Limnol. Oceanogr., 38(l),
0 1993, by the American
1993, 1 12-127
Society of Limnology
and Oceanography,
Inc.
Ecosystem analysis based on biomass size distributions:
study of a plankton community in a large lake
A case
Ursula Gaedke
Limnologisches
Institut,
Universitat
Konstanz,
P.O. Box 5560, D-7750 Konstanz,
Germany
Abstract
The plankton biomass size distribution
and its seasonal changes were used to estimate seasonal fluctuations of the metabolic activity of the community and of the efficiency to transfer biomass to larger
sized organisms in a large and deep prealpine lake (Bodensee: Lake Constance). The efficiency of transfer
of biomass from small (e.g. autotrophic)
to larger (e.g. herbivorous)
organisms increased considerably
during the first half of the year and reached maximum values when daphnid densities were high. This
trend was attributed to the different generation times of the organisms involved in the food web. The
trophic transfer efficiency may depend on the predator-prey weight ratios, and the efficiency of growth
and exploitation
of the constituent organisms. The contribution
of these factors to the overall change of
the transfer efficiency was estimated from additional information
on the food-web structure. The results
derived from the size spectra agreed reasonably well with previous studies of single populations, suggesting
that biomass size distributions may substantially contribute to ecosystem analysis. The seasonal trend in
slopes of the size spectrum was related to predictions derived from conceptual models. Empirical results
from Lake Constance could be reconciled with those models accounting for seasonal changes of exploitation efficiency. Inference from the size spectra supported the hypothesis that natural assemblages of
pelagic bacteria are unlikely to attain the potential productivity
implied by allometric relationships.
Biomass size distributions provide a holistic
ecosystem description that facilitates ecosystem comparisons in time and space. Biomass
size distributions
may also provide a tool for
ecosystem analysis owing to the close relationships between body mass and metabolic
processes and between body mass and related
ecological properties of the organisms, especially in pelagic ecosystems (e.g. seasonal
variability,
type of nutrition).
Total biomass
tended to be approximately uniformly distributed over logarithmically
equally spaced size
classes in the pelagic zone of some large aquatic
environments (Sheldon et al. 1972, 1977; Witek and Krajewska-Soltys
1989; Gaedke
Acknowledgments
Data acquisition and the present study were performed
in Special Collaborative
Program (SFB) 248 “Cycling of
Matter in Lake Constance” supported by Deutsche Forschungsgemeinschaft and headed by M. M. Tilzer.
I thank the scientists (R. Berberovic, C. Braunwarth, R.
Eckmann, A. Giani, W. Geller, U. Kenter, H. Miiller, H.R. Pauli, A. Schweizer, M. Simon, D. Springmann, H.-H.
Stabel, U. Theurer, M. Tilzer, N. Wang, T. Weisse, and
S. Wiilfl) who developed the data base. Comments on the
manuscript were provided by Wolfgang Ebenhoh, Hans
Giide, Claudia Pahl-Wostl, John Lehman, and Walter
Geller who pointed out the possibility of comparing biomass and energy spectra. I thank Trevor Platt and an
anonymous referee for improving the content and style of
the manuscript.
1992a). Hence, a continuum of organisms exists with respect to body mass which fills the
potential niches defined by body mass and related parameters (e.g. generation times, turnover rates) within the size range of plankton
organisms.
Several theoretical approaches have been
developed to explain the striking regularity in
the distribution
of biomass with body mass.
Platt and Denman (1978) introduced a theoretical concept that considered the biomass flux
to larger organisms as a continuous process
rather than a transfer between discrete trophic
levels. Another approach, suggested by Sheldon et al. ( 1977) and Sprules (1988), is closely
related to common ecological concepts on energy transfer within food webs. This “discretestep” model is based on the concept of trophic
levels, where the biomass flow to larger sized
organisms is governed by distinct predatorprey relationships. A comparison of these and
other models was provided by Borgmann
(1987) who showed that all models gave similar results if they were based on the same assumptions.
The models rely on empirically established
allometric relationships between body weight
and metabolic processes, suggesting that biomass size spectra reveal an interplay between
physiological properties of individual
organ112
Biomass size distribution
113
isms and community structure. The slope of Platt and Denman 1978; Sheldon et al. 1977)
the spectrum indicates the efficiency of bio- - are of only limited value in explaining size
distributions that include bacteria for two reamass transfer to larger organisms. For example, a uniform distribution of biomass over all sons. First, they assume a biomass flux exclusize classes indicates that losses in transfer to sively from small to large organisms. However, the trophic structure of the plankton
larger organisms are compensated by higher
community at the lower end of the size range
P : B ratios of smaller organisms, implying longer energy residence times for the larger sized (i.e. in the range of autotrophs and bacteria)
appears to differ in principle from that in the
individuals.
On the basis of the scaling exporange of larger organisms for which the asnent of allometric relationships,
the relative
seasonal changes of the metabolic activity of sumption of a biomass flux toward larger orthe entire community or of its subgroups can ganisms is suitable. Pelagic bacteria live predominately on organic matter originating from
be estimated from biomass size distributions
and their seasonal variation (Platt et al. 1984). larger sized organisms, especially from phyA detailed analysis has been performed on toplankton (Simon and Tilzer 1987). Hence,
primary production enters and cycles in the
the seasonal dynamics of the biomass size distribution in a large and deep lake (Constance)
heterotrophic food web via two different pathways:. by grazing, which fits into the concept
that covered the entire size range of plankton
organisms from bacteria (1 O- I4 g C cell- I) to of a biomass flux up the spectrum, and by
large crustaceans (1 Od4 g C ind.- l). This analrelease of organic substances (e.g. exudation),
ysis confirmed that the simple relationship be- which implies transfer of organic matter to
tween body mass and biomass already estab- smaller organisms.
Second, the theoretical concepts mentioned
lished in marine systems also existed in a large
above rely on allometric equations. Allometric
freshwater ecosystem on a seasonal average
analysis has been well established for eutherian
(Gaedke 1992a). A potential mechanism provoking a regular biomass size distribution and mammals, supplemented with comprehensive
some life-history features of keystone species measurements for invertebrates and some data
causing deviations from this overall rule have on heterotrophic
eucaryotic unicells. Autobeen discussed elsewhere (Gaedke 19923). In trophs and procaryotes have rarely been inaddition, the ecologies of the major organisms
cluded in allometric relationships
on which
in this lake are well-known,
allowing one to theoretical approaches to biomass spectra are
relate seasonal changes in size distributions to based. The respiratory mass dependence among
the seasonal waxing and waning of their comsmall invertebrates likely follows that of all
ponent organisms and to compare the seasonal
living things. However this statement may not
variation of the metabolic activity derived from
hold consistently for intrinsic growth rates, esthe size spectra with previous production es- pecially among certain taxa (Banse 1982).
timates (Geller et al. 199 1).
Additional
difficulties may arise when apSeveral closely related questions are ad- plying allometric relationships to bacteria. One
dressed here. How do the metabolic activity
school of thought maintains that a large part
of the community and the trophic transfer ef- of bacteria is metabolically inert most of the
ficiencies as estimated from the biomass size time in pelagic ecosystems (e.g. Stevenson
distribution change during the season? Do these
1978; Glide 1989). Simon (1987) observed that
calculations agree with independent produconly a variable fraction of the bacterial cells
tion estimates and studies on population dyin Lake Constance assimilated amino acids.
namics? Can the current theoretical models be Cole et al. (1988) found a significant correlareconciled with the observed seasonal changes tion between bacterial production
and cell
of slopes of the size spectra? Model parameters
numbers (r2 = 0.63) in a cross-system commay change during the season. Are the re- parison including aquatic ecosystems with exquired parameter changes in accord with bitremely different productivity.
However, in
ological observations? Which seasonal changes Lake Constance, seasonal changes of bacterial
of the pelagic ecosystem are reflected in bioproduction correlated only weakly with those
mass size distributions?
of bacterial biomass parameters (Simon and
Current theories about biomass spectra (e.g. Tilzer 1987) and bacterial production fluctu-
114
Gaedke
ated 10 times more than cell numbers over the
entire year (Simon 1987). These and other
studies indicate that bacterial biomass and
weight-specific metabolic activity may not be
tightly coupled, although such coupling is implied in allometric analysis of populations and
biomass size spectra.
On the basis of these arguments, analysis of
observed plankton size spectra will be done
separately for the entire range of body mass
from bacteria to carnivorous crustaceans and
for a reduced size spectrum ranging from eucaryotic phytoplankton
(22 pg C cell-l) to
“herbivorous”
crustaceans (including omnivorous adult cyclopoids). The two largest size
classes formed by carnivorous crustaceans are
omitted for the sake of simplicity (see below).
Comparison with theoretical concepts
The present evaluations concentrate on seasonal changes of the slopes of straight lines
fitted to the size spectra. These slopes provide
the most suitable measure of biomass size distributions to investigate the correspondence of
observations
and theoretical
concepts and
contain information
on the transfer efficiency
along the spectrum. The intercepts of the fitted
lines vary seasonally as well, depending on the
slopes and the total plankton biomass which
is not further analyzed here. The ratio of biomasses in different size classes (which may represent different trophic levels) can be computed from the slope of a biomass spectrum
and vice versa. For example, an equal distribution of biomass over all size classes corresponds to a zero slope of a line fitted to a
Sheldon-type size spectrum (i.e. the biomass
per size class is displayed as a function of body
weight on a logarithmic scale, e.g. Sheldon et
al. 1972), and to a slope of - 1 of the normalized spectrum (Platt et al. 1984). In normalized spectra, an approximate measure corresponding to the abundance of organisms per
size class is displayed as a function of body
weight on a logarithmic scale (e.g. see Platt and
Denman 1978). Both measures-the
slope and
the biomass ratio-are
used interchangeably
for practical purposes.
The observed seasonal trends in slopes of
biomass size distributions
from Lake Constance will be compared to predictions derived
from the continuum model (Platt and Denman
1978) and the discrete-step model (Sheldon et
al. 1977; Sprules 1988). The continuum model
consists of allometric growth and loss functions derived from body-weight-dependent
turnover times and respiration rates, respectively. Both terms are density-independent.
Additionally,
detritus production was considered in the model, but turned out to be quantitatively unimportant
and is neglected here.
The model predicted that the biomass ratios,
Bj : Bi, of differently sized organisms with body
weight Wj and Wi follow the relationship
BJ
B,
-
Wj
‘-ltol
0w,
where b represents the scaling exponent and A
and (x the proportionally
coefficient of the allometric relationships of turnover time, T(W)
= Ati, and the individual respiration rate, R(w)
= ~ywl-~. Assuming parameter estimates for 6,
A, and a as given by Fenchel(l974),
the slope
of the normalized spectrum was predicted to
be - 1.22 if the component organisms were
heterotherms (b = 0.28, aA = 0.5) and -0.82
if they were unicells (b = 0.28, CUA= 0.1) (Platt
and Denman 1978). Recent investigations
generally confirmed the estimate of b given by
Fenchel (1974) or slightly lower values (b =
0.25, Peters 1983), but indicated that the unicell-multicell
division regarding a! and A may
not be consistent for all process rates (Moloney
and Field 1989). For example, planktonic organisms that take up dissolved nutrients from
solution (e.g. bacteria and phytoplankton)
may
have lower weight-specific
respiration rates
compared with either unicellular or multicellular heterotrophs that ingest particles.
The discrete-step model involves the same
basic assumptions as the continuum
model,
namely a uniform ratio of predator to prey size
(w, : w,) throughout the food web, allometric
relationships between body mass and weightspecific P: B ratios, and constant growth efficiency throughout the food web. Additionally,
the discrete-step model accounts for the efficiency of exploitation.
The growth efficiency,
K,, is defined as the ratio between production
and consumption. It is influenced by physiological processes (e.g. respiration), ration, and
food quality. The exploitation efficiency, C, is
defined as the fraction of prey production consumed by predators. It accounts for nonpredatory losses like sedimentation and depends
on species composition,
food-web structure,
and other nonphysiological
factors. Thus, the
Biomass size distribution
discrete-step model considers loss terms, reducing the transfer of biomass to larger organisms on two different levels of ecosystem organization.
I show that the seasonal trend in metabolic
activity as estimated from the biomass size
distribution
agrees with independent production estimates for the eucaryotic community.
The biomass size distributions indicate, in accord with previous field studies, an increase of
the combined growth and exploitation
efficiency in the eucaryotic plankton community
during spring development. Individual
body
mass proves a suitable ataxonomic attribute
to describe plankton spring succession.
Materials and methods
Lake Constance (Bodensee) is a large (476
km2), deep (zmax= 252 m), prealpine (47’50’N)
lake of warm-monomictic
character. It is presently undergoing reoligotrophication
and can
be characterized as meso-eutrophic.
The import of labile allochthonous
organic material
and the flow of matter from the benthic and
littoral community into the pelagic plankton
is considered to be small (Glide 1990a; Frenzel
pers. comm.).
Measurements of biomass size distributions-The present study was undertaken in
the Special Collaboration Program “Cycling of
Matter in Lake Constance.” During the 1987
growing season (23 March-16 November), a
large team of scientists measured the abundance of all known groups of organisms in the
pelagic community
(see Geller et al. 199 1;
Gaedke 1992a).
Sampling was done weekly (larger phytoplankton twice a week) at different depths at
a 147-m-deep sampling site in the northwestern part of the lake (Uberlingersee). All plankton organisms were assessed with microscopy
by different sampling and counting techniques
appropriate for the size and fragility of the
organisms. The counting volumes were adjusted to the numerical density of the respective organisms. The observed plankton abundances at the sampling site may have been
influenced considerably by changes of waterlayer thicknesses induced by internal seiches.
Observed abundances of strongly affected
plankton groups (bacteria, autotrophic picoplankton-APP,
heterotrophic flagellates, and
larger phytoplankton)
were corrected for this
effect (Gaedke and Schimmele 199 1).
115
Size frequency distributions
within the respective populations and their seasonal changes
were established for small organisms like bacteria, autotrophic picoplankton,
and heterotrophic flagellates. For medium-sized
organisms (larger phytoplankton,
ciliates, rotifers),
30-80 morphologically
different forms were
distinguished,
and size measurements were
carried out regularly for each taxon. Size distributions
of herbivorous
crustaceans were
measured from each sample with 2-5 size
classes for each species and converted to units
of dry weight with length-weight relationships
established for the lake. For the zooplanktivorous crustaceans, Bythotrephes longimanus
and Leptodora kindtii, ranges of body mass
were taken from the literature. Original measurements of body size were converted to units
of carbon with measurements from Lake Constance or from the literature. Some data on
size frequency distributions, vertical gradients
in abundance at greater depths, and conversion factors to units of C were not measured
in 1987 but in other years. Details on measurements and computation
of biomass size
spectra are given by Gaedke (1992a) and references cited therein.
period was divided into
The investigation
10 time intervals of unequal length for which
separate biomass size spectra were computed
to describe the seasonal changes in ecosystem
structure.
Estimating growth and exploitation eficiency and the metabolic activity from size spectra -The discrete-step model is used to estimate the combined growth and exploitation
efficiencies, K,C. The model can be summarized as follows (Sprules 1988). Production on
a higher trophic level (P2) was derived from
production at the next lower trophic level (P,)
by
P2 = P, K,C.
(1)
P/B = c, w-”
(2)
Using
where c1 is the constant of proportionality
of
the allometric relationship,
we can calculate
the biomass ratio of two adjacent trophic levels
(B2 : B,) as
KJ.
(3)
B, is defined as the biomass of a prey with
Gaedke
116
body weight wl, and B2 represents the biomass
of the corresponding predator with body weight
w2. The biomass ratio of predator and prey
(B2 : B,) depends on the size-dependent scaling exponent of the specific production rates
(b), on the step size between adjacent trophic
levels (w2/w1), and on the efficiencies of biomass transfer from one trophic level to the next
VGC).
KIC will be estimated according to Eq. 3
from the slope (a) of a straight line fitted to
the biomass size spectrum which reveals the
biomass ratio between adjacent trophic levels.
A line fitted to a Sheldon-type biomass size
distribution
presented on a log-log scale is
equivalent to a power law:
B(g) = c2Sa@)
(4)
Grazing pressure of all herbivores which comprise a size range of - 19 size classes (130 pg
C cell- L to 3 3 pg C ind. - I) concentrates on the
size range of small algae (up to -170-l 50 pg
C cell-‘) throughout the season (Knisely and
Geller 1986; Gaedke 1992b). Since most herbivores feed on about the same size range of
phytoplankton,
seasonal changes of predatorprey weight ratios for the reduced size spectrum (ranging from eucaryotic phytoplankton
to herbivorous crustaceans) can be estimated
from the seasonal changes of average body mass
of herbivores.
A weighted average body mass for herbivores ( wh) was calculated by weighting the mean
body weight in each size class (wJ by the total
herbivorous metabolism in that class (c3wi- bBi).
That is
with size classes
wh
dw) = bs(w~wo)
where c2 is a constant and w. the mean body
weight of the smallest size class. B(g) represents
the biomass and w the average body mass in
size class g. The mean body mass in two consecutive size classes differs by a factor of S (in
this study S = 2, see Gaedke 1992a). The biomass ratio between predator and prey can be
calculated from the slope of the spectrum as
a
B2
-
=
pMw2)-sw,)l
=
.
(5)
&
Combining
and rearranging Eq. 3 and 5 yields
(6)
In conclusion, calculation of the combined
growth and exploitation efficiency (K, c) relies
on the slope of the size spectrum (a), the scaling
exponent (b), and the predator-prey weight ratio (w, : w,). The value of a has been measured.
The value of b is taken as 0.25 (if not indicated
otherwise) based on a large body of empirical
evidence (e.g. Peters 1983). The predator-prey
weight ratios are difficult to assess experimentally for this system, owing to the small size
and the complex and variable feeding habits
of many component organisms. However, the
reduced size spectrum is mainly composed of
phytoplankton
and of ciliates, rotifers, and
herbivorous crustaceans that feed predominantly on the phytoplankton
(Starkweather
1980; Geller et al. 199 1; Miiller et al. 199 1).
= Z(WiC3WimbBi)IZ (C3WipbBi)
(7)
where Bi represents the herbivorous biomass
per size class. This method accounted for the
fact that small organisms have a higher metabolic activity per unit of biomass and time
than larger ones. It was assumed that the
weight-specific metabolic rates (e.g. the ingestion rate per unit of biomass and time) obey
an allometric relationship with the scaling exponent b = 0.25 and the constant of proportionality c3. The latter was assumed to be equal
for all herbivores and constant during the season. Its value could be set to 1 because the
metabolic activity was only used as a relative
weighting factor.
The metabolic activity (.A4) of the plankton
community or subgroups was calculated as
M=
BiWi-0.25
(8)
where Bi represents the biomass per size class.
The value of c, is presently not well established
for the small organisms included in the size
distribution.
It was not fixed to avoid the impression of unjustified accuracy. Hence, no
magnitude was attached to the metabolic activity of the community and only the relative
seasonal changes are presented in the figures.
A most probable number for c4 can be calculated from production
measurements
and
compared to literature data (see discussion).
CUE
Results
Biomass ratios and metabolic activity-The
slope of a line fitted to the normalized spectrum (seasonal average) was - 1.OO when the
Biomass size distribution
slope
I
body weight
Fig. 1. Seasonal trend of slopes of the reduced normalized size spectra (W) and of the average body weight (0) of
herbivores. As expected by theoretical concepts, large predator-prey
weight ratios (indicated by large herbivores)
correspond to less negative slopes which point to a higher trophic transfer efficiency (details given in text).
spectrum covered the entire range of body mass
from bacteria to carnivorous crustaceans and
was averaged over the water column (Gaedke
1992a). The slope was steepest in early spring
(- 1.16) and shallowest
in early summer
(- 0.94). The slope of the normalized spectrum
ranging from phytoplankton
to herbivorous
crustaceans is also significantly steeper in early
spring (- 1.23) than in early (-0.90) and late
(- 0.82) summer; the seasonal average is - 0.97
(Fig. 1).
A slope of - 1.16 of the normalized spectra
(spring situation of the entire spectrum) implies a biomass ratio between adjacent size
classes of 1 : 0.90. The corresponding biomass
ratio for a slope of -0.94 (early summer) is
1 : 1.04. Regarding the reduced spectrum covering autotrophs
and herbivores,
seasonal
changes are more pronounced. Biomass ratios
of adjacent size classes change significantly,
from 1 : 0.85 in early spring to 1 : 1.08 (1.13)
in early (late) summer.
Additionally,
biomass ratios between consecutive trophic levels can be estimated from
the slopes of the size spectra if the predatorprey weight ratios can be estimated and if a
constant width of the size ranges of prey and
predator is assumed. For the reduced spec-
trum, calculations (Eq. 7) suggest an increase
of the predator-prey weight ratios from 1 : 28
= 256 (early spring) to 1 : 212.6 = 6,200 (early
summer) (seeFig. I and Table I). The biomass
ratio of the two consecutive trophic levels of
the reduced spectrum (B2 : B,) increases by a
factor of 8.9 from early spring to early summer.
Such a change of biomass ratios between predator and prey suggests a considerable increase
of the efficiency of biomass transfer to larger
organisms during the first half of the year.
The seasonal patterns of eucaryotic plankton
biomass and metabolic activity differ remarkably, owing to the smaller size of the organisms
in spring. The metabolic activity as estimated
from the size spectrum (Eq. 8) reaches its maximum in spring (April-June)
suggesting that
during this period P: B ratios and fluxes are at
maximum in the eucaryotic community.
In
contrast, standing stocks are highest in summer (Fig. 2). The seasonal pattern of the metabolic activity remains similar if a scaling exponent of -0.15 is assumed, as hypothesized
by Joint and Pomroy (1988) and Joint (1991)
for marine phytoplankton.
The size distribution of the metabolic activity can be calculated from the biomass size
distribution
with Eq. 8 (Fig. 3A; seasonal av-
Gaedke
118
I
1
ol,d
A
M
J
J
A
S
0
r
Fig. 2. Seasonal patterns of eucaryotic plankton biomass (solid line) and of the corresponding metabolic activity (broken line) as estimated from biomass size distributions (Eq. 8).
erage). Maximum metabolic activity per size
class is exhibited by bacteria if the same allometric relationship is applied for the entire
size range. Under these conditions, the metabolic activity of the entire plankton community, including procaryotes, and its seasonal changes are strongly governed by bacteria.
If the metabolic activity of bacteria is reduced
by a factor of -0.05 or more as suggested (e.g.)
by a comparison of measurements of turnover
times of bacteria with other plankton organisms (seediscussion), autotrophs contribute the
highest metabolic
activity
per size class
throughout the season. The location of the
maximum changes seasonally within the size
range of the autotrophs. Most of the time, medium-sized cells contribute the largest share to
the overall autotrophic metabolism but during
some periods autotrophic picoplankton gains
considerable importance. These results are in
general agreement with size-fractionated measurements of primary production in the lake
(Schweizer pers. comm.). The metabolic activity of herbivores per size class generally decreases with body size according to expectations (see discussion).
Reconciliation of empirical results with theoretical concepts on biomass size spectra -The
following evaluations are restricted to the reduced spectrum because the theoretical concepts do not provide a suitable representation
of the procaryotic food-web structure. The flow
of matter from autotrophs to heterotrophs, estimated as a fraction of primary production,
was large compared to the rate of biomass
change. Total biomass increased on average
by 2% per day from late winter to early sum-
mer. The increase of total herbivorous biomass from minimum values in late April to
maximum values in July amounted to 2.8% of
the primary production as measured by 14C
fixation (Tilzer unpubl. data) during the corresponding period of time. Hence, although
primary production is not completely transferred to larger organisms, nondynamic models describing the flow of biomass to larger
organisms in an equilibrium
state can approximate the present case.
Regarding the continuum model of Platt and
Denman (197 8), no significant differences exist
between observed slopes and those predicted
by the model. Observed slopes range from
- 1.23 (early spring) to -0.82 (late summer)
and predicted ones from - 1.22 for systems
dominated by heterotherms to -0.82 for systems governed by unicellulars. About half of
the size range of the entire plankton size spectrum is dominated by unicellular organisms.
Bacteria contribute a substantial, but not dominant, fraction to the total plankton biomass.
The share of procaryotes (17-39%; seasonal
avg, 25%) fluctuates less than the contribution
of all unicells (3 l-89%; seasonal avg, 63%)
(Fig. 4).
However, the direction of the observed and
predicted seasonal trends in slopes is contradictory. During periods when unicellulars contribute a large fraction to the total plankton
biomass, slopes are more negative, and vice
versa (Figs. 1,4). This argument holds equally
well for both the entire and the reduced spectrum. In contrast, the model predicts shallower
slopes if the spectrum is derived from a community dominated by unicellular organisms
and steeper ones if heterotherms dominate.
This behavior would originate in the model if
the constants of proportionality
of allometric
relationships established for unicellulars are
smaller than for invertebrate heterotherms as
suggested by Fenchel(l974).
The potential differences between the proportionality
coefficients imply that unicellulars have lower metabolic costs than equally sized heterotherms.
The observed range of slopes also agrees with
the biomass ratios predicted by the discretestep model of Sprules (198 8) with biologically
plausible parameters. The different models
cannot be distinguished on this basis. Conformity of the observed and predicted seasonal
trend of slopes can be examined by investigating potential seasonal changes of model pa-
Biomass size distribution
-7
-5
-3
-1
1
3
5
7
9
11
13
15
17
bl,(bOdY
19 21
23
25
27
mass) (PS C)
r
energy quality
Fig. 3. A. Size distribution
of the metabolic activity calculated according to Eq. 8, averaged over the water column
and season (solid line). Broken line indicates metabolic activity if the bacterial activity is multiplied by a factor of 0.0 1
(details given in text). Diagonal line shows the relative change of turnover times with body weight, assuming a scaling
exponent of the allometric relationship of 0.25. The unit corresponds approximately
to days. Horizontal bar marks
the size range of autotrophic dominance (i.e. external energy input). B. Energy spectrum for an open system with an
energy source of medium quality. The arm to the left of the maximum represents the transition of energy to lower
quality states (decay). The arm to the right represents transfer to higher quality (e.g. larger organisms) (modified from
Odum 1983).
rameters. Relevant parameters are (see Eq. 3)
the predator-prey
weight ratio (w2 : w,), the
growth efficiency (K,), and the exploitation efficiency (C).
The biomass ratios of predator and prey (B2 :
B,), as indicated by the slopes of the spectra,
change 8.9 times from spring to early summer
(Fig. 1; see above). Such fluctuations cannot be
explained solely by seasonal changes of one of
the three parameters. If one sets b = 0.25,
average predator-prey size ratios would have
to vary by a factor of >6,000 to provoke an
120
Gaedke
“, 0.8
m”
E
0
06.
‘5
73
s
0
04.
2
m
.
32
0.2
0
Fig. 4. Seasonal changes of the relative contribution
of different-sized
organisms to the entire plankton biomass.
Size classes below the lower heavy line are dominated by procaryotes, size classes between the two heavy lines are
ruled by eucaryotic unicellulars, and size classes above the upper heavy line are dominated by metazoans.
increase of B2 : B1 by a factor of 8.9 (Eq. 3).
Such a variation appears unrealistically
high
when compared with measurements (Fig. 1).
To explain the observed seasonal changes of
B2 : B1 solely by changes of K1 or C requires
1 .o
0.8
0.6
0.4
0.2
‘*”
A ’ M ’ J ’ J ’ A ’ S ’ 0’
Fig. 5. Seasonal pattern of the relative importance
the metabolic activity of different groups of herbivores
computed from Eq. 8.
of
as
low values of proportional variability in spring
and high values in summer. The following results suggest that the observed change of size
distributions is likely to be the result of alterations of all three parameters.
The average body mass of herbivores increases from early spring to early summer by
a factor of 24 or 90 by late summer owing to
a succession in dominance from ciliates to rotifers and daphnids (Figs. 1, 5). The fluctuations of the average body mass of herbivores
are taken as indicators of the changes of the
dominant predator-prey weight ratio within the
reduced size spectrum because most herbivores feed predominantly
on similar-sized algae throughout the season, and proportional
changes between the predator-prey weight ratio and the average body mass of herbivores
are assumed. According to the theoretical concepts, large predator-prey weight ratios imply
less negative slopes of size spectra. Observed
seasonal changes of slopes and of average body
mass of herbivores covary as predicted by the
Biomass size distribution
models, especially during the first half of the
year. Steep slopes coincide with small herbivores and vice versa (Fig. 1). A change of the
predator-prey weight ratio by a factor of 24 (or
90) implies a change of the biomass ratio by
a factor of 2.2 (or 3.1) according to Eq. 3. The
increase in average body mass of herbivores
may, thus, account for a substantial fraction
of the increase in transfer efficiency during the
first half of the year. The remaining fraction is
attributable to an increase of the growth and
(or) exploitation
efficiencies--K,
and C from
spring to summer according to the discretestep model. This model prediction is at least
qualitatively
validated
by observations
of
plankton succession in the lake (see discus-
sion).
Estimation of K,C from the discrete-step
model- The combined growth and exploitation efficiency (K,C) and its seasonal changes
are estimated according to Eq. 6 from the slopes
of the biomass size spectra and the predatorprey size ratios, assuming an average cell size
of the predominantly
grazed algae of 32 pg C
and an allometric scaling exponent of 0.25 (Table 1). K,C increases continuously from early
spring until the clear-water phase and early
summer. It drops during the following period
of cold, rainy weather and increases again toward the end of summer. The inequality signs
in Table 1 originate from the presumption that
the system under consideration is not truly in
equilibrium.
For example, the flux of biomass
up the spectrum is somewhat underestimated
by an equilibrium model in early spring when
herbivorous biomass increases. In contrast,
trophic transfer efficiencies are probably overestimated during periods of high daphnid densities because high numbers of large herbivores
cannot be sustained for long.
Discussion
Biomass ratios and metabolic activity- Seasonal dynamics of the metabolic activity of the
eucaryotic plankton community, as estimated
from biomass size distributions and allometric
relationships (Eq. 8), correspond closely to respective community
production
estimates
provided by Geller et al. (199 1) (Fig. 6). After
low values in late winter, production and metabolic activity reached maximum values in
spring and an intermediate level in summer.
The production estimates were dominated by
121
Table 1. Estimates of the combined growth and exploitation efficiency (K, C) for different time intervals from
the slopes of the Sheldon-type biomass size spectra and
the predator-prey weight ratios, W, : w, (see Eq. 6).
Time
interval
Early spring
Early summer
Midsummer
Late summer
Seasonal avg
w, : w,
28
212.”
28.7
214.5
210.3
SIOPC
K,C
-0.23
0.10
0.03
0.18
0.03
>0.07
~0.28
0.26
CO.50
0.21
primary production,
although 14C measurements were reduced by 25% to account for
respiration and exudation. Production estimates of heterotrophs were close to net production or to net population growth, depending on the group of organisms.
The correlations between the production estimates and the estimates of the metabolic activity calculated with scaling exponents of 0.25
and 0.15 are highly significant (r2 = 0.82, P I
0.0003). The linkage is very close during the
first half of the year. Largest differences occur
during a short period of cold, rainy weather in
late July-early August and at the end of the
season. Deviations may be caused partially by
a varying degree of food limitation
or temperature preventing maximum growth rates
and by changes in the community composition
since it is possible that the coefficients of proportionality of the allometric relationship vary
among taxa and during the season (Banse 1982;
Moloney and Field 1989). The correlation between biomass and production or metabolic
activity is weak (r2 = 0.30, P 5 0.1; r2 = 0.14,
P I 0.3) (Figs. 2, 5).
If the coefficient of proportionality
(c4 in Eq.
8) is chosen so that the calculated metabolic
activity equals community production, values
of about 2 pg Co.25d-l are obtained for time
intervals of good correspondence (entire range
1.2-3.7). These values can be roughly compared to allometric
analyses of maximum
weight-specific production or respiration rates,
although this comparison is frequently complicated by the different slopes used in regression analysis. Moloney and Field ( 1989) fixed
the slope to -0.25 as they were computing
metabolic activity. They obtained proportionality coefficients of 1.7 and 14 pg Co.25d-l for
respiration rates of phytoplankton
and bacteria (data from Banse 1982) and particle-feeding heterotrophs.
122
Gaedke
A
M
J
J
A
S
0
Fig. 6. Comparison of the metabolic activity (broken
line) with direct production estimates (solid line, redrawn
from Geller et al. 199 1) of the eucaryotic plankton community.
The value of the coefficient c4 derived from
the size distribution
is close to the value obtained for phytoplankton
and low when compared to the value established for heterotrophs
by allometric analysis. The difference between
the value obtained by allometric analysis and
the one derived from the size distribution and
community production could be caused by four
factors. First, production estimates are likely
to reflect a value somewhere between net production and net population
growth but no
maximum growth rates. Second, community
production is dominated by phytoplankton.
Third, respiration frequently exceeds production according to other allometric analyses.
Fourth, the heterotrophs included in the analysis of Moloney and Field were generally much
larger than those in Lake Constance and their
relationship overestimated the respiration rates
of small heterotrophs by a factor of - 3-5.
The correlation
between production
and
metabolic activity of the entire plankton community is statistically significant (r2 = 0.54, P
I O.Ol), but weaker than for the eucaryotic
community.
The seasonal patterns do not
match: estimated metabolic activity of the entire community exhibits a peak in early summer with the biomass maximum, but not in
spring when community production is at its
maximum. In contrast, biomass (dominated
by eucaryotes) and metabolic activity (dominated by bacterial biomass) are more strongly
correlated in the entire community (r2 = 0.60,
P I 0.008) than in the eucaryotic community
alone.
These findings support the idea that in vivo
bacterial metabolism does not obey allometric
rules established for larger sized organisms.
Bacterial production was estimated to amount
to at most 30% of measured primary production (Giide 1990a,b). However, computing the
metabolic activity from biomass size distributions results in a bacterial contribution
of
66-90% (seasonal avg, 80%) to total community activity and in a ratio of metabolic activity
of autotrophs to bacteria of 20-45%. These
values appear unrealistic in view of empirical
results and the consideration of energy conservation (e.g. Strayer 1988), especially if the
presumably low growth efficiency of bacteria
is taken into account (Giide 1990a). Measurements by Joint (199 1) in the Celtic Sea also
indicated that natural assemblages of bacteria
were unlikely to attain the potential productivity suggested from an allometric relationship established for phytoplankton.
Present results thus suggest that the metabolic activity
as estimated from biomass size distributions
provides a useful indicator for seasonal changes
of eucaryotic community production and P : B
ratios.
The size distribution of the metabolic activity can be compared to predictions derived
from an approach describing the flow of matter
and energy in ecosystems (and other open systems) (Odum 1983) that is more general than
the theoretical concepts on size spectra considered so far. Odum’s (1983) approach considered energy distributions where large flows
of low quality energy are transformed into and
support smaller and smaller flows of higher
and higher quality types of energy. The energy
distributions
are represented graphically by
energy spectra in which the quantity of energy
flow is plotted as a function of the energy quality (Fig. 3B).
To compare the predictions of this concept
with findings from the plankton ecosystem in
Lake Constance, we relate such energy spectra
to the size spectrum of metabolic activity of
the plankton, based on Odum’s concept of
“embodied energy.” He suggested that biomass formed by large organisms (i.e. predators) has a higher energy quality than the biomass of small organisms (i.e. prey organisms).
In the present context, the term energy quality
can be interpreted to mean the population biomass of small organisms is differently packaged than that of large organisms, i.e. the aggregation of biomass differs.
Biomass size distribution
Regarding the entire size range of pelagic
organisms in Lake Constance, it is reasonable
to assume that the trophic level of constituent
organisms increases roughly with body weight
(e.g. Borgmann 1982; Gaedke 19923). Transferring biomass from one trophic level to the
next (i.e. increasing the aggregation of biomass) requires a considerable amount of energy. Thus, in the present context, energy quality represents
a measure
of biomass
aggregation, and one criterion for defining it is
the amount of energy (e.g. primary production)
required to build up a certain amount of its
biomass. The energy quality of bacterial biomass can be categorized as low from the viewpoint of larger grazers, owing to the small size
of bacteria. In conclusion, body weight provides a suitable indicator of the energy quality
as defined by Odum, and, in contrast to the
concepts previously mentioned, this approach
is also applicable to the size range of organisms
smaller than autotrophs (e.g. bacteria). The
quantity of energy flow at each level of energy
quality can be estimated from the size distribution of the metabolic activity.
Odum postulated, for obvious reasons, that
values of energy flow in the range of the energy
quality of the incoming energy source would
be maximal and decrease exponentially
from
the maximum in both directions if the graph
of the energy distribution
included the range
of energy quality below that of the incoming
energy source (Fig. 3B). A comparison of the
observed and predicted location of the maximum metabolic activity per size class points
again to pronounced overestimation
of the
bacterial activity by allometric relationships.
This statement is likely to hold although, in
contrast to the energy flow model of Odum,
bacteria get a considerable amount of energy
from organisms larger than autotrophs, and
bacterial biomass is concentrated in three size
classes in contrast to (e.g.) the autotrophs which
spread over 13 size classes. These two factors
may somewhat enlarge the bacterial biomass
and metabolic activity per size class compared
to other groups of organisms. Reducing bacterial metabolic activity in each size class by
a constant factor may be a conservative simplification because large bacteria are regarded
as more active than very small ones.
In conclusion, the size distribution of energy
flows in the planktonic ecosystem of Lake Con-
123
stance meets general expectations derived for
open systems if a positive correlation between
energy quality and body weight is assumed and
if bacterial metabolic activity is calculated from
production estimates but not from allometric
relationships.
Reconciliation of empirical results with theoretical concepts-The assumption of proximate steady state conditions for the different
time intervals is a reasonable approximation
for the computation
of transfer efficiencies,
considering the ratio between biomass changes
and fluxes and the accuracy of the other parameters. The subdivision of the season into
10 time intervals allows us to track the major
seasonal changes of KIC because the rate of
change of the processes determining K,C is
most likely influenced by the generation times
of the crustaceans. However, to gain a deeper
understanding of the functional processes underlying the changes of the biomass size distribution, dynamic models will be required that
describe the spring development of the size
spectra as a wavelike instability moving from
primary producers to larger organisms. The
first general models of this kind were suggested
by Silver-t and Platt (1978, 1980).
The continuum model of Platt and Denman
( 1978) did not reproduce the observed seasonal trend, suggesting that a significant feature
was omitted. The model described the trophic
energy flow without specifying trophic levels
of the constituent organisms. A shortcoming
of this appealing concept was that nonpredatory losses of prey production and density-dependent effects were ignored. The model did
not admit the seasonal fluctuations in foodweb structure that could lead to a fluctuating
degree of utilization of prey production by the
next trophic level. The only model parameters
that potentially changed seasonally were influenced by the relative share of unicellulars and
metazoan plankton. Physiological differences
between these groups might affect the slope.
The observed trend in the relative contribution
of unicells and multicells, however, would promote a trend in slopes opposite to the one
observed. Hence, this mechanism appears to
be less important for the slope of the size spectrum (i.e. the trophic transfer efficiency).
In contrast, the discrete-step model (Sheldon et al. 1977; Sprules 1988) could reproduce
the seasonal trend of slopes with parameter
124
Gaedke
combinations which vary seasonally in a way
consistent with observations (see below). This
type of model involved ambiguities imposed
by generalizations about trophic levels in complex food webs. The analysis of the reduced
size spectrum was based on the assumption
that it covered only two trophic levels, here
called autotrophs and herbivores. Classifying
all ciliates, rotifers, and crustaceans (except
Leptodora and Bythotrephes) as herbivorous is
a simplification.
However, phytoplankton
is
the dominant food source of these organisms
(Pourriot 1977; Starkweather 1980; Knisely
and Geller 1986; Geller et al. 199 1; Miiller et
al. 1991). Furthermore, feeding on organisms
other than autotrophs (e.g. heterotrophic nanoflagellates) does not affect estimation of KIC
as long as the number of trophic levels and the
approximate
predator-prey
weight ratio remain unchanged. Species diversity and most
probably the importance of omnivory increases in summer (see below). The seasonal variability of K, C may account for density-dependent, nonlinear
processes in this model
approach. Empirical results from Lake Constance can be reconciled with the current theoretical concepts on biomass size distributions
only if the models account for nonpredatory
loss terms caused by incomplete utilization of
production of small organisms by larger ones.
Accuracy of estimates ojK,C- Computation
of the combined growth and exploitation
efficiency (K,C) from Eq. 6 involved three different parameters: the slope of the size spectrum (a), the exponent of the allometric
relationship (b), and the predator-prey weight
ratio (w2 : w,). The parameters have associated
errors which, if cumulative, might render the
absolute estimates of KIC meaningless. The
seasonal trend can be expected to be less sensitive.
The breadth of the confidence intervals associated with a was relatively small and has
been discussed by Gaedke (1992a). A large
body of experimental evidence covering almost all taxonomical groups suggested values
for b around 0.25 (e.g. Peters 1983). However,
occasionally other values have been found and
evidence for very small organisms is still scarce.
A value of 0.25 implies a doubling of the turnover time if the weight of the organisms increases by a factor of 24 = 16, i.e. with every
fourth size class (Fig. 3A). The suitability of
this assumption for the plankton community
of the lake can be checked with various field
measurements that allow estimates of turnover
times for differently sized plankton organisms.
The generation times of the dominant cladocerans (daphnids and Bosmina; body wt, l40 pg C) were in the range of 1 l-47 d, whereas
copepods had somewhat longer generation
times (37-84 d) (Geller 1986). Calculations of
the mean turnover time of the daphnid population yielded 1O-2 1 d (Geller 198 5), partially
ignoring the effect of food limitation
which
plays a role in summer.
The turnover times of phytoplankton can be
estimated from measurements of primary production ( 14C incorporation,
Tilzer et al. 199 1).
For the entire phytoplankton community (size
range, 0.06-4,OOO pg C) turnover times were
- 1.7 d assuming that 25% of the originally
fixed C was lost by respiration and exudation.
Turnover times of autotrophic picoplankton
(size range, -0.06-0.5
pg C) in the upper 10
m of the water fluctuated between 0.2 and 0.7
d during the season (estimated from the frequency of dividing
cells, Schweizer pers.
comm.). A comparison of the turnover times
of crustaceans and autotrophic picoplankton
suggests values for the scaling exponent b between 0.20 and 0.27. In conclusion, no contradictions arise between the assumption of b
= 0.25 and evidence from field measurements
(excluding bacteria).
The extrapolation of the allometric relationship to the size range of bacteria (- 15 fg C
cell-l) yields turnover rates of -0.15 d (3-4
h); such growth rates can be achieved under
laboratory conditions (Neidhardt et al. 1990).
For the pelagic zone of the lake, however, measurements of turnover rates were in the range
of 340 d (Glide et al. 1985; Glide 1986,199Ob;
Simon 1988, pers. comm.). Hence, observed
bacterial R-B ratios were considerably lower
than those of phytoplankton
and were at most
one or a few percent of those expected by the
allometric relationship. The low growth rates
of heterotrophic bacteria in vivo may be attributed to resource limitation (e.g. Glide 1989).
The final caveat involved in calculating K, C
concerns the estimation of the average body
mass of autotrophs and heterotrophs to estimate w, : wl. Numerous studies on food preferences are available
for the dominating
daphnids but not for ciliates and rotifers, which
prevents computation of exact predator-prey
weight ratios for individual species under nat-
125
Biomass size distribution
ural conditions. Assuming a constant average
body mass of the palatable fraction of the autotrophs during the season may have contributed to overestimation of K1 C in late summer.
However, calculations of KIC are more sensitive to errors involved in estimates of the
slope (a) and the scaling exponent (b) than of
w2 : w, owing to the nonlinearity of Eq. 6. The
three parameters were altered within a biologically reasonable range to illustrate the sensitivity of KIC to potential errors (Table 2).
Separate impact of KI and C-The separate
impact of KI and Con the seasonal fluctuations
of KIC can be analyzed with a quantitative
relationship between K1 and w2 : w1 (Borgmann
1982) describing a decrease of .the growth efficiency with increasing predator-prey weight
ratios:
log(K,) = --e log(w,lw,)
or rewritten
K, = (w~/w~)-~
(9)
where E is particle-size-conversion
efficiency.
Some measurements, mainly on carnivorous
zooplankton, indicated values in the range of
-0.17-0.25
for E. On the basis of this relationship, Eq. 6 can be written as
c = (W2/Wl)a-b+‘.
(10)
Equation 10 provides a simple way to estimate the exploitation
efficiency C from the
slope of the biomass size distribution,
provided that the parameters are known with sufficient reliability. This condition may not yet be
fulfilled, especially for E, which precluded a
separate computation of C in Table 1. However, assuming a decrease of K, solely with
increasing values of w2 : w, (i.e. E > 0) already
suggests that C changes seasonally more than
KI C because large predator-prey weight ratios
(i.e. low K,) coincide with high estimates of
K, C and vice versa.
Seasonal analysis of size distributions and of
&C-The
seasonal analysis of the biomass size
distributions and transfer efficiencies allows a
holistic description of the seasonal plankton
development from an alternative point of view
that can be compared with results from comprehensive field studies on the ecologies of individual groups of organisms from 1987 and
subsequent years. The size spectra indicate low
exploitation efficiencies in spring that may be
Table 2. Examples illustrating
estimate of K,C against potential
parameter estimates (see Eq. 6).
w* : w,
Slope
Exponent
K,C
210.3
0.03
0.03
0.03
-0.01
0.07
0.07
0.25
0.25
0.25
0.25
0.25
0.20
0.21
0.18
0.24
0.16
0.28
0.43
-0.01
0.30
0.08
211.3
29.3
210.3
210.3
29.3
211.3
the sensitivity
errors involved
of the
in the
Remarks
Standard (seasonal avg)
W, : W, large
w2: w, small
Low value for the slope
High value for the slope
Extreme case, all
parameters at an
upper bound
Extreme case, all
parameters at a
lower bound
attributed to differences in the generation times
of the organisms involved in the food web.
They prevent simultaneous development
of
predator and prey, and the high production of
small organisms in early spring is not efficiently used by larger ones with longer generation
times because most large organisms are not yet
present in sufficiently high numbers. Previous
analyses of plankton dynamics support this
hypothesis and confirm the seasonal trend of
K, C qualitatively.
According to these studies, individual body
size proves a powerful ataxonomic attribute to
predict spring succession of different plankton
groups. Early spring provided excellent growth
conditions for primary producers and small,
fast-growing algae rapidly built up high biomass concentrations (Tilzer and Beese 1988).
They formed a high-quality
food source for
herbivorous ciliates, rotifers, and crustaceans.
To exploit this resource efficiently, herbivores
had to develop simultaneously with the algae.
However, the larger body mass of herbivores
as compared to algae implied longer generation
times for herbivores. The slower reaction rate
of the consumers resulted in a time-lag between the build-up of algal and herbivorous
biomass. The time lag in the increase of biomass of the different groups of herbivores,
ranging over five orders of magnitude in body
weight, was strongly correlated with body mass
(Fig. 5, but see also Gaedke 1992b).
Small algivorous ciliates (e.g. Pseudobalanion planctonicum) were the first to react almost
simultaneously
to the algal blooms (Miiller
199 1; Miiller et al. 199 1). They were most likely not food limited during this period (Miiller
126
Gaedke
et al. 199 1). The high concentrations of edible
algae combined with low densities of herbivores pointed to low exploitation
efficiencies
between autotrophs and (small) herbivores and
the absence of a tight coupling between adjacent trophic levels. During an early spring
bloom in 198 8, an equal share of - 14% of the
primary production was used by ciliates and
metazoan zooplankton (i.e. rotifers and crustaceans) respectively (Weisse et al. 1990). Additionally,
predation on ciliates can be assumed to be low in spring because their
predators still occurred in low numbers, implying a low efficiency of biomass transfer to
larger organisms. Furthermore, due to the high
food supply, ingestion of large rations was likely to occur, indicating low growth efficiencies
(Dickie et al. 1987).
For rotifers, processes similar to those described for ciliates can be postulated during
spring development,
except for their longer
response time. Rotifers occurred in very high
numbers at the end of the spring bloom in 19 8 7
and most likely were responsible for the subsequent clear-water phase (Geller et al. 199 1)
which was relatively weakly expressed when
compared to other years. Daphnids played a
minor role in spring development
in 1987
(Fig. 5).
Around the clear-water phase, food availability for algivorous ciliates was low and the
grazing impact by larger zooplankton
increased (Miiller et al. 199 1). Hence, it can be
assumed that K, increased and that the coupling between trophic levels became tighter,
implying a higher value of C. The shallow
slopes of the size spectrum in July and September-October
(i.e. high K,C) are mainly
caused by pronounced maxima of daphnids
(Gaedke 1992a,b). This observation agrees with
the idea that Daphnia transfers pica- and
nanoplankton production to larger organisms
with high efficiency (e.g. Stockner and Porter
1988).
The sudden onset of high primary production in spring thus provoked a pronounced disequilibrium
in the food web, comprising differently sized organisms with different reaction
rates and low values of K,C. The reaction rate
of the system to balance this pulse depended
mainly on the time required by the largest herbivores to build up their populations.
In summer. changes in community
com-
position are thought to be more strongly influenced by nonlinear biological interactions than
by external perturbations, and species diversity and diversity of feeding types are at their
maximum (Sommer et al. 1986; Sommer 1987;
Tilzer and Beese 1988; Miiller et al. 199 1). The
relatively large discrepancies between measurements and model predictions and the extremely high estimate of K,C in late summer
(Figs. 1, 6) can be taken as an indication that
the main features of system behavior are less
well described by the simple discrete-step
model during this period.
The present study suggests that the analysis
of biomass size distributions provides holistic
ecosystem descriptions and a promising tool
to investigate standing stocks and fluxes in
complex pelagic food webs.
References
BANSE, K. 1982. Mass-scaled rates of respiration and
intrinsic growth in very small invertebrates. Mar. Ecol.
Prog. Ser. 9: 281-297.
BORGMANN, U. 1982. Particle-size-conversion
efficiency
and total animal production in pelagic ecosystems.
Can. J. Fish. Aquat. Sci. 39: 668-674.
-.
1987. Models of the slope of, and biomass flow
up, the biomass size spectrum. Can. J. Fish. Aquat.
Sci. 44(suppl. 2): 136-140.
COLE, J.J.,S. FINDLAY,AND M. L. PACE. 1988. Bacterial
production in fresh and saltwater ecosystems: A crosssystem overview. Mar. Ecol. Prog. Ser. 43: I-10.
DICIUE, L.M.,S.R.
KERR, AND P.R. BOUDREAU. 1987.
Size-dependent processes underlying regularities in
ecosystem structure. Ecol. Monogr. 57: 233-250.
FENCHEL, T. 1974. Intrinsic rate of natural increase: The
relationship with body size. Oecologia 14: 317-326.
GAEDKE, U. 1992a. The size distribution
of plankton
biomass in a large lake and its seasonal variability.
Limnol. Oceanogr. 37: 1202-l 220.
-.
1992b. Identifying ecosystem properties: A case
study using plankton biomass size distributions. Ecol.
Model. 63: 277-298.
-,
AND M. SCHIMMELE. 199 1. Internal seiches in
Lake Constance: Influence on plankton abundance at
a fixed sampling site. J. Plankton Res. 13: 743-754.
GELLER, W. 1985. Production, food utilization and losses
of two coexisting, ecologically different Daphnia species. Ergeb. Limnol, 21: 67-79.
1986. Diurnal vertical migration of zooplankton
-.
in a temperate great lake (L. Constance): A starvation
avoidance mechanism? Arch. Hydrobiol.
Suppl. 74,
p. l-60.
-,
AND OTHERS. 199 1. Relations among the components of autotrophic
and heterotrophic
plankton
during the seasonal cycle 1987 in Lake Constance.
Int. Ver. Theor. Angew. Limnol. Verh. 24: 831-836.
G~IJDE, H. 1986. Loss processes influencing growth of
planktonic bacterial populations in Lake Constance.
J. Plankton Res. 8: 795-810.
Biomass size distribution
127
SILVERT, W., AND T. PLATT. 1978. Energy flux in the
. 1989. The role of grazing on bacteria in plankton
pelagic ecosystem: A time-dependent equation. Limsuccession, p. 337-364. In U. Sommer [cd.], Planknol. Oceanogr. 23: 8 13-8 16.
ton ecology: Succession in plankton communities.
-,
AND -.
1980. Dynamic energy-flow model
Springer.
of the particle size distribution in pelagic ecosystems.
1990a. Bacterial production and the flow of orAm. Sot. Limnol. Oceanogr. Spec. Symp. 3: 754-763.
ganic matter in Lake Constance, p. 489-502. Zn M.
New England.
M. Tilzer and C. Serruya [eds.], Large lakes-ecologSIMON, M. 1987. Biomass and production of small and
ical structure and function. Springer.
large free-living and attached bacteria in Lake Con-.
1990b. Bacterial net production
approaching
stance. Limnol. Oceanogr. 32: 59 l-607.
zero-a
frequent phenomenon in pelagic environ_
ments? Ergeb. Limnol. 34: 165-169.
-.
1988. Growth characteristics of small and large
free-living and attached bacteria in Lake Constance.
-,
B. HAIBEL, AND H. MILLER. 1985. Development
Microb. Ecol. 15: 151-163.
of planktonic bacterial populations in a water column
of Lake Constance (Bodensee-Obersee).
Arch. HyAND M. M. TILZER. 1987. Bacterial response to
seasonal changes in primary production and phytodrobiol. 105: 59-77.
JOINT, I. R. 199 1. The allometric determination
of peplankton biomass in Lake Constance. J. Plankton Res.
9: 535-552.
lagic production rates. J. Plankton Res. 13(suppl.):
SOMMER, U. 1987. Factors controlling the seasonal vari69-8 1.
ation in phytoplankton
species composition-a
case
-,
AND A. J. POMROY. 1988. Allometric estimation
study for a deep, nutrient rich lake (Lake Constance).
of the productivity of phytoplankton assemblages. Mar.
Prog. Phycol. Res. 5: 123-178.
Ecol. Prog. Ser. 47: 161-168.
-,
Z. M. GLIWICZ, W. LAMPERT, AND A. DUNCAN.
KNISELY, K., AND W. GELLER. 1986. Selective feeding of
1986. The PEG-model
of seasonal succession of
four zooplankton species on natural lake phytoplankplanktonic events in fresh waters. Arch. Hydrobiol.
ton. Oecologia 69: 86-94.
106: 433-47 1.
MOLONEY, C. L., AND J. G. FIELD. 1989. General allometric equations for rates of nutrient uptake, ingesSPRULES,W. G. 1988. Effects of trophic interactions on
the shape of pelagic size spectra. Int. Ver. Theor. Antion, and respiration in plankton organisms. Limnol.
gew. Limnol. Verh. 23: 234-240.
Oceanogr. 34: 1290-l 299.
STARKWEATHER, P. L. 1980. Aspects of the feeding beMUELLER, H. 199 1. Pseudobalanion planctonicum (Ciliophora, Prostomatida):
Ecological significance of an
havior and trophic ecology of suspension-feeding rotifers. Hydrobiologia
73: 63-72.
algivorous nanociliate in a deep meso-eutrophic lake.
J. Plankton Res. 13: 247-262.
STEVENSON, L. H. 1978. A case for bacterial dormancy
-,
A. SCH~NE, R. M. PINTO-C• ELHO, A. SCHWEIZE~,
in aquatic systems. Microb. Ecol. 4: 127-133.
AND T. WEISSE. 199 1. Seasonal succession of ciliates
STOCKNER, J. G., AND K. G. PORTER. 1988. Microbial
in Lake Constance. Microb. Ecol. 21: 119-138.
food webs in freshwater planktonic ecosystems, p. 69NEIDHARDT, F. C., J. L. INGRAHAM, AND M. SCHAECHTER.
83. Zn S. R. Carpenter [ed.], Complex interactions in
1990. Physiology of the bacterial cell. A molecular
lake communities. Springer.
approach. Sinauer.
STRAYER, D. 1988. On the limits to secondary producODUM, H. T. 1983. Systems ecology: An introduction.
tion. Limnol. Oceanogr. 33: 12 17-l 220.
Wiley.
TILZER, M. M., AND B. BEESE. 1988. The seasonal proPETERS,R. H. 1983. The ecological implications of body
ductivity cycle of phytoplankton
and controlling facsize. Cambridge.
tors in Lake Constance. Schwciz. Z. Hydrol. 50: lPLATT, T., AND K. DENMAN. 1978. The structure of pe39.
lagic marine ecosystems. Rapp. P.-V. Reun. Cons. Int.
-,
U. GAEDKE, A. SCHWEIZER,B. BEESE,AND T. WIESExplor. Mer 173: 60-65.
ER. 199 1. Interannual variability
of phytoplankton
-,
M. LEWIS, AND R. GEIDER. 1984. Thermodyproductivity
and related parameters in Lake Connamics of the pelagic ecosystem: Elementary closure
stance: No response to decreased phosphorus loading?
conditions for biological production in the open ocean,
J. Plankton Res. 13: 755-777.
p. 49-84. Zn Flows of energy and material in marine
WEISSE,T., AND OTHERS. 1990. Response ofthe microbial
ecosystems. NATO Conf. Ser. 4, Mar. Sci. V. 13.
loop to the phytoplankton
spring bloom in a large
Plenum.
prealpine lake. Limnol. Oceanogr. 35: 78 l-794.
POURRIOT, R. 1977. Food and feeding habits of Rotifera.
WITEK, Z., AND A. KRAJEWSKA-SOLTYS. 1989. Some exErgeb. Limnol, 8: 243-260.
amples of the epipelagic plankton size structure in
SHELDON, R. W., A. PRAKASH, AND W. H. SUTCLIFFE, JR.
high latitude oceans. J. Plankton Res. 11: 1143-l 155.
1972. The size distribution of particles in the ocean.
Limnol. Oceanogr. 17: 327-340.
-,
W. H. SUTCLIFFE, AND M. A. PAFUNJAPE. 1977.
Submitted: 6 November 1991
Structure of pelagic food chains and relationship beAccepted: 3 June 1992
tween plankton and fish production. J. Fish. Res. Bd.
Revised: 11 August 1992
Can. 34: 2344-2353.
-