Umnol. Oceanogr., 30(1), 1985, 202-212
© 1985, by the American Society of Limnology and Oceanography, Inc.
The prediction of cladoceran grazing rate spectra1
Abstract—Reanalysis of published observa
tions on the ingestion of artificial particles by
cladocerans confirmed the statistical significance
of particle size selection in situ. Three statistical
approaches were tested to seek a framework for
a general theory of cladoceran particle size selec
tion: the algebraic continuous model, the alge
braic discrete model, and the distributional mod-
1 A contribution to the Groupe d'Ecologie des Eaux
douces ofl'Universite de Montreal and the Lake Memphremagog Project of McGill University. This work
was supported by the Natural Sciences and Engineering
Research Council of Canada, the Canadian National
Sportsmen's Fund, the Lake Memphremagog Project,
and the Department of Education of the province of
Quebec.
el. The first two approaches can predict the shape
of grazing rate: particle size spectra but make
biased predictions. The last approach, in which
equations are used to predict the parameters of
the negative binomial distribution which mimics
grazing rate spectra, makes fairly precise (r2 =
0.67) and unbiased predictions. Improvement of
this kind of model is suggested as a step toward
quantification of the role played by zooplankton
in the dynamics of phytoplankton communities.
Particle size selection by zooplankton
predators is considered responsible in part
for the structure of phytoplankton com
munities (Porter 1973; McCauley and
Briand 1979). Lam and Frost (1976) sug-
Notes
203
30-
20
SIZE OF
30
40
50
PARTICLE
Ojiti dlam )
0
5
10
15
20
25
30
Fig. 2. Size-frequency distribution of organic poly
mer particles in grazing experiments conducted in Mikolajskie Lake during 1973. (Drawn from Gliwicz 1977:
table 1.)
SIZE OF PARTICLE (p; jjm dlam)
Fig. 1. Grazing rate (mean and standard deviation
of the sample) of Daphnia cucullata (Kp) on organic
polymer particles of various sizes (p) during July, Au
gust, and September 1973. (Redrawn from Gliwicz
1977: fig. 1.) Each of these three plots is here referred
to as a "grazing rate spectrum."
gested that the size composition of the phytoplankton influences the length and com
plexity of planktonic food webs and thus
that particle size selection by zooplankton
should be included in simulation models of
planktonic communities. The ability ofzooplankton to ingest various sizes of algae has
also been thought to mold zooplankton
community structure in lakes of different
trophic status (Brooks and Dodson 1965;
Makarewicz and Likens 1979; McCauley
and Kalff 1981; McCauley 1983). Lehman
(1976) even suggested that a model to pre
dict the behavior of filter feeders is incom
plete if it ignores the size-selective ingestion
of food particles. Food particle size selec
tion by zooplankton has been found in lab
oratory experiments (e.g. Mullin 1963; Gli
wicz 1970; McQueen 1970; Arnold 1971;
DeMott 1982), and Peters and Downing
(1984) have tried to quantify the general
effect of food particle size on grazing rate.
However there have been few attempts to
measure in situ particle size selection, and
therefore the literature lacks a general model
or framework for future studies. The im
portance of such a general model can be
underscored by the recent proliferation of
models of planktonic communities that
make simple assumptions regarding particle
size selection by zooplankton (e.g. Jernigan
andTsokos 1980; Sjoberg 1980; Wulff 1980;
Arnold and Voss 1981; Brown et al. 1982;
Montague et al. 1982).
Gliwicz (1977) examined in situ particle
size selection by feeding the natural zoo
plankton of Mikolajskie Lake beads of or
ganic polymer of different sizes in addition
to their natural food. Animals were re
trieved after a short feeding period and the
number of beads in each of 10 size classes
was counted in their guts. Grazing rates 0*1
anim."1 h"1) for each size class were calcu
lated by comparing the number of particles
ingested to the number of particles of that
size available per unit volume of lake water.
Histograms with standard deviations were
presented to show how grazing rate varied
with particle size in five cladoceran species.
204
Notes
The general form of the histograms (Fig. 1)
suggests that positive selection is strongest
for small particles (< 10 nm) and that neg
ative selection is strongest against large nannoplankton (15-50 nm).
Two types ofinvestigation should be made
before we can use these results to theorize
regarding the effects of cladocerans on phytoplankton communities. First, it is not clear
how much of the variability in the grazing
rates found by Gliwicz could have resulted
from the experimental conditions rather
than the behavior of the animals. The par
ticle size distribution offered the animals
was highly skewed (Fig. 2); thus, unless
counts were pooled from hundreds of ani
mals, the ingestion of large particles would
be rare, even ifgrazing were independent of
particle size. Ifthe concentration ofparticles
of a given size is very low then the proba
bility of random uptake of a single particle
is small. Fractions of particles cannot be
ingested. Therefore, if sample sizes are not
large, grazing rates will be apparently zero,
underestimating the more accurate small,
positive value. This could account for some
of the apparent selection against large par
ticles shown by Gliwicz's histograms. In fact,
his calculations show that grazing rates
within species-date combinations are al
most always significantly correlated (P <
0.05) with the density of plastic particles.
Second, the data are presented as 25 sepa
rate observations without general connec
tion. Because these are the best field exper
iments done on cladoceran particle size
selection to date, it is tempting to use the
data to produce a preliminary general the
ory to predict zooplankton predation dam
age to phytoplankton. At the very least, an
analysis ofthese data might suggest a format
for future studies.
Our purpose here is to examine Gliwicz's
data in greater detail, to determine the sig
nificance of departures from random par
ticle uptake, and to test a series of statistical
approaches through which a more general
theory might be produced. We thank M.
Gliwicz for sharing his thoughts and data.
Comments on the manuscript by R. Peters,
M. Pace, J. Bence, and D. Smith are also
appreciated.
We originally intended to evaluate the size
range through which grazing rates deter
mined with small particles (1-4 jum) could
be representative of the grazing rates on
larger sized particles (5-35 pm) (see Down
ing and Peters 1980; Downing 1981). The
grazing rates on various sizes of particles
(Vp, where p is the midpoint of the particle
size range in nm, e.g. F25, V-,-5, etc.) and the
bounds of the approximate 95% confidence
intervals for replicate determinations were
taken from figures 1-4 of Gliwicz (1977).
Grazing rates (V, /xl anim."1 h"1) were de
termined to within 0.1 fil anim."1 h~' with
calipers and some photo-enlargements of
these figures. Mean body lengths of various
species in Gliwicz's experiments were taken
from his table 2. The data so derived con
sisted of grazing rates, confidence intervals,
body lengths, and particle diameter mid
point for Daphnia cucullata, Daphnia
longispina, Bosmina coregoni, Diaphanosoma brachyurum, and Chydorus sphaericus during May, June, July, August,
September, and October 1973. Some
species-month cells are empty but we had
a total of 25 different grazing rate: particle
size distributions.
We wanted to determine both the fre
quency with which the grazing rate distri
butions of Gliwicz would be expected to
occur as a result of nonselective uptake of
particles, and the particle sizes for which
significant deviations occur. A x2 compar
ison ofgrazing rate spectra with Fig. 2 would
satisfy the first goal but would yield no in
formation on the positive or negative selec
tion for specific sizes of particles. Instead,
we simulated the experimental protocol but
used a random number generator instead of
animals to ingest the particles. In the in situ
experiments, each of the grazing rate: par
ticle size curves was a result of 3-5 replicate
determinations, each consisting of the par
ticles ingested by 3-10 animals, during a
period less than the gut passage time (about
10 min). Thus, we assumed that each rep
licate arose from the particles ingested in
100 animal-min (10 animals feeding for 10
min). We used this estimate to back-cal
culate the average number ofbeads that were
ingested and counted in each replicate de
termination for each of the 25 experiments.
We then used the random number generator
Notes
(random at P < 0.01) to "ingest" this same
number of beads from the size distribution
in Fig. 2 for each of five replicates. Each
single particle in Fig. 2 thus had an equal
probability of being ingested. The grazing
rate that would be obtained if selection were
random (Vp) was then calculated from the
number of particles of each size range in
gested. If Gliwicz's results are simply an
expression of random uptake, then in re
peated simulations, 95% of the Vp should
lie within the confidence interval found by
Gliwicz(i.e. Vp ± f005SE).In nsimulations,
the probability that the observed grazing rate
results arose from random uptake of par
ticles can be calculated: n/0.95n, where n is
the number of simulations in which Vp fell
within the confidence interval for Vp re
ported by Gliwicz. Theoretically, n could
be greater than 0.95«, indicating that ran
dom uptake is a more precise descriptor of
Gliwicz's data than the data themselves.
This was not a common occurrence. We
performed this simulation between 100 and
1,000 times for each of the 25 species-date
combinations; more simulations would be
prohibitively expensive and result in little
increase in precision (J. Downing unpubl.
data).
Table 1 shows that some of the apparent
particle size selection can be attributed to
random uptake but that cladocerans are sig
nificantly size-selective. Random uptake is
especially prevalent at small and large par
ticle sizes. The uptake of large particles ap
pears random simply because the particle
size distribution offered was highly skewed
(see asterisks: Table 1). The cladocerans
ingested very few (if any) particles >40 pm
in diameter, but given the particles offered,
the random number generator would en
counter these particles with a probability of
only 0.0009! Thus, it is obvious that the
apparent size of the largest particle ingested
by a filter-feeding animal (cf. Burns 1968a)
will be a function of the shape of the food
spectrum offered and the total number of
particles censused. This is true even if there
is no size selection. Random uptake at
smaller particle sizes appears to be real but
varies over the season, which suggests that
animals are able to vary their uptake effi
ciency seasonally, but this could be due to
205
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206
Notes
behavioral or mechanical plasticity, or ge
netic variability. Also notable is the rarity
of positive selection, suggesting that cladocerans do not often seek out preferred par
ticle sizes but reject those that are less ac
ceptable.
The dominating observation, however, is
that cladocerans select against particles be
tween 10 and 35 nm in diameter (Table 1).
Some of the shape in Gliwicz's curves (e.g.
Fig. 1) is thus due to behavioral or me
chanical selectivity by cladocerans, not sim
ply the statistical aspects of the size spec
trum offered. The importance ofthis finding
to the modeling of phytoplankton com
munities is clear. If we assume that all nannoplankton (e.g. <35 mhi) is removed from
the water by cladocerans at equal propor
tional rates, then predation pressure should
lead to the dominance of those algae that
have superior rates of growth (i.e. small al
gae; see Banse 1976; Friebele et al. 1978;
Foy 1980; Malone 1980; Schlesinger et al.
1981; Smith and Kalff 1982). On the other
hand, if predation pressure is proportionally
lower on those algae that are growing most
slowly, then the differential predation rate
may allow coexistence of large and small
algae or even dominance of slow growing
forms under some conditions. It is thus im
portant that we be able to predict differences
in proportional predation rates on different
size categories of phytoplankton.
We here propose three different statistical
approaches that could be used to make these
predictions and compare them to find which
yields the most accurate and precise pre
dictions of grazing rate of cladocerans on
algae of different sizes. We call these three
approaches the algebraic continuous model,
the algebraic discrete model, and the dis
tributional model. The three types are cer
tainly not exhaustive but include the most
prevalent classes of analysis in ecology to
day.
The algebraic continuous model was sug
gested by work showing that the grazing rate
of a cladoceran is a continuous function of
its body size and of the concentration of
food offered to it (Downing and Peters 1980;
Downing 1981; Peters 1984). The effect of
body size (L; length, mm) is usually positive
(Burns 1969; Egloffand Palmer 1971; Chis-
holm et al. 1975; Geller 1975; Peterson et
al. 1978), while the additional effect of food
concentration is usually negative (McMahon and Rigler 1965; Burns 1968a;
Chisholmetal. 1975; Geller 1975; Kersting
and van der Leeuw 1976). The particle size
(P) in question also determines the grazing
rate of those cells, with lower values seen at
higher P and perhaps at lower P as well
(Burns 19686; Gliwicz 1969; Porter 1973;
Peterson et al. 1978; Peters and Downing
1984). Thus, the grazing rate response in
Gliwicz's data should be approximated by
the simple function:
Vp = a + b log L + cP - dP2 - eS (1)
where S is the food concentration, P is the
particle size (jim diam), and a, b, c, d, and
e are fitted constants. Unfortunately, we do
not know S for Gliwicz's experiments. The
effect of food concentration can be account
ed for, however, by using the grazing rate
at 2.5 nm (V2.5) which should be negatively
correlated with S, as an independent vari
able to predict K75to F475. This is especially
useful since in situ grazing rates are often
approximated with particles ofthis size range
(Haney 1973; Downing and Peters 1980).
Thus, the expected algebraic equation to
predict Vp (exclusive of V2 5, ofcourse) would
be
Vp = a + b log L + cP - dP2 + <?K2.5.(2)
We fitted this equation to Gliwicz's data
using least-squares regression (Draper and
Smith 1966) and backwards elimination to
find the best equation (Hocking 1976;
Downing 1981).
A highly significant regression equation
could be derived by this technique. Over
the small range of L, however, the logarith
mic transformation of body length yielded
no significant (P < 0.01) improvement over
the linear form. In addition, there was no
significant curvilinear effect of particle size
(P2) on Vp. The best equation to predict Vp
was therefore
Vp = 4.897 + 0.021L - 0.958P
+ 0.415F,2.5-
(3)
This equation has an overall /''-value of 65
(n = 129, r2 = 0.61), and partial F-values of
all regression coefficients are highly signif-
Notes
207
Although this equation fits the data well,
on average, there is one important failure
in this approach. Figure 3 shows a plot of
£
20
40
60
OBSERVED GRAZING RATE Oil anlm.-'h"1)
Fig. 3. The relationship between observed grazing
rates and those predicted using the algebraic continu
ous model. Predictions are from Eq. 3. The solid line
indicates a 1:1 correspondence between observations
and predictions. The model gives rise to negative graz
ing rates, is positively biased between 5 and 30 fd anim."1
h~', and is negatively biased at high grazing rates (>40
nl anim."1 h~*)-
icant (P <§: 0.01). We also tried logarithmic
transformations of Fand P, but the result
ing equations made poorer predictions of
Vp. The effect of body size is positively lin
ear, the effect of particle size is negatively
linear, and F2.s acts as a positive scaling
factor raising or lowering the response,
probably corresponding to variations in food
concentration.
predictions vs. observations for these data.
If Eq. 3 were an unbiased predictor of Vp
(the grazing rate on the midpoint of size
class p) then the observations would fall
evenly along the "1:1" line. Throughout
much of the range of Vp, however, Eq. 3
yields overestimates. It also fails in two oth
er ways. First, predictions ofvery low values
are poor and often negative; a negative val
ue of Vp is impossible unless animals are
producing algae. Second, Eq. 3 fails to pre
dict very high observations of Vp. These
failings result from the complex curvilinearity of the actual response and the linear
ity of the fitted model. This is not to suggest
that this approach cannot yield good pre
dictions of grazing rate when new data are
added, only that it is not sophisticated
enough to yield an unbiased fit to these data.
The algebraic discrete model involved the
construction of a series of multivariate
equations that describe how the grazing rate
on independent size classes of prey varies
as a function of cladoceran body size and
the grazing rate on the 2.5-iim reference par
ticle. This yielded a set of six multivariate
equations (Table 2; part 1), one to predict
grazing rates for each ofthe prey size classes.
Significant (P < 0.01) relationships were
Table 2. Equations to predict grazing rate spectra for cladocerans using either (part 1) discrete multivariate
equations or (part 2) a model based on the negative binomial distribution. Vp is the grazing rate on prey size
class p (jim diam), L is the body length in mm, X is the mean grazing rate over the grazing rate spectrum
calculated on the basis of a size-class frequency distribution, and N is the definite integral of the grazing rate
spectrum.
1. Discrete multivariate equations:
Prey size
class (p)
b
c
7.5
12.5
0.000704
0.00119
0.01557
0.01388
17.5
0.00172
22.5
27.5
32.5
0.00106
0.000105
-0.000103
0.01104
0.01451
0.00518
0.00431
2. Distributional terms:
logI0* == 0.697 log10L - 0.164 logiOV2S - 0.80
S* == 2.779JE0-5 - 2.337
log,0AT == 0.0022L - 0.0408 V2i + 1.705
a
0.446
-0.034
-0.447
-0.427
-0.057
-0.011
r
F
0.897
0.795
96.2
47.6
0.781
0.666
0.323
0.186
r
0.71
0.81
0.96
39.4
22.0
6.2
2.5
F
37.8
43.9
142.2
Notes
208
E
80-
o
3
UJ
•
-
•
60-
•
q:
z
40-
N
-
©
20-
0 UJ
q.
0
20
40
60
OBSERVED GRAZING RATE
(jul anim:1 tT1)
Fig. 4. The relationship between observed grazing
rates and those predicted using the algebraic discrete
model. Predictions are from equations in part 1 of Ta
ble 2. The solid line represents a 1:1 correspondence
between observations and predictions. The relation
ship between observed (Vp) and predicted (Vp) grazing
rates can be characterized as Vp = 1.935 + 0.801 Vp
(r* = 0.71; F= 385). The model is biased, especially
for predicting low grazing rates (i.e. <10 /tl anim."1
h-).
found for only four of the six size classes
<35-fim diam (Table 2). Observations of
grazing rates on particles >35 tim were
nearly all zero and so were not examined
further. Grazing rates on particles between
25 and 35 /-im were not functions of body
size of cladocerans or of grazing rate on the
reference particle. To examine the overall
ability of the models to predict variation in
grazing rates, we examined the relationship
between predicted and observed values for
the equations presented in Table 2 (Fig. 4).
Regression analysis indicates that although
the multivariate equations could account for
more than 70% of the variance in grazing
rate, the predictions were biased. The slope
of the relationship between predicted and
observed rates was significantly different
from one (P < 0.005), and the intercept de
viated significantly from zero (P < 0.005).
20
OBSERVED
o
40
GRAZING
60
RATE
(p\ aninvV)
Fig. 5. The ability of the negative binomial distri
bution to approximate Gliwicz's 25 grazing rate spec
tra. The negative binomial distribution was fitted by
expanding the individual terms of the negative bino
mial distribution (Elliott 1977) based on mean, vari
ance, k, and N calculated directly from each of the
spectra. The solid line represents a 1:1 correspondence
between calculated (Vp) and observed (Vp) grazing rates.
The relationship can be characterized as V'p = 0.02 +
1.02 Vp (r2 = 0.88; F = 1,498). Grazing rate spectra can
thus be fitted accurately by negative binomial distri
butions.
These equations overestimate grazing rates
for values <10 yl anim."1 h"1. This bias
could not be removed by further transfor
mation of the independent and dependent
variables. Because of this bias, we consid
ered these models, too, to be inadequate for
predictive purposes.
The distributional model was based on
the observation that the relationship be
tween grazing rates and prey size for cladoc
erans (Gliwicz 1977) resembles a negative
binomial distribution. In this approach, the
dependent variable is not a set of single val
ues of grazing rate on particular particle size
classes but rather an estimate of the param
eters required to expand the individual terms
of the negative binomial distribution to fit
the grazing rate spectrum for each datespecies combination. The individual terms
can be expanded in a recursive model (El-
Notes
209
liott 1977), if we know the mean {x), vari
ance (s2), total number of observations (N),
and the expansion coefficient (k). There are
two methods commonly used to calculate
h, these are the product-moment and max
imum likelihood techniques. The former
method, where
k = x/(s2 - x),
(4)
is recommended for distributions measured
with small sample size, because it is the most
efficient (Pieters et al. 1977).
To find whether the observed relationship
between grazing rate and prey size can be
described by the negative binomial distri
bution, we converted each grazing rate dis
tribution to a frequency distribution and
calculated the terms of the negative bino
mial (x, s2, N, and k). N was calculated as
the definite integral of the grazing rate spec
trum. Expanding the terms yielded a differ
ent fitted or calculated distribution for each
ofthe observed distributions. By comparing
the fitted value for each size class with the
observed grazing rates, we can determine
whether the negative binomial distribution
can be used to describe individual filtering
rate spectra.
This comparison is shown in Fig. 5 for
the 25 observed distributions. In general,
the negative binomial distribution is a good
descriptor ofthe observed variation in graz
ing rates. Regression analysis shows that
there is no bias introduced in fitting the dis
tributions to the individual relationships.
The slope is not significantly different from
one (P < 0.01) and the intercept is not sig
nificantly different from zero (P < 0.01). In
addition, the F-value and correlation coef
ficient indicate significant agreement be
tween the distributions and the observed
relationships. This only means that filtering
rate spectra can be fitted using a negative
binomial, not necessarily that it can be used
for prediction.
To attempt these predictions, we con
structed empirical relationships between es
timates of the parameters of the negative
binomial distribution and the independent
variables (body size and the grazing rate on
the 2.5-/im reference particle). This analysis
yielded three relationships (Table 2; part 2)
that can be used to predict the variation in
0
20
OBSERVED
40
60
GRAZING RATE
(jul animT'h"1)
Fig. 6. The relationship between observed grazing
rates and those predicted using the distributional mod
el. The predictions are made by expanding a negative
binomial distribution of grazing rate against particle
size using the expansion coefficients predicted from the
equations in part 2 of Table 2 (see text). The solid line
represents a 1:1 correspondence between predicted (Vp)
and observed (Vp) grazing rates. The actual relation
ship can be characterized as Vp = 0.03 + 1.02F, (r2 =
0.67; F = 385). The distributional model makes un
biased predictions of grazing rates on various particle
sizes with body size of cladoceran and V2i as inde
pendent variables.
grazing rate on prey items of different sizes.
The variables x and AT were predictable from
body size and the grazing rate on the 2.5nm particle, while s2 was predictable from
x. There was no significant relationship be
tween k and the independent variables, but
this parameter can be estimated from pre
dicted estimates of x and s2 (Eq. 4).
Figure 6 shows predicted and observed
rates with the negative binomial relation
ships. Predicted values are based on the ex
pansion of the negative binomial distribu
tion (Elliott 1977) using estimates of the
required parameters from the regressions in
part 2 of Table 2. Regression analysis in
dicates no detectable bias with these rela
tionships because the slope and intercept
are not significantly different (P < 0.05)
from one and zero. In addition, more than
210
Notes
67% of the variation in grazing rates can be
explained with this approach. At very high
grazing rates, predicted values deviate from
the observed, although this deviation does
not appear to be systematic.
The analyses presented here represent a
first attempt to construct empirical rela
tionships that predict variations in grazing
rates by cladoceran zooplankton on artifi
cial prey items of different sizes. Our results
complement other studies showing that the
body size of zooplankton is useful for pre
dicting grazing rates on single sized particles
(e.g. Burns 19686; Downing and Peters 1980)
by quantifying the relationship between
body size and variation in grazing rates on
prey particles of different sizes. The results
also suggest a format for future studies to
predict this variation. Empirical relation
ships based on either discrete multivariate
equations or transformed polynomial
regressions, which have been used success
fully to predict other aspects ofzooplankton
feeding (Downing and Peters 1980; Down
ing 1981; Peters and Downing 1984), were
shown to be inadequate because they yield
ed biased predictions of grazing rates. The
distributional technique provides estimates
that are not biased and that explain a similar
or larger percentage of the variance. These
techniques are therefore recommended over
the other two methods.
Our study was restricted by the avail
ability of data. We found no other data that
could be used to test the generality of this
approach for cladocerans (e.g. Gliwicz 1969;
Kersting and Holtermann 1973; Berman and
Richman 1974; Neill 1975). Data for copepods are less rare but the danger of par
ticle size modification {see Peters 1984)
makes interpretation of some size classes
difficult. The distribution of the grazing rates
of copepods on different sized prey is either
more symmetrical (Vanderploeg 1981) than
that of cladocerans, or positively skewed
(Richman et al. 1980) rather than negatively
as it is for cladocerans. If the variation in
the grazing rate distributions of copepods
can be related to their body size, then it may
be possible to produce a single empirical
model for copepods and cladocerans through
the use ofdummy variables (Gujarati 1978).
This would yield a more general theory, de
scribing the variation of grazing rates for
crustaceans on prey items of different sizes.
The models presented here could also be
improved by incorporating the abundance
of prey in different size categories as inde
pendent variables. This would add infor
mation concerning the functional response
of zooplankton, which describes the varia
tion ofingestion rates in response to changes
in prey abundance (Holling 1959, 1965;
Schoener 1971; Murdoch and Oaten 1975;
Downing 1981). Unfortunately, Gliwicz
(1977) did not report such data for the feed
ing experiments with cladocerans so that
surrogate data had to be used instead. Add
ing prey concentration for various size
classes as independent variables may ac
count for some of the unexplained variance
seen by this approximation. Comparisons
should also be made with size selectivity of
individuals, since lumping of data from dif
ferent sized organisms could give rise to
some of the apparent size selectivity.
The synthesis of information about zoo
plankton feeding through the use of empir
ical relationships such as those presented
here should eventually allow quantitative
predictions of loss rates by algae of different
sizes. Tests of these predictions against new
observations ofgrazing rates on natural par
ticles can lead to the improvement of the
models. In addition, since these models use
the body size of zooplankton as an inde
pendent variable, shifts in the distribution
of loss rates could be predicted from ob
served changes in the size structure of zoo
plankton communities. With these models,
information from detailed studies offeeding
behavior could be used to make quantita
tive predictions about the role of zooplank
ton in the dynamics of phytoplankton com
munities.
Edward McCauley2
Department of Biology
McGill University
1205 Ave. Dr. Penfield
Montreal, Quebec H3A 1B1
2 Present address: Department of Biological Sci
ences, University of California, Santa Barbara 93106.
Notes
John A. Downing
Departement de Sciences Biologiques
Universite de Montreal
C.P. 6128, Succursale 'A'
Montreal, Quebec H3C 3J7
211
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1978. Relationship between phytoplankton cell
size and the rate of orthophosphate uptake: In situ
observations on an estuarine population. Mar. Biol.
45: 39-52.
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Submitted: 24 October 1983
Accepted: 5 July 1984