230
available, rates (or rate constants) can be estimated
using very simple or relatively complicated models.
When using a modeling approach with numerical
approximation, separate, but identical submodels
are used to describe flow of the two isotopes (natural and added isotopes) through the system. All of
the rate constants used in the two submodels are
linked mathematically so that as the rate constant
for one process is adjusted, flow of both isotopes
changes. Initial values for pool sizes (concentrations) and rate constants are provided for the model,
either based on actual data or best guesses, and a
simulation is performed. At the end of the simulation, the enrichment predicted by the model for one
of the sink pools is compared with the actual enrichment measured for that pool during experimentation. Rate constants are adjusted, and a new simulation is performed. Enrichments are compared
again, and rate constants are readjusted. This iterative process continues until the error between predicted and actual enrichments becomes lower than
some value predetermined by the modeler. While
this approach requires some proficiency in programming, modeling software, such as Time-Zero
(Quaternary Software, Fort Collins, CO), is available that greatly simplifies the numerical approximation procedure. In addition, software is currently
available that uses numerical methods to estimate
gross rates of specific processes such as N mineralization, immobilization, and nitrification (e.g.,
Mary et al. 1998).
Natural Abundance Isotope Methods
Isotope fractionation and discrimination processes
cause the relative abundance of naturally occurring
isotopes to differ slightly from one pool to another.
For example, N2 in the atmosphere is 0.3663% 15N
and 99.6337% 14N (on a mole basis), whereas N in
soil typically ranges from about 0.3670 to 0.3718%
15N (Shearer et al. 1978). Changes in the relative
abundance of naturally occurring isotopes from one
pool to another have been used to estimate gross
rates of nutrient transformations. Natural abundance approaches fall into two categories: kinetic
models and source-identification approaches. The
approach using kinetic models is nearly identical to
the modeling and numerical approximation method
described in the previous section. The only difference is that slightly different rate constants are used
John M. Stark
for the two isotopes to model fractionation or discrimination processes. For example, during nitrification, the rate constant for 14NHt oxidation is
about 3% higher than the rate constant for 15NHt
(i.e., ~ = 1.03) (Handley and Raven 1992). In contrast, during N fixation, the rate constant for 14N2
reduction is nearly equal to the rate constant for
15N2 (~ = 1.002). Relatively few kinetic models
have been used to estimate transformation rates in
ecosystems, however (e.g., Shearer et al. 1974;
Herman and RundelI989).
The most frequent way that natural isotope abundances are used to estimate transformation rates is
by combining a source identification approach with
net rate measurements. Source identification approaches are used when an element flows into a
sink pool from two sources, and the two sources
differ significantly in isotope composition. For example, a source identification approach has been
frequently used to estimate rates of N fixation by
plants of natural and agro-ecosystems (Shearer and
Kohl 1986; Handley and Raven 1992; Ladha et al.
1993). The two sources ofN for N-fixing plants are
the soil and the atmosphere. As discussed earlier,
the N from these two sources may differ by as much
as 0.006 atom % 15N (or 15%0). Isotope discrimination during fixation of atmospheric N and during
uptake of soil N is relatively small (Handley and
Raven 1992). Therefore, if a plant obtains 100% of
its N from N fixation, then the isotope abundance
of the plant N will be approximately equal to that
of the atmosphere. Conversely, if the plant obtains
100% of its N from the soil, then the isotope abundance of the plant N will be approximately equal
to that of the soil plant -available N pool. If the plant
N is derived from both sources, then the isotope
abundance will be a weighted average of the abundances of the atmosphere and the soil, where the
weights are the proportion of N obtained from each
source. Typically the 15N abundance of the soil
plant available N pool cannot be measured directly,
but instead the 15N abundance in a non-N-fixing
"control" plant, that obtains all of its N from the
soil, is measured and assumed to represent the
plant-available N pool (e.g., Ladha et al. 1993).
These source identification calculations only provide information on the relative amount of N obtained from two different sources. To convert these
relative flow rates to absolute rates, the total rate of
increase of N in the plant must also be measured.
available, rates (or rate constants) can be estimated
using very simple or relatively complicated models.
When using a modeling approach with numerical
approximation, separate, but identical submodels
are used to describe flow of the two isotopes (natural and added isotopes) through the system. All of
the rate constants used in the two submodels are
linked mathematically so that as the rate constant
for one process is adjusted, flow of both isotopes
changes. Initial values for pool sizes (concentrations) and rate constants are provided for the model,
either based on actual data or best guesses, and a
simulation is performed. At the end of the simulation, the enrichment predicted by the model for one
of the sink pools is compared with the actual enrichment measured for that pool during experimentation. Rate constants are adjusted, and a new simulation is performed. Enrichments are compared
again, and rate constants are readjusted. This iterative process continues until the error between predicted and actual enrichments becomes lower than
some value predetermined by the modeler. While
this approach requires some proficiency in programming, modeling software, such as Time-Zero
(Quaternary Software, Fort Collins, CO), is available that greatly simplifies the numerical approximation procedure. In addition, software is currently
available that uses numerical methods to estimate
gross rates of specific processes such as N mineralization, immobilization, and nitrification (e.g.,
Mary et al. 1998).
Natural Abundance Isotope Methods
Isotope fractionation and discrimination processes
cause the relative abundance of naturally occurring
isotopes to differ slightly from one pool to another.
For example, N2 in the atmosphere is 0.3663% 15N
and 99.6337% 14N (on a mole basis), whereas N in
soil typically ranges from about 0.3670 to 0.3718%
15N (Shearer et al. 1978). Changes in the relative
abundance of naturally occurring isotopes from one
pool to another have been used to estimate gross
rates of nutrient transformations. Natural abundance approaches fall into two categories: kinetic
models and source-identification approaches. The
approach using kinetic models is nearly identical to
the modeling and numerical approximation method
described in the previous section. The only difference is that slightly different rate constants are used
John M. Stark
for the two isotopes to model fractionation or discrimination processes. For example, during nitrification, the rate constant for 14NHt oxidation is
about 3% higher than the rate constant for 15NHt
(i.e., ~ = 1.03) (Handley and Raven 1992). In contrast, during N fixation, the rate constant for 14N2
reduction is nearly equal to the rate constant for
15N2 (~ = 1.002). Relatively few kinetic models
have been used to estimate transformation rates in
ecosystems, however (e.g., Shearer et al. 1974;
Herman and RundelI989).
The most frequent way that natural isotope abundances are used to estimate transformation rates is
by combining a source identification approach with
net rate measurements. Source identification approaches are used when an element flows into a
sink pool from two sources, and the two sources
differ significantly in isotope composition. For example, a source identification approach has been
frequently used to estimate rates of N fixation by
plants of natural and agro-ecosystems (Shearer and
Kohl 1986; Handley and Raven 1992; Ladha et al.
1993). The two sources ofN for N-fixing plants are
the soil and the atmosphere. As discussed earlier,
the N from these two sources may differ by as much
as 0.006 atom % 15N (or 15%0). Isotope discrimination during fixation of atmospheric N and during
uptake of soil N is relatively small (Handley and
Raven 1992). Therefore, if a plant obtains 100% of
its N from N fixation, then the isotope abundance
of the plant N will be approximately equal to that
of the atmosphere. Conversely, if the plant obtains
100% of its N from the soil, then the isotope abundance of the plant N will be approximately equal
to that of the soil plant -available N pool. If the plant
N is derived from both sources, then the isotope
abundance will be a weighted average of the abundances of the atmosphere and the soil, where the
weights are the proportion of N obtained from each
source. Typically the 15N abundance of the soil
plant available N pool cannot be measured directly,
but instead the 15N abundance in a non-N-fixing
"control" plant, that obtains all of its N from the
soil, is measured and assumed to represent the
plant-available N pool (e.g., Ladha et al. 1993).
These source identification calculations only provide information on the relative amount of N obtained from two different sources. To convert these
relative flow rates to absolute rates, the total rate of
increase of N in the plant must also be measured.