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Limnol.
Oceanogr., 31(l), 1986, 34-44
0 1986, by the American
Society of Limnology
and Oceanography,
Inc.
Dependence of the rate of release of phosphorus by
zooplankton on the P : C ratio in the food supply,
as calculated by a recycling model1
Yngvar Olsen, Arne Jensen, Helge Reinertsen
Institute of Marine Biochemistry, University of Trondheim, N-7034 Trondheim-NTH,
Norway
Knut Yngve Borsheim and Mikal Heldal
Institute of Microbiology and Plant Physiology, University of Bergen, N-5000 Bergen, Norway
Arnjinn Langeland
Directorate for Wildlife and Freshwater Fish, Tungasletta 2, N-7000 Trondheim, Norway
Abstract
In two enclosure experiments, Daphnia pulex ingested cryptophytes, bacteria, and probably
detritus particles. The specific clearance rate of the zooplankton increased when the concentration
of food decreased. The P : C ratio of the food also increased. More than 92% of the particulate
phosphorus was located in the living cells (algae and bacteria); the detritus was practically phosphorus-free. The specific release rate of phosphorus estimated for the daphnids by use of the
recycling model increased as the P : C ratio of the food increased and became zero at a critical low
P : C ratio, Q. of 6-8 pg P mg-’ C. At this concentration, all the ingested phosphorus is needed
for growth and reproduction, and no release of the element can be expected. This indicates that
Daphnia may experience P limitation in nature, since the P : C ratio of P-starved algae and detritus
may be considerably ~6-8 pg P mg-l C.
The use of mass balance also appears to be suitable for modeling phosphorus and carbon fluxes
through zooplankton in pelagic ecosystems.
The problem of estimating the release or
excretion of phosphorus from zooplankton
has attracted considerable attention during
the last decade. Several methods have been
suggested (cf. Olsen and Ostgaard 1985), but
quantification is difficult, especially for natural populations
which include
phosphorus-limited
algae. In such cases, the released phosphorus is rapidly taken up by
algae or bacteria (Gotham and Rhee 198 1;
Taylor and Lean 198 1; Chen 1974), and no
increase in the ambient concentration of the
element is observed (Lehman. 1980).
Olsen and Ostgaard (1985) proposed a
recycling model for the estimation of phosphorus release from zooplankton
and
adapted equations which permit estimation
of release rates from incubation
experiments. Application of the method to natural
populations introduces problems regarding
distribution
of phosphorus in seston particles and selective grazing. These factors must
1This study forms part of the research program on
eutrophication of inland waters financed by the Norwegian Council for Scientific and Industrial Research.
34
be carefully examined to ensure correct estimates of the variables of the model.
We here apply the recycling model to a
natural plankton community. The input data
were taken from two enclosure experiments.
Because the algal biomass declined during
the experiments, we could test the model
over a wide range of food concentrations.
A characterization of the food, its contents,
and internal distribution
of phosphorus is
presented, as well as the feeding kinetics of
the animals and their phosphorus release.
We thank B. Naess and 0. Tumyr for technical assistance.
Materials and methods
Experimental -The enclosure
experiments were done in a small, eutrophic lake,
Nesjovatn,
in central Norway (69”8’N,
11”50’E, 12 MSL) in late July 1981. Polyethylene cylinders, 1.5 m in diameter and
4.5 m deep and closed at the bottom were
filled with lake water in the evening; animals
were added the following morning, and the
first sampling was at noon that day (day 1).
The initial conditions in the two enclosures
Release of P by Daphnia
Table 1. Initial situation of the two enclosures. The
enclosures were well mixed, and the temperature was
16’3 1°C throughout.
Enclosure
Parameter
Zooplankton biomass, mg dry
wt liter-’
Algal biomass, mg C liter-’
Total particulate C, mg C liter-’
1
2
0.3
1.1
1.2
1.6
1.2
1.6
are shown in Table 1. During the next 8
days, both enclosures were sampled on five
occasions.
Zooplankton
for the grazing and phosphorus release experiments was collected in
a zooplankton net hauled vertically from
the bottom of the enclosures. Suitable subsamples (2-20 mg dry wt) were carefully
rinsed and washed before being transferred
to the bottles used for the incubations (Pyrex, 1.2 liter). The water in the bottles was
always taken from the same enclosure as the
zooplankton and was filtered twice through
a 30-pm plankton net to remove animals
and larger detritus particles. Four bottles
were prepared for each enclosure and day;
animals were added to two, and two served
as controls. The bottles were kept in dim
light and incubated for about 2 h (1.7-2.2
h) at 3-m depth, where no or little algal
fixation of carbon took place. The time between collection of water and animals to the
start of the incubation was < 1 h. Incubations were run from about 1100 to 1300
hours at a constant temperature of 16°C.
The animals were then removed by filtration through a 120qm plankton net. The
animals retained by the net were immediately transferred to a preweighed glass-fiber
filter and dried at 60°C to constant weight
(l-2 days). The length of the animals and
the number of their eggs were measured for
a prefixed sample taken from the zooplankton net sample. Length was converted to
units of dry weight according to W(pg dry
wt ind-l) = 6.9 1L(mm)3.0s (Langeland et al.
1984).
Several samples were taken from the bottles after incubation. Samples for particulate carbon and phosphorus were collected
on GF-F glass-fiber filters and ignited or
washed by acid. Dissolved phosphorus in
35
Table 2. List of symbols.
Concentrations:
N = food concentration
P = concentration of particulate phosphorus
P, = concentration of dissolved phosphorus
Q, = phosphorus : carbon (phosphorus : dry wt) ratio
Q0 = lower limit of Q,,, subsistence quota
Q, = lower limit of Q, yielding positive release rate
OfP
Z = zooplankton biomass
Plow rates:
P, = release rate 0fP
Pi = ingestion rate of P
P, = incorporation rate of P (growth + reproduction)
R = specific release rate of P
I, = specific ingestion rate of P
c, = ingestion rate of food
I = specific ingestion rate of food
CR = specific clearance rate of food
p, = specific growth rate of zooplankton
E = specific excretion rate of P as given by the Peters (1975) model, upper limit
Others:
L. = individual length of animals
W = individual dry weight of animals
T = incubation time
the filtrate was determined. Filter samples
were kept frozen (- 1SOC) and water samples were preserved with 0.09 N H,SO,.
Carbon was estimated with a Carlo Erba
elemental analyzer, model 1104, after treatment of samples with acidic fumes to remove inorganic carbon. Total phosphorus
was estimated in the filter samples (diluted
with distilled water) and in the dissolved
fractions after digestion in acidic persulfate
for 30 min at 120°C (Koroleff 1976). Random errors within replicates were normally
small in all analytical procedures (C.V. <
5%). Algal samples were preserved with Lugol’s solution and counted in an inverted
microscope. Volumes of the algal cells were
converted to carbon units with conversion
factors established in pure cultures of Rhodomonas Zacustris. On average, the carbon
content of the present Rhodomonas species
was 33 pg C cell-‘. Bacterial samples were
preserved with 8% glutaraldehyde
and
counted after staining with acridine orange
(Hobbie et al. 1977). Bacterial volume and
carbon content were measured as described
by Bakken and Olsen (1983).
Calculations-The specific ingestion rate
36
Olsen et al.
of food by zooplankton
according to
(I) was calculated
The symbols are given in Table 2; the subscript T represents the value for experimental bottles with added animals, 0 represents control cultures without
added
animals or controls at time zero. The animals’ specific clearance rate of food (CR) is
estimated as
Wo - Nd
(2)
ZT(No + NT)
and their specific release rate of phosphorus
(R) was calculated from the recycling model
of Olsen and Ostgaard ( 198 5) [Note: This
is the corrected version of their eq. 17.1:
CR =
- Rio
+PTNo
-
PONT
NT-No
NT
*In N
.
( 0 )I
Results
Preliminary experiment-The
results of a
preliminary experiment to identify acceptable experimental conditions are shown in
Table 3. The fraction of Rhodomonas cells
removed (RF) varied between 8.4 and
70.7%. The estimated clearance rates (CR)
were equal in all bottles, except those operated under extreme conditions (bottles 1
and 6). The ingestion rate of Rhodomonas
cells (I) was fairly constant, except in bottle
1. The estimated release rates of phosphorus
(R), according to the recycling model, were
more or less equal for all bottles (C.V. =
8.9%) and seem therefore not to be more
sensitive to the experimental conditions than
the clearance and ingestion rates. The excretion rates of phosphorus (E) predicted by
the Peters (197 5) model were on average
89% of the release rates.
In accordance with these results, we chose
the following conditions for the incubation
experiments. Food concentration should not
drop below 0.2-0.3 mg C liter-’ during incubation (incipient limiting food concen-
I I I I I
37
Release of P by Daphnia
BACTERIA
2r
E -
to the time-zero situation. From 60 to 630
animals per liter were added to the bottles
(mean 285), depending on food concentration.
Enclosure experiment -At the time of the
experiment the lake had a phytoplankton
community
of only cryptophytes.
There
were three species present: R. lacustris,
Cryptomonas erosa, and Cryptomonas
marssonii.*The first was the most abundant
(>95% of cell number and >75% of cell
carbon). The shapes and the sizes of these
species and of the bacteria present are shown
in Fig. 1.
The concentration of food carbon in the
enclosures is shown in Fig. 2; algal, bacterial, and detrital carbon are expressed as
ratios of the total particulate carbon. The
development was more or less the same in
the two enclosures. Algae were the most important potential source of food carbon at
the start of the experiment, detritus and bacteria toward the end. Death and sedimen-
-I
ALGAE
Fig. 1. Shapes and sizes of the important groups of
bacteria and species of algae.
tration normally found for Daphnia). The
fraction of algal cells removed (CF) should
be in the range of 20-50%, the higher values
being acceptable only at high food concentrations. The incubations were run for short
periods (2 h) in subdued light to avoid any
development in the control cultures relative
1.5
E-l
t
17
7z
.e
-
Detrital
C
ii.:?.::::
i.:.
i..
: Bacterial
i~.‘:‘j:
C
qii.:
1.0,
. .-.*.a
...
.>>I.
. ....*.a
..
.:.:.:.
....
.‘...‘.
.>:.:.
.. ..‘.‘.
...
.:.>>
.*.*.*a
. .*.*.*a
...
.:.:.:.
.-.*.*a
...a.-<
E
+
ti
0.5
O-
;.:.:
..
)>I
,-.-.
,-.a.
,*.a.
,a.-.
,a.-.
..*
:::::
:::::
:::p
2
h
E-2
*
::::
:I::
w
.:.:::
:. :
.:j,:.:
&
4
6
8
1
2
4
6
8
Day
Fig. 2. Development of the different food carbon fractions during the experimental period. Detrital carbon
has been defined as the difference between total particulate carbon (TC) and algal plus bacterial carbon. Bars
indicate 1 SE of the estimates.
Olsen et al.
38
E-l
0: :
E-2
Dissolved
P
.:i:..,:
:
III!iillj:li,lParticulate p
6
8
6
8
Day
Fig. 3. Development of particulate and dissolved phosphorus during the experimental period. Bars indicate
1 SE of the estimates.
tation of algae were more important than
grazing in removing carbon from the water
during the first days. This explains why the
two enclosures, which received different
amounts of zooplankton, behaved in a similar way.
The changes of particulate and dissolved
phosphorus in the enclosures are shown in
Fig. 3. Although both dissolved and particulate phosphorus decreased during the experimental period, the reduction was less
than that of particulate carbon. For the last
3 days of incubation, the concentrations of
particulate phosphorus in the total fraction
(Fl) (cf. Fig. 3) and in the fraction which
passed a 1-pm-pore Nuclepore filter (F2) are
given in Table 4. Most of the particulate
phosphorus (on average 8 7%, range 7 5-96%)
was in small (< 1 pm) particles. The specific
phosphorus contents of algae (Qpma)and bacteria (Q,-,) are also given. We assume that
F2 represents bacterial phosphorus and
Fl - F2 represents algal phosphorus. Microscopic examination verified that very few
algal cells passed the filters, whereas the sus-
pended bacteria did. The validity of this
assumption is further discussed below.
The P: C ratios for the algae were extremely variable. This is not surprising, because the difference between the phosphorus in the Fl fraction and that in the F2
fraction is small compared to the absolute
values for Fl and F2. The range, however,
agreed well with results for R. Zacustris in
culture (Table 5).
The P : C ratios for the bacteria were less
variable and gave better confidence intervals. In general, these values were higher
than those for the algae and in good agreement with others reported for bacteria (Fuhs
et al. 1972; Chen 1974; Vadstein 1983).
A detailed study of the distribution
of
phosphorus in the individual
suspended,
smaller particles was made by X-ray microanalysis (Heldal et al. 1985) on the unfixed samples from enclosure 1, taken on
day 4. The results (Table 6) indicate that
only 8% of the phosphorus was located in
detritus particles, although all bacterial
groups were rich in this element. Thus the
39
Release of P by Daphnia
Table 4. Distribution of phosphorus in two fractions (IL 1 SE) (Fl: x < 30 pm and F2: x < 1 pm) on the
last 3 days of incubation together with estimates of the P : C ratios of the algae (Q,J and bacteria (Q,+). (Details
given in text.)
Day 4
Day 6
Day 8
9.lkO.19
6.8kO.02
13.9+ 1.2
61.8k2.6
6.7k0.27
6.4kO.04
4.11 k3.7
70.0f3.4
5.8zkO.02
5.3k0.76
23.8k36.2
72.7kll.l
7.2k5.1
6.7k0.23
3.3k3.7
78.8k4.4
6.1kO.28
5.6kO.17
13.5k8.8
65.8k3.4
5.1 Iko.37
4.OkO.04
55.0* 18.6
50.5* 1.7
Parameter
Enclosure 1
Fl, pg P liter-l
F2, pg P liter-’
Q,,-,,a P mg-’ C
QpMb,
CLgP mg-’ C
Enclosure 2
FI , pg P liter-’
F2, pg P liter-l
Q,.,,a P mg-’ C
Qpeb7
PLgP mg- ’ C
phosphorus in the particulate matter was
located in living algae and bacteria (cf. Tables 4 and 6). These food particles were
cleared from the water at about the same
rate by Daphnia pulex (Bsrsheim and Olsen
1984). Particulate phosphorus per algal-plusbacterial carbon (QpWa,)may therefore be
taken as an estimate of the phosphorus content of that specific food compartment. The
development of Qp+,,,in the enclosure communities (Fig. 4) showed a significant increase (P < 0.05) as the experiment proceeded. The values for the first days equalled
those for cultures of R. Zacustris (Table 5).
Toward the end of the experiment, when
the bacterial biomass exceeded that of the
algae, the values rose to levels normally
found for bacteria.
The development and specific clearance
rates of D. pulex, which made up at least
96% of the dry weight of the zooplankton,
are shown in Table 7. The biomass was fairly constant through the experimental period
in both enclosures, and most of the individuals were adults. The estimated clearance rates for algae and bacteria increased
as the experiment proceeded or as the food
concentration
decreased (cf. Fig. 2). The
rates were consistently in good agreement
with those of Geller (1975) for D. pulex.
Our results do not permit a direct estimate of the ingestion rate of carbon, because
the ingestion rate of detritus particles was
not determined. On day 1 the detritus particles constituted only a minor fraction of
the particulate organic matter, and no serious error is introduced if the ingestion rate
of carbon (I,) is estimated as clearance rate
times total particulate carbon (I = CR x
TC; cf. Eq. 1 and 2) on this day. This gives
an average (&SE) ingestion rate of 14.3 +
0.6 pg C (mg dry wt)-’ h-l for both enclosures.
The estimated specific release rates of
phosphorus (R) for the enclosure experiment are shown in Fig. 5, together with pre-
Table 5. P : C ratios of some freshwater food algae and bacteria.
Q,,a P mg-’
(range)
3.3-80*
3.7-88*
2.5-26
4-25
C
Chlorella pyrenoidosa
Selenastrum capricornutum
Chlamydomonas
reinhardtii
Rhodomonas Iacustris
Corynebacterium
bovis
Pseudomonas aeruginosa (P starved)
Bacillus subtilis (P starved)
Mixed bacterial community, year
succession in Nesjovatn
* C obtained
t C obtained
as 40% of dry wt.
assuming 0.12 pg C pm-‘.
98-220-f
61-t
97-t
41-230t
Reference
Nyholm 1977
Nyholm 1977
Olsen et al. 1983
Olsen unpubl.
Chen 1974
Fuhs et al. 1972
Fuhs et al. 1972
Vadstein 1983
40
OZser2e It al.
as a function of the phosphorus content of
the algal-bacterial food compartment;
we
have also included data from the laboratory
experiments of Olsen and Ostgaard (1985).
Linear regression data for the relationship
are given in Table 9. The relationship was
significantly positive and the slope close to
unity, especially when the three values
shown “crossed” in Fig. 6 were excluded.
The curve tended to intercept the Qpmab
axis
at a positive value; we call this Q,. The estimated value of Q, remained quite constant
irrespective of the exclusion of the three deviating values. The probability for Q, > 0
was >90% in both cases (Table 9).
800
o
7
E”
a
EL
-z
60-
40-
ci
20-
0
I:‘,
1
1
2
I
I
4
I
1
6
I
I
8
Discussion
Day
Fig. 4. Phosphorus concentration of the algal-bacterial food carbon compartment (Q,-,,) during the experimental period. Enclosure 1-O; enclosure 2 - +.
dictions of the upper limit of phosphorus
excretion rate according to Peters (1975). In
both enclosures, the release rate tended to
increase toward the end of the experiment.
The values were well below the predicted
excretion rates at the start, but in reasonable
agreement by the last day of incubation.
The relationships between the release rate
of phosphorus and a number of variables
expressing the feeding conditions and actiyity of the animals are given in Table 8. No
positive relationship was found between the
release rate and the concentrations of the
various food sources nor that of particulate
phosphorus; there was a positive relationship with the clearance rate and the P : C
ratio of the food. The last relationship is
shown in Fig. 6, in which the amount of
phosphorus released per unit of algal and
bacterial carbon ingested has been plotted
For reliable results in experiments with
algae and zooplankton incubated in bottles,
it is important that we choose the correct
conditions. Crucial factors are animal biomass, incubation time, and the concentration of food present (Johannes and Webb
1970). The guidelines for such incubations
given above were found to be acceptable for
measurements of both the animals’ specific
clearance rate and the specific release rate
of phosphorus according to the recycling
model (Eq. 3). This conclusion was supported by the filtering kinetics obtained; the
clearance rates of both algae and bacteria
decreased as the concentration of food carbon increased, indicating that the food concentration was above the incipient limiting
level for the animals. Moreover, the magnitude of the rates was well in agreement
with those published for the species by Geller (1975).
We treated algal plus bacterial biomass as
one food compartment of the grazers. This
was possible because both types of food particles were cleared from the water at the
Table 6. Relative distribution of phosphorus in small particles (detritus and bacteria) estimated by X-ray
microanalysis.
Bacteria
Detritus
Particle diam, pm
Relative No.
Particles containing
P (%)
Total P in the
sample (%)
CO.3
700
0.3-0.8
600
>0.8
100
0.36
26
0.46
80
0.69
32
1.1
8
1.2
6
1.3
1
10
5
50
100
100
100
100
100
100
0
4
4
2
12
24
9
43
2
Release of P by Daphnia
41
Table 7. Development and feeding activity of Daphnia pulex in the enclosures (HE). Symbols are given in
Table 2.
Day
Enclosure 1
L, mm (n = 50)
W, pg dry wt ind-’
Z, mg dry wt liter-l
% adult (n = 100)
CR,,, ml (mg dry wt)-’ h-l
Enclosure 2
L, mm (n = 50)
W, pg dry wt ind-*
Z, mg dry wt liter-’
% adult (n = 100)
CR,,, ml (mg dry wt)-’ h-l
1
Day 2
Day 4
Day 6
Day 8
1.39kO.07
27k3.6
0.24kO.03
50
9.Ok 1.8
1.3OkO.08
25k4.3
0.35f0.06
10.2kO.4
1.55kO.07
36k4.6
0.37kO.05
50
19.7f3.9
1.34kO.07
26k4.3
0.37kO.06
32.1 f9.0
1.32kO.09
3Ozk6.3
0.27 20.06
36
61.5k12.3
1.53kO.06
31 k3.1
l.l-+O.ll
57
8.8k3.8
1.55kO.06
32t-3.6
0.98kO.11
15.4k2.5
1.38kO.06
24k2.8
1.0+0.12
53
21.5k2.3
1.63kO.07
39k4.3
0.82kO.09
34.8k0.7
1.71kO.07
46k4.6
0.8OzkO.09
63
5 1.8k4.5
same rate by D. pulex during these enclosure
experiments (Borsheim and Olsen 1984).
Additionally,
it was shown that most of the
particulate phosphorus was located in this
specific food compartment with only a small
proportion in the detritus particles. Accord-
ingly, by substituting algal + bacterial carbon for N in Eq. 3, and total particulate
phosphorus for P, we could avoid the problem of estimating the ingestion rate of detritus particles by the grazers. This measurement could hardly be made directly.
E-2
E-l
8
1
2
4
6
8
Fig. 5. Estimated specific release rate of phosphorus (R) in the enclosure experiments. Solid circles indicate
the excretion rate predicted according to Peters (1975, upper limit) and bars 1 SE of the estimates.
Olsen et al.
42
Table 8. Regression parameters expressing the relationship between the release rate of phosphorus (R)
and several variables expressing the feeding conditions
and activities of the animals.
Regression
paramctcrs
Relationship
R
R
R
R
R
Qpaw pP mg%
Fig. 6. The amount of phosphorus released by the
animals (P,) per unit of algal and bacterial carbon which
is ingested (Ci) as a function of the mean phosphorus
content of the respective food (&,,). Regression line
and its 95% C.I. for all experimental values is drawn.
Qp++,is defined as the mean Qpmab
of experimental and
control bottles. Enclosure 1-O; enclosure 2- +; preliminary experiment-A; experiment 1 (Olsen and 0stgaard 1985)--V, experiment 2 (Olsen and 0stgaard
1985)-o; values omitted in regression (cf. Table
9)-K
Ingestion of P-free detritus is of no importance for the phosphorus mass balance of
the animals or for the release rate of this
element (cf. Olsen and Ostgaard 1985).
The specific release rates of phosphorus
in the enclosure experiment did show a pronounced increase as the experimental period proceeded. Compared to the excretion
rates predicted by the Peters (1975) model,
our release rates were in agreement at the
end of the experimental period and in the
preliminary
experiment.
Otherwise, our
rates were considerably lower than the predicted values. Although the release rate, as
defined here, is not directly comparable with
the excretion rate since fecal compounds do
not enter the latter process, a rough comparison is still possible. The low release rates
at the start of the experimental period were
probably an effect of phosphorus subsaturation in the food organisms; under such conditions, the P : C ratio of algae and bacteria
vs.
vs.
vs.
vs.
vs.
total particulate C
algal C + bacterial C
particulate P
P : C ratio of food (Q,.,,,)
clearance rate (CR,J
-0.635
-0.493
-0.540
0.746
0.918
0.133
0.169
0.158
0.099
0.035
is lower than that of P-saturated organisms
(Table 5). We do not contend that both algae
and bacteria were P limited at the start of
the experiment, but the P: C ratio of the
complete algal-bacterial
community
was
lower than at the end of the experiment (Fig.
5). The influence of the P : C ratio of the
food on the release rate of phosphorus is
clearly seen in Fig. 6, in which the phosphorus released per unit of ingested carbon
(PrCi-‘) was plotted against the P : C ratio of
the actual food compartment (Qpeab).This
curve intercepted the Qpeabaxis at a positive
value (cf. Table 9), indicating that the release rate of phosphorus by the animals became zero when the P : C ratio of the food
was below a certain critical value, Q,, here
estimated as 6-8 yg P mg-’ C. Above this
value, the release rate was proportional
to
the P : C ratio of the food at a given ingestion
rate of food carbon.
The above value of Q, is not expected to
be valid for other groups or species of zooplankton having different growth characteristics from the daphnids (cf. Allen 1976). A
mathematical representation of Qc is given
by
PZQp-Z
Qc = --y-
(4)
C
showing that Q, is proportional to the growth
and reproductive rate (& of the animals
and to their body phosphorus concentration
(Q,J, and inversely related to their specific
ingestion rate of food carbon (Ic). Accordingly, for a given situation, Qc is predictable
if these variables are known. Only the specific ingestion rate of carbon has been determined here [Ic = 14.3pgC(mgdrywt)-’
h-l], but independent experiments in the
lake provided the data necessary to compute
43
Release of P by Daphnia
Table 9. Regression parameters for
Qp-abaxiS <QJ.
All values
Three values excluded*
* Shown
P,Ci-’
vs.
Qpmab;
95% C.I. are given for slope and the intercept with the
QC
r
P
0.843
0.920
co.05
co.03
Slope
1.13kO.26
1.011kO.16
(~3 p mg- I Cl
tQc: 0)
7.90(-3.25-14.9)
6.07(-1.30-l 1.4)
>0.90
>0.95
I( on Fig. 6.
Q, according to Eq. 4. These additional experiments included measurement of the
P : dry wt ratio of the animals and an in situ
life-history
experiment
with D. pulex
(Langeland et al. 1984). In the latter experiment, the growth and reproductive rate of
individuals (40 hg dry wt, mean individual
biomass of the animals in Fig. 6) was 0.008
h-l, and the body phosphorus concentration was 15.1 pg P mg- 1 dry wt. On this
basis an independent estimate of Q,, calculated from Eq. 4, was 8.4 pg P mg-’ C.
Although this calculation is rough, the value
for Q, agreed well with those given in Table
9, obtained by extrapolation.
These calculations indicate that D. pulex
may become phosphorus limited if fed sufficient quantities of food containing ~6-8
E.cg
P mg- I C. In general, P limitation in such
a situation occurs if
where p, is the growth and reproduction rate
of the animals, QpSZis their concentration
of body phosphorus, and Ip is the specific
ingestion rate of phosphorus of the animals.
It is an interesting question whether natural
populations of Daphnia might experience P
limitation. To evaluate this, we have assembled P : C ratios of some freshwater food
algae (Table 5). There is a wide range, with
values well below the Q, value for Daphnia
in the case of P-starved algae and values
considerably higher for bacteria. Therefore,
P limitation in daphnids is a theoretical possibility if P-starved algae or detritus particles are the major components of the diet.
However, a small proportion of bacteria or
P-sufficient algae in the food is enough to
meet the animals’ requirement for phosphorus, and we tend to believe that the
probability
of this group of animals encountering P limitation
in nature is very
low. Other factors, such as the availability
of the food phosphorus and the possibility
that the animals have developed other strategies of avoiding P limitation are not considered here, but may be important. The
estimated values of Q, were based on the
assumption that all phosphorus in the food
was assimilated by the animals. If some
fraction, for example the inorganic polyphosphates, was poorly assimilated, P limitation would occur at even higher P : C ratios, so that P limitation in nature may be
more frequent. This is, however, still not
known.
The recycling model proposes that release
of phosphorus by the zooplankton is directly coupled to its ingestion and use for
growth and reproduction.
Individual
animals do not generate phosphorus at a rate
independent of its intake. The phosphorus
concentration of the food has rarely been
taken into consideration as a factor affecting
the release rate of phosphorus (Thingstad
and Pengerud 1985). Peters and Rigler
(1973) have discussed the nature of the extreme variation in the excretion/release rates
of phosphorus reported in the literature, and
they concluded that methodological
problems are the reason. We agree, but suggest
that the phosphorus content of the food is
another important
factor not taken into
consideration by the authors of the papers
that they reviewed. The variation in the P : C
ratio alone causes variations of several orders of magnitude in the release rate, since
the rate may approach zero for low phosphorus concentrations in the food.
The theoretical characteristics of the recycling model make it convenient for estimating or modeling phosphorus release in
open systems (i.e. not bottles). The fundamental mass balance equation,
pr = Pi - P,,
(6)
stating that the flux of released phosphorus
44
Olsen et al.
(P,) is given by the difference between what
is ingested (Pi) and what is used for growth
and reproduction
(P,) (Taylor 1984), is
equivalent to
R = IF - QcL = Ip - P,Q,-z
(7)
(symbols given in Table 2). Different experimental approaches may be used to estimate release rates of phosphorus by zooplankton according to the above equation.
The effect of temperature, food concentration, species, and other critical factors on
the release rate is incorporated in the variables of Eq. 7, which constitutes a link between the carbon and phosphorus fluxes of
the animals. Equations 6 and 7 are therefore
well suited for modeling carbon and phosphorus fluxes through zooplankton in pelagic ecosystems.
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Submitted: 5 February 198.5
Accepted: 8 July 1985