Lake Kinneret: A seasonal model for carbon flux through ......Lake Kinneret: A seasonal model for carbon flux through the planktonic biota Lewi Stone and Tom Berman Yigal Allon Kinneret

Limnol. Oceanogr., 38(8), 1993, 1680-1695 Q 1993, by the American Society of Limnology and Oceanography, Inc.

Lake Kinneret: A seasonal model for carbon flux through the planktonic biota

Lewi Stone and Tom Berman Yigal Allon Kinneret Limnological Laboratory, Israel Oceanographic & Limnological Research, P.O. Box 345, Tiberias 14102, Israel

Richard Bonner, Stephen Barry, and Scott W. Weeks Faculty of Environmental Scicnccs, Griffith University, Nathan, Queensland 4111, Australia

Abstract Carbon standing stock distribution in the cuphotic zone of Lake Kinneret and the immediate fate of

primary-produced carbon arc very different during late winter-early spring (with the occurrence of the annual dinollagellate bloom) than they are in late summer (when nanophytoplankton are the dominant primary producers). We used a linear programming model to construct balanced carbon flow charts for these two seasons based on measured primary productivity; on carbon standing stocks of algae, bacteria, flagellates, ciliates, cladocerans, rotifers, and fish; and on data on turnover times, respiration, and grazing rates obtained in 1989. The charts were compiled to fit as closely as possible all obscrvcd and inferred estimates of carbon fluxes while simultaneously ensuring that mass balance and key biological constraints were maintained for each of the 10 compartments representing the principal biota of the Kinneret food web. We used the model to examine the extent to which individual intercompartmental flux rates were free to vary while the mass-balance and biological constraints were enforced. The model was also capable of generating different yet feasible flow-chart scenarios; it thus proved useful in suggesting alternative hypotheses concerning the role of the microbial food web in the euphotic waters of Lake Kinneret.

A major aim of both theoretical and applied aquatic research has long been to understand the patterns of flow of carbon and other elc- ments through the pelagic biota in lakes and seas. Within the last decade it has become in- creasingly evident that the complex communities of microbial organisms in the pelagic zone in both marine and freshwater environments play a key role in processing and trans- ferring carbon, nitrogen, and phosphorus from primary producers to metazoan plankton and fish (Pomeroy 1974; Azam et al. 1983; Berman 1990). Much debate has been generated concerning the function of microbial food webs as

Acknowledgments WC are indebted to B. Azoulai, K. D. Hambright, M.

Gophen, G. Nahum, 0. Hadas, U. Pollinghcr, Y. 2. Ya- cobi, and T. Zohary for data, discussion, and dissent. We are grateful for the comments of two rcvicwcrs that enabled us to improve and revise the original version of the paper.

This work was supported in part by grant 87-00006 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, by a grant from the Basic Re- search Foundation of the Israel Academy of Sciences and Humanities and by the Ian Potter Foundation.

A contribution of Israel Oceanographic and Limnolog- ical Research.

net sinks or sources in aquatic systems (Duck- low et al. 1986; Sherr et al. 1987) because the extent to which carbon fixed in microbial biomass passes to other trophic levels rarely has been quantified. Nevertheless, there is some evidence that protozoans may be important food sources for mctazoan zooplankton (Gif- ford 199 1; Stoecker and McDowell Capuzzo 1990) and recently Carrick et al. (199 1) suggested that in Lake Michigan protozoan as- semblages ranging in size from 3 to 20 pm were equally as important as phytoplankton for zooplankton nutrition. These investigators calculated that - 15% of the bacterial production was passed to macrozooplankton by a simple two-step coupling.

Using the well-known mathematical technique of linear programming, we have devcl- oped a computerized model which takes into account the activities of the microbial biota and helps quantify carbon flux through major groups of organisms in aquatic ecosystems. The model is designed to generate flow charts with compartments that satisfy mass-balance laws and basic biological’ constraints. It also provides reasonable estimates for poorly quantified flows. Furthermore, the model can be used to produce quite different food-web charts, each

1680

Carbon flux model 1681

of which can offer a plausible solution within the obscrvcd and estimated measurements of the system. This ability to generate alternative solutions allows us to examine alternative hypotheses concerning a particular food-web structure.

As an initial exercise, we have tested the model by applying it to the quantification of carbon flux through major groups of organisms in the euphotic zone of Lake Kinneret (Israel). The extensive monitoring and research program that has been carried out on the lake since 1969 enabled us to obtain experimentally determined data for many of the relevant param- eters, including measured values of standing stocks of phytoplankton, zooplankton (cladocera, copepods, and rotifers), bacteria, protozoans (flagellates, ciliates), and fish. Data for phytoplankton and bacterial carbon uptake, respiration, release or excretion of particulate or dissolved organic carbon (POC and DOC), and turnover rates of the various biotic compartments were either measured or taken from the literature. We used these data and known biological constraints as inputs to the model to construct plausible flow charts depicting a simplified food web in the cuphotic zone of the lake at two different seasons. Our results indicate that this technique may have considerable potential for the study and delineation of carbon flows in aquatic systems.

Methods Model structure-In a previous study, Scr-

ruya ct al. (1980) attempted to quantify the carbon flows in the pelagic waters of Lake Kin- neret, taking as their example a year (1972) with high standing stocks of the annual bloom- forming dinoflagellate, Peridinium, and a year ( 1975) with relatively low algal biomass. Al- though some of the main assumptions of that study remain valid, others must bc revised in light of new knowledge. A major amendment has been made in the present model by including the components of the microbial food web (Azam et al. 1983), thus emphasizing the potential role of bacteria and protozoans as modulators of pelagic carbon flux.

We have applied our model to depict two seasons in the euphotic zone (depth, -20 m) of the lake representing different limnological states (Scrruya et al. 1980; Berman et al. 1992) that recur from year to year (Serruya 1978):

late winter-early spring (March-April 1989), the peak of the annual dinoflagellate bloom; and late summer (August-Septcmbcr 1989), characterized by minimal levels of algal biomass consisting mainly of nanoplanktonic chlorophytes. Our analysis examined the lake for the year 1989 because standing stock data for bacterial and protozoan compartments were unavailable for preceding years.

The outline of the model, given in Fig. 1, shows the major carbon pathways between a set of 10 “compartments” chosen as representative for the Kinneret ecosystem. No attempt has been made to depict intracompartmcntal flows other than “cannibalism,” which we de- iine as predation whether between or within species pooled in the same compartment. The components of the model are described below.

Two phytoplankton compartments, one consisting of Pyrrophyta (mainly Peridinium gatunense), a large thecate dinoflagellate that contributes 80-95% of the total algal C during the bloom season, and one consisting of other algae, here termed “nonpyrrophytes” (mostly nanoplanktonic chlorophytes accompanied by some diatoms and blue-greens, Berman et al. 1992). This second category also includes the picophytoplankton (mainly picocyanobacter- ia, Malinsky-Rushansky and Berman 199 1).

Previous studies have indicated that most of the dinoflagellate cells in the lake are de- graded in the water column or on the sediment surface (Hertzig et al. 198 1) and that essen- tially none of their carbon content is directly transferred to metazoan grazers (Serruya et al. 1980). In contrast, all other phytoplankton are assumed to be grazed by herbivorous metazoan zooplankton. We are aware that some of the pica- and nanophytoplankton may be grazed by ciliates (Sherr et al. 1991) but have not included this pathway in the present mod- Cl.

Three zooplankton compartments (cladocerans, copepods, and rot$ers) comprising the major metazooplankton groups found in the lake (Gophen 1978a). The cladocerans are the main herbivorous metazoan zooplankters and are dominated by Bosmina longirostris, Cer- iodaphnia reticulata, and Diaphanosoma brachyurum. The cyclopoid copepods are usu- ally represented by Mesocyclops ogunnus and Thermocyclops dybowskii. The adults of these organisms are assumed to be strict predators

1682 Stone et al.

Primary Prod. Prod. Primary a SEDIMENTATION NON-

PYRROPHYTA PYRROPHYTES I I

Bacterial Production

FLAGELLATES

v 1’ +

CILIATES -

I I

-A- l c )

FISH -----e---m---

Growth-Export

Fig. 1. Carbon flux model for the euphotic zone of Lake Kinneret, March-April and August-September 1989, showing the biotic and detrital C compartments and the major fluxes into, out of, and between compartments. Dashed lines indicate fluxes from microbial food-web compartments to zooplankton and fish. Respiration fluxes are indicated by the “ground” symbol common to every compartment in the food web. B, F, and C symbolize fluxes from bacteria, flagellates, and ciliates. Cannibalism indicated as intracompartmental loop.

and we have included an intracompartmental predation loop for this compartment. Note that nauplii and copepodite stages, which are partly herbivorous, are not shown separately in the model. Thus, some of the carbon flux that appears in the model as passing from phytoplankton to cladocerans should in fact be at- tributed to algal grazing by juvenile copepod forms.

Rotifers generally comprise a low propor- tion (< 10%) of the zooplankton biomass in the lake, but in March-April 1989 there were exceptionally high numbers of these organisms (M. Gophen pers. comm.).

Three microbial food- web compartments

(bacteria, heterotrophic nonpigmented jlagel- lates, and ciliates). WC have assumed that bacterial C is either respired or consumed by bac- terivores with no direct release of DOC. Mixotrophic flagellates, which can sometimes be numerous but were not observed in high numbers during the two periods examined (N. Paran pers. comm.), were not included in the model. A cannibalism loop appears in the ciliate compartment to account for intcrspecics predation.

Ajsh compartment. There are some 20 different fish species (Ben-Tuvia 1978) in the lake, but the bulk of the fish standing stock consists of Mirogrex terraesanctae (the Kinneret sar-


dine). Other commercially significant species include the cichlids Sarotherodon galilaea (St. Pctcr’s fish) and Sarotherodon aurea. Although there are no important piscivorous species in the lake, WC have provided for some intracompartmcntal predation. However, we have not attempted to quantify carbon fluxes for different spccics or lift stages of the fish.

A single detrital carbon compartment rep- rcscnting both POC and DOC (similar in form to the model of Vadstein ct al. 1989). Her-c the POC represents only particulate organic matter that is either solubilizcd directly to DOC, for example through the action of extracellular hydrolytic enzymes, or sediments out of the euphotic zone. Note that this does not include particulate organic matter which is directly used by detritivores. Thus, for example, detritus dc- riving from nonpyrrophytes which is grazed by cladocerans is included in the flux from nonpyrrophytes to cladocerans. Organic detritus may also be an important source of nutrition for organisms such as metazoan zooplankton and larval fish (Riemann and Sondergaard 1986). In Lake Kinneret, organic detritus consists largely of aggregates deriving from algal particles colonized by bacteria and protozoans. Much of the use of detritus may in fact also include consumption of attached and as- sociated microorganisms belonging to the microbial food-web compartments of the model.

We are well aware that this model contains simplistic assumptions about the homoge- neous nature of the biotic compartments. Thus, all copepods are considcrcd carnivorous and no attempt has been made to differcntiatc be- twccn diITcrent species or lift stages of fish, although these certainly have very different fccding patterns and probably very different carbon turnover times. Our purpose here was the depiction of a general scheme that would include the major categories of pelagic biota rather than a detailed model of ccosystcm sub- components.

Model design and framework-We used a mathematical model to estimate the daily carbon flux passing through and bctwcen the 10 compartments for each of the two seasons. The average of measured or estimated biomass and flux values for the two periods, March-April and August-September 1989, is used to form a template chart on which the model imposes the basic constraint of mass balance. In this

respect, each season can be considcrcd to exist at quasi-equilibrium and its llow chart is designed to represent a “typical day” of the season or, more precisely, the seasonal daily average. In doing so, WC assume that the biomass of every biotic compartment remains constant during the typical day. One could view the charts as a kind of snapshot of the lake with the camera shutter opening set for one season.

Although the assumption of a seasonal steady state is to some extent limiting, it is certainly far less restrictive than modeling the lake sys- tcm as though it were in equilibrium over the cntirc year. As will bc demonstrated, a comparison of two seasonal states reveals important details that would never be brought out by considering Lake Kinneret as if it wcrc an “annual average” system. We also extend the analysis further in order to examine the effects of variability within a given season.

The mathematical model cnsurcs that all compartments obey simple mass-balance constraints, i.e. the sum of the fluxes cntcring any particular compartment must balance the sum of all exiting fluxes. This sum of fluxes is known as the compartment’s throughflow or, cquiv- alently, its demand. Although it is certainly possible to construct balanced llow charts for each season manually (i.e. with pen and paper), experience shows that even for a system with only 10 compartments the task becomes ex- traordinarily laborious. Tcchniqucs for constructing flow charts with the aid of mathematical modeling have been described in the literature (Ducklow et al. 1989; Kleppcr and Van DC Kamer 1987; Vezina and Platt 1988) and these form the basis for our study.

Similar to the inverse methods outlined by Vezina and Platt (1988), our model combines data of biomass and carbon uptake and release, as well as measured or assumed assimilation efficiencies and respiration rates of particular compartments to build a feasible chart. How- ever, rather than make use of the singular value-decomposition method of Vezina and Platt, the flow chart is balanced by USC of linear programming techniques. These two mcthodolo- gies have much in common, the latter having developed into a well-established branch of mathematics specifically intended to solve the problem discussed hcrc.

A key fcaturc of the model is that it takes into account that in nature all biological fluxes

1684 Stone et al.

fluctuate in time and space. Thus, different plausible charts for a single food web need not represent fluxes as fixed constants but may show them to differ from their estimated values by an amount that lies within bounds set by measurement and estimation errors and variations expected from natural cnvironmen- tal and ecological variability. The computer program can be run to yield a set of flow charts representative for a given season, each chart differing in a manner that could reflect natural variability. This set of charts is taken to represent realistic states or configurations in which the ecosystem may reside on a typical day for a particular season. It then becomes possible to explore the features of a range of model food webs. In this methodology it is necessary to assume that the charts portraying the seasonal daily average (see Figs. 2 and 3) could in fact be representative of a particular single day. This seems to be a reasonable first approximation, but may in some cases fail if biomass and flows change significantly and nonlinearly over the season.

As it is currently set up, the model reads in and accepts initial flux rate observations in two distinct formats: either as direct flux-rate observations (mg C me2 d-l) or as percentage throughflows. Flux rates based either on ob- servational or experimental measurements or on values taken from the literature are entered into the computer as default values to form an initial but unbalanced flow chart. Addition- ally, the computer program requires approxi- mate error ranges to be set for each flux. We found the second category, percentage throughflow, useful in the Kinneret model when we attempted to deal with respiration losses that were estimated as a fixed percentage of the total carbon demand ofeach compartment.

To our knowledge, except for the work of Vezina and Platt (1988), flux models accept data either as perccntagc throughflows (e.g. Fasham 1985; Newell and Linley 1984) or as direct flow estimates (c.g. Klepper and Van De Kamer 1987) but not both simultaneously. In some studies, flow charts appear to have been constructed from ad hoc considerations (e.g. Suttle ct al. 1990; Vadstein et al. 1989; Weisse ct al. 1990). Although techniques based exclu- sively on percentage throughflows certainly have value for theoretical studies (Fasham 1985), these techniques have limitations for

workers interested in applied ecosystem modeling where many observations are in the form of direct flow measurements. Difficulties often arise when one attempts to transform these direct flow measurements to percentage throughflows while simultaneously keeping the entire flow chart in balance when it is subject to a given set of complicated constraints on parameter ranges. In fact, the problem of bal- ancing a chart becomes extremely difficult when both forms of observations arc allowed for; spreadsheet approaches generally prove inad- equate in these situations. Fortunately, linear programming grew out of the need to solve such problems.

The above description of Lake Kinneret yielded 45 flows that either interconnected the 10 core compartments or were lost from the system in the form of respiration or exports. In mathematical terms, 10 equations were required to maintain mass balances for all compartments simultaneously. These equations were required to conform to a basic set of biological constraints, namely each known flux variable was constrained to lie within specified maximal and minimal bounds as dictated by measurement error as well as by natural ecological variability.

For the Kinneret data set, we initially assumed that all measured or estimated flows were accurate to within + 10% of their pos- tulated values and that this would be a reasonable (though possibly minimal) range that might allow for natural variability over a typical day. Although not done here, an alternative procedure might use sample variances of the field measurements for determining error ranges. However, estimates of variances are not often easily obtainable for flux rates that are inferred from turnover times, efficiencies, etc. For either method, two inequalities can be deiined for each flux (i.e. a total of 90 inequalities). The problem may then be recast in terms of a standard linear programming formulation that requires satisfying 10 equations subject to 90 constraints.

Once all fluxes are read in, the computer program produces a balanced flow chart. How- ever, since many such balanced charts exist, the program can be set to search for the chart that is “closest” to the original set of estimates, using techniques similar to those of Klepper and Van De Kamcr (1987). Here the closest

Carbon jlux model 1685

chart means that balanced chart whose sum of deviations from the initially given estimated values is minimal. For the purposes of at- tempting to find a solution that is closest to the initial input data set, this approach has the potential to yield more realistic solutions than other techniques which, for example, minimize the total sum of flows (Vezina and Platt 1988).

Axsb (5)

where x is a vector of the n flows -xii,

and n a (2n + m)-x-n matrix and b a vector of dimension (2n + m) with components pij, qij, and zeroes.

The computer’s user-friendly interface easily allows changes to be made to any flux rates for which the initial values have been only crudely estimated. Such changes may have effects that reverberate throughout the system and are readily observed on the output of the new chart.

Model theory- Here we outline the technical details of the linear programming methodology. The less mathematically inclined reader may skip this section without any loss of con- tinuity. A more complete description will be presented elsewhere. ,

Consider a food web with m compartments. Let xij represent the rate ofcarbon flowing from compartment i to compartment j and assume that there is a total of n such flows. The csti- mated or observed values of these flows will be notated as -)zij. The intervals within which x,] values are confined to lie are defined by the known (assumed) quantities pii and qu:

po 5 xg 5 qu. (1) These constraints (Eq. 1) can be broken into 2n inequalities:

The above formulation is now well suited to a linear programming analysis. It is possible, for example, to dcterminc a balanced flow chart that satisfies all the constraints given by Eq. 5 and also minimizes S, the total sum of all flows xii in the food web (similar to Vezina and Platt 1988). In the terminology of linear programming, we call S the objective function, and the problem can bc written as

minimize S = z xij

subject to the constraints A x I b.

The simplex routines of, for cxamplc, Press et al. (1987) can be used to compute the solution.

However in the work described here, rather than minimize the sum of flows we used a more complicated procedure that computed the balanced chart that was “closest” (according to some chosen norm) to the set of estimated values, Zi. Using the L, norm, we translate this to

minimize T = C 1 X0 - -;Cij 1

subject to A x I b. Xij 5 qij (2)

and -Xij I -Pljs (3)

The laws of mass balance dictate that the sum of flows entering any compartment must equal the sum of flows leaving that same compartment. For compartment i:

sum of flows in = sum of flows out

zXJi= ZXij

j j

or

We refer the reader to Kleppcr and Van de Kamer (1987) for further details of this approach. It can be seen that setting the estimated values & to zero will result in an objective function that minimizes the sum of fluxes. This property suggests a possible option of setting Zij to zero for all fluxes xij whose estimates are unknown.

z (Xji - Xii) = 0 i= 1,2 ,..., m. (4) i

A whole range of balanced flow charts can be produced by slightly varying one or more of the estimates iij, but keeping them well within the accepted ranges given by Eq. 5. All the operator needs to do then is balance the chart while noting that the solution will differ whenever the estimates are varied.

Note that Eq. 2-4 represent 2n + m equations One of the key features of the model lies in and inequalities. Equivalently, we can write its ability to handle percentage throughflows Ea. 2-4 in the form toeether with constraints aivcn in the form of

1686 Stone et al.

Table 1. Carbon biomass of compartments and initial input values of key fluxes. A-March-April 1989; B- August-Septcmbcr 1989. Compartmental respiration rates given in text.

Biomass* C demand : C biomasst Total C demand* Detrital C relcasel &Cm ‘) (turnover time, d ‘) (mg m I d I) (% demand)

A B A B A B A B

Pyrrophytcs 33.40(85.0) 1.71(21.9) Nonpyrrophytes 0.8 l(2.1) 2.15(27.6) Bacteria l.00(2.5) 0.67(8.6) Flagellates 0.12(0.3) 0.06(0.8) Ciliates 0.36(0.9) 0.20(2.6) Cladocerans 0.32(0.8) 0.36(4.6) Copepods 0.1 l(O.3) 0.24(3.1) Roti rcrs 0.18(0.5) 0.0 12(0.1) Fish 3.00(7.6) 2.40(30.1)

- - 1,650 - - 600

- 500 1.2 1.0 144 0.6 1.0 206 0.8 1.6 256 0.8 0.7 88 0.6 0.8 108 0.09 0.03 270

85 40 25 1,760 15 25

470 0 0 60 20 20

200 20 20 570 50 40 168 50 40

10 50 40 72 50 40

* Pcrccntagcs of total C biomass given in parentheses. t Values for flagellates and ciliates from Hadas et al. 1990 and Berman unpubl.; for zooplankton from Gophcn 1976a,h, 19786, I98 Ia& for fish from Walline

et al. 1992, pers. comm. $ These values incorporate the etfccts of cannibalism in the case of ciliates, copepods, and lish. Values for pyrrhophytcs and nonpyrrophytcs measured by “‘C

uptake (Y.Z. Yacobi pcrs. comm.) and bacteria by [‘HIthymidine incorporation (T. Berman unpubl.). Other values of C demand obtained by multiplying C biomass (column I) and C demand : C biomass (column 2).

8 “Best initial estimates” for protozoa and fish. Values for phytoplankton from Berman 1976, unpubl.; for zooplankton based on Gophen 1976a, b, 1981a.b.

Eq. 1. Suppose, for example, that the flow x, must lie between c&o and @“/o of the total flow through compartment r. Let the total throughflow of compartment r be U = z) Xjr. We re- quire j

x, 52 per/100 (6)

and

-x,, 5 -cuu/100. (7)

It is easy to see that after a simple subtraction which transforms the right-hand sides of the inequalities to zero, Eq. 6 and 7 conform ex- actly to the format of Eq. 5.

A standard linear programming technique allows evaluation of the full possible range of values for a given how xij when the food web is constrained by Eq. 5. We explore this further below, but point out here that the extreme values of the range can be found by solving

minimize Xij

subject to A x I b

and

minimize -Xlj

subject to A x 4 b

(see also Chvatal 1983; Klcppcr and Van De Kamcr 1987).

Data set for Lake Kinneret (I 989) -We now apply the model using the data input from Lake

Kinneret averaged for March-April and Au- gust-September 1989. In Table 1 we list the carbon biomass (given as g C mF2) for the major biotic compartments in the photic zone averaged over each of the two seasons. Phy- toplankton wet weight biomasses were determined by microscopy on samples taken weekly or biweekly (data provided by U. Pollingher). Carbon content was taken as 10% of wet weight, except for dinoflagellates, mainly P. gatunense, for which a value of 20% C had been detcr- mined experimentally (Berman et al. 1992). The areal biomass of phytoplankton C (g C m-2) was calculated from a linear integration of 6-8 discrete depth determinations for the euphotic water column (15-20 m). Zooplank- ton abundances were based on unpublished averaged monthly data of M. Gophen. The biomasses we dcrivcd are, if anything, conser- vative and possibly underestimate the zooplankton standing stocks (M. Gophen pcrs. comm.), but are of sufficient accuracy for this modeling exercise.

Bacteria and protozoans were sampled every 2 weeks at six discrctc depths. Bacteria were counted by means of DAPI staining under epifluorescent microscopy (Porter and Fcig 1980). To obtain carbon biomass, we used an averaged bacterial volume of 0.1 pm’ and 0.22 pg C pm-3 (Bratbak 1985), or -0.03 pg C (bacterial cell)- I. The flagellates and ciliates were also stained with DAPI and their biovolume determined with epifluorescent microscopy. Carbon content was estimated with a conver-


sion value of 0.2 pg C pm3 (Borsheim and Bratbak 1987). Fish biomass was based on values derived from acoustical surveys conducted by Walline et al. (1992) with C as 10% of wet weight (Vinogradov 1983). Total DOC, as measured with a standard acid hydrolysis technique (Am. Public Health Assoc. 198 I), averaged 47 and 28 g C m-2 in March-April and August-September, respectively, but presumably only a small fraction of this pool was la- bile. No measurements of POC were available.

Carbon flows for each of the system compartments were estimated, where possible, on the basis of measured data in a manner similar to that of Newell and Linley (1984). Table 1 gives the mean measured primary and bacterial production, daily gross carbon demand, and estimated proportions of the intake which are excreted or cgested. All flow rates were expressed as mg C m-2 d-l. Primary production was directly measured by Y. Z. Yacobi using [ 14C]bicarbonatc uptake (Berman and Pollingher 1974) and was partitioned bctwcen nonpyrrophytcs and pyrrophytes on the basis of experimentally determined, size-partitioned photosynthetic activities (Pollingher and Berman 1982). The incorporation of [3H]thymidine (as modified by Wicks and Ro- barts 1987) was used to estimate bacterial production (cells mm3 d-l) with an empirically determined calibration factor for the lake. This value was then expressed in terms of mg C m-3 d- 1 (see the conversion factor given above), and the total daily C demand was calculated by correcting for bacterial respiration losses of 30% (March-April) and 40% (August-Septem- ber). We assumed no extracellular release of DOC by bacteria. The carbon demands for other compartments were estimated as the total biomass of each compartment divided by its turnover time. (The turnover times are dc- termined from Table 1 as the reciprocal of the C demand : C biomass ratio in column 2.)

For zooplankton, gross daily C intake requirements and excretion plus egestion rates were based on experimental observations (Go- phen 1976a,b, 19783, 1981a,b, pcrs. comm.). For the C requirements of protozoa, calculations were based either on protozoan genera- tion times or on grazing rates on bacteria as measured by Hadas et al. (1990). For fish, we set the daily C demand as 8% of body C weight in March-April when many larvae and small

fingerlings arc present, and 3% in August-Sep- tember when fish growth may bc limited by food sources (Landau et al. 1988). These values, especially for March-April, may be over- estimated because a yearly demand : biomass (Q : B) ratio of 10.0 has been recently suggested for most Lake Kinneret fish (P. Walline pcrs. comm.).

No experimental measurements of grazing or predation by metazoan zooplankters on protozoa in the lake are presently available, although such flows have been documented for other systems (Stoecker and McDowell Cap- puzo 1990). Initial values for these and other unknown flows (detrital C release by protozoa and fish), surmised on the basis of our biological intuition, were given wider error ranges (typically f 50%). Subsequently, slightly modified rates were “determined” by the model. Table 1 provides a summary of the initial input values used for carbon demands and detrital C release and their derivation.

Respiration levels were assumed to be similar for all compartments of the pelagic biota and were set at an average of 30 and 40% (+ 10%) of gross C uptake in March-April and August-September (the average lake epilimnic temperatures at these two seasons were -20 and 25°C). Although the implication that all biotic compartments show similar respiration losses is undoubtedly a simplification of the situation in nature, these assumed respiration values fit reasonably well to measurements that have been made for phytoplankton (Berman and Pollingher 1974) and bacteria (Berman et al. 1979). Thcsc respiration rates are some- what higher than some experimental measurements with zooplankton (which ranged from 7 to 35%, Gophen 198 1 a, b) but lower than other estimates for zooplankton and fish respiration (Newell and Linley 1984). Because respiration rates may vary considerably for different organisms at the same temperatures, it is difficult to pinpoint more accurate rates when dealing with heterogeneous compartments. In this respect, our assumptions are reasonable for the present modeling exercise.

For these flow charts, we posit that there are no significant external inputs of POC or DOC to the pelagic euphotic zone. Some detritus as POC derived from phytoplankton and fish reaches the hypolimnion or lake bottom and is removed from the system. Other organic

Stone et al.

‘rimary Prod. SEDIMENTATION - Prim. Prod* a 1650 600

PYRROPHYTA NON- 82 PYRROPHYTES

300

82 81 3acterial Production 170 49

1 A 127 r

163 v v

212 5

6C + FISH 13

119 ' --_---------

Growth-Export( 13)

Fig. 2. Carbon flow chart for euphotic zone biota of Lake Kinneret, March-April 1989. All values given in mg C m 2 d-l. In each compartment, the upper number refers to gross uptake flux, the lower number to net carbon export rate (gross uptake minus respiration and excretion losses). Losses to the detrital C pool from phytoplankton include 5% extracellular release (Berman 1976) indicated in parentheses (legend as for Fig. 1).

detritus is assumed to be solubilized within the water column or consumed by zooplankton or fish (see above). The remaining carbon losses from the system are due to respiration and removal by fishery. These assumptions are undoubtedly simplistic but are nevertheless realistic enough to permit the construction of first approximation models for the pelagic cco- system in the lake.

Results and discussion Flow charts-Charts showing the carbon

flows calculated by the model for March-April and August-September 1989 are given in Figs. 2 and 3. The C uptake or demand for each

compartment (measured as gross intake g C m-2 d-l) is given in Table 1. A remarkable feature for March-April was the relatively high contribution of nonpyrrophyte algae to the total primary production (N 600 out of a total of 2,250 mg C me2 d-l) despite their low biomass. This characteristic was implied by the model of Serruya et al. (1980), and measurements in the lake by Pollingher and Berman (1982) indicated that nanoplanktonic algae generally had much higher specific photosynthetic rates and a more rapid turnover of carbon (N 1.4 d) than the large dinoflagellates (-20.2 d). In contrast, in August-September 95% of the photosynthetic activity was carried

Carbon Jlux model 1689

I 38(+4)

PYRROPHYTA

439(-t88)

1 SEDIMENTATION Prim, Prod.

1757+- NON-

PYRROPHYTES 528

16 I


470 54 BACTERIA -h

282 I I

60 I I I I

508 4 A 228 b

241 16 I

I

16 I I

168 V I

184 64 ; CILIATES - 40 ):

64

+80

25 v* ,

Fl?H

1

4c *

8 29 _-_-_---__---

7 t Growth-Export(s)

Fig. 3. As Fig. 1, but for August-Scptcmber 1989.

out by nanoplanktonic algae. Bacterial scc- ondary productivity was 22 and 26% of primary production in March-April and August- Scptcmber-close to the average pcrccntage suggested by Cole et al. ( 1988) for a wide range of aquatic environments. Of the metazoan zooplankters, cladocerans were especially active in terms of carbon flow in August-Sep-

_I tcmbcr. Carbon uptake by the fish population was highest in March-April when there were large numbers of metabolically active fingcr- lings. The sum of all carbon throughflows in the pelagic biota in August-Septcmbcr was only reduced by - 10% in comparison to that of March-April, even though the carbon biomass of phytoplankton had dropped by 80% (Table 1).

In March-April, -85% of all living C (total 39.9 g C me2) was sequestered in the Pyrro- phyta biomass, followed by 7.6% in fish and 2.5% in bacteria. All other biotic compartments contained ~5% of the total C (Table 1).

In August-Scptembcr, total living carbon standing stock had decreased to 7.8 g m-2. The phytoplankton still accounted for most of the carbon (- 50%), with -28% and 22% sequestered in nonpyrrophytes and pyrrophytes. The next highest percentage of living carbon (- 3 1%) was in fish biomass. At this season, the carbon pool of bacteria (8.6%) and cladocerans (4.6%) was relatively important. To- tal C standing stock in August-September was only -20% of that observed in March-April (Table 1).

1690 Stone et al.

Table 2. Percentage contribution of each biotic compartment to total carbon flux. A-March-April 1989; B- August-Scptcmber 1989. All numbers are given as pcr- centagcs of the total carbon flux in biotic compartments of the model.

Jklrital C Demand Respiration excretion

A B A B A B

Pyrrophytes 44.2 2.5 43.4 2.5 67.4 4.4 Nonpyrrophytes 16.1 52.4 15.8 51.8 7.5 55.5 Bacteria 13.4 14.0 13.1 13.9 - - Flagellates 4.0 1.8 3.9 1.7 1.9 1.3 Ciliates 5.0 5.5 5.1 5.9 2.5 4.2 Cladocerans 6.8 17.0 6.7 16.8 8.0 24.0 Copepods 2.0 4.5 2.2 4.9 2.1 7.1 Rotifers 2.7 0.3 2.7 0.3 3.2 0.4 Fish 5.7 2.0 7.0 2.1 7.5 3.1

During both seasons, most of the community respiration derived from the phytoplankton. In summer, cladocerans (16.8%) and bacteria (13.9%) were relatively important contributors to community respiration (Table 2). The seasonal patterns of release of POC or DOC (Table 2) followed the changes in C demand, with cladocerans being prominent in rcleasc of detrital C during August-September (24.0%). In March-April, fish and cladocerans both contributed about the same percentage (7-S%) to detrital C release. The rates of POC sedimentation out of the euphotic zone as derived by the model from mass-balance considerations were within the range of POC fluxes determined experimentally with sediment traps (A. Nishri pers. comm.).

The model indicates that in March-April (August-September) only - 5% (10%) of gross photosynthetic C fixation from the pyrrophytes was transferred directly to fish. In ac- cordance with previous assumptions (Scrruya et al. 1980), we have posited that no living pyrrophyte C was directly taken up by the hcr- bivorous zooplankton. Most of the C photo- synthetically fixed by the dinoflagellates was lost to respiration (30%) and to the detrital C pool (65%). A substantial portion of POC sedi- mcnting out of the euphotic zone in March- April consists of Peridinium theta (T. Zohary pers. comm.). At this time, the nanophytoplankton, although a relatively minor biomass fraction of the algae, supplied a dispropor- tionate amount of carbon for fish, cladocerans, and rotifers (38, 67, and 48% of their requirc-

ments, respectively). This finding supports other studies of the Kinneret system (Serruya et al. 1980; Drenncr et al. 1987). About 60% of the C demand by herbivorous zooplankton was supplied by nanoplanktonic algae and -40% by organisms of the microbial food web in March-April. From a net bacterial production of 350 mg C m-* d-i, -50% was passed either directly or via protozoa to the zooplankton, and the rest was lost as respiratory CO2 or recycled to the detrital C pool. Copepods were dependent on ciliates as a carbon source to a considerable extent (46%).

A major difference in flux pattern was observed in August-September when the hcrbiv- orous zooplankton (mainly Cladocera) derived almost 90% of their C from nanoplanktonic phytoplankton with only a minor part of their needs supplied by the microbial food web. Co- pcpods, however, still received a substantial portion of their carbon requirement (36%) from ciliates. In August-September, -45% of the bacterial production was transferred either directly or via protozoa to the zooplankton. The model suggests that -50% of the daily fish rcquircment was provided by metazoan zooplankton and ciliates, 34% by phytoplankton or algal detritus, and 10% from interspccics predation (cannibalism).

WC found that the role of cannibalism may bc quite important in food webs and conse- quently attempted to analyze its effects, even if crudely. For example, the ciliate compartment in the August-September period, according to calculations based on turnover considerations, required 200 mg C m-* d-i (as seen in Table 1 or Fig. 3). However, since part of this flux requirement actually included intracompartmental predation or cannibalism, the C input to the ciliate compartment was in fact 10% less, N 184 mg C m-* d-i (see Fig. 3). This type of effect is similar to that discussed by Strayer (1988). His argument dealt only with the impact of intercompartmental recirculation, but it may also have meaning when examining intracompartmental recirculation. The phenomenon explains how the total C requirements of a compartment (200 mg C m-* d-i in the ciliate example) can sometimes exceed the sum of its inputs (184 mg C r-r-* d-l).

&jfY?cts of variability-One fcaturc of the model is the way in which it can cxplorc the


effects of a hcterogcneous environment. In the natural world, biological lluxcs do not exist at fixed, unvarying values but fluctuate in time and space; we take advantage of linear programming theory to examine how changing flux rates might affect the food web. As discussed previously, our assumption here is that the seasonal daily average flow charts (Figs. 2 and 3) are to some extent representative of the lake ecosystem on a particular single day. We now explore fcaturcs of a range of model ecosystems similar in configuration to the charts portraying the seasonal daily averages.

strained with zero system variability (as discussed above).

By a linear programming technique (see model theory section), it is possible to calculate balanced external solutions that exist in this cnsemblc of model food webs (Chvatal 1983; Klepper and Van De Kamcr 1987). We need to ask: What is the maximum or minimum of any single flux, say flux A, while all other fluxes arc allowed to fluctuate by some specified amount?

Any study of fixed flow charts that ignores the ramifications of natural variability could result in misleading conclusions. Zero system variability tightly constrains charts and does not portray the range of feasible solutions. Small amounts of flux variability that must be present in a fluctuating environment have the potential to produce large changes in individual flows. WC have examined this subject in more depth elscwhcre (Stone and Berman 1993) and have shown that the variability of fluxes could bc a major factor in influencing the dynamics of the microbial food web, with effects that are capable of resonating through the entire ecosystem.

To further examinc what we mean by this, WC first consider the cast in which all fluxes, except for A, arc held constant. In this situation there is zero “system variability,” and the mass-balance conditions are highly constraining. In fact, the chart has a unique solution, and flux A can take on only a fixed constant value.

A further point of interest can bc found in the results shown in Table 3. Column 2 gives the values of flows as estimated by the model for the Kinneret charts (Figs. 2 and 3). For most fluxes, these values lie about midway bc- twccn the minimum and maximum possible values (as given in columns 1 and 3). This result implies that the charts prescntcd here as characteristic for two seasons in Lake Kinneret do not represent extreme solutions but reasonably portray “average” configurations of the fluctuating model system.

Suppose WC now allow all fluxes except A to fluctuate by up to 10% of their estimated value (i.e. a system variability of 10%). Such an amount would reflect the minimal variability that might be cxpccted in a changing cnviron- ment. We then ask: What restrictions does this put on flux A, and what are the extremal (maximum or minimum) values which A may at- tain? In terms of the linear programming model, this question can bc answered by constructing an objective function that maxi- mizes or minimizes flux A while clamping all other fluxes so that they do not change by > 10% from their initial estimated values.

Note that a number of the flows are zero in Table 3 and could thus in some casts portray unrealistic charts that do not make sense bi- ologically (e.g. a chart in which fish do not eat copepods). However, because we interpret each chart as a possible state or configuration of the system over a season, an extrcmal chart would have meaning over a brief time scale. Such a chart would correspond to an extreme configuration and its chance and length of occurrence would presumably be very small. In “all like- lihood the system would mostly fit close to the average charts given in Figs. 2 and 3, but the ranges of fluctuation about the average might well be large.

Our results for the Kinneret system, shown Alternativesummerflowchart-Although the in Table 3, are surprising. Despite what might microbial food web is now a well-established be considered tight mass-balance constraints feature of aquatic food webs, considerable un- enforced on the system, we found that even certainty remains about the extent to which C with an overall system variability as small as or other nutrients are passed from microor- lo%, each of the flows can change considerably ganisms to metazoan zooplankton or to fish. (often by factors exceeding 100%) while still For example, from their model of food webs maintaining a balanced chart. This result is in in the Celtic Sea, Taylor and Joint (1990) con- sharp contrast to that found in flow charts concluded that bacteria were relatively unimpor-

1692 Stone et al.

Table 3. Permissible ranges for carbon fluxes (mg C m-2 d ‘) between compartments (fluxes to detrital C compartment omitted). These ranges were evaluated by constraining all fluxes, except for say flux X, to range between + 10% of the values listed in the solution flow charts (Figs. 2 and 3). WC then computed the range of flux X. Detailed explanation given in text.

March-April AugustSeptember

Min Act Max Min Act Max

Pyrrophytes* Nonpyrrophytes* Bactcriat Pyrrophytes to fish Nonpyrrophytes to cladocerans Nonpyrrophytes to rotifers Nonpyrrophytcs to fish Bacteria to cladocerans Bacteria to rotifers Bacteria to flagellates Bacteria to ciliates Cladocerans to copepods Cladocerans to fish Rotifers to copepods Rotifers to fish Flagellates to cladocerans Flagellates to rotifers Flagellates to ciliates Copepods to fish Ciliates to cladocerans Ciliates to rotifers Ciliates to copepods Ciliates to fish

1,299 473 394 22

107 22 21 0 0

119 106

0 0 0 0 0 0

3 0 0

0

1,650 2,118 600 770 500 642 82 162

170 250 49 83 81 161 25 119 25 61

150 194 150 205 26 44 25 87 15 34 5 30

25 59 16 51 35 68 13 34 35 78 12 49 35 52

6 36

66 1,356

363 0

373

0 0

46 122 54 0 0 0 0 0 5 0 0 0

22 0

85 112 1,756 2,32 1

470 620 9 28

508 699 4 8

16 41 50 153 4 8

60 79 168 229 96 151 19 43

16 17

54 91 4 24

3 20

5 28 42 30

* Primary production. t Bacterial production.

tant and that the microbial food web was not copepods from 54 to 12 mg C m-* d- l (-t 20%). a significant carbon source to other biotic com- Under the initial constraints, the computer ponents in this system. In contrast, Wiadnyana program was unable to balance the chart with and Rassoulzadegan (1989), working in the these major changes. Therefore, to preserve western Mediterranean, presented evidence overall balance, we were forced to relax the that a considerable amount of the nutrients original 10% constraints on some fluxes as fol- required by metazoans could derive from pro- lows: cladocerans to copepods (f. 25%), ciliates tozoans. A recent review by Stoecker and Mc- to detrital C (+ 35%), bacteria to ciliates Dowell Cappuzo (1990) also concluded that in (+ 20%), and bacterial secondary production many marine systems protozoans can be an important food source for zooplankton. Most

(+20%). These choices were designed to significantly reduce the flows from microbial or-

probably the relative importance of the mi- ganisms to the rest of the food web. At the crobial food web as a “source” or “sink” of C same time it was necessary to increase the varies for different environments and different “slackness” or variability within the microbial seasons or times (Berman 1990). food web to accommodate this major change.

In view of the above, we explored the pos- sibility of constructing a variant of the Kin- neret model for August-September 1989 in which the fluxes of bacteria and ciliates to metazoans were drastically reduced. We generated charts in which the fluxes from bacteria to cladocerans were arbitrarily lowered from 50 to 10 mg C m-* d- l (+ 20%) and from ciliates to

The resulting chart (Fig. 4) differs in several aspects from the previous version. Total C inputs from the microbial food web to metazoan zooplankton have been reduced by 63%. Pri- mary production by nonpyrrophytes and input to the detrital C compartment are increased by -9 and -7% respectively, while there is a simultaneous increase in sedimentation rate of

Carbon ji’ux model 1693

Fig. 4.

474(96)

Primary Prod. SEDIMENTATION Prim. Prod. 11914

~-1 PYRHPPH;3 1

I


61 cl FLAGELLATES 22

5581 4 II\ 234

I b l

Alternative carbon flow chart for euphotic zone biota of Lake Kinneret, August-September 1989, with minimal transfer of carbon from bacteria and ciliates to mctazoan zooplankters (legend as for Figs. 1 and 2).

some 30%. Secondary production of bacteria is reduced by -20%. As a consequence, the estimated carbon turnover time for bacteria would increase from 1.4 to 1.8 d during the season when water temperatures are greatest and bacterial activity should be maximum- a value that is still not unreasonable. Thus, Fig. 4 indicates a plausible food-web scenario in-which only 6% of the C requirement of zooplankton and fish is supplied by the microbial food web, contrasted with 16% in the original scheme (Fig. 3). Also, only 10% (as opposed to 40%) of the C requirement of copepods is supplied by ciliates in this alternative chart.

Given the dearth of experimental data on the fluxes between the microbial food-web

compartments and those of the zooplankton in Lake Kinneret, it is hard to judge which chart for August-September (Fig. 3 or 4) is more realistic. Except for the fluxes related to the microbial food web, Fig. 4 does not depart drastically from the original set of data input to the model; nevertheless, it leads to a con- flicting conclusion with regard to the importance of the microbial food web in carbon flux during late summer. The fact that two plausible scenarios can be obtained with the model emphasizes the riced to obtain better input data and indicates where research focus and expcr- imental measurements are critically required. In the present cast, fluxes between protozoans and zooplankton are not easily quantified with

1694 Stone ( ?t al.

a high degree of accuracy, but it should be possible to determine which alternative be- twcen, say, a flux of 10 or 50 mg C rnh2 d-l from bacteria to cladocerans is more realistic.

Conclusion We have used a linear programming model

to examinc the flows of carbon in Lake Kin- neret over two distinctive seasons by exploit- ing comprchcnsive data collected in 1989. For our purposes, this steady state flow-chart approach seemed preferable to dynamical models based on time-dependent diffcrcntial cqua- tions (Field et al. 1989). These latter methods arc best suited to small systems, and, although they have the potential to provide important qualitative insights, they are less capable of dealing with quantitative empirical obscrva- tions as in the scheme rcquircd here. The difficulties involved in performing what was at first felt to bc a straightforward task- balanc- ing a flow chart- in the end proved to be an claboratc and challenging problem.

The present model may be of general use in examining patterns of carbon (or other nutrient) flux in aquatic systems. The balanced charts that are generated are an essential pre- requisite for any serious study of more subtle system properties (e.g. indirect flux flows, re- cycling indices, sensitivity analyses) which WC hope to detail in future work.

Finally, a word of caution: As Riemann and Sondergaard (1986, p. 267) stated,

Generalizing diagrams sometimes have a tendency to bc vicwcd in a very rigid and definitive manner as if they contain the whole and final story. This is never the cast, as a diagram presents a “frozen” picture of a complex series of dynamic events. Fur- thermore, such diagrams are always biased by present knowledge.

Flow charts such as those shown hcrc should not be regarded as definitive, ultimate state- ments of actual carbon fluxes in Lake Kinncr- et, but rather should be considcrcd as working hypotheses to be subjected to further testing and research. The correct application of such models should be the exploration of possible scenarios and the gaining of an overall per- spective. By adjusting parameter values and constraints and examining the limitations pos- itcd by alternative charts, “most reasonable” schemes may be achieved. These should point

the way for further refinements in cxpcrimcn- tation and theory.

References

AMERICANPUBLICHEALTHASSOCIATION. 1981. Standard methods for the examination ofwatcr and wastewater, 15th ed. APHA.

AZAM, F., AND OTHERS. 1983. The ecological role of water-column microbes in the sea. Mar. Ecol. Prog. Ser. 10:257-263.

BEN-TUVIA, A. 1978. Fishes, p. 407430. In C. Scrruya [cd.], Lake Kinneret. Junk.

BERMAN, T. 1976. Release of dissolved organic matter by photosynthesizing algae in Lake Kinneret. Frcsh- water Biol. 6: 13-l 8.

- 1990. Microbial food webs and nutrient cycling in ‘lakes: Changing pcrspcctivcs, p. 5 1 l-526. In M. Tilzcr and C. Serruya [eds.], Dynamic proccsscs in large lakes. Springer.

-, 0. HADAS, AND U. MARCHAIM. 1979. Hetero- trophic glucose uptake and respiration in Lake Kin- nerct. Hydrobiologia 62: 275-282.

-, AND U. POLLINGHER. 1974. Annual and seasonal variations of phytoplankton, chlorophyll, and pho- tosynthesis in Lake Kinneret. Limnol. Oceanogr. 19: 31-55.

-,Y.Z.YACOBI,AND U. POLLINGHER. 1992. Lake Kinneret phytoplankton: Stability and variability during twenty years (I 970-l 989). Aquat. Sci. 54: 104- 127.

BORSHEIM, K. Y., ANDG. BRATBAK. 1987. Cell volume to cell carbon conversion factors for a bactcriovorous Monas sp. enriched from seawater. Mar. Ecol. Prog. Ser. 36: 171-175.

BRATBAK, G. 1985. Bacterial biovolume and biomass estimation. Appl. Environ. Microbial. 49: 1488-1493.

CARRICK, H. S.,G. L. FAHNENSTIEL, E. F. STOERMER,AND R. G. WETZEL. 199 1. The importance of zooplankton-protozoan trophic couplings in Lake Michigan. Limnol. Oceanogr. 36: 1335-l 345.

CHVATAL, V. 1983. Linear programming. Freeman. COLE, J.J.,M. L. PACE, ANDS. FINDLEY. 1988. Bacterial

production in fresh and salt water ecosystems. A cross system overview. Mar. Ecol. Prog. Ser. 43: I-10.

DRENNER, R. W., K. D. HAMBRIGHT, G. L. VINYARD, M. GOPHEN,AND U. POLLINGHER. 1987. Experimental study of size-sclcctive phytoplankton grazing by a fl- ter-feeding cichlid and the cichlid’s effects on plankton community structure. Limnol. Oceanogr. 32: 1 I38- 1144.

DUCKLOW, H. W., M.J. R. FASHAM, AND A. F. VBZINA. 1989. Derivation and analysts of Bow networks for open ocean plankton systems, p. 159-205. Zn Nct- work analysis in marine ecology: Methods and applications. Coastal Estuarine Stud. V. 32. Springer.

-, D. A. PURDIE, P. J. LEB. WILLIAMS, AND J. M. DAVIES. 1986. Bacterioplankton: A sink for carbon in a coastal marine plankton community. Scicncc 232: 865-867.

FASHAM, M. J. R. 1985. Flow analysis of materials in the marine euphotic zone, p. 139-l 62. In Ecosystem theory for biological oceanography. Can. Bull. Fish. Aquat. Sci. 213.


FIELD, J. G., C. L. MOLONEY, AND K. H. MANN. 1989. Network analysis of simulated succession after up- welling, p. 132-158. In Network analysis in marinc ecology: Methods and applications. Coastal Estuaries Stud. 32. Springer.

GIFFORD, D. J. 199 1. The protozoan metazoan trophic link in pelagic ecosystems. J. Protozool. 38: 81-86.

GOPHEN, M. 1976~. Temperature dcpcndcncc of food intake ammonia excretion and respiration in Cerio- daphnia reticulata (Jurinc) (Lake Kinneret, Israel). Freshwater Biol. 6: 45 l-455.

-. 19766. Temperature &ccl on lifespan, mctab- olism and development time ofMesocyclops leuckarti (Claus). Occologia 25: 27 l-277.

- 1978a. Zooplankton, p. 297-3 11. Zn C. Scrruya [cd.], Lake Kinncrct. Junk.

-. 1978h. The productivity of Mc~socyclops Ieuck- arti (Claus) in Lake Kinneret (Israel). Hydrobiologia 60: 17-22.

-. 198 lu. The metabolism of adult Mesocyclops leuckarti populations in Lake Kinneret (Israel) during 1969-1978. Int. Vcr. Thcor. Angew. Limnol. Verh. 21: 1563-l 572.

- 198 I h. Metabolic activities of herbivorous zooplankton in Lake Kinncrct (Israel) during 1972-l 977. J. Plankton Rcs. 3: 15-24.

HADAS, O., AND OTHERS. 1990. The clIcct of detrital addition on the development of nanoflagellates and bacteria in Lake Kinncrct water. J. Plankton Rcs. 12: 185-199.

HERTZIG, R., Z. DUBINSKY, AND T. BERMAN. 1981. Breakdown of Peridinium biomass in Lake Kinneret, p. 179-186. In H. Shuval [cd.], Dcvelopmcnts in arid zone ecology and cnvironmcntal quality. Balaban.

KLEPPER, O., AND J. P. G. VAN DE KAMER. 1987. The use of mass balances to test and improve the cstimatcs of carbon fluxes in an ecosystem. Math. Biosci. 85: 37-49.

LANDAU, R. M., M. GOPHEN, AND P. WALLINE. 1988. Larval Mirogrex terrasanctae (Cyprinidae) of Lake Kinneret (Israel): Growth rate, plankton selectivities, consumption rates and interaction with rotifers. Hy- drobiologia 169: 9 1- 106.

MALINSKY-RUSHANSKY, N., AND T. BERMAN. 199 1. Pi- cocyanobactcria and bacteria in Lake Kinneret. Int. Rev. Gcsamten Hydrobiol. 76: 555-564.

NEWELL, R. C., AND I. A. S. LINLEY. 1984. Significance of microheterotrophs in the decomposition of phytoplankton: Estimates of carbon and nitrogen flow based on the biomass of plankton communities. Mar. Ecol. Prog. Ser. 16: 105-l 19.

POLLINGHER, T., AND T. BERMAN. 1982. Relative con- tributions of net and nano phytoplankton to primary production in Lake Kinncrct. Arch. Hydrobiol. 96: 33-46.

POMEROY, L. R. 1974. The ocean’s food web, a changing paradigm. BioSciencc 24: 499-504.

PORTER, K. G., AND Y. S. FEIG. 1980. The USC of DAPI for identifying and counting aquatic microflora. Lim- nol. Oceanogr. 25: 943-948.

PRESS, W. H., B. P. FLANNERY, S. A. TEUKOLSKY, AND W.

T. VETTERLUNG. 1987. Numerical recipes: The art of scientific computing. Cambridge.

RIEMANN, B., AND M. SONDERGAARD [EDS.]. 1986. Car- bon dynamics in cutrophic temperate lakes. Elsevicr.

SERRUYA, C. [ED.]. 1978. Lake Kinneret. Junk. -, M. GOPHEN, AND U. POLLINGHER. 1980. Lake

Kinneret: Carbon flow patterns and ecosystems man- agemcnt. Arch. Hydrobiol. 88: 265-302.

SHERR, E. B., B. F. SHERR, AND L. J. ALBRIGHT. 1987. Bacteria: Link or sink? Science 235: 88.

- - T. BERMAN, AND 0. HADAS. 1991. High abundance of picoplankton ingesting ciliates during late fall in Lake Kinneret, Israel. J. Plankton Res. 13: 789-799.

STOECKER, D. K., AND J. MCDOWELL CAPUZZO. 1990. Predation on protozoa: Its importance to zooplankton. J. Plankton Rcs. 12: 891-908.

STONE, L., AND T. BERMAN. 1993. Positive feedback in aquatic ecosystems: The case of the microbial loop. Bull. Math. Biol. 55: 9 19-936.

STRAYER, D. 1988. On the limits to secondary production. Limnol. Oceanogr. 33: 12 17-l 220.

SUTTLE, C. A., J. A. FUHRMAN, AND D. G. CAIWNE. 1990. Rapid ammonium cycling and concentration-dcpen- dent partitioning of ammonium and phosphate: Im- plications for carbon transfer in planktonic communities. Limnol. Oceanogr. 35: 424-433.

TAYLOR, A. H., AND I. JOINT. 1990. A steady-state analysis ofthc “microbial loop” in stratified systems. Mar. Ecol. Prog. Ser. 59: l-17.

VADSTEIN, O., B. 0. HARKJERR, A. JENSEN, Y. OLSEN, AND H. REINERTSEN. 1989. Cycling of organic carbon in the photic zone of a cutrophic lake with special ref- crcncc to the heterotrophic bacteria. Limnol. Occan- ogr. 33: 489-503.

V~ZINA, A. F., AND T. PL,A~. 1988. Food web dynamics in the ocean. 1: Best estimates of flow networks using invcrsc methods. Mar. Ecol. Prog. Ser. 42: 269-287.

VINOGRAWV, A. P. 1983. The clcmentary chemical composition of marinc organisms. Sears Found. Mar. Res. Yale.

WALLINE, P. D., S. PISANTY, AND T. LINDEM. 1992. Acoustic assessment of the number of pelagic fish in Lake Kinneret Israel. Hydrobiologia 231: 153-163.

WEISSE, T., ANDOTHERS. 1990. Response ofthc microbial loop to the phytoplankton spring bloom in a large prealpinc lake. Limnol. Oceanogr. 35: 78 l-794.

WIADNYANA, N. N., AND F. RASSOULZADEGAN. 1989. Se- lcctivc f&ding ofAcartia clausi and CentropageLy typ- icus on microzooplankton. Mar. Ecol. Prog. Ser. 53: 37-45.

WICKS, R. J., AND R. D. ROBARTS. 1987. The extraction and purification of DNA labcllcd with [methyPH] thymidine in aquatic production studies. J. Plankton Rcs. 9: 1159-l 166.

Submitted: 30 September I992 Accepted: 2.5 May 1993

Revised: 20 July 1993

Documents

Lake Kinneret: A seasonal model for carbon flux through ......Lake Kinneret: A seasonal model for carbon flux through the planktonic biota Lewi Stone and Tom Berman Yigal Allon Kinneret