading but are actually -20.3832 ‰, -39.3989 ‰, and -48.4319 ‰, respectively, for panels (a–c). These
values are drawn from the curve at a depth of 40 cm.
While 14C is a radioactive isotope and thus decays with time, the
half-life is sufficiently long so that 14CO2 behaves similarly to
stable isotopes on the timescales at which diffusion occurs in a soil gas
system. In this way, δ13C diffusive
fractionation theory can be applied to the radiocarbon isotopic composition,
δ14C, so long as we account for the mass difference. The larger
mass of 14C means that the diffusion fractionation factor is calculated
to be 8.8 ‰ based on the atomic masses of
14CO2, 12CO2, and bulk air (Southon, 2011).
We can show that the 14CO2 distribution in soils will be like that
of 13CO2 if we model its distribution through depth in the same
synthetic soil gas environment. In Fig. 1b we present a modeled soil
environment with defined atmospheric and production source CO2 isotopic
composition boundary conditions for δ14C, the 14C
equivalent to δ13C (Stuiver and Polach, 1977):
δ14C=AsAabs-11000,
where δ14C is the isotopic composition in
per mill, As is the measured activity of the sample, and
Aabs is the activity of the oxalic acid standard (both unitless). As in
Fig. 1a, in panel (b), the profile with lower soil diffusivity, the
downward penetration of atmospheric CO2 into the soil profile is
reduced, and as a consequence the isotopic depth profile more closely
reflects (but does not equal) the composition of production (-50 ‰; dashed line). When the diffusion rate is high and
transport is rapid, the atmospheric source is more readily able to penetrate
the profile and mix with the production source. In both profiles, the
measured value of soil CO2 at a given depth will not equal
the isotopic production value of -50 ‰ because of
diffusion and diffusive mixing. Similar profiles of δ14C of
soil CO2 with depth, highlighting the diffusive effects, have been
presented by Wang et al. (1994).
Since δ14C transport of soil CO2 is like that of δ13C, it follows that we should apply corrections for δ14C
like those in Eq. () in order to calculate the isotopic composition of
production. The δ14C reformulation of Davidson's
δJ13 equation is as follows:
δJ14=Csδs14-8.8-Ca(δa14-8.8)1.0088(Cs-Ca),
where δJ14 is the δ14C composition of soil
production, Cs and δs14 are the mole fraction and δ14C composition of the soil CO2, and Ca and δa14 are the mole fraction and δ14C composition of
CO2 in the air just above the soil. This Davidson reformulation for
δ14C, δJ14, was applied to a model-generated
profile of soil δ14C at a 40 cm depth in Fig. 2b, like in
panel (a) for δ13C (Cs= 14 780 ppm, δs14=-39.3989 ‰, Ca=380 ppm, and
δa14=45.5276 ‰; see inset
box, Fig. 2b). As was the case for δ13C in Fig. 2a, the
modeled values of Cs and δs14 at any depth will yield
the true isotopic composition of production, -50 ‰ (dashed line), because this approach accounts for diffusion and diffusive
mixing.
The typical approach that has been used for interpreting the 14C
composition of soil CO2 and soil-respired CO2 (e.g.,
Trumbore, 2000) differs from the δ14C example above
because a δ13C correction is applied to account for
the mass-dependent isotopic fractionation of biochemical origin, ultimately
converting δ14C to a variant called Δ14C
(Stuiver and Polach, 1977). The derivation of the mass-dependent
correction is provided in Stuiver and Robinson (1974), wherein
observations are normalized to an arbitrary baseline value of -25 ‰ for δ13C (a value for terrestrial wood),
and the 13C fractionation factors are squared to account for the
14C/12C fractionation factor as follows:
ASN=AsRs-25Rs2,=As1-251000×RVPDB21+δ13C1000×RVPDB2,=As1-25100021+δ13C10002,
where ASN is the normalized sample activity, As is the sample
activity, and δ13C is the isotopic composition of the sample
(soil CO2 in our case). As explained in Stuiver and Robinson (1974),
the 0.975 term sometimes used in forms of ASN is equivalent to 1-251000, which we will retain for clarity. The equation
for Δ14C, the δ13C-corrected variant of δ14C, can then be created from Eq. () by substituting in delta
notation for Δ14C of Δ14C= (ASN/Aabs
-1) × 1000 following Stuiver and Robinson (1974):
Δ14C=1+δ14C10001-25100021+δ13C10002-11000.
Combining Eqs. () and () leads to
Δ14Cold=AsAabs1-25100021+δ13C10002-11000.
For more information on the derivation of Eqs. () and () see Stuiver and
Robinson (1974), page 88. In Eq. () we have added the subscript “old” to
highlight that this is the common approach used to date for soil gas
applications – we will introduce a “new” method with Eq. (). The terms on
the left-hand side of Eqs. () and () are identical. Note that Aabs in
our notation is equivalent to AO in Stuiver and Robinson (1974).
Equation (7) uses δ13C as an input parameter to make a mass-dependent
correction to obtain Δ14C, but the profiles of δ13C and δ14C of soil CO2 (Fig. 1) highlight the fact that
both vary within the soil because of diffusion and diffusive
mixing. This makes it unclear what form of δ13C should actually
be used in the place of the mass-dependent correction in the soil gas
environment (δ13C of the soil CO2 is measured but δ13C of biological production is not) as diffusive mixing is not a
mass-dependent process. When Δ14Cold is modeled through
depth like δ13C and δ14C in Figs. 1 and 2 it also
varies with depth as shown in Fig. 2c. However, using a Δ14C
variant of Davidson's δJ (as for δ14C in Fig. 2b) at the same 40 cm depth does not correctly reproduce the
specified model value for the Δ14C of production of -50 ‰ like it did for δ13C and δ14C (Cs= 14 780 ppm, Δs=-48.4319 ‰, Ca=380 ppm, and Δa=10 ‰; see inset box, 2c). We therefore adapted the
mass-dependent correction in Δ14Cold using Davidson's (1995) theory to demonstrate how and why it should be used for Δ14C soil gas applications.
Methods – model description
We used an analytical gas transport model to simulate a range of natural
soil profiles of 12CO2, 13CO2, and 14CO2 in
order to present soil gas transport theory. The model is based on Fick's
second law of diffusion:
θ∂Conc∂t=∂∂zDz,t∂Conc∂z+Pz,t,
where θ is the soil air-filled pore space, Conc is the concentration,
t is time, D(z,t) is the soil gas diffusion function, and P(z,t) is the biological
production function, with the latter two dependent on both depth z and time
t.
The model was run in steady state,
∂Conc∂t=0,
and both diffusion and production rates were constant with depth:
10Dz=D,11Pz=P.
The following boundary conditions were used:
12Cz=0=Concatm,13∂C∂z|z=L=0,
where Concatm is the concentration of CO2 in air just above the soil
and L is the model lower spatial boundary, the point below which no
production or diffusion occurs. Equation () is solved analytically to yield the
following equation:
Concz=P/LDL×z-z2z+Concatm.
In the model, isotopologues of CO2 are treated as independent gases,
with their own specific concentration gradients and diffusion rates
(Cerling et al., 1991; Risk and Kellman, 2008; Nickerson and Risk, 2009). We assume total CO2 to be 12CO2
because of its high abundance. The error associated with this
assumption is less than 0.01 % (Amundson et al., 1998). Equation () is thus
applied for 13CO2 and 14CO2. For the full derivation see
Nickerson et al. (2014) Sect. 2.3.
The analytical gas transport model was applied across a range of soil
diffusivity (1×10-7, 1×10-6, and 1×10-5 m2 s-1) and
soil production rates (0.5, 1, 2, and 4 µmolCO2 m-3 s-1). The specific soil diffusivity and production rates used to
generate each profile are stated in the figure caption of that profile. We
used a δ13C of biological production (-25 ‰) and atmospheric CO2 (δa; -8‰) and Δ14C of biological production (-50 ‰) and atmospheric CO2 (Δa; 10 ‰) to represent realistic conditions found in
nature. The other model boundary conditions were as follows: L=0.8 m, z=0.025 m, and Concatm= 15 833 µmol m-3 (∼380 ppm). The output of the model under these applied conditions were profiles
of 12CO2, 13CO2, and 14CO2 for each depth
(z) down to the bottom boundary (L).
Modeled steady-state diffusive vertical depth profiles for
Δ14Cold (solid line; same profile as in Fig. 2c) and
Δ14Cnew (dashed line) of soil CO2. The Δ14Cnew soil profile was calculated from the profiles in Fig. 2
(soil production and diffusivity rates of 2 µmol m-3 s-1 and
1×10-6 m2 s-1, respectively). The inset “Calculated” panels
show how, using input data read directly from the depth profile of Δ14Cnew, a user would arrive at the correct value of production
using a Davidson approach to adjust for in-soil gas transport. The
atmospheric source (Ca) composition is presented as a white circle, the soil
CO2 composition (Cs) is a black circle, and the isotopic
composition of production is a black square. Note that values for the
isotopic composition of soil and atmosphere are rounded for ease of reading
but are actually -39.3989 ‰ and 45.5276 ‰, respectively. These values are drawn from the curve
at a depth of 40 cm.
ResultsAdapted correction for interpreting radiocarbon values of soil and
soil-respired CO2
Based on Davidson's (1995)
theory and what we demonstrated with Fig. 2c, rather than using the
δ13C soil pore space as a mass-dependent correction, we suggest
instead using the value δJ13 (Eq. ), the
biological production of δ13C, in its place in the denominator
of Eq. () as follows:
Δ14Cnew=AsAabs1-25100021+δJ1310002-11000.
Values of Δ14Cnew through depth represent
transport-fractionation-corrected soil CO2 values of radiocarbon, and
in comparison to Δ14Cold, they are corrected for
mass-independent diffusive mixing.
A depth profile of Δ14Cnew is presented in Fig. 3 (dashed
line). To generate this soil depth profile we used the numbers from the
simulated profiles in Fig. 2 and inserted them into Eq. (2) to determine
δJ13 at each depth. These values were then used in
Eq. (15) to obtain Δ14Cnew of soil CO2 through depth.
The Δ14Cnew profile (dashed line) is more isotopically
enriched compared to the Δ14Cold profile (solid line) in
Fig. 3. Values sampled from the Δ14Cold profile (the
same as the one presented in Fig. 2c) were not able to reproduce the
specified model value for the Δ14C of production of -50 ‰ using a Δ14C variant of Davidson's
δJ. To demonstrate that Δ14Cnew does correct
for gas transport fractionations, it can be placed into ΔJ14,
a Δ14C adaption of Davidson (1995) for 14C (Eq. ), as
follows:
ΔJ14=CsΔ14Cnew-8.8-CaΔa14-8.81.0088(Cs-Ca),
where ΔJ14 is the Δ14C composition of soil
production, Cs and Δ14Cnew are the mole fraction
and Δ14C composition of the soil CO2, and Ca and
Δa14 are the mole fraction and Δ14C composition
of CO2 in the air just above the soil.
Unlike in the case of Δ14Cold demonstrated in the inset
box in Fig. 2c, using the same 40 cm depth from the Δ14Cnew profile, we were able to reproduce the specified model
value for the Δ14C of production of -50 ‰ (Cs= 1 780 ppm, Δs=-39.3989 ‰,
Ca=380 ppm, and Δa=45.5276 ‰;
see inset box, Fig. 3).
Work-arounds and establishing new best practice
In the soil gas environment, Δ14Cnew convention should be
used to properly interpret soil-respired CO2 from soil CO2, as it
corrects for all related transport fractionations. For researchers who have
soil CO2 data previously interpreted using Δ14Cold,
the following steps will help correct for transport fractionations: (1) use
δs13 and Δ14Cold to back out the
activity of the sample (As); (2) calculate the isotopic composition of
production for δ13C using Eq. (), δJ13;
(3) use δJ13 and As in Eq. () to calculate
Δ14Cnew; and finally (4) determine the radiocarbon isotopic
composition of production using Eq. (), ΔJ14.
Going forward, several changes to best practice are recommended. On a lab
level, for new soil CO2 data, we propose that laboratories report
radiocarbon using Eq. () for δ14C, the uncorrected radiocarbon
variant, so that the first step above (use δs13
and Δ14Cold to back out the activity of the sample; As) can be avoided, and researchers can proceed with steps 2–4. We
also suggest that researchers measure δ13 alongside Δ14C so that they are not dependent on the AMS-measured δ13 for potential back corrections.
The Davidson (1995) δJ method was the gradient approach we used
in our study, but alternative gradient approaches, such as those presented
for δ13C by Goffin et al. (2014) and Nickerson et al. (2014) and for Δ14C by Phillips et al. (2013), would likely be similarly successful
in producing depth-dependent compositions of production. They are, however,
not quite as straightforward as the δJ method.
Conclusions
This traditional Δ14C solution, which uses δ13C of soil CO2 as a mass-dependent correction, is not
appropriate for the soil gas environment, as it does not account for
mass-independent mixing processes. We propose a new best practice for
Δ14C work in the soil gas environment that accounts for gas
transport fractionations and produces true estimates of Δ14C of production.
Data availability
No data sets were used in this article.
Author contributions
JEE, DRB, and DAR conceptualized the theory and method for proving the new
solution for radiocarbon applications in the soil gas environment. JEE
carried out the modeling, validation, visualization, and writing of the
original draft. DRB, DAR, and JEE reviewed and edited the draft.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Thanks to Thure Cerling for helpful discussions on the paper and to anonymous reviewers whose input was important in shaping the final presentation of this material.
Financial support
Jocelyn E. Egan is grateful for support from a Research-in-Residence Award from the Inter-University Training in Continental-scale Ecology Project, National Science Foundation, Directorate for Biological Sciences (grant no. EF-1137336). Jocelyn E. Egan was also funded by the Natural Sciences and Engineering Research Council of Canada (NSERC). This research was also supported by the US Department of Energy, Office of Science (grant no. DE-SC0010625).
Review statement
This paper was edited by Dan Yakir and reviewed by three anonymous referees.
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