Abstract

The Lake Erie Ecological Model (LEEM) arose as a modeling framework to address both scientific and management uncertainties about causes of recent instabilities of the Lake Erie ecosystem. Model design and implementation decisions were guided and reviewed by a group of managers and scientists under the aegis of the International Joint Commissions' Lake Erie Task Force. Design criteria required that the model provide a framework for joint consideration of lake-wide effects of invasion of zebra mussels, declining phosphorus loading, continuing toxic contamination, and fish harvesting on the structure of the fish community of Lake Erie. Meeting these criteria required explicit representation of trophic structure and nutrient limitations on primary production. Solutions to the problems of deciding on scope and resolution of the model are discussed. These trade-off decisions about model design have important implications for the scientific and practical usefulness of the modeling framework.

Introduction

With the adoption of the 1995 Priorities and earlier initiatives of the Council of Great Lakes Managers, the International Joint Commission has explored the potential of mathematical models to help with the implementation and assessment of an ecosystem approach to management. In the 1995 Priorities (IJC 1995), the Lake Erie Task Force created the Lake Erie Ecosystem Modelling Project as part of the Commission’s 1995 priority for Lake Erie. The priority arose from concern about the rapid changes that had occurred in the Lake Erie ecosystem over the previous five years in association with the invasion of zebra mussels. Under guidance of the Lake Erie Task Force and with the assistance of a core group of Lake Erie managers¹, the Lake Erie Ecosystem Modelling Project produced a prototype Lake Erie Ecological Model (LEEM) that focused on overlapping interests of fishery and water quality managers. The goal of this paper is to report on the full implementation of LEEM² in the context of a regional ecological risk assessment project funded by the U.S. Environmental Protection Agency³ and to review its contribution to ecosystem based management of the Lake Erie ecosystem.

LEEM Description

Modeling Framework

LEEM is a simplified representation of the food web of the Lake Erie ecosystem. The model simulates energy flow and contaminant movement by implementing a set of rules, which describe the feeding behavior of individual animals (Figure 1). By assuming that phosphorus loading limits the overall productivity of the Lake Erie ecosystem, LEEM constrains food web energetics to obtain consistency with observed productivity and biomass levels. Phosphorus loading thus acts as the main forcing function through regulation of primary production, which depends jointly upon phosphorus loading and internal recycling by zebra mussels. LEEM also implicitly⁴ incorporates physical habitat constraints by relating fish reproduction to availability of suitable habitat and by incorporating habitat structure into predator-prey interactions. With the explicit representation of two types of fisheries and the possibility of augmenting natural reproduction by stocking of hatchery-reared fish, LEEM further provides the option of exploring effects of exploitation policies on harvest and fish community structure. The modular structure of LEEM allows exploration of future appearance of non-indigenous fish species.

Figure 1

Schematic diagram of the Lake Erie Ecological Model, showing an explicit primary production component and emphasizing feedback of zebra mussels on the magnitude (through effects on phosphorus cycling) and allocation of primary production to edible and inedible components due to effects of grazing. Contaminant movement through the food chain is also shown.

Assumptions

A major simplification in LEEM is the choice of spatial and temporal scales for representing interactions in the Lake Erie ecosystem. The model assumes a whole-lake spatial⁵ aggregation and simulates changes in the ecosystem at a minimum of one-year intervals. This assumption means that the model is most realistic for fish populations and progressively less realistic for zebra mussels, zoobenthos, and zooplankton, whose populations exhibit substantial seasonal variability. Zooplankton and zoobenthos dynamics, therefore, are simplified to steady-state approximations of mean annual abundance and productivity. Zebra mussels and Quagga mussel are treated as a single mussel type with only annual total biomass dynamics. Fish migration is assumed to average lake-wide gradients in productivity, but spatial heterogeneity of fish populations is preserved through the explicit consideration of habitat overlap among fish species and lower trophic level components of the ecosystem. Nearshore and tributary habitat also act to limit recruitment of year-class cohorts to fish populations.

Phytoplankton and other primary producers are represented implicitly in the model. The model assumes that phosphorus loading determines lake-wide primary productivity. Productivity of zooplankton and zoobenthos thus depend upon phosphorus loading through primary productivity. The model separates primary production into two phytoplankton components: edible (available for zooplankton grazing) and inedible (mainly blue-green algae), which enter the food web through the benthos. Zebra mussel density partitions primary into these two fractions. Biomass of each fraction is a function of the production to biomass ratio, which is assumed to be size dependent.

The model simulates four contaminants (PCB, DDT, Atrazine, and Mercury). Contaminant loadings and mass balances are not explicitly represented. The model assumes an input data set consisting of annual mean concentrations of each contaminant in lake water. Contaminant body burdents of organisms at lower trophic level are predicted from estimated bioaccumulation factors, and contaminant body burdens of all other individuals depends upon the annual balance of contaminant uptake (ingestion and absorption) and excretion.

Growth of individual fish depends upon feeding according to annualized, theoretical expectations from bioenergetics models. Except for rainbow trout and lake trout, all fish species rely on natural reproduction for recruitment. Predicted reproduction depends upon fecundity and fertility coefficients, which vary by species and age. Habitat limitations are imposed through coefficients affecting egg mortality and through a density dependent limitation of spawning and nursery habitat supply limitation. Reproduction also depends upon an annually varying stochastic factor that represents effects on climate factors on spawning success and early life-history survival of each fish species.

Feeding by all age groups of fish depends upon a common set of rules rather than upon a predefined set of feeding relations. Predators are assumed to search a defined habitat volume and randomly encounter prey items. Probability of capture of a prey item depends upon the ratio of prey to predator size and on a habitat overlap coefficient.

Model Structure

LEEM explicitly incorporates three categories of state variables (Table 1). The model recognizes 7 to 14 age-structured, fish species, three lower trophic levels groups, and contaminant body burdens for each of the trophic variables. The whole lake version includes 669 state variables. Implicitly, the model also includes two more phytoplankton state variables, but growth of zooplankton, zoobenthos, and zebra mussels depend upon primary production rather than biomass.

Phosphorus loading is the fundamental driving variable for the model. State variable dynamics also depend upon ambient contaminant concentrations, climate influence on fish reproduction, suitability of nearshore and tributary habitat, and annual fishing effort for commercial and recreational fishing. For stocked fish species, the model requires annual amounts of stocking as yearling-equivalents.

Including control of annual nutrient loading, LEEM provides for fish management control through fishing and stocking. The model provides two types of fisheries (commercial and recreational) with age-specific catchability schedules varying by species. Options are also available for stocking to supplement natural reproduction for any species. Since LEEM does not have fixed feeding relations, the model allows exploration of the consequences of possible intentional or unintentional introduction of exotic fish species.

LEEM Application

Because LEEM is a simplification of a complex ecosystem, the applications are primarily heuristic. As Oreskes et al. (1994) have noted, models of large-scale, complex systems all share the problem of fundamental incompleteness in system description. Peters (1991, p. 110-128) has argued that the reductionism required to formulate any ecosystem model severely restricts its rejection on the basis on incorrect predictions⁶. The dilemma created with modeling a complex system is that any simplification or attempt represent the structure of a real system is false at some level and will thus yield incorrect predictions of system behavior. Solutions to this dilemma depend on the context of applications.

Judgment about the validity of model or its predictions depends on a specific problem setting. From a scientific point of view, a model is no different from any other hypothesis. Solving a problem or advancing understanding requires hypothesis testing through error detection. In this sense, heuristic application of a model is like other hypothesis testing, which requires making potentially refutable predictions. The context for application of a model depends upon criteria for determining whether a prediction is true or not. As in general hypothesis testing, heuristic applications of models must iteratively cycle between hypothesis generation and hypothesis testing. True predictions of a model or derivative hypothesis must be challenged more rigorously. Alternatively, incorrect predictions require exploration of possible sources of the error in model assumptions, structure, and test implications. The credibility and usefulness of a model, therefore, emerges from its contribution to the understanding of a particular management question or scientific problem.

Testing, Calibration, and Validation

For LEEM, model calibration and testing has focused on understanding recent changes in the Lake Erie fish community. After an impressive recovery from a depressed state in the 1960s Hatch et al. (1987), walleye populations had begun to decrease along with yellow perch and smelt (Koonce et al. 1999). Initial prototype development and model testing began with a Western Basin version of the model (Koonce and Locci 1995), which had only 7 fish species. IJC convened two modeling summits (1995 and 1996) to evaluate the adequacy of the model and recommend changes. The current version of the model (14 fish species with a whole lake spatial resolution) emerged from this evaluation process (Koonce and Locci 1996). In response to specific concerns with declining productivity of the Eastern Basin, Lake Erie fisheries biologists assisted with the development of an Eastern Basin version that includes 10 fish species.

Estimation of model parameters depended upon literature values and on Lake Erie data. The model requires estimation of 1,942 parameters. Many of these parameters are linked through biological processes and have fixed rules for their relationships. Even with optimistic assessment of the ability to estimate these biological relationships from "first principles," however, the model is over-determined with respect to calibration data sets. Although detailed studies of parameter uncertainty are ongoing⁷, model calibration primarily has focused on recruitment and habitat overlap parameters. Virtual population reconstructions of walleye and yellow perch along with diet studies provided by fishery agencies were the basis of initial model calibration. Koonce et al. (1999) and Locci and Koonce (1999) contain additional details of model calibration and testing.

Predictive Capability

Heuristic applications do involve predictions. However, falsifiable predictions tend to be about general characteristics of system rather than specific future states. Figure 2, for example, shows a testable prediction derived from repeated scenarios of LEEM. Simpler models such as the Lotka-Volterra predator-prey models, predict limit cycles of predator and prey with amplitude of the cycle dependent upon initial displacement from the equilibrium abundance of prey and predator as determined by model parameters. Introducing satiation feeding into such models (i.e. increasing their realism), leads to damped oscillations instead of stable limit cycles. To assist in the evaluation of the hypothesis that the decline in walleye abundance in the 1990s was the result of a predator-prey oscillation, a number of LEEM scenarios were run to explore the effects of various rates of increase of walleye. These simulations indicated that there appeared to be a threshold of the ratio of predator to total fish biomass at which increasing predator biomass would induce an oscillation. Below this threshold, predator and prey biomass would approach a steady-state without an oscillation. Since lack of quantitative estimates of total fish biomass preclude estimation of this ratio in most large aquatic ecosystems, we found that walleye proportion of total percid biomass was an acceptable surrogate. In Lake Erie, this threshold appeared to be crossed in the early 1980s—several years before walleye reached peak biomass. This hypothesis is not specific to Lake Erie, and could be tested with observations in other percid dominated systems.

Figure 2. LEMM simulations of walleye recovery for varying levels of exploitation. Dotted lines are scenarios that did not result in a predator-prey oscillation. the horizontal dashed line is the apparent threshold of percent walley biomass of total percid biomass at which a predator-prey oscillation is induced in simulations.

The role of LEEM in the testing of this hypothesis was to assist in the formulation of a testable prediction. In similar applications, Koonce et al. (1999) showed effects of alteration of lower trophic level productivity (simulating effects of reduced phosphorus loading or possible effects of the invasion of zebra mussels on pelagic productivity) would propagate through the Lake Erie food web differently than observed. In fact, the difference in expected timing of decline of various fish species is a critical divergence of predictions of "lower trophic level" and predator-prey oscillation hypotheses for explaining the decline of walleye, yellow perch, and smelt during the 1990s.

Discussion

Understanding how models will be tested is essential to model design. Without a context for judging extent of model error, it is nearly impossible to resist the lure of completeness offered by reductionism. All models are simplifications of real systems and are thus incorrect at some level of detail. In the development of LEEM, there were many criticisms raised about the adequacy of the model’s representation of lower trophic level complexity or of the lack of explicit spatial resolution that were attempted in the earlier water quality models of DiToro and Connolly (1980) and Lam et al. (1987). Balancing these calls for increasing resolution were the preferences of members of the Core Advisory Group to address primarily issues of common concern. Their needs were for a framework within which they could evaluate management options to deal with causes of declining fish populations. They did not perceive a need for detailed lower trophic level models or detailed nutrient mass-balance estimations, but they also did not know whether these details would be required for correct predictions of fish population dynamics. A fundamental challenge in the development of LEEM, therefore, was to find the proper balance between complexity of model design and simplicity of interpretation.

Experience with the application of LEEM to aid understanding of recent instability of the Lake Erie ecosystem has taught us the value of setting model resolution nearer the simplistic end of the complexity spectrum for any problem. Two examples of our own attempts to find model error illustrate the merit of beginning simply and adding detail only when it can not be avoided. The first example began with an effort to increase the resolution of the lower trophic level representation in LEEM. These attempts were the work of Sturtevant and Heath at Kent State University and Ghan and Johannsson of the Department of Fisheries and Oceans Canada, but they were similar in scope to the earlier International Biological Programme models (Huff et al. 1973, Park et al. 1975, and Walters et al. 1980). Central difficulties in this disaggregation of LEEM were determining numbers of functional groups of zooplankton and phytoplankton and determining the interaction of temporal and spatial scaling. The first problem is the familiar problem of potentially endless reductionism, but the second problem is actually more formidable. Simulating rapidly changing abundance of phytoplankton and zooplankton requires short time steps (of days or less), but at these time scales, spatial pattern dynamics also become significant to local population dynamics. Increasing time resolution without increasing spatial resolution requires ignoring the contribution of spatial pattern dynamics (i.e. diurnal migration or aggregation in fronts). However, including spatial pattern dynamics greatly increases model complexity—perhaps even beyond reasonable computational demands. The whole-lake spatial resolution of LEEM avoids this difficulty by assuming that annual fish movement patterns compensate for spatial pattern dynamics. On an annual basis, it is sufficient to describe the probability distribution for occurrence in habitat regions to predict the interactions of species. LEEM relies on a habitat overlap coefficient to define these interactions. This assumption is not valid for basin specific versions of LEEM. In the basin specific versions, effects of fish migration among basins must be included in mortality parameters.

The second example deals with decisions on aggregation of state variables more directly. May et al. (1979) proposed a multi-species fishery model based on a much simpler representation of a fish community than LEEM’s. The main simplifying assumption in their model was elimination of age structure. With the help of Atkinson and Zaremba (Department of Biology, Case Western Reserve University), we explored the effect of age-group aggregation on model predictions. In this case, we found substantial differences in model behavior were induced by inclusion of age-structure. In particular, models without age structure tend to damp variability much more rapidly than age-structured models. Because these differences in predicted behavior matter to fishery managers, who must deal with year-to-year variability in fish abundance, the computational simplification obtained by eliminating age structure renders such a model less relevant to the problem of interest. Without this reference problem, however, we would have much greater difficulty in finding criteria with which to judge model adequacy.

From the beginning of model development, the Lake Erie Ecological Modelling Project has sought to fulfill two purposes. First, trying to provide managers a framework within which to consider the management implications of recent changes in the Lake Erie ecosystem required involvement of a core group of managers to decide on types of problems to address and the levels of resolution required to address them. Because framework creation is an iterative process, the Lake Erie Ecological Model had to be flexible and easy to modify. The second purpose of model development was to obtain additional experience with the ways models of various types can be linked to enhance understanding of the ecological factors that are contributing to the rapid changes in the Lake Erie ecosystem. LEEM has been used to explore the interactions of factors contributing to the recent decline of important fisheries in Lake Erie (Koonce et al. 1999, and Locci and Koonce 1999). These applications indicate that the model has the potential to make these two contributions. LEEM, however, will not address all ecological issues confronting management of Lake Erie. From the outset, we have emphasized that LEEM will have a primarily heuristic value, and we find that using a model heuristically requires linkage of the process of evaluation of management issues and model development. Model development without linkage to use ultimately loses criteria for judging model adequacy.

Without application of a model to a specific problem context, many of the issues raised in evaluation and testing can not be resolved. LEEM and other similar models seem to sit on a cusp of complexity and simplicity. Attempts by Sturtevant and Heath to include more resolution of structure of primary producers in LEEM encounters formidable obstacles of defining appropriate spatial and temporal resolution as well as parameter estimates. Similarly, with the development of an ecosystem model for Lake Ontario, DiPinto and Jain (1995) reported that lack of data precluded the application of a detailed model of energy and nutrient flows and compelled use of a simpler model. These experiences echo the findings from efforts during the International Biological Programme to develop comprehensive ecosystem models (Huff et al. 1973, Park et al. 1975). While it was possible to construct models linking hydrology of watersheds with detailed biology of lake ecosystems, the behavior of these systems was not all that different from predictions based on much simpler models (Walters et al. 1980).

Application of LEEM to the problem of understanding recent changes in the Lake Erie fish community has also confirmed the existence of fundamental gaps in research and monitoring. In attempting to find errors in model predictions, we have encountered a lack of some very basic data from the Lake Erie ecosystem. Since the early recognition of possible eutrophication problems in Lake Erie, phosphorus loading has been considered an important factor to regulate. Unfortunately, we no longer have reliable estimates of annual loading, and, more significantly, we know even less about the biological availability of phosphorus loading now entering the Lake Erie ecosystem. The lack of understanding of phosphorus and productivity linkage is further eroded by the lack of lake-wide estimates of primary production. The recent publication of results of lake-wide sampling of phytoplankton and zooplankton (Graham et al. 1996) provides some information, but we still do not have estimates of whole lake biomass productivity. Without such estimates, we have found it very difficult to set reasonable constraints on fish productivity. This is a particular problem in reconciling the estimates of walleye abundance through virtual population reconstruction with the levels of productivity indicated in Graham et al. (1996). It is also clear from our model studies that the fish species have far more reproductive capacity than observed. A critical missing element is adequate understanding of the role of habitat limitation in the regulation of recruitment of dominant fish species.

¹ The Core Advisory Group included representatives from each State with Lake Erie jurisdiction (Michigan Department of Natural Resources, Ohio Department of Natural Resources, Pennsylvaina Boat and Fish Commission, and the Ney York Department of Environmental Conservation), the Province of Ontario, U.S. Fish and Wildlife service, and Environment Canada

² http://environment.cwru.edu/framindx.htm

³ EPA project number R825150-01-0, Modeling and Multiobjective Risk Decision Tools for Assessment and Management of Great Lakes Ecosystems.

⁴ Implicit incorporation refers to the representation of ecosystem structure through parameter values. Explicit incorporation of ecosystem structure occurs through state variable specification.

⁵Alternative versions of the model provide varying spatial resolution. A western basin model simulates seven fish species within the western basin of Lake Erie. An eastern basin version provids the option of exploring reduced nutrient inputs to the eastern basin with explicit focus on the 10 most important fish species in eastern Lake Erie.

⁶Peters developed this theme more extensively in Rigler and Peters (1995, p. 95-114).

⁷The analysis of parameter uncertainty of LEMM is being undertaken by Benjamin Hobbs and Richard Anderson (Dept of Geography and Environmental Engineering, Johns Hopkins Univiersity) in the context of the EPA funded project on Ecological Risk Assessment.

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