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Journal of Plankton Research Vol.17 no.6 pp.1273-1305, 1995 A comparison of whole-community and ecosystem approaches (biomass size distributions, food web analysis, network analysis, simulation models) to study the structure, function and regulation of pelagic food webs Ursula Gaedke Limnologisches Institut, Universitdt Konstanz, PO Box 5560, D-78434 Konstanz, FRG Abstract A step-by-step procedure for investigating the structure, function and regulation of pelagic communities as an entirety is suggested which proceeds along gradients of increasing requirements for data and knowledge, and of growing understanding of ecosystem functioning. It comprises methodologies based on biomass size distributions, followed by food web analysis, network analysis and dynamic simulation models. The different approaches are compared with respect to data requirements, theoretical foundations, operational problems, time and computational effort, and the different types of information they provide on food web structure and dynamics. These ideas are illustrated with data from Lake Constance. Biomass size distributions provide a structural and energetic food web analysis based only on measurements of abundances and body sizes, and a few general assumptions mainly on size relationships of metabolic activities and trophodynamics. Food web analysis considers binary webs depicting qualitatively trophic links between species or trophic guilds and provides profound information about the food web structure. Mass-balanced flow diagrams (trophic webs) take into account the magnitude of flows between living and non-living compartments, and provide comprehensive descriptions of fluxes and cycling of matter and the trophic food web structure when evaluated by network analysis. These three static approaches are contrasted with tactical dynamic simulation models depicting interaction webs and representing unique possibilities of studying the dynamic nature, spatio-temporal organization, direct and indirect cause-effect relationships, and impact of physical forcing. However, these capabilities are only achievable on the expenditure of a very large research effort. Introduction Now, more than ever, a comprehensive understanding of the structure, function and regulation of major ecosystems is necessary to face the world's ever growing environmental problems. Urgently needed is a strategic approach to predict the development of community structures and the functional responses of ecosystems to different anthropogenic environmental impacts. The dynamics and regulation of food webs cannot be understood, however, unless one simultaneously considers processes at the level of individual populations in concert with those acting over the domain of the entire community. All populations are embedded in an ecological context, i.e. processes that accrue at the population level permanently change properties of the whole system. These, in turn, impose new constraints back upon the individual populations (e.g. Mann, 1988; Pahl-Wostl, 1993b, 1995). Approaching this idea in practice is made problematic, however, by the extreme complexity of natural ecosystems which does not allow us to treat ecosystem dynamics in their entirety. Rather, one is forced to abstract from the situation, i.e. to select only certain data and questions to be asked and to neglect O Oxford University Press 1273 U.Gaedke the rest. Which of the many possible conceptions one chooses to elaborate and examine depends on many factors. For example, one's choice is strongly influenced by the availability of data, their training, working conditions and sociocultural milieu. The same factors affect the temporal and spatial scales with which an investigator observes ecosystem development. Therefore, one must approach the attributes of ecosystems from as many angles as possible—a task made feasible to an extent by the use of conceptual and mathematical models. Because they are simplified descriptions of the real world, there is no reason to expect any individual approach to be unequivocally right or wrong. Rather, each will differ in its capabilities to portray distinct features of the same natural system. In the end, however, they should complement each other, by virtue of the fact that each separate abstraction poses somewhat different questions and uses distinct types of information. An operational procedure that takes these problems into account could take the form of a step-by-step procedure for the analysis of ecological communities and ecosystems. Investigation proceeds in a stepwise fashion that requires ever more data and knowledge at each juncture, but which in turn yields a progressive understanding of ecosystem functioning (Figure 1). It takes explicit account of the effort and operational problems involved in the measurement of features of pelagic systems and in the subsequent data analysis. Along the way, the perspective changes from a focus on the community to an ecosystem point of low high low n*gl»ot«d low high low high oonsldsrsd high effort & Information content of the data base rel. contribution of local field work blomass sirs distribution food wab analysis (binary food waba) network analysis (trophic food waba) dynamic simulation modal (Intaractlon waba) - rigid adapthra potential contribution from other ecosystems & lab. studies interactions with the abiotic environment mechanlstical details Fig. 1. Sketch of a hierarchical order of different ecosystem approaches underlying Table I which provides more detailed information. The effort to establish the data base and the information content is roughly estimated by the multiplicity of knowledge required to apply a specific methodology. The increasing effort required to obtain additional information beyond standing stocks goes along with an increase of generality of this knowledge for similar ecosystems. For example, the abundance of a species in a particular ecosystem is relatively easy to measure as compared to its feeding habits. The latter, in tum, may be more alike among different habitats (for details see the text). 1274 Investigating pelagic food webs view by explicitly incorporating more numerous abiotic processes that may significantly affect food web dynamics. Prior or supplementary to setting up a dynamic, fully interactive simulation model for a particular ecosystem, it may be appropriate to explore other available methodologies, such as biomass size distributions, food web analysis and network analysis. Because they demand fewer data, these methodologies are usually less time consuming and expensive. Furthermore, they are likely to involve a smaller number of assumptions that can be communicated more succinctly. Table I provides a summary of the data requirements, potentials and limitations for various methods of studying entire food webs. Only those approaches that are capable of characterizing food webs in their entirety, and for which more or less well-defined theoretical foundations have already been developed, are considered. Hence, phenomena or modelling techniques that pertain only to individual populations (e.g. individual-based modelling) are excluded from the discussion. The contribution to theoretical ecology made by strategic models formulated in terms of analytically solvable differential equations is explicitly acknowledged (e.g. those that address the coexistence of species in a fluctuating environment; Ebenhoh, 1988; Yodzis, 1989), but a full consideration of these techniques lies beyond the scope of this paper. Some methodologies pertain mostly to pelagic and locally sustained food webs, but most technologies are more generally applicable. I illustrate most methods with examples from the pelagic zone of Lake Constance. Table I. Overview of the data requirements, concepts and potential insights to be gained by various ecosystem approaches Observational basis Concepts and techniques Potential insights abundances and body mass —» biomass biological species, allometric relationships, time-series analysis, biomass size distribution, trophic continuum concept species list, quantitative importance of species in respect to biomass (and process rates) size-conversion efficiency, variation in time and space, (structure, function, regulation) + abiotic parameters regression analysis potential abiotic impacts + trophic interactions —> binary web aggregation of species to trophic guilds, food web analysis food web structure, connectance, linkage density, potential direct interactions + process rates (e.g. production, respiration) and diet compositions -»trophic web population dynamics, flow analysis, network analysis, cycle analysis, trophic level concept mass-balanced flow diagrams, recycling of C and nutrients, trophic transfer efficiencies, trophic structure and function (direct and indirect effects) consistency checks + regulation of flows -> rigid interaction web dynamic simulation models with a set community structure direct and indirect effects and interactions, dynamic consistency checks + adaptability -» adaptive interaction web folly reactive and predictive simulation models with a flexible community structure prediction of community structure and function for different environmental scenarios 1275 U.Gaedke Lake Constance (in German: Bodensee) is a large (476 km2), deep (zmax = 256 m, mean depth 100 m), mesotrophic lake situated at the northern fringe of the Alps. It represents a large open-water body with presumably little labile allochthonous imports and a pronounced seasonally. A comprehensive data base is available on almost all abiotic and biotic parameters. For example, most physicochemical parameters and the abundance of all plankton organisms have been assessed by weekly sampling and elaborate microscopic counting techniques for several years. Additionally, production and other metabolic rates have been studied in detail. The measurements have been performed by a large team of scientists within the special collaborative programme 'Cycling of matter in Lake Constance'. This outstanding data set has been analysed in detail at the population level (e.g. Simon, 1988; Tilzer and Beese, 1988; Glide, 1990; Muller et al., 1991; Weisse, 1991) and at the community level (Geller et al., 1991) using biomass size distributions (Gaedke, 1992a,b, 1993), food web analysis (M.M.Lang, unpublished), and network analysis (Gaedke and Straile, 1994a,b; Straile, 1994; Gaedke et al., 1995). Further references on sampling techniques and production estimates are given by Gaedke (1992a) and Gaedke and Straile (1994b), and the literature cited therein. To conclude, the basic objective here is to suggest a strategy with which to investigate the functioning of a distinct pelagic community at the ecosystem level. A full discussion is given describing the measurements required to understand specific details of food web structure and function. Similarly, given a specific set of data, I discuss what kind of approach is the most suitable to apply. The paper aims to provide a comparison of methodologies by examining for each particular approach data requirements, theoretical foundation, time and computational effort, and capabilities and limitations of understanding of ecosystem structure, function and regulation. References for more comprehensive reviews and recent developments of the individual approaches and unresolved problems are given to the best of my knowledge. After some general remarks on an appropriate sampling strategy, I examine in depth the four key modelling approaches: biomass size spectra, food web analysis, network analysis and dynamic simulation models. Measurement strategy Field observations may be performed with different accuracy, and with different spatial and temporal resolution. Phytoplankton biomass and species composition, for example, may be roughly but more rapidly assessed by microscopy which requires up to 10 h of work time per sample, depending on the requested accuracy and taxonomic resolution. It may also be assessed by measuring pigment concentrations either in situ or by remote sensing. The space of potential sampling schemes may be imagined as a three-dimensional cube where the j-axis represents the temporal, the >»-axis the spatial resolution and the z-axis the effort in making the observations (Figure 2). Of course, it is most desirable to achieve high-quality measurements with a high spatio-temporal resolution. Given the usual limitations of a typical sampling programme, however, this will 1276 Investigating pelagic food webs quality of measurements spatial resolution of measurements temporal frequency of measurements Fig. 2. Three-dimensional cube to illustrate the potential sampling space along the gradients of temporal and spatial resolution and of the accuracy of measurements. Owing to the limited sampling capacity, trade-offs between the different optimization criteria are in general required. Total sampling effort should be distributed over various sampling strategies represented by different points within the cube in order to obtain information on different spatio-temporal scales. not be possible in general. Consequently, less accurate techniques (e.g. fluorescent probes or remote sensing) will have to be used in order to increase the spatio-temporal resolution. Long-term data series, where data acquisition is repeatedly performed in the same way, show a great potential for many studies and are essential for some. However, ecosystem functioning is determined by a multitude of processes acting on a large range of spatio-temporal scales which have to be studied appropriately (e.g. Field et ai, 1985). Concepts such as stability, resilience or equilibrium are contingent on the spatial and temporal scales of observation (e.g. Pahl-Wostl, 1993a,c, 1995, and references cited therein), and cross-system comparisons of food web structure and dynamics are only meaningful when one accounts for the spatio-temporal variability. Thus, the available sampling capacity should not be concentrated on one point within the cube of potential sampling schemes, but different locations in it have to be covered providing information on different aspects of food web dynamics. Community analysis based on measurements of abundances and body sizes: biomass size distributions (trophic continuum) When starting research on a particular open-water ecosystem, organismal abundances and body masses are among the first biological observations as they are relatively easy to establish in pelagic environments and essential for all subsequent analyses. They form the basis for the hierarchy of methodologies suggested in Table I by providing basic information on the species list and the quantitative importance of the different groups as assessed by biomass. Using allometric relationships, contributions to metabolic community processes like production and respiration may be roughly inferred as well (see below). Organismal abundances have to be observed specifically for individual ecosystems and periods of seasonal succession, and can hardly be inferred reliably from knowledge about other ecosystems. In contrast, estimates of body 1277 U.Gaedke masses and conversion factors from body length or fresh weight to units of dry weight and carbon may be gained for many taxa from studies undertaken in similar ecosystems. The spatio-temporal variability and pattern formation in standing stocks may be investigated by time-series analysis and other techniques that correlate the various parameter combinations (e.g. herbivorous and algal biomass). This analysis allows the formulation of first hypotheses concerning biological interactions. Accompanying measurements of physicochemical factors (e.g. temperature, light, nutrient concentrations), which are commonly obtained simultaneously with the basic biological parameters, allow a first investigation of the reaction of the biological system to environmental fluctuations occurring during the period of investigation (Table I). These techniques generally do not take a whole food web viewpoint, but provide basic information for the models that are to follow. In contrast, a complete analysis of species size distributions of abundance, biomass and metabolic activity can provide information about structural and energetic aspects of pelagic food webs in their entirety based on these data, as illustrated below. General description and data requirements Biomass size distributions are constructed by allocating all organisms into logarithmically spaced size classes according to their individual body weight and summing up the biomass in each size class. Such spectra have been established for small and large limnetic and marine systems, and show the remarkable regularity with which biomass is frequently distributed in a continuous manner across the entire range of logarithmic size classes. In large open-water ecosystems like Lake Constance and the open ocean, no gaps (i.e. size classes without detectable biomass) are observed along the size gradient (e.g. Sheldon et al., 1972; Rodriguez and Mullin, 1986; Gaedke, 1992a). Furthermore, biomass tends to be in general evenly distributed over all size classes ranging from bacteria (10 14 g C cell ') to carnivorous crustaceans (10^* g C ind."1) on a seasonal average in Lake Constance (Figure 3). This regularity implies that the abundance of organisms per size class is inversely proportional to their body weight, which enables an estimate of the minimum counting volumes required to assess abundances of all size categories with equal accuracy. Some of the oceanic systems show a gradual and regular decrease of biomass with body size. Microscopic counting of an entire plankton community ensures detailed insight into the species composition, which enables a more profound functional analysis and provides the basis for the subsequent approaches. However, because it requires a great amount of time, it becomes impossible to attain a good spatio-temporal resolution. The latter may be improved considerably at the expense of taxonomic resolution by using automated particle analysers like inductive particle counters (e.g. the Coulter counter) or, more powerful, flow cytometers and (in the future) other optical techniques, as well as echo-sounders for crustaceans and larger organisms. Coulter counters were used to establish the first particle size distributions for many different regions in the open ocean 1278 Investigating pelagic food webs 10.000 1.000 E 100 o 11 14 17 20 23 26 log 2 (body weight) [pg C] Fig. 3. A plankton biomass size distribution of Lake Constance, time-averaged over the seasonal course in 1987 (redrawn from Gaedke, 1992a). (Sheldon et al., 1972), but do not allow discrimination between living and dead particles. The most advanced flow cytometers equipped with different scatters, excitations and emission channels, as well as sorting capacities, will permit a rough identification of shapes and emission spectra over a broad size range, making living organisms and dead material distinguishable. Furthermore, measurements of autofluorescence enable a distinction to be made between pigmented (i.e. autotrophs) and non-pigmented cells (i.e. heterotrophs). Future development of staining techniques (e.g. for proteins) may improve the capabilities of this method to estimate biomass. Given that some knowledge of the species composition, biomass conversion factors and food web structure is available, biomass size spectra based on such data are an effective technique to study the structure of and the energy flow within the food web (see below). This approach appears particularly useful for long-term monitoring and for large heterogeneous areas with possibly fast dynamics. Theoretical framework and underlying assumptions Body mass is frequently the single most useful quantity for study. Elton (1927) has already attempted to reduce the enormous complexity of pelagic food webs by emphasizing the generalizing capacity of body size. Allometric relationships between body size and weight-specific process rates enable a rough prediction of metabolic properties of (parts of) the entire community from body mass (e.g. Banse and Mosher, 1980; Platt et al., 1984). The metabolic activity, M,, of the organisms within size class i may be estimated from the size class-specific biomass, Bh and the average body mass, w,, of the respective size class: M, = c Bt w[*. The constant c depends on the physiological process under consideration (e.g. production, respiration). Its value may differ among major taxonomic groups (e.g. homeotherms and heterotherms, osmotrophs and phagotrophs; 1279 U.Gaedke Moloney and Field, 1989) and can probably not yet be specified as reliably as the scaling exponent b (e.g. Platt, 1985). A value of 0.25 is commonly assumed for b for all kind of processes (e.g. Peters, 1983; Moloney and Field, 1989). However, this value might be too large for (small) plankton organisms (Platt and Silvert, 1981; Banse, 1982; Sommer, 1989). A reasonable agreement was found between seasonal changes in the metabolic activity of the eukaryotic plankton community in Lake Constance derived by this method and of more direct and largely independent production estimates (e.g. 14C technique; Geller et al., 1991; Gaedke, 1993). This allometnc approach was used to parameterize a dynamic simulation model in a coherent way for a region where direct measurements of process rates were mostly lacking (Moloney and Field, 1991; see below). Additionally, body size has great predictive power for ecological processes (e.g. Platt et al., 1984; Calder, 1985; Cousins, 1985; Platt, 1985). In Lake Constance, for example, spring succession (i.e. the response time to an external perturbation) of dominant herbivores (ciliates, rotifers and crustaceans like daphnids) was strongly related to body size, as was the magnitude of seasonal fluctuations of plankton standing stocks per size class. In pelagic systems, body size gains additional predictive power at the community level since body size and trophic position are related to each other, especially if the grazing and detritus chain are considered separately (see below). This regularity derives from the fact that autotrophs tend to be relatively small and predators are generally to a certain extent larger than their prey, i.e. the predator size allows predictions about the size of food particles eaten. After the first empirical establishment of continuous and regularly shaped biomass size distributions, some models were developed to explain this regularity (e.g. Sheldon et al., 1977; Platt and Denman, 1978; Silvert and Platt, 1978, 1980; Borgmann, 1987) which formed the theoretical foundation for all subsequent analyses. They have basically three characteristic features, (i) They utilize the correlation between body size and trophic position in pelagic systems and describe a mostly continuous flow of matter from small to larger organisms, (ii) They are based on allometric relationships between body weight and metabolic processes, (iii) (Constant) predator-prey weight ratios, indicating the width of each trophic step along the size gradient, are used in some models to relate the flow of matter along the size gradient to trophic transfer efficiencies. The suitability of models assuming size-dependent metabolic rates and trophodynamics was experimentally analysed for lake plankton using a radiotracer (32P) (Vezina, 1986). A more detailed model considering differently sized autotrophs, heterotrophs and detrital particles has been suggested by Cousins (1985). Bacteria are the exception to models of this type since the basic assumptions of a flow of matter along the size gradient and predictability of growth rates from allometric relationships are not valid for these organisms (Giide, 1990). A continuum of biomass in respect to body size indicates the existence of a continuum of functional guilds in the planktonic food web owing to the close relationship between body size and physiological and ecological features. For example, herbivorous plankton ranges over a large size range and exhibits a correspondingly wide and continuous range of response times to a phytoplank1280 Investigating pelagic food webs ton bloom. Fast reactions are commonly achieved at the expense of other factors like vulnerability to grazing. This perception is in contrast to a more traditional view which emphasized differences in life history features among distinct taxonomic groups. Perceiving the pelagic community as a continuum of ecotypes has recently stimulated some preliminary hypotheses to explain the emergence of regular size distributions as an interplay between processes at the population and system level (Silvert, 1984; Gaedke, 1992b; Pahl-Wostl, 1995). Predator biomasses equal or exceeding those of their prey are energetically possible because small organisms have higher weight-specific metabolic rates than larger ones. Flat size spectra indicate that size-related differences in weight-specific metabolic rates compensate for the losses implied by the transfer of biomass from one trophic level to the next. The steepness of a size spectrum's slope reflects the efficiency of transferring biomass from small to larger sized organisms. A more negative slope of a straight line fitted to the (normalized) biomass size spectrum implies that a relatively large amount of small organisms supports only a relatively small biomass of larger ones and vice versa. By these means, biomass size distributions provide insight into the energy flow and transfer efficiency along the size gradient in complex pelagic food webs without the necessity to define distinct trophic levels or to distinguish taxonomic gToups as long as the size range under consideration is sufficiently broad to justify the assumption of an energy flow along the size gradient. Between others, this technique may provide rough predictions of potential fish yield from plankton measurements (Mann, 1988). The efficiency of transferring biomass along the size gradient by trophic interactions (i.e. not growth) depends on usual trophic transfer efficiencies (including exploitation and growth efficiencies) involved in each predator-prey interaction, and on the predator-prey weight ratios which determine the 'step size' by which biomass is transferred to larger sized organisms. If predators are only moderately larger than their prey items, a larger number of trophic interactions is required to transfer e.g. bacterial production to large crustaceans as compared to food chains dominated by filter feeders with large predator-prey weight ratios. Thus, trophic transfer efficiencies may be derived from the slope of biomass size spectra if average predator-prey weight ratios can be estimated (Gaedke, 1993). According to expectations, slopes become less negative with increasing eutrophication (Ahrens and Peters, 1991). Standardized measures, time and computational effort A biomass spectrum is mostly characterized by two features: the overall slope of a fitted line and the deviation from this line, which indicates the smoothness of the spectrum. The spectrum's shape reacts sensitively to insufficient assessment of particular size ranges, whereas the slope on which the functional analysis is based is less affected (Gaedke, 1992a, and references cited therein). Computations of biomass size spectra and related measures are straightforward and quickly done when the data are arranged in a proper way. This, however, may demand some effort, as measurements of abundance of all organisms have to be 1281 U.Gaedke merged with corresponding body sizes or size frequency distributions. Analyses of size spectra may be performed on PCs without specific training in mathematics or computer science. Comparison with other approaches The data base required to establish size distributions is close to the form in which the raw data are obtained. Models for the energetic analysis demand the parameterization of only very few constants as compared to network analysis and tactical simulation models. These highly aggregated models appear capable of explaining the major energy flows (Vezina, 1986; Gaedke, 1994a), although they do not account for mechanistic details, e.g. a detailed evaluation of the recycling of matter via the microbial loop. It has been postulated that size-related models may achieve a larger predictive power than (less aggregated) mechanistic box models (Mann, 1988; see below). The double logarithmic plot of biomass versus body size provides only a coarse representation of the community structure and reflects only substantial changes. A major shortcoming of actual models on biomass size distributions and flow networks as compared to dynamic simulation models is that they are nondynamic. One way to depict seasonal changes is to discretize the plankton development artificially by splitting the seasonal course into different time intervals. Size distributions and trophic food webs may then be established for each time interval assuming steady-state conditions. This procedure may give reasonable information on the average structure and fluxes during the respective periods, but it is not suitable for grasping fast dynamics and the processes driving them properly. Truly dynamic models for size distributions have rarely been developed (Silvert and Platt, 1978, 1980; Parkin and Cousins, 1981) and have hardly been tested with a particular data set (but see Vezina, 1986), partially because they provide a very idealized view of the energy flow (see the section on interaction webs for tactical simulation models using body size as aggregation scheme). Conclusion and future development Size-related approaches allow evaluations of the structure and energy flow in complex pelagic food webs. Abundance, metabolic activity, seasonal variability, reaction time to external perturbations, trophic position, prey size ranges and other attributes may be predicted from body mass. This empirical evidence (as well as recently developed theory) suggests that size-related descriptions have some potential for the analysis and modelling of pelagic food webs which needs to be explored more strongly in the future. Size-related approaches may turn out to be relatively cost efficient and reproducible for different pelagic ecosystems since only relatively accessible measurements (especially when modern automated particle analysers become generally available) and a few general assumptions are required (see also Platt, 1985). To utilize this potential, more effort should be directed to a better quantification of aUometric relationships for small plankton organisms and to analyse 'size conversion efficiencies' as compared to trophic transfer efficiencies. 1282 Investigating pelagic food webs Community analysis based on additional information of trophic interactions: food web analysis (binary food webs) General description and data requirements Based on a species list, binary community food webs may be established by compiling knowledge on all trophic interactions occurring within the food web (Table I). The name binary web indicates that only the presence or absence of a feeding link is considered, but not its magnitude or interaction strength. All organisms within an ecosystem influence each other directly or indirectly, which makes detailed information on the food web structure essential for functional ecosystem analysis. This is one reason why binary food webs were established for almost all types of ecosystems ranging from large open-water bodies and deserts to water-filled tree holes. Furthermore, binary webs are used to search for phenomenological regularities in food web structures (e.g. the number of feeding links per species, the number of predators per prey species, food chain lengths, the connectance; see 'standardized measures' below) across different habitats, and their dependence e.g. on food web size (i.e. the number of species or guilds), habitat characteristics (e.g. productivity, environmental fluctuations, size, pelagic versus terrestric, dimensionality) and the history of assembly (e.g. Cohen et al., 1990; Havens, 1992; Hall and Raffaelli, 1993). Such regularities are of major concern for disputes on food web stability and resilience which were investigated using dynamic population models, the behaviour of which depended on their trophic structure (e.g. Yodzis, 1988). For example, species-rich and highly connected model systems tended to be less 'stable' and it was postulated that natural webs should display patterns which enhance stability (Pimm et al., 1991; but see also Yodzis, 1993). To conclude, most studies of binary food webs were either performed as essential prerequisites of more functional analyses, or in the context of cross-system comparisons and stability analyses. The potential direct contribution of food web analysis to the solution of applied problems in particular ecosystems requires further evaluation. Figure 4 displays an example of a binary food web model of the pelagic community of Lake Constance (M.M.Lang and U.Gaedke, unpublished). Knowledge on potential trophic interactions between pelagic organisms may be derived from direct observation, stomach content and faecal pellet analysis, by immunological and isotopic techniques and, to some extent, from laboratory studies and the morphology and feeding behaviour of a potential predator combined with the relative prey size and its potential predator avoidance strategies [for a more comprehensive discussion, see Paine (1988)]. Diet compositions of large zooplankton and fish are in general well established as compared to smaller plankton. Observations on feeding links obtained for a particular ecosystem may be considerably supplemented from the literature since adaptation of feeding behaviour to prey availability (e.g. by adjusting mesh sizes) and temporal and geographical diet heterogeneity may be regarded as low, especially for small plankton. Parasitic interactions were generally ignored in pelagic systems. Including or excluding a less known or quantitatively minor 1283 U.Gaedke •D O S Fig. 4. A binary food web of the pelagic community of Lake Constance. Approximately 280 morphologically different forms were aggregated into 26 trophic guilds. (1) Bacteria; (2) autotrophic picoplankton (APP); (3-8) larger phytoplankton; (5) heterotrophic flagellates; (9-13) ciliates; (14-17) rotifers; (18-22) crustaceans; (23-26) fish (larvae) (M.M.Lang and U.Gaedke, unpublished). feeding link in a particular web remains to some extent subjective [for further discussion, see Yodzis (1993)]. Comprehensive and standardized documentation may partially overcome this problem (Cohen et al., 1993). Food web analysis is basically a non-dynamic approach. Spatio-temporal variability of the food web structure may be inferred from changes in the species lists. However, the absence of a species in the (probably varying) counting volume does not necessarily imply its absence in the natural habitat. Most species occur year round, but in very different densities. Thus, defining a species and its feeding links as present or absent generally requires the definition of an arbitrary threshold which tends to complicate cross-system comparisons (Winemiller, 1990; Closs and Lake, 1994). Theoretical framework and underlying assumptions Binary food web 'models' are purely descriptive and empirical graphs. Consequently, operational issues concerning e.g. the aggregation, definition of system boundaries, and the quality and comparability of the data base are the dominating factors determining their reliability. Aggregation. In food web studies, it appears most logical to take a trophic point of view and to aggregate or split biological species into trophic guilds (synonym: trophospecies) which do not represent units of reproduction, but units of organisms which share the same predators and prey (e.g. Cohen et al., 1993; Yodzis, 1993). Ontogenetic changes of predators and prey ranges of individual 1284 Investigating pelagic food webs species (e.g. by cyclopoid copepods) may exceed the differences between biological species (e.g. Daphnia hyalina and D.galeata) and very small plankton organisms can hardly be distinguished at the biological species level. Additionally, intra-guild predation is avoided by aggregation at the level of trophic guilds which facilitates subsequent computations. Aggregating or splitting biological species into trophic guilds may also help to reduce the effort to be spent on establishing the matrix of trophic links, and to avoid the impression of unjustified accuracy. Although the majority of all potential trophic interactions in species-rich communities may immediately be ruled out by common sense, many thousands remain to be checked when working at the biological species level, suggesting that a trade-off between the call for exhaustiveness and practicalities will be required even if funding is generous. The use of trophic guilds as the basic unit in food web analysis has been criticized because their definition is to some extent tautological and subjective, and this motivated recent work on the biological species level (e.g. Closs and Lake, 1994). Body size has been suggested as a more objective criterion for aggregation, i.e. defining for each size range the same number of trophic guilds (Pahl-Wostl, 1993a). The expressions trophic guilds and species are used interchangeably in the following text. The definition of system boundaries (e.g. the inclusion or exclusion of littoral, benthic, migrating or transient species). Its necessity arises in all kinds of ecosystem studies. It is, however, particularly difficult to resolve for binary food webs because the magnitude of fluxes or interaction strength is not a suitable decision criterion. The actual quality and comparability of the data base. This varies greatly because most studies of binary food webs available so far were not primarily designed for systematic cross-system comparisons (however, see e.g. Winemiller, 1990; Polis, 1991; Martinez, 1993; Closs and Lake, 1994), but were often by-products of research with other aims. Consequently, emphasis given to various parts of the food webs and the spatio-temporal scale varies between studies. For example, commercial fish species may receive more attention than other organisms and diet compositions of small organisms are less studied than those of large plankton, which favours a stronger aggregation at the lower end of the size gradient. A more detailed discussion on operational problems and potential improvements is given, for example, by Paine (1988), Cohen et al. (1993), and Hall and Raffaelli (1993). Standardized measures Purely graphical representations of complex food webs are incomprehensible and a number of different measures have been suggested to summarize relevant structural properties of complex food webs (e.g. Cohen et al., 1990; Yodzis, 1993, and literature cited therein). Basic statistics include the number of species (5) and links (L) per web, the proportions of top (T), intermediate (/) and basal (B) 1285 U.Gtedke trophic species, and the ratio of the number of prey species to the number of predator species (or consumers), ((T + /)/(/ + B)). The mean chain length represents the average number of links connecting top to basal species. Related descriptors include the maximum chain length and maximum number of trophic levels, as well as the frequency distribution of chain lengths connecting basal and top species. The number of links per species (linkage density: D = US) and the ratio of the number of observed links to the number of all possible links (directed connectance: C = US2 = D/S) describe the degree of connectedness within community food webs. Empirically established values of the connectance and related metrics were used to parameterize dynamic models studying the relationship between stability and complexity. The dependence and sensitivity of these quantities to the size of the natural web and the aggregation of the food web model are under debate owing to the weakness of the data base (see below) (e.g. Cohen et al., 1990; Martinez, 1992, 1993; Hall and Raffaelli, 1993). Inconsistencies in the resolution of web entities both within and between webs so far prevent clear statements about the relationship between the above-mentioned measures and habitat characteristics, and about their latent information on functional or dynamic properties of the respective communities. Scale invariance has been postulated for the connectance which would imply that the linkage density increases proportionally with S. Consequently, species would maintain on average more trophic interactions in large than in small webs (e.g. have a broader diet composition) which might have consequences for system stability. This hypothesis is contrasted by the iink-species scaling law' which conjectures an approximately constant linkage density independent of S (i.e. the connectance decreases hyperbolically with S) [see the review by Hall and Raffaelli (1993)]. Time and computational effort Computation of most measures is straightforward if no cycles between trophic guilds occur (cycles between living components are rare and usually of very small magnitude in natural food webs; Pimm, 1982), but may demand a powerful PC if the web is large. Standardized programmes are not yet available. Calculations demand little time as compared to the effort usually required to establish the feeding links, and to compare the results with other studies. If carefully done, the latter may become very time consuming owing to the above-mentioned dependencies of many indices on model assumptions and lack of standardization (e.g. Closs and Lake, 1994). Comparison with other approaches A major characteristic of this food web approach is that it requires no quantitative information on biomasses, diet compositions and fluxes which allows a high resolution of the food web and avoids the introduction of a large degree of uncertainty if the data base is weak. Food web analysis has a great power to summarize structural patterns of complex food webs at the expense of probably little capacity to study functional and dynamic aspects directly. 1286 Investigating pelagic food webs Disregarding the actual operational problems, a better understanding of food web organization can contribute to applied questions like strategies on wildlife conservation and ecosystem stress detection. Food web analysis may complement the common practice of inspecting species lists or the occurrence or absence of characteristic species by taking a whole community viewpoint and including indirect interactions. For example, a recent study showed that several parameters of lake food webs reacted sensitively to strong acidification (Havens, 1993). Conclusion and future development Food web analysis provides an effective tool for the structural analysis of complex food webs which is an important prerequisite for more functionally orientated approaches. Universal properties of food webs from different habitats are searched for in order to understand principal differences between types of ecosystems. However, the many imperfections in the current data base strongly complicate the unambiguous establishment of regularities in food web structures. It is a common feeling that future work should be directed to straightening out and using standardized aggregation procedures, which advance the evaluation of the ecological implications of the numerous food web descriptors, and of the mechanisms of how the observed patterns may have evolved (Hall and Raffaelli, 1993). Community analysis based on additional information of the magnitudes of flows: mass-balanced flow diagrams and network analysis (trophic food webs) General description and data requirements The binary food web is extended to a trophic one by considering the quantitative importance of the individual flows, and by including the fluxes to and from the pool of dead organic matter (Table I). The trophic food web is depicted by a number of compartments to which all organisms are allocated and which are interconnected by fluxes of matter. To estimate the magnitude of these fluxes, measurements or estimates on major process rates like ingestion, respiration, production and the release of dead organic matter are required for each living compartment, as well as quantitative information on the diet composition of omnivores. Mass-balance conditions have to be fulfilled for individual compartments (i.e. ingestion representing the input must balance the sum of the outputs consisting of e.g. respiration, production, egestion, release of organic substances), as well as for the entire system. For example, total primary production must balance the sum of community respiration, sedimentation and changes in standing stocks in autochthonous systems. A typical example for such a massbalanced flow diagram is shown in Figure 5. Flux estimates are obtained by a broad range of techniques depending on the processes and organisms under consideration. In situ process rates, especially on respiration and the release of organic substances, tend to be more difficult to obtain than data on standing stocks. Fortunately, the increasing effort proceeds 1287 U.Gaedke with an increase of alternative possibilities to estimate the range a flux may achieve (Figure 1). Information may be derived from laboratory studies, and from measurements on potential weight-specific rates, assimilation and net growth efficiencies. Furthermore, the mass-balance constraints reduce the potential range of flux values. Given a sufficient data base, they enable a rigorous consistency check of the different bits of information used to quantify the flow diagram, and allow 'guestimates' of some fluxes which are particularly inaccessible to measurements. Most flow diagrams to date have been quantified in units of carbon, indicating the flow of energy. However, some studies use the most limiting nutrient. In natural systems, mass-balance conditions are fulfilled for all biogenic elements. The consideration of multiple commodities (e.g. carbon, nutrients, oxygen, energy) in balanced flow diagrams and its computational handling is still in its infancy (Vezina and Platt, 1988; Constanza and Hannon, 1989; Jackson and Eldridge, 1992; L.Stone, S.Barry and S.Hochstadter, unpublished). It improves the realism of the analysis and imposes additional constraints which reduce the degrees of freedom when setting up the flow model. However, the representativeness of point observations and laboratory studies for the entire ecosystem should be questioned owing to the adaptability, dynamic nature and spatial heterogeneity of natural systems. Natural systems vary on many scales and these variabilities are beyond the potential of observation, which enlarges the inevitability of gaps in the observational variables. For these and other reasons, 177 | herb. cm. !n ;i ho, 1095 :f-t O fish ', j 11 I h 79 phytopl. 281 263 j 219 o !._:_.! 131 ? 381! car. cru. -•??-.' 60 I—i--—-j 67 ! O2 18. sad. ! 54 31 HF oa? 38 -260 i—:::, 27' _ POC/DOC-pool _ * _ _ 13 88 "<L. - 160|sed. Fig. 5. A mass-balanced trophic food web of the pelagic community of Lake Constance in high summer 1987, quantified in units of carbon (mg C m"2 day"1) (Gaedie and Straile, 1994b; Straile, 1994). HF stands for heterotrophic flagellates; herb. cru. and cam. cru. stand for predominantly herbivorous and carnivorous crustaceans, respectively. Circles within compartments represent changes of standing stocks (increase if <0 and decrease if >0), circles outside compartments are intracompartmental predation. X symbolires respiration. 1288 Investigating pelagic food webs a considerable degree of uncertainty about the magnitude of individual fluxes and the diet compositions will remain even for systems which are very well studied according to actual standards (e.g. Stdne et al., 1993; Gaedke and Straile, 1994b). Consequently, different techniques were suggested to establish mass-balanced charts from incomplete data sets (e.g. Vezina and Platt, 1988; Wulff et al., 1989, and references cited therein; Jackson and Eldridge, 1992). Some account explicitly for errors in the measurements and stochasticity of the environment by including a consistency range for each flux and biomass estimate in the input data set (e.g. best estimate 100 units, reasonable range 50-200 units). This enables, for example, the computation of the minimum and maximum value a (group of) fluxes may take without causing inconsistencies with the other data (McManus, 1991; Stone et al., 1993). Questions like 'What is the maximum value algal dark respiration may take without causing unreasonable values for other fluxes and efficiencies in the food web model?' are evaluated. The relevance of uncertainty about individual processes for the overall results may be assessed systematically and this has the potential to facilitate an efficient allocation of future research directions. Network analysis, as defined by Wulff et al. (1989), extracts from massbalanced flow charts comprehensive information on the flow and cycling of matter, the trophic structure and transfer efficiencies, and the organization of the food web (see below). Detailed studies were performed for Chesapeake Bay (Baird and Ulanowicz, 1989), Narragansett Bay (Kremer and Nixon, 1989), an open ocean plankton system (Ducklow et al., 1989), Lake Kinneret (Stone et al., 1993), Lake Constance (Gaedke and Straile, 1994b; Straile, 1994), and some other systems (Christensen and Pauly, 1993), partially in combination with dynamic simulation models (e.g. Field et al., 1989; Moloney et al., 1991). Theoretical framework and underlying assumptions Ecological network analysis has several roots. Many concepts and computational techniques were developed primarily in other disciplines that include economics, control theory and electrical networks, and later adapted to ecological networks (Wulff et al., 1989). Influenced by thermodynamics, network analysis relies entirely on the exchange of material between organismal groups and their environment which is a prerequisite for life to exist (Ulanowicz and Platt, 1985). Quantitative flows are assumed to integrate and reflect to a large extent the various ways by which organisms interact in nature. However, the magnitude of matter exchange is not necessarily directly proportional to the flow of information which restricts the potential of network analysis (see below). For example, from the view point of plants pollination by bees involves an extremely small flow of energy, which is, however, of outstanding importance for population dynamics. At the present state of the art, restricted knowledge on flows and diet compositions generally demands a stronger aggregation of trophic webs than that used for binary ones. This complicates a satisfactory accounting of the reticulate 1289 U.Gaedlte trophic interconnections of real food webs (Polis and Strong, 1994). Allocating organisms to a small number of trophic compartments and following the flow of matter through this model food web may relate to the discrete trophic level concept sensu Lindeman which has frequently been criticized, e.g. for the operational problems to handle omnivores unambiguously (e.g. Cousins, 1987). Trophic analysis in the context of network analysis accounts for omnivorous nutrition by describing the trophic food web structure in two ways. First, the trophic position of a compartment is calculated as the weighted average of the trophic positions of its prey compartments. Thus, the trophic positions of omnivores are non-integer values which reflect the average number of trophic transfers their prey items have passed before consumption. Second, the contributions of the individual compartments to the distinct trophic levels sensu Lindeman are calculated based on their relative share of ingestion (or biomass), i.e. omnivorous compartments are distributed over several trophic levels depending on their diet compositions. Knowledge of indirect effects which are transmitted by two or more (trophic) interactions between different members of a food web is essential for the overall understanding of ecosystem functioning (Yodzis, 1988). Interactions which appear detrimental when regarding only the direct effects at the population level may turn out to be advantageous in the community context and vice versa (Stone, 1990; Stone and Roberts, 1991). For example, an increase in algal abundance may enhance growth of herbivorous ciliates (positive direct effect), but it may also be detrimental to ciliates as densities of omnivorous ciliate predators like daphnids may also increase with increasing algal food supply (negative indirect effect). Some techniques have been suggested to evaluate indirect effects from flow diagrams (e.g. Ulanowicz and Puccia, 1990). Such computations are, however, unlikely to reflect true mutual dependencies for several reasons (cf. also Wiegert and Kozlowski, 1984). First, flow diagrams are commonly quantified and analysed in one commodity, either carbon or a limiting nutrient. However, the interplay between energy and nutrients may present a key factor in ecosystem functioning, and the strength of the effects may depend strongly on the commodity used (Stone and Weisburd, 1992). Secondly, the importance of an interaction is deduced from the relative amounts of flows between the organisms. This relationship may not hold for several reasons (Power, 1992). For example, omnivorous predators may be able to switch to another prey if the previous one is depleted. Thus, their dependency may be overestimated by a rigid and non-adaptive model (e.g. Polis and Strong, 1994). Third, evaluations of indirect effects may demand a comparison of positive and negative effects (Stone, 1990) for which controversial definitions have been suggested. Like binary webs, flow diagrams were used as basis for computations of interaction strengths between compartments near equilibrium (de Ruiter et al., 1995). This subject requires further evaluations. Standardized measures Similar to food web analysis, comparative indices have been established to quantify trophic structure, intercompartmental dependencies, nutrient cycling, 1290 Investigating pelagic food webs compartmental and system residence times, and the organization of trophic webs. A comprehensive overview of their theoretical basis and application in marine systems can be found in Wulff et al. (1989) and the literature cited therein. The ecological interpretation of most measures is largely unambiguous and straightforward, and does not demand assumptions other than those made when establishing the flow chart. Such measures include a cycling index which represents the portion of flows that is recycled compared with the total flow within the system. Long cycles involving several living compartments and a substantial amount of matter are regarded as indicators of undisturbed systems. The average path length measures the average number of trophic transfers a unit of matter travels from its entry into the system (e.g. by primary production) until it leaves the system (e.g. by respiration or sedimentation) and, thus, provides a weighted average of the food 'chain' length. The total system throughput represents the sum of all fluxes within a trophic web and may be regarded as an indicator of its size. So-called 'dependency coefficients' inform about the direct and indirect contribution of one compartment to the diet of any other one. For example, the importance of microbial production for the nutrition of larger zooplankton may be evaluated by these means. In Lake Constance, fish derive 2-8% of their nutrition from bacterial production, the remaining fraction originates directly from autotrophs (via the grazing chain) (Straile, 1994). The effective trophic position as defined above is obtained from a so-called theoretical 'Lindeman Matrix' which also provides an abstract food chain consisting of the various trophic levels ('Lindeman Spine'). Graphical representations of the latter display the quantitative importance of flows between the levels, and the respiration and recycling of matter from each level (Figure 6). Additionally, the contribution of individual compartments to distinct trophic levels may be examined. The ascendency is defined as the product of the total system throughput and the food web organization inferred from flow diversity (Ulanowicz, 1986). Its maximum value is called developmental capacity since it was primarily speculated that the ascendency increases as the system matures (Ulanowicz, 1986), which is in conflict with recent findings (Christensen, 1994; Straile, 1994). Another measure tackling a very important and demanding issue, but yet delivering disputable results (e.g. Loehle, 1990), are the coefficients of indirect effects (see above). Mass-balanced flow diagrams can additionally be used to formulate simple linear models which trace the pathway of one unit of matter ('tracer', e.g. primary production or organic matter taken up by bacteria) through the food web as a function of time. The velocity by which organic matter is channelled through, and lost from, the food web, and its accumulation within different compartments of the food web, are computed based on compartmental residence times, i.e. the ratio of biomass to ingestion. Residence times, accumulation and elimination of toxic or otherwise harmful substances may be evaluated by these means (e.g. Anderson, 1983; Jackson and Eldridge, 1992; Eldridge and Jackson, 1993; Higashi et al, 1993; Gaedke et al, 1995). In Lake Constance, the residence time of primary production was low in spring when 50% of the algal standing stock was lost from the system after 2 days. In early and midsummer, system 1291 U.Gaedke 124.6 F' .3 2014 140 8 75 4.86 0 22 0 07 * A 2740 u 282 III 48.8 •4* IV 341 V 0.38 VI * * VII VIII • < - Fig. 6. A 'Lindemans Spine' of the pelagic community of Lake Constance (early spring, 1987). The Roman numbers within the boxes indicate the trophic level (D stands for the pool of dead organic matter). The numbers above the boxes provide exports from the system and the numbers below the recycling of dead material. 4 symbolizes respiration. Values are only given for fluxes >0.01 mg C m"2 day"1 (Straile, 1994). residence times were 2-3 times as long which may reflect an increase of community organization. The temporal development of the relative distribution of the tracer within the food web exhibited pronounced seasonal changes as well. In early spring, primary production was passed quickly to the ciliate compartment and then to the pool of dead organic material which implied that cycling of considerable amounts of carbon was performed within a few days. In summer, herbivores and predators with longer residence times prevailed, which resulted in a slower flow to bacteria and fish than in early spring. In addition to the static descriptions of the trophic food web structure mentioned so far, dynamic considerations of food web regulation were developed which assume among other things that the major groups of organisms can be allocated to discrete trophic levels which represent functional units. Such concepts delivered reasonable predictions and management tools for some systems. For example, a trophic cascade may be found where large populations of secondary carnivores (e.g. piscivorous fish) suppress primary carnivores (e.g. planktivorous fish), which leads to high standing stocks of herbivores and correspondingly low abundances of primary producers (Benndorf et al., 1988; Carpenter and Kitchell, 1993). However, such appealingly simple mechanisms of food web regulation appear to be restricted to a limited number of systems (Reynolds, 1994; Polis and Strong, 1994). The reasons for the diverging findings can partly be analysed at the level of static flow diagrams (e.g. composition of trophic levels, importance of omnivorous nutrition), but may also require knowledge on dynamic interactions as described in the following section. The present level of data acquisition (i.e. standing stocks, body sizes and quantitative trophic interactions) additionally allows the computation of average predator-prey weight ratios for parts or the entire food web which are weighted according to their quantitative importance (Table I). These are relevant for all size-related energy transfer models. Time and computational effort A network analysis for a particular ecosystem may in general be performed within a few years, depending on the availability of biomass and flux estimates, 1292 Investigating pelagic food webs and on the degree of aggregation (e.g. number of compartments and fluxes, spatio-temporal resolution). Achieving mass-balance conditions and calculating the various network indices requires a considerable computational effort, even for small systems with up to 10 compartments. Two (non-commercial) software packages are readily available for personal computers which provide limited facilities to obtain mass-balanced charts and compute the measures mentioned above (NETWRK and AUTOMOD, Ulanowicz and Kay, 1991; ECOPATH, Christensen and Pauly, 1992) (for other programmes, see above). Careful interpretation of the results sometimes demands detailed knowledge of the underlying algorithms which are mostly based on matrix operations. Comparison with other approaches The compartmental model approach and numeric simulation models as described below promote a perception of the pelagic community as being composed of distinct non-overlapping groups of organisms in contrast to a trophic spectrum as it is emphasized by size distributions. The philosophy of aggregation may influence the results. In contrast to biomass size distributions, network analysis relies mostly on flux estimates rather than observations of standing stocks which, however, may influence flux estimates if weight-specific rates are used rather than independent rate measurements (e.g. by the I4C technique). Given sufficient knowledge, network analysis allows more detailed evaluations of the trophic structure and energy flow than biomass size distributions, e.g. concerning the relevance of the detritus chain. The larger reductionism is commonly achieved at the expense of demanding a considerable number of parameter estimates, some of which are impossible to determine with sufficient accuracy (e.g. on diet compositions) and ad hoc considerations. Despite these differences, the two approaches may deliver similar results, e.g. with respect to the overall energy transfer through the eukaryotic food web. The absolute values and the seasonal course of trophic transfer efficiencies derived by network analysis and from the slope of biomass size distributions using allometric relationships and average predator-prey weight ratios were in reasonable agreement for most of the seasonal course of 1987 in Lake Constance (Gaedke and Straile, 1994a). Although magnitudes of fluxes do not necessarily indicate their overall importance, a trophic web is likely to provide considerably more information on ecosystem functioning than binary webs. Nevertheless, the potential power of network analysis (i.e. ignoring all uncertainties in the model assumptions) to explain the probable causality of food web flow dynamics in a mechanistic sense is restricted when compared to dynamic adaptive simulation models. Summary and future development Mass-balanced flow diagrams evaluated by network analysis and related techniques provide an outstanding tool for the description of fluxes and cycling of matter in food webs. They overcome a number of limitations of actual sizerelated and food web approaches. Future work in this area should be directed (i) 1293 U.Gaedke to formalize, optimize and standardize mass-balancing procedures which account explicitly for errors in the measurements and for natural variability, (ii) to improve the theoretical and computational basis to deal with different units like carbon and nutrients simultaneously, (iii) to reconsider the methods to evaluate indirect effects from flow diagrams, and (iv) to further improve the (non-trivial) consideration of the dynamic nature and spatio-temporal organization of natural systems at the ecosystem level, e.g. by establishing time-resolved measures (e.g. ascendency) (Pahl-Wostl, 1990, 1993a, 1995). Ecosystem analysis based on additional information of flux regulation and adaptability: dynamic simulation models (interaction webs) General description and data requirements The transition from a trophic to an interaction web describing most direct and indirect interdependencies between the groups of organisms and their abiotic environment is one of the most difficult and challenging tasks in systems ecology, even for a set community structure and environment. It requires in addition to quantitative flux estimates, a profound understanding of the forces which drive them (Table I). Information on direct and indirect interdependencies is again less accessible by direct in situ measurements and has often to be inferred from long-term data series, cross-system comparisons, pulse and press perturbation experiments (Bender et al., 1984), exclusion- and laboratory experiments, indirect evidence, and first principles. Thus, qualitative and informal knowledge considerably complements hard data which are mostly used for model calibration and validation (W.Ebenhoh, in preparation). In general, extensive quantitative data bases are available for some interdependencies (e.g. the relationship between temperature and physiological rates under laboratory conditions) and lacking for others (e.g. in situ growth rates of a predator at various concentrations of differently exploitable prey items). The interaction strength representing a pairwise per capita effect of one group on another is not necessarily proportional to the magnitude of flow [see above and, for example, Polis and Strong (1994)], nor to its importance for the community and its stability as a whole owing to, for example, indirect effects (Hall and Raffaelli, 1993; de Ruiter et al., 1995) and specific life history features which makes reliable predictions of system behaviour largely elusive based on such data (Power, 1992). The results of simulated press perturbation experiments in a modelling study were highly indeterminate in respect to the direction of changes of standing stocks, and to the relative importance of individual interactions when the interaction strengths were assumed to be known within an order of magnitude (Yodzis, 1988). Empirical interaction webs have so far only been established for parts of complex natural ecosystems (e.g. Paine, 1992). Inference on whole community interaction webs from inevitably incomplete data sets requires again a mathematical formalism which may be provided by dynamic simulation models. Dynamic simulation models describing explicitly the major dynamics and interactions between the important functional groups and with abiotic processes 1294 Investigating pelagic food webs in a particular ecosystem, are called tactical simulation models, in contrast to strategic ones which aim to identify possible ecological principles by considering few state variables. The latter provide mostly abstract descriptions of individual processes isolated from the ecosystem context and are often solved analytically. Large tactical models are based on non-linear systems of coupled differential or difference equations which have to be solved numerically on a large computer (e.g. Jorgensen, 1986). Examples include models for coastal areas (Kremer and Nixon, 1978; Baretta and Ruardij, 1988; Moloney and Field, 1991; Taylor et al., 1993; Baretta et al., 1994,1995) and lakes (Scavia and Robertson, 1979). Complexity and scale. The difficulty of transcending scale is inherent to all ecosystem studies since the many-layered complexity of natural ecosystems can never be depicted in a single (mathematical) model, and the principal aim of any kind of model is not a perfect reproduction of the natural system, but to reduce the incredible natural complexity to a degree we can hope to cope with. If a mathematical model were to approach a complexity similar to that of nature, the investigation of its behaviour would be almost as difficult as that of the natural system itself. Consequently, mathematical models are always designed to answer more or less narrowly defined questions and should only include the processes which are regarded as essential for this purpose. Carefully chosen trade-offs are required between realism, generality of the results, possibilities to analyse the model behaviour, and the effort spent in model construction and testing. An unsystematic incorporation of details into the model is counterproductive for a better understanding and fit of the model, for various reasons (e.g. Wiegert, 1977; W.Ebenhoh, in preparation). The criteria and the level of aggregation influence essential properties of model behaviour like stability, elasticity, adaptability to changing conditions, and the capacities for temporal and spatial serf-organization. The latter demand internal degrees of freedom and redundancies e.g. in the model food web and community structure, and the introduction of additional dynamic variables which describe properties of other state variables, e.g. by reflecting the species composition of functional groups (Ebenhoh, 1994). Most frequently component organisms are aggregated into functional groups which may have the side effect that the expression of chaotic behaviour is reduced (EbenhOh et al., 1995). After realizing the predictive power of body size for physiological and ecological properties (see the section on biomass size distributions), body size is increasingly used as an aggregation scheme in dynamic simulation models (e.g. Moloney and Field, 1991; Silvert, 1993). Discrete trophic levels represent an alternative aggregation scheme. However, its applicability seems to be restricted to a limited number of systems (see above). To conclude, finding the optimal degree of aggregation for a model appropriate to answer specific questions is in itself a challenging task (Silvert, 1981), as are related subjects like parameterization, a comprehensive discussion of which is beyond the scope of the present paper. Nevertheless, being forced to select and model in mathematical terms the processes thought to be most relevant is of great value for the participating scientists as this promotes systematic thinking on system behaviour (Baretta and Ruardij, 1988), even if the 1295 U.Gaedke model outcome has serious deficiencies. This work may be facilitated by all kinds of studies which improve the understanding of ecosystem functioning, e.g. analysing the system with the previously mentioned methodologies, and developing tactical and strategic submodels for different key processes on a lower level of organization (e.g. phytoplankton growth in dependence on the physicochemical environment, competition of algae and bacteria for limiting nutrients). The restriction of the model to a particular question also implies the consideration of a particular scale in time and space. This is complicated by the fact that the intrinsic temporal and spatial scales of the component organisms of the entire food web differ by orders of magnitude, which requires the coupling of different scales in the model. The time step of pelagic simulation models on the ecosystem level is often 1 day, and simulation runs cover a few years which accounts for the usual predominance of the seasonal cycle as primary signal of interest (e.g. Baretta et al., 1995), and excludes consideration of evolutionary processes. Effects of processes acting on a finer time scale than 1 day may be introduced into the main model using time-averaged results from temporally finer resolved submodels. Large-scale spatial heterogeneity is often considered by subdividing the area of investigation into discrete spatial compartments (horizontally and/or vertically) for which simulations are performed separately using different boundary conditions. In this case, the biological model is in general linked to a physical one which describes the inter-compartmental horizontal and vertical transport and mixing of dissolved and particulate substances, including plankton organisms. Like short-term variation, small-scale patchiness is generally not modelled explicitly in the main model, but its (often significant) impact has to be considered when selecting suitable parameter values or, if available, by using averaged results from spatially finer resolved submodels. At least part of the year, physical forcing (e.g. by temperature, irradiance, stratification and mixing) can be the dominant factor determining the structure and function of pelagic communities, especially when regarding the lower trophic levels (Baretta et al., 1994). Its adequate representation in the model may require an interactive coupling of physical and ecological models, which again increases the complexity to be coped with. The seasonal courses of abiotic parameters which are only marginally influenced by the biological system at the spatio-temporal scale under consideration (e.g. surface irradiance, wind) are introduced as independent time series into the model. Dealing with multiple commodities is well established in numerical simulation models. The most advanced models consider the mass balance of the flows of carbon as a substitute for energy as well as those of the limiting nutrients and all other conservative substances which influence the biological system significantly (e.g. oxygen or sulphate concentrations) (e.g. Baretta and Ruardij, 1988; EbenhOh et al., 1995). In this context, the definition of system boundaries needs careful consideration (e.g. accounting for interacting processes with benthic and/or littoral systems may be required for a sufficiently realistic description of remineralization and nutrient dynamics; Baretta etal., 1994). Predictability. A clear distinction should be made between simulation models 12% Investigating pelagic food webs aiming to reproduce natural patterns observed in a particular ecosystem and those designed to derive additionally predictions outside the experience on which they are based, e.g. the system's response to major environmental changes. Predictive models require sufficiently realistic capabilities to adapt to alternative environmental scenarios, e.g. by modifying their community and food web structure and related parameters accordingly. Reliance mostly on field observations rather than well-designed experiments and extensive cross-system comparisons limits our knowledge to the naturally occurring combination of abiotic factors during the observational period. The predictive power of most models is further reduced by the usual necessity to fit some of the parameters, inbuilt predetermination, lack of adaptability, and in any case by the existence of positive feedback mechanisms, the chaotic nature of many ecological processes (e.g. Hastings et al., 1993; Pahl-Wostl, 1993c) and the (hardly known) selforganizing capacity of the ecosystem. Fully responsive and predictive ecosystem models have not yet been achieved, they present major objects of investigation for international programmes to be established during the next years. For the reasons mentioned above, we will always have to accept an irreducible extent of uncertainties (Breckling and MUller, 1994) which stimulated a fruitful and ongoing effort to Gnd useful ecosystem models (Ulanowicz and Platt, 1985; Mann, 1988). Present evidence suggests that the uncertainties are smaller on the higher levels of aggregation (e.g. the production and dynamics of individual species are less predictable than those of large functional guilds) (e.g. PahlWostl, 1995). A reasonable degree of predictability may be expected for spatially and temporally averaged qualitative patterns at the system or community level, but not for small-scale processes at the population level (e.g. the local outburst of specific pest species). Nevertheless, the improved understanding of ecosystem functioning and regulation gained during model development increases the reliability of qualitative predictions made by the modellers themselves. Constructing and analysing ecologically reasonable simulation models, considering many functional guilds explicitly without major flaws, is a science in itself and cannot be dealt with here in further detail, although it has hardly been discussed in the published literature (Baretta et al., 1995; W.Ebenhoh, in preparation). The objective of the following section is to briefly contrast tactical simulation models to the previously mentioned approaches in order to allow the reader a first judgement about the suitability and practicability of this technique for her or his project. Theoretical framework and underlying assumptions Simulation models represent a mechanistic approach which explicitly postulates a dominant role of cause-effect relationships. However, recent developments towards a more 'fuzzy' way of modelling aim to consider naturalflexibilityas well (Breckling and MUller, 1994; W.Ebenhoh, 1994 and in preparation). The theoretical framework underlying tactical simulation models is less well defined as compared to the previous mentioned approaches. It involves an entire body of theoretical concepts derived from all fields of theoretical ecology, system, 1297 U.Gaedke information and chaos theory, and related disciplines. A general theory of complex systems is still lacking although interdisciplinary studies identified some common features of complex systems like non-predictability, but universal order in chaos, and spatio-temporal self-organization. In ecosystems, the latter may derive from the co-existence of many similar species which may both rely on and increase local spatio-temporal variability and decrease global fluctuations (Pahl-Wostl, 1995). The actually very limited understanding of the organization principles of natural ecosystems is a major difficulty in developing realistic models (W.Ebenhoh, in preparation). Time and computational effort The time scope required for model evaluation and testing depends on the particular goal since a refinement of the questions we ask demands an increase in the complexity of the models we need to answer these questions. Investigations on fully responsive and predictive models require a large and interdisciplinary team of scientists collaborating intensively for years. Apart from a well-defined scientific scope, such models require a long-term funding scheme which favours the free exchange of data and ideas. Long-term group selection may need to be strengthened as compared to the actually common way of exclusively judging individual scientists frequently. Nowadays there is a trend of coding site-specific models in such a way that they can easily be modified to apply to similar systems, which greatly reduces the effort of future model development, and implies an efficient transfer of knowledge between systems and working groups (Baretta el al., 1995; Ruardij et al., 1995; W.Ebenhoh, personal communication). The analysis of simulation results of large models with many state variables demands computational aid and automated procedures. Results may be summarized using previously described techniques (e.g. flow diagrams, Lindeman spines; Moloney et al., 1991; Ebenhoh et al., 1995). Regarding computations, most tactical models require larger computers than PCs, e.g. well-equipped workstations or main frames. Commercial and noncommercial simulation environments (i.e. software packages) for models of different size, goals and complexity are available which facilitate, for example, compiling and linking of submodels, definition of model parameters, error analysis, integration, and the numerical and graphical output as well as the comparison with field data (e.g. Baretta and Ruardij, 1988; Ruardij et al., 1995). Comparison with other approaches The advantages of dynamic simulation models, as compared to the previously mentioned approaches, include the unique possibility of studying the dynamic nature and spatio-temporal organization, which are of outstanding importance in natural systems (e.g. Ebenhoh, 1988; Gaedke and Ebenhoh, 1991; Stone and Berman, 1993). Simulation models represent a coherent way to investigate direct and indirect cause-effect relationships of a large number of dynamic interacting processes, although their predictive power should not be overestimated [Yodzis (1988) and see above]. They may overcome many of the restrictions of network 1298 Investigating pelagic food webs analysis mentioned above, particularly if they involve sufficient adaptation capabilities. The often considerable impact of physical forcing can be analysed explicitly, which is less feasible with the above-mentioned static approaches. Dynamic simulation models offer powerful tools for consistency checks of input data and assumptions, testing of hypotheses, systematic integration of qualitative and quantitative knowledge of an interdisciplinary team, and the transfer of this knowledge to other ecosystems and research groups (e.g. Baretta and Ruardij, 1988). Tactical models have recently been criticized for the way they portray a far too mechanistic and rigid picture of natural ecosystems. Also, the large number of parameters that are required introduce numerous assumptions and uncertainties which might render model results meaningless for poorly specified systems. Deterministic models are often misinterpreted as having the ability to provide unjustifiably arbitrary precision. In most cases, they are unable to describe the natural variability that is ubiquitous in real ecosystems, which prevents meaningful confidence limits being assigned to their outputs. The research effort is great and the number of potential pitfalls is numerous. The almost unlimited freedom in model construction is achieved at the expense that all concepts, equations, parameters and assumptions have to be laid open in order to enable a full understanding of the model outcome. Complex models developed by cooperating groups of scientists are tedious to check by single scientists, which partially reduces their acceptance in the scientific community. Summary and future development Tactical simulation models with built-in degrees of freedom for self-organization, and changes of community structure and species composition have an outstanding potential to promote a functional ecosystem understanding. Such models require the mathematical formulation of non-linear functions which describe the interdependencies between the numerous physicochemical and biological state variables, and detailed information on the adaptation and organization principles of the system under study. Unfortunately, much of this information is hardly available. This suggests that building and analysing such complex models without major errors is a most difficult and time-consuming task, and appropriate techniques are only now being developed. Although the overall potentials and limitations are heavily debated, environmental threats like global warming, as well as the increasingly successful utilization of simulations in other sciences, promote further efforts to develop a new generation of ecological simulation models aiming to account for the criticism mentioned above (Breckling and Mtiller, 1994). Discussion and conclusions The present considerations are thought to provide a pragmatic guide to pelagic ecosystem research that describes well-established ecosystem approaches. Alternative ways of ecosystem description are under development and it is to be hoped that they will take into account the above-mentioned problems, reflect 1299 U.Gaedke recent changes in ecological perceptions and complement the current views. Most recent developments include concepts based on information theory (Hauhs, 1992) and individual orientated approaches which, for example, aim to explain properties emergent at the ecosystem level with processes acting at a local scale. Some goal functions like emergy, exergy and ascendency (e.g. Jorgensen, 1986, 1992; Ulanowicz, 1986; Odum, 1988; Christensen, 1994) have been suggested as highly aggregated measures of the overall development of ecosystems. The actual comparison of different methodologies proceeded largely towards the consideration of more and more data and details apparently providing a deeper and deeper insight into ecosystem functioning. As briefly mentioned in the last section, an excessive continuation of this trend is neither feasible nor desirable, but various trade-offs need to be evaluated. The complete reducibility of ecosystems to physics and chemistry by some form of algorithmic reasoning has to be questioned, and 'hyper-complex' models of any kind are unlikely to deliver complete understanding and reliable predictions for many reasons, some of which were touched on above (Mann, 1988; Yodzis, 1988; Wissel, 1992). Empirical evidence shows that (highly aggregated) models may have predictive power independent of a successful analysis of the underlying mechanisms (Peters, 1991; Hauhs, 1992). However, these predictions are only reliably applicable to previously experienced conditions. To face environmental problems like global warming, we need methodologies based on a more comprehensive understanding of ecosystem functioning, regulation and adaptation. It has previously been acknowledged that empirical ecosystem studies demand simultaneous investigations of all relevant biotic and abiotic parameters by a team of field workers. In analogy, modellers favouring different theoretical frameworks and modelling techniques should combine their efforts as well by analysing the same ecosystem with different methodologies. First results from Lake Ciso (Pedros-Alio and Guerrer, 1993) and Lake Constance (U.Gaedke, in preparation) indicate that this enables an efficient supplement of insights and more profound comparisons of the capacity of the various approaches to portray essential features of the natural system. Acknowledgements The present study, as well as data acquisition, were performed within the Special Collaborative Programme (SFB) 248 'Cycling of Matter in Lake Constance' supported by the Deutsche Forschungsgemeinschaft. Martin M.Lang performed most of the work on binary food webs in Lake Constance, as did Dietmar Straile and Silke Hochstadter on the trophic webs which were used for illustration. 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