226
tification" approach (Handley and Raven 1992)
which I describe in the section on natural abundance methods. In this chapter, I use the term isotope dilution in the same sense as Kirkham and Bartholomew (1954).
The isotope dilution equations of Kirkham and
Bartholomew (1954) calculate gross production
and consumption rates based on how rapidly isotope enrichment declines and how rapidly isotope
disappears from the labeled pool. In contrast to
tracer techniques, the researcher adds isotope to the
pool that is the product of the transformation of
interest. The gross production rate is then estimated
from the rate at which the added isotope (e.g., 15N)
is "diluted" by influx of the natural isotope (e.g.,
14N) (Fig. 14.7). The gross consumption rate can
also be calculated based on the rate at which the
isotope disappears from the pool. To calculate gross
_p_ro_d_uc_t_io_n-l"~{~} consumption ..
~
60~------------'
50 ................•....•.• [I~ P"~Qg!l~t!Qn •
~ 40
~
E 30
:\
,
o
ca 20
10
, , , " " ' .. .. .. _ QO_ consumption
--- ---2
3
4
5
relative incubation time
(incub. time/MRT)
FIGURE 14.7. Changes in isotopic enrichment during an
15N isotope dilution experiment when either production
rates are zero, consumption rates are zero, or the produc·
tion rate equals the consumption rate. The incubation
time is expressed relative to the mean residence time
(MRT) for the pool (initial pool size/flow rate). For ex·
ample, in the case in which production = consumption,
if the pool has a MRT of 1 day and the experiment is
carried out for 2 days, the atom % 15N excess will decline
from 50 to 7%.
John M. Stark
rates of production and consumption, data are required on the nutrient concentration and isotopic
enrichment at the beginning and end of the incubation (Hart et al. 1994b):
Gross production rate (GPR)
Po
Pt
t
(14.9)
Gross consumption rate
= GPR
(14.10)
where Po is nutrient concentration at the beginning
of the incubation (e.g., mg N kg- 1 soil); P t is nutrient concentration at the end of the incubation; Io
is the relative amount of isotope, in excess of background, that is found in the nutrient pool at the beginning of the incubation (measured as atom % excess if a stable isotope is used or specific activity
if a radioactive isotope is used); It is the relative
amount of isotope, in excess of background, that is
present in the nutrient pool at the end of the incubation; and t is the length of the incubation time.
Some of the same assumptions required for
tracer techniques are required for isotope dilution
techniques: The added isotope acts the same as the
naturally occurring isotope, and the pool is uniformly labeled by the isotope. Additional assumptions are that rates are constant during the incubation period, and the isotopic enrichment of the
source pool is constant (i.e., there is no recycling
of isotope back into the source pool during the incubation) (Kirkham and Bartholomew 1954).
The isotope dilution method works best when
used with short-term laboratory incubations of
mixed water, sediment, or soil samples (e.g., Blackburn 1979; Glibert et al. 1982, Vitousek and Andariese 1986; Hart et al. 1994a, Stark and Firestone
1996; Low et al. 1997). Short incubation periods
(24 to 48 hr for many N transformation rates) usually prevent significant recycling of isotope into the
source pool. Incubation in the laboratory allows
temperature control so that rates are less likely to
fluctuate, and use of mixed samples promotes uniform distribution of isotope and reduces the subsample variance.
The isotope dilution method has also been used
with field incubations of intact soil cores (e.g.,
Schimel et al. 1989; Davidson et al. 1990; Davidson et al. 1992; Stark and Hart 1997). Isotope di-
tification" approach (Handley and Raven 1992)
which I describe in the section on natural abundance methods. In this chapter, I use the term isotope dilution in the same sense as Kirkham and Bartholomew (1954).
The isotope dilution equations of Kirkham and
Bartholomew (1954) calculate gross production
and consumption rates based on how rapidly isotope enrichment declines and how rapidly isotope
disappears from the labeled pool. In contrast to
tracer techniques, the researcher adds isotope to the
pool that is the product of the transformation of
interest. The gross production rate is then estimated
from the rate at which the added isotope (e.g., 15N)
is "diluted" by influx of the natural isotope (e.g.,
14N) (Fig. 14.7). The gross consumption rate can
also be calculated based on the rate at which the
isotope disappears from the pool. To calculate gross
_p_ro_d_uc_t_io_n-l"~{~} consumption ..
~
60~------------'
50 ................•....•.• [I~ P"~Qg!l~t!Qn •
~ 40
~
E 30
:\
,
o
ca 20
10
, , , " " ' .. .. .. _ QO_ consumption
--- ---2
3
4
5
relative incubation time
(incub. time/MRT)
FIGURE 14.7. Changes in isotopic enrichment during an
15N isotope dilution experiment when either production
rates are zero, consumption rates are zero, or the produc·
tion rate equals the consumption rate. The incubation
time is expressed relative to the mean residence time
(MRT) for the pool (initial pool size/flow rate). For ex·
ample, in the case in which production = consumption,
if the pool has a MRT of 1 day and the experiment is
carried out for 2 days, the atom % 15N excess will decline
from 50 to 7%.
John M. Stark
rates of production and consumption, data are required on the nutrient concentration and isotopic
enrichment at the beginning and end of the incubation (Hart et al. 1994b):
Gross production rate (GPR)
Po
Pt
t
(14.9)
Gross consumption rate
= GPR
(14.10)
where Po is nutrient concentration at the beginning
of the incubation (e.g., mg N kg- 1 soil); P t is nutrient concentration at the end of the incubation; Io
is the relative amount of isotope, in excess of background, that is found in the nutrient pool at the beginning of the incubation (measured as atom % excess if a stable isotope is used or specific activity
if a radioactive isotope is used); It is the relative
amount of isotope, in excess of background, that is
present in the nutrient pool at the end of the incubation; and t is the length of the incubation time.
Some of the same assumptions required for
tracer techniques are required for isotope dilution
techniques: The added isotope acts the same as the
naturally occurring isotope, and the pool is uniformly labeled by the isotope. Additional assumptions are that rates are constant during the incubation period, and the isotopic enrichment of the
source pool is constant (i.e., there is no recycling
of isotope back into the source pool during the incubation) (Kirkham and Bartholomew 1954).
The isotope dilution method works best when
used with short-term laboratory incubations of
mixed water, sediment, or soil samples (e.g., Blackburn 1979; Glibert et al. 1982, Vitousek and Andariese 1986; Hart et al. 1994a, Stark and Firestone
1996; Low et al. 1997). Short incubation periods
(24 to 48 hr for many N transformation rates) usually prevent significant recycling of isotope into the
source pool. Incubation in the laboratory allows
temperature control so that rates are less likely to
fluctuate, and use of mixed samples promotes uniform distribution of isotope and reduces the subsample variance.
The isotope dilution method has also been used
with field incubations of intact soil cores (e.g.,
Schimel et al. 1989; Davidson et al. 1990; Davidson et al. 1992; Stark and Hart 1997). Isotope di-