14. Nutrient Transfonnations
estimates of gross rates can be obtained even in
complex systems where production and consumption occur simultaneously. Second, isotope is added
to the product pool rather than the substrate pool,
and thus, gross production rates will not be stimulated by addition of substrate. The isotope dilution
equations also provide an estimate of gross consumption rates; however, these rates may be stimulated due to addition of isotope (Hart et al. 1994b).
The gross production rate estimated by isotope
dilution is for all production processes combined.
If production consists of more than one process and
rate estimates of individual processes are desired,
it may be possible to use isotope dilution in combination with inhibitors to estimate gross rates of
individual processes.
The gross consumption rate estimated by isotope
dilution is also for all consumption processes combined. In contrast to production rates, gross rates of
individual consumption processes can be measured
directly based on appearance of the isotope in other
pools. For example, in an experiment in which
15N03- is added to soil as part of an isotope dilution
experiment, measurement of 15N in the plant and
microbial biomass at the end of the incubation allows one to estimate how much of the consumption
was due to either plant or microbial uptake. This
approach is similar to the tracer approach described
previously (Equation 14.6); however, it is necessary
to use equations slightly more complicated than the
simple tracer equation because the isotopic enrichment of the source pool (e.g., 15N03") changes
throughout the incubation. Depending on how rapidly the source pool is diluted, one of two equations
should be used. If rates are slow relative to the size
of the pool or the length of the incubation, the enrichment of the source pool will decline in a nearly
linear fashion. In this case, the mean enrichment of
the source pool can be used in place of the initial
enrichment of the source pool (I A ) in the tracer
equation (Equation 14.6):
M
-
PBt · IBt
AB - (lAO + IAt)/2
(14.11)
where MAB is the total amount of nutrient (added
plus natural isotopes) that flowed from the source
pool (A) to the sink pool (B) during the incubation
(e.g., mg N kg - 1 soil); P Bt is the concentration of
B (the sink pool) at the end of the incubation (e.g.,
mg N kg - 1 soil); IBt is the relative amount of iso229
tope, in excess of background, that is found in pool
B at end of the incubation; lAO is the relative amount
of isotope, in excess of background, that is present
in the source pool at the beginning of the incubation; and IAt is the relative amount of isotope, in
excess of background, that is present in the source
pool at the end of the incubation.
On the other hand, if rates are rapid relative to
the concentration or incubation period, the enrichment of the source pool will decline exponentially,
rather than linearly. In this case, the following equation provides a better estimate of the total amount
of nutrient that flows into the sink (Davidson et al.
1991):
PBt·IBt
MAB = -----,--I Ao (l - e k)/k
(14.12)
where k = In(IAofIAt)/t, and t is the length of the
incubation time. As with the tracer equation, MAB
must be divided by the length of the incubation
period to calculate the gross rate. This method has
some of the same limitations as the tracer method:
Increased substrate concentration due to addition of
isotope may stimulate rates, and movement of isotope out of sinks will result in underestimation of
rates.
Estimation of Rates
by Modeling Methods
In many experiments, it may not be possible to meet
the assumptions required for the isotope dilution
approach. Rates may not be constant throughout the
incubation period, and isotope may recycle back
into the source pool. Simulation modeling combined with a numerical approximation technique
provides an extremely powerful tool for estimating
gross rates in more complex experimental systems
(Myrold and Tiedje 1986; Barraclough and Smith
1987, Bjarnson 1988; Tietema and Van Dam 1996;
Mary et al. 1998). While the isotope dilution equations described previously (Equations 14.9 to
14.11) require the assumption of zero order kinetics, simulation modeling allows one to describe individual rates with first order, mixed order (e.g.
Michaelis-Menten), or higher order kinetics. Modeling also allows one to include the influence of
temperature, moisture, or other variables on rate
constants. Depending on how much information is
estimates of gross rates can be obtained even in
complex systems where production and consumption occur simultaneously. Second, isotope is added
to the product pool rather than the substrate pool,
and thus, gross production rates will not be stimulated by addition of substrate. The isotope dilution
equations also provide an estimate of gross consumption rates; however, these rates may be stimulated due to addition of isotope (Hart et al. 1994b).
The gross production rate estimated by isotope
dilution is for all production processes combined.
If production consists of more than one process and
rate estimates of individual processes are desired,
it may be possible to use isotope dilution in combination with inhibitors to estimate gross rates of
individual processes.
The gross consumption rate estimated by isotope
dilution is also for all consumption processes combined. In contrast to production rates, gross rates of
individual consumption processes can be measured
directly based on appearance of the isotope in other
pools. For example, in an experiment in which
15N03- is added to soil as part of an isotope dilution
experiment, measurement of 15N in the plant and
microbial biomass at the end of the incubation allows one to estimate how much of the consumption
was due to either plant or microbial uptake. This
approach is similar to the tracer approach described
previously (Equation 14.6); however, it is necessary
to use equations slightly more complicated than the
simple tracer equation because the isotopic enrichment of the source pool (e.g., 15N03") changes
throughout the incubation. Depending on how rapidly the source pool is diluted, one of two equations
should be used. If rates are slow relative to the size
of the pool or the length of the incubation, the enrichment of the source pool will decline in a nearly
linear fashion. In this case, the mean enrichment of
the source pool can be used in place of the initial
enrichment of the source pool (I A ) in the tracer
equation (Equation 14.6):
M
-
PBt · IBt
AB - (lAO + IAt)/2
(14.11)
where MAB is the total amount of nutrient (added
plus natural isotopes) that flowed from the source
pool (A) to the sink pool (B) during the incubation
(e.g., mg N kg - 1 soil); P Bt is the concentration of
B (the sink pool) at the end of the incubation (e.g.,
mg N kg - 1 soil); IBt is the relative amount of iso229
tope, in excess of background, that is found in pool
B at end of the incubation; lAO is the relative amount
of isotope, in excess of background, that is present
in the source pool at the beginning of the incubation; and IAt is the relative amount of isotope, in
excess of background, that is present in the source
pool at the end of the incubation.
On the other hand, if rates are rapid relative to
the concentration or incubation period, the enrichment of the source pool will decline exponentially,
rather than linearly. In this case, the following equation provides a better estimate of the total amount
of nutrient that flows into the sink (Davidson et al.
1991):
PBt·IBt
MAB = -----,--I Ao (l - e k)/k
(14.12)
where k = In(IAofIAt)/t, and t is the length of the
incubation time. As with the tracer equation, MAB
must be divided by the length of the incubation
period to calculate the gross rate. This method has
some of the same limitations as the tracer method:
Increased substrate concentration due to addition of
isotope may stimulate rates, and movement of isotope out of sinks will result in underestimation of
rates.
Estimation of Rates
by Modeling Methods
In many experiments, it may not be possible to meet
the assumptions required for the isotope dilution
approach. Rates may not be constant throughout the
incubation period, and isotope may recycle back
into the source pool. Simulation modeling combined with a numerical approximation technique
provides an extremely powerful tool for estimating
gross rates in more complex experimental systems
(Myrold and Tiedje 1986; Barraclough and Smith
1987, Bjarnson 1988; Tietema and Van Dam 1996;
Mary et al. 1998). While the isotope dilution equations described previously (Equations 14.9 to
14.11) require the assumption of zero order kinetics, simulation modeling allows one to describe individual rates with first order, mixed order (e.g.
Michaelis-Menten), or higher order kinetics. Modeling also allows one to include the influence of
temperature, moisture, or other variables on rate
constants. Depending on how much information is