Journal of Plankton Research Vol. 19 no. 2 pp. 263-271, 1996
SHORT COMMUNICATION
Estimation of N or C uptake rates by phytoplankton using
15
N or 13 C: revisiting the usual computation formulae
Louis Legendre and Michel Gosselin1
Department de biologie, Universite Laval, Quebec, QC G1K 7P4 and ' Department
d'oce'anographie, Universite du Quebec a Rimouski, 310 Allee des Ursulines,
Rimouski, QC G5L 3A1, Canada
Abstract. The uptake of N by phytoplankton is generally estimated using the I5 N technique and,
under some circumstances, the uptake of C is estimated using 13 C. Rigorous examination of formulae
for computing net transport rates leads to several interesting and even unexpected conclusions. These
are that the I5 N or B C technique formula for computing net transport rates (p) is identical to that of
the 14C technique, in spite of apparent dissimilarities which reflect differences in equipment used for
determining non-radioactive and radioactive isotopes; the so-called specific uptake rates (V) should
not be used with natural samples, except as a step in the calculation of transport rates (p); estimation
of p is unaffected by the presence/absence of non-phytoplanktonic paniculate organic matter (POM)
in the incubated sample; the practice of adding the concentration of tracer to the denominator of
expression representing the concentration of tracer in the dissolved phase at the beginning of incubation should be discontinued; and the concentration of POM should be determined from the inoculated sample at the end of incubation (or, alternatively, from a sample incubated in parallel) and
not from a water sample taken at the beginning of the incubation.
Thirty-five years ago, Dugdale et al. (1961) introduced to biological oceanography the I5 N technique to determine the uptake rates of nitrogen by phytoplankton. More than 15 years later, Slawyk et al. (1977, 1979) conducted the
first dual tracer measurements using the stable isotopes 13C and I5 N, to simultaneously estimate the uptake rates of dissolved inorganic carbon and nitrogen.
A number of different formulae have been used to calculate the uptake rates of
nitrogen (e.g. Neess et al., 1962; Dugdale and Goering, 1967; Eppley et al.,
1977) and carbon (e.g. Slawyk et al., 1977; Hama et al., 1983). These were
reviewed and compared by Collos and Slawyk (1985) and Collos (1987). Dugdale and Wilkerson (1986) and Collos (1987) recommend two different equations
to calculate N transport (also called absolute uptake) rates. One is to be used
when the concentration of particulate organic nitrogen (PON) is measured at
the end of incubation, and the other, for situations when PON is determined at
the beginning. The two equations provide equivalent results when phytoplankton use only one source of nitrogen. When algae use several sources of nitrogen,
as is generally the case in natural populations, the only valid equation for calculating transport rates is the first (i.e. PON measured at the end of incubation).
The two equations can also be used for computing C transport rates (13C
method; Collos and Slawyk, 1985). In addition, Lund (1987) developed equations to calculate N transport rates when the initial concentration of PON is
known instead of the final, and when there is simultaneous uptake of several N
sources. Recent papers (Bronk et al., 1994; Slawyk and Raimbault, 1995) have
shown that part of the nitrogen taken up by phytoplankton may be lost during
© Oxford University Press
263
L.Legendre and M.Gosselin
incubation, so that one must distinguish between gross and net transport rates.
Here, the two equations generally used for computing net transport rates of dissolved inorganic carbon and nitrogen in the stable isotope ( I5 N and/or I3C) technique are critically examined. The exercise leads to several interesting, and
sometimes unexpected, conclusions.
The two usual equations for computing net transport rates (p: mass volume"1
time"') are both derived from the following general equation (equation 3 in
Collos, 1987):
AP + AP* _ %/>«(/>, + />*) - % f g(fo + PS)
At
%D*At
P
l
'
All symbols are denned in Table I. The sums (Po + PJ) a n d (A + P*) correspond to the concentrations of particulate organic matter (POM) in the sample
before and after incubation, respectively.
Given that:
AP + AP* = (Pt + P*) - (P o + P*o)
(2)
it follows from equation 1 that:
pA* = (P t + P*) - (Po + PJ)
(3)
Using equation 3, it is easy to derive two forms of equation 1:
P
P
%P*(Pt + P?) - %Pg[(Pt + P\) - p At]
%D*At
(
_ %P*[p At + (Pp + PS)] ~ %P*Q(Po + Pj)
%D\At
'
,„
K)
Equations (4) and (5) can be developed to isolate p on the left-hand side. For
equation 4, this gives:
p(%D* - %P*)At = (%P* - %Po")(P, + PJ)
which provides the formula for calculating p when (P t + P*) is known:
P
(%p* - %PS)
(%D* - %P*)
(Pt + Pp
At
K
'
In a similar way, equation 5 provides the formula for cases when (Po + P*,) is
used instead of (P t + P*):
P
(%Pr - %P$) (Pp + PS)
(%£>? - %Pt)
At
m
l
'
The two equations are both derived from equation 1, so that they are mathematically equivalent.
The net transport rate of N (or C) is generally computed using equation 6
(which corresponds to equation 2 in Dugdale and Wilkerson, 1986, and equation
4 in Collos, 1987). A slightly different form of this equation is:
264
Formulae for N and C uptake by phytoplankton
Table I. Definitions of symbols in the text and the equations
Concentrations and changes in concentrations (mass volume'1)
D*
Concentration of tracer (heavy isotope) added to the sample at beginning of incubation.
Do
Concentration of light isotope in the dissolved phase before incubation (natural
concentration).
Dp
Concentration of heavy isotope in the dissolved phase before incubation (nat. cone.)
P,
Concentration of light isotope in the particulate phase after incubation.
/**
Concentration of heavy isotope in the particulate phase after incubation,
^o
Concentration of light isotope in the particulate phase before incubation (nat. cone.)
PQ
Concentration of heavy isotope in the particulate phase before incubation (nat. cone.)
AP
Increase of light isotope in the particulate phase during incubation.
AP*
Increase of heavy isotope in the particulate phase during incubation.
AP*noc
Increase of heavy isotope in the particulate phase during incubation for the inoculated
sample
A/'Jj,
Increase of heavy isotope in the particulate phase during incubation for a sample
incubated in parallel (without tracer, i.e. natural water).
Concentrations (atom %)
%D*
Concentration of heavy isotope
incubation (i.e. after addition
%DQ
Concentration of heavy isotope
%P*
Concentration of heavy isotope
%P*,
Concentration of heavy isotope
in the dissolved phase of the sample at beginning of
of the tracer).
in the dissolved phase in the natural environment.
in the particulate phase after incubation.
in the particulate phase before incubation.
Time and rates
At
Incubation time.
V
Specific uptake rate (time" 1 ).
p
Net transport rate (mass volume"1 time"').
=
(%p* - %pg) (ft + Pf)
(/oi/j — /OUQ)
m
AI
where %/"5 in the denominator is replaced by %DQ. This is based on the
assumption that %D*Q = %PQ (%D*, is not determined in field applications).
According to Collos and Slawyk (1985), Dugdale and Wilkerson (1986), and
Collos (1987), equations 6 or 8 yield unbiased results even when more than one
N or C source is taken up by phytoplankton.
There are two alternative ways of computing %D*:
%D*=(D*+D*0)/(D0 + D*0)
%D* = (D* + D*0)/(D0 + D*0+ D*)
(9)
(10)
The two equations are equivalent when D* is small relative to (Do + DJ). Using
the first definition of %D* (equation 9), equation 8 can be developed as follows:
/
* n T "T
, + Pl + AP+AP*
r
n
Pp + Py
(Pp + P*o + AP + AP*)
265
L.Legendre and M.Gosselin
If equation 10 is used instead of equation 9, as is generally the case in the literature, p is then computed as:
/
P*Q + AP*
_ \PQ
\ »+
P*Ou + AP +
P ~~
D*+D*o
D0 + D*0+D*
P*o \
AP* PO» + »P*J/ ( o +
D*o \
+ AP*)
o
A
,
D0 + D*J
The consequences of using equations 11 or 12 will be examined below.
Equation 11 can be further developed as follows:
PpAP*
-P*OAP
Expanding the numerator of equation 13 gives:
D* o
Do+D*
At
In natural waters, the concentrations of heavy isotopes I5 N or 13C in the POM
are much smaller than those of the corresponding light isotopes 14N or 12 C.
Values for isotopic ratios in the literature are expressed as 5 15 N and 513C:
I5
C/ I 2 C in the sample
-ljxlOOO
VI 3 C/ I 2 C in the standard
_ /
~
in the sample
X
N/ I 4 N in the standard - )
I3
(16)
For 5 I 5 N, the standard is atmospheric N 2 , in which 15 N/ 14 N = 0.0036765; the
values for isotopic ratios in marine seston generally range between 815N = +2
and +10 (e.g. Voss et al., 1996). For 5 13 C, the standard is Pee Dee Belemnite,
whose 1 3 C/ I 2 C = 0.011327; the values for marine seston are 5 I3 C =
approx. —25 (e.g. Voss et al., 1996). It follows from equations 15 and 16 that, in
most phytoplankton samples, 1 5 N/ I 4 N = 0.004 and 1 3 C/ I 2 C = 0.01. This allows
the computation of values for two expressions in the numerator of equation 14:
forN
P£P*=0"6
and
' T^T/T 0 - 9 8 9
and
'
forC
266
^ r
Formulae for N and C uptake by phytoplankton
Identical results (to the third decimal) would be obtained for 8 I 5 N ranging
between - 2 1 and +224 and 5 I3 C between - 4 8 and +32. It follows from the
two equations that, for both N and C:
-%1
and
„
°
**0
(19)
Given equation 19, equation 14 becomes:
P
= ^(D0
+
D*0)-L
(20)
It is interesting to note that, even if the concentration of POM (/\ + P*) is an
explicit term in equation 8, it is cancelled out by other terms, so that it does not
appear in the final form (equation 20). When calculating the net transport of N
and C using the I5 N or I3 C tracers, equation 20 can be rewritten as:
P = 4^Xt
[N-nutrient]0
P = 7 ^ Pick
(21)
(22)
where [N-nutrient]o is the ambient concentration, at the beginning of incubation,
of the dissolved N-nutrient whose net transport is being estimated, and [DIC]o is
the concentration of dissolved inorganic carbon in sea water. It must be noted
that equation 22 is identical to the formula used to determine primary productivity with the I4 C radioactive tracer (refs. in Peterson, 1980):
AI4C
Primary productivity = -^-^
[DIC]0
(23)
Equations 20 to 22 show that equation 8 estimates:
P =
fraction of tracer taken by phytoplankton x concentration of substrate in water
incubation time
The form of equation 8 compared with that of equation 23 is dictated by the fact
that a mass spectrometer provides ratios of isotopic abundances of the light and
heavy isotopes in particulate matter, whereas a liquid scintillation counter determines the activities of radioactive isotopes. A basic assumption of methods using
either stable or radioactive isotopes is that isotope discrimination by phytoplankton is negligible. This leads to two important conclusions.
Firstly, one finds in the literature, in addition to the net transport rate (p), the
so-called specific uptake rate (V). The latter is the transport rate divided by the
concentration of POM:
V = p/POM
(24)
267
L.Legendre and M.Gosselin
Several authors first compute V and use it to calculate p:
p = V x POM
As long as most of the measured POM is phytoplankton, equation 24 provides a
valid normalization. However, when a significant proportion of POM is not phytoplankton, as is often the case in natural waters, dividing phytoplankton N or
C net transport rates (equations 21 and 22) by PON or POC concentrations (in
which there are large non-phytoplanktonic components) does not provide a
valid normalization. This is why primary productivity, when determined on natural phytoplankton using the 14C technique (equation 23), is never normalized to
POC but always to chlorophyll a (chl a). There is no reason why the same rule
should not apply to p. This is consistent with the recent practice (e.g. Levasseur
el ai, 1990; Dickson and Wheeler, 1995) of normalizing nitrogen transport
rates to chl a (p/chl a). However, since there is no constant ratio of chl a to phytoplankton carbon, nitrogen, or cell volume, normalization to chl a is by no
means ideal but chl a is, at least, specific to phytoplankton. It follows that computed V values are generally not true specific rates, so that V should not be used
with natural samples, except as a step in the calculation of p.
Secondly, the fact that POM is not in the final form of the equation used to
compute p (equation 20) means that p is unaffected by the presence or not of
non-phytoplanktonic POM in the incubated sample. The same conclusion had
already been reached by Dugdale and Goering (1967) and Dugdale and Wilkerson (1986), based on a different reasoning.
The above discussion was based on equation 9. However, the definition of
%£>* in equation 10 is presently more frequently used than that in equation 9,
and the following development examines the consequence of using equation 10
instead of equation 9. Developing equation 12, which was derived from equation
10, gives:
p = ^l(D0
+ D*0)— (\+D{}
' " ' ), where I ^ - J - ^ I should be « 1 (25)
Because, in equation 25, the additional term relative to equation 20 should be
quite small, the difference in calculated p values would also be small. However,
since equation 20 clearly shows that equation 11 estimates net transport rates,
there seems to be no reason to use the definition of %D* in equation 10 instead
of that in equation 9. Hence, when D* is small relative to Do, the practice of
adding D* to the denominator of %D* should be discontinued. When D* is
not small relative to Do, there is no way of computing unbiased p, as shown in
the next paragraph.
There are situations when the amount of heavy isotope added to the sample is
high relative to the natural concentration, e.g. when N transport is estimated in
oligotrophic waters. In such cases, the term (DJ -f D*)/Do is not negligible (it
can even be >1) so that, as shown by equation 25, equation 11 would overestimate p. In fact, when the amount of tracer is high relative to the natural
concentration and is thus an enrichment, no equation can correct for the fact
268
Formulae for N and C uptake by phytoplankton
that N transport in the incubated sample does not represent transport under the
natural, lower N concentration. The problem does not occur when determining
C transport by marine phytoplankton because, in oceans, DIC concentrations
are high relative to the amount of added I3 C tracer. The situation may be
different in fresh waters, where DIC concentrations are sometimes relatively
low.
There is no absolute rule for deciding whether D* is small or large relative
to DQ. In waters with high concentrations of nitrogenous nutrients (i.e.
A> + Z>o >0.5uM), £>? should not exceed 10% of the ambient value (Dugdale
and Goering, 1967; Dugdale and Wilkerson, 1986). Hence, (D*o + D*)/Do <0.1
(equation 25). In waters with low concentrations of nitrogenous nutrients (i.e.
DO + DQ < 0 . 5 U M ) , /)* must not exceed the limit of detection of the nutrient
(McCarthy, 1980), which is ~0.05uM for dissolved inorganic nitrogen. In oligotrophic waters, (DQ + D*)/D$ may thus lie between 0.5 and 1.0, which would
overestimate p as discussed in the previous paragraph. This may nevertheless be
acceptable for some purposes.
The final case to be examined is the computation of p using the concentration
of POM in a water sample taken at the beginning of incubation, instead of that
in the sample at the end of incubation. As shown above, p is then calculated
with equation 7 (Collos and Slawyk, 1985, their equation 4; Dugdale and Wilkerson, 1986, their equation 7; Collos, 1987, his equation 5). According to
Collos and Slawyk (1985) and Collos (1987), equation 7 can be used only when
algae take a single source of nitrogen (or carbon). Since this is generally not
the case for natural populations, equation 7 should not be used and the concentration of POM should thus be determined on the inoculated sample at the end
of incubation (or, alternatively, on a sample incubated in parallel) and not on a
water sample taken at the beginning of incubation. Determination of POM on
the inoculated sample or, alternatively, on a sample incubated in parallel
depends on whether the available equipment measures, on a single filter, the relative concentrations of light and heavy isotopes and the absolute concentration of
POM. If so, isotope and POM concentrations are determined simultaneously on
the incubated sample. If not, isotope and POM concentrations must be determined independently, on either two samples incubated in parallel (with and without added tracer, respectively) or two fractions of a large-volume inoculated
sample.
In cases when the concentration of POM is determined on a sample (without
added tracer) incubated in parallel to the inoculated sample (end of previous
paragraph), equation 11 becomes:
•
P
f
.
/n*
i n*
n \
inoc
n*
P
PO++ Pll
V (PQ + P*Q +
AP+,
Using equation 19, development of equation 26 gives:
269
L.Legendre and M.Gosselin
P =
AP* ._
D*
.. 1
h
u
= 1
(27)
However, because AP*noc and AP* at are small relative to Po + PQ + AP, equation 27 shows that using POM measured on a sample incubated in parallel to
the inoculated sample would only slightly underestimate p (equation 20).
Lund (1987) proposed a set of equations to calculate p when only the initial
(and not the final) PON is known and when there is simultaneous uptake of
other (unlabelled) N sources. In order to use these equations, the uptake of
each N source must be determined separately. The same set of equations could
perhaps also be used, when only the initial PON or POC are known, to compute
C and N uptake (two tracers) or, as discussed by Collos and Slawyk (1985), to
assess the simultaneous uptake of DIC and dissolved organic carbon. In several
instances, determining the net transport of all N and/or C sources taken up by
natural phytoplankton may be quite demanding.
In summary, the above results show that: (i) the 15N or I3 C technique formula
for computing net transport rates (p) is identical to that of the I4 C technique,
apparent dissimilarities reflecting differences in equipment used for determining
non-radioactive and radioactive isotopes; (ii) the so-called specific uptake rates
(V) should not be used with natural samples, except as a step in the calculation
of transport rates (p); (iii) estimation of p is unaffected by the presence or
absence of non-phytoplanktonic POM in the incubated sample; (iv) the practice
of adding the concentration of tracer to the denominator of expression representing the concentration of tracer in the dissolved phase at the beginning of
incubation should be discontinued; and (v) the concentration of POM should
be determined on the inoculated sample at the end of incubation (or, alternatively, on a sample incubated in parallel) and not on a water sample taken at
the beginning of incubation.
Acknowledgements
Contribution to the programmes of CIROQ (Groupe interuniversitaire de
recherches oceanographiques du Quebec) and GREC (Groupe de recherche en
environnement cotier). The authors thank the two reviewers and Drs. Jacques
Dionne, Bert Klein and Warwick F. Vincent for useful suggestions. Research
grants from the Natural Sciences and Engineering Research Council of Canada
were instrumental in completion of the work.
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270
Formulae for N and C uptake by phytoplankton
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Received on April 2, 1996; accepted on September 30, 1996
271