Much of economic modeling involves optimizing behavior by agents who interact in institutions with other optimizing agents to shape equilibrium outcomes. For example, economists postulate that consumers and producers are motivated by utility and profit, and they respond to incentives in the form of prices that are generated by their individual choices within market institutions. Of course, real people may be motivated by many factors; nevertheless, by focusing on utility and profit and assuming rational behavior economic models are useful in predicting the impact of policies on the prices, quantities, incomes and profits that follow from individual choices.

With some modification, this modeling framework applies equally well to plants and animals living in ecological systems. Individual plants and animals can be modeled as motivated by fitness. Theyrespond to incentives in the form of energy prices that are generated by their individual choices and the choices of other plants and animals within predator-prey and competitive relationships. And while plants and animals exhibit a bewildering array of strategies in the pursuit of fitness, by assuming consistent behavior, which may be less stringent than assuming rational behavior by humans, the economic modeling approach can be useful for predicting the impact of policies on plant and animal biomass demands and supplies, energy prices, and population dynamics that follow from individual choices.

Also like economies, ecosystems can be modeled in either a partial equilibrium or a general equilibrium framework. The former framework in economics requires isolating one or a few markets while fixing demands and supplies in other markets, and assuming that there are no feedback effects to those other markets from the markets under scrutiny. Similarly, in ecosystems partial equilibrium analysis requires isolating one or a few species while fixing the biomass demands and supplies of other species and assuming no feedback effects. Partial equilibrium is often adequate for understanding individual choices in isolated circumstances, although if there are important feedback effects, it can lead to seriously wrong conclusions about system wide outcomes [1,2]. Because feedbacks abound in both economies and ecosystems, there are many problems that are intrinsically general equilibrium in nature.

In this paper we take as given that integrating economics and ecology for better policy making is appropriate and desirable [3-6]. To this end, we draw upon the numerous similarities between economies and ecosystems to construct linked general equilibrium models of both systems. This approach avoids the tradition in economics of modeling ecosystems as a mere technical constraint on economic activity. The technical constraint usually is the logistic curve, and it is derived from an extreme partial-equilibrium version of an ecosystem. The curve depicts the growth of a single species while all other species are represented by a fixed carrying capacity. There is no underlying optimization by purposeful individuals, and there are no general equilibrium feedbacks. Such models miss the entire biological nature of nature.

Economic management policies derived from single species models inevitably will generate impacts on many other species in the ecosystem. These impacts move the ecosystem to a different equilibrium that may be an unintended consequence of the policy, thereby generating ecosystem externalities in the economy [7]. Moreover, people have demonstrated time and again that they have preferences about ecosystem externalities; that is, they are concerned not only with the policy goals but with the process that leads to the goals. “Because economic values depend on individuals' own assessments of their well-being, an understanding of the ways in which specific impairments of an ecosystem diminish their lives is essential.” [5] (p. 1388). Examples of such impairments are: the loss of cultural ecosystem services when bison that wander out of the Yellowstone Park on snowmobile trails are culled, the loss of marine ecosystem diversity when forage fish are harvested to feed hatchery salmon, and economic growth leading to the loss of charismatic birds and the cultural and supporting ecosystem services they provide [8]. Without a model that describes species interactions, one may miss different types of interactions between people and the ecosystem, because one cannot trace the ecosystem externalities that create the impairments.

Our linked general equilibrium approach describes the relationship between parallel, linked adaptive systems [9-11]. It is applied to a North Carolina estuary in which agricultural runoff altersphytoplankton densities and the resulting hypoxia leads to diminished fisheries. The general equilibrium economic model and the general equilibrium ecological model are connected through agricultural runoff and the fisheries, and important issues that are addressed include: (i) the choice of compatible spatial and temporal scales across the two systems; (ii) the role of dynamics; (iii) the boundaries of the systems and how entry and exit of firms and species occurs; and (iv) what outcomes from the systems are important and how they can be measured. The effects of hypoxia on multiple species across space are analyzed and the joint economic and ecosystem wide response to a policy of reduced runoff is quantified. The approach provides an assessment of changes in ecological welfare (in terms of species populations) and economic welfare (in terms of equivalent variations) following reductions in runoff. After developing the general equilibrium models, we highlight the advantages of a linked approach.

GEEM combines two disparate ecological modeling approaches: optimum foraging models and dynamic population models. The former approach has been likened to consumer theory [12] and describes how individual predators search for, attack and handle prey to maximize net energy intake per unit time. The approach does not account for multiple species in complex food webs and it does not track species population changes. The latter approach tracks population changes by using a difference or differential equation for each species. The familiar logistic-growth model used extensively in the economics literature is the simplest example, although extensions include resource competition models, e.g., [13], and multi-species models, for example, [14-22]. However, the parameters in the dynamic equations represent species-level aggregate behavior: optimization by individual plants or animals or by the species is absent. Alternatively, GEEM employs optimization at the individual level as in foraging models, and uses the results of the optimization to develop difference equations that track population changes.

GEEM also differs from large simulation models, e.g., [23,24]. First, its basic unit is an individual organism and not a species, and decisions are made by the individual. Second, it recognizes that natural selection requires plants and animals to maximize their net energy flows; thus an optimization approach is used to capture efficient energy use by all individuals. Third, species' population update equations are derived from individual behavior and linked to individual energy efficiency. Estimates of lumped parameters in the update equations are not needed.

In sum, GEEM combines general equilibrium calculations, similar to those used in Computable General Equilibrium (CGE) economic models, with dynamic population updating used in ecology. By tracking multiple populations GEEM is a step toward ecosystem-based management in which the importance of non-target species is recognized and preserving biodiversity is a goal [25].

Applying GEEM is an exercise similar to applying a basic CGE model. CGE models translate an economy into a mathematical formulation. While there are numerous methods of approaching the problem, the most common method uses individual optimization problems of firms and consumers to derive demand and supply functions. These functions describe how these agents react to prices and perturbations in other variables, and they are used to construct the equilibrium conditions of the model. Thus the problem is converted to solving a square system of equations, where optimal individual behaviors are embedded in the system. The numerical solution finds values of endogenous variablesfor given values of exogenous parameters. Endogenous variables include outputs, prices, and demands, while exogenous parameters include preferences, technologies, and factor endowments.

The initial data for a CGE is usually represented by a rectangular matrix known as a social accounting matrix (SAM). A SAM basically broadens a traditional input-output table to encapsulate all monetary and real flows in an economy. SAMs present what is assumed to be an observed equilibrium for an economy, and provide a tabular description of the circular flows of commodities and money throughout an economy. They display all the consumer and firm receipts and expenditures, with the requirement that in equilibrium receipts and expenditures balance.

Before running a CGE model a validity test is conducted in which the CGE is required to replicate the SAM equilibrium. To find parameters that are not available in the initial data, the SAM benchmark endogenous variables are used to calibrate the model to the observed equilibrium. Following calibration the CGE is run using the parameters and it is validated if it replicates the SAM.

GEEM also uses individual optimization problems to derive demand and supply functions, although the individuals are plants and animals who are maximizing their net energy devoted to reproduction. Quantities are in biomass units and prices are in energy units: for example, a predator expends energy to capture and consume prey biomass. As with CGE, the numerical solution finds values of endogenous variables for given values of exogenous parameters. Endogenous variables include biomass demands and supplies and energy prices, while exogenous parameters include individuals' respiration and predation parameters, weights, embodied energies and species populations.

Initial data is needed for GEEM that may be labeled an ecological accounting matrix (EAM). EAMs provide what is assumed to be an observed equilibrium for an ecosystem, and provide a tabular description of the circular flows of biomass and energy throughout an ecosystem. They display all the plant and animal biomass receipts and energy expenditures, with the requirement that in equilibrium receipts and expenditures balance. Again as with CGE, a validity test is conducted wherein the EAM is assumed to be an observed equilibrium and GEEM is required to replicate this equilibrium.

Where GEEM departs from CGE is in tracking the species populations. That is, in CGE the numbers of consumers or firms are exogenous, but treating species populations as exogenous would miss what may be the most important characteristic of the ecosystem—how populations are changing over time. To determine population changes, after each general equilibrium calculation, the individuals' optimum net energies are used to update the populations. Therefore, populations are exogenous for each general equilibrium calculation but endogenous over time, and GEEM should be thought of as a series of general equilibrium calculations in which the numbers of individuals are changing between calculations. If the numbers of individuals cease to change, then a steady state is said to be attained.

The North Carolina economy is described by a closed CGE model of an economy with a fishery sector. The “closed economy” assumptions of all economic production and consumption taking place within North Carolina allows a focus on the impacts of the policy throughout the North Carolina and the Neuse ecosystem. But these assumptions have consequences on the results as they neglect any responses of the greater economic and ecological systems surrounding North Carolina and the Neuse.

Within the economy, all agents are assumed to be perfectly myopic, consistent with open access in blue crab harvesting, and all savings and investment behavior omitted such that factor stocks remain constant over time. Government is included in the model only through command and control N emissions practices.

The economy has three production sectors: the blue crab fishery B, agriculture A, and composite goods C. Profit-maximizing, price-taking firms employ harvests of blue crabs in the fishery, and capital and labor in all sectors, to produce their outputs in a continuous, nonreversible, and bounded process. Outputs from the fishery, agriculture, and composite goods are sold in closed regional marketsto regional households. Capital K and labor L are homogeneous and defined in service units per period. They are also perfectly mobile between sectors and between periods. Sector i factor employment levels are given by K_i and L_i (i = B, A, C).

In simulations, commodity prices, final demands, factor employments, factor rewards, consumer incomes, species populations and harvests are endogenously determined. Changes in these variables and welfare measures are observed as N loadings are reduced. The general methods employed in the CGE model follow [55-57]. Only unique features of the methods employed are presented in detail, standard features relegated to the Appendix. Unique components of the model are the treatment of the fishery sector and agricultural costs of a N reduction policy. The blue crab fishery adapts the bioeconomics of [15] to the CGE framework following [58].

Incorporating a fishery into a CGE framework raises issues that require modifications to the standard fishery models. First, where most of the fishery literature employs effort as the single human factor of production [59,60], capital and labor must be included in CGE so that the fishery interacts with other sectors. Second, the non fishery sectors hire capital and labor in service units per time period, in this case one year, but in the fishery factors may be employed considerably less than one year. Third, harvests are spatially distinct which requires further modifications to the fishery.

To include these modifications in the CGE framework we use a nesting structure. Aggregate (non-spatially explicit) industry behavior is summarized by expressions (3.1) and (3.2): (3.1) H B = d B T α B n 7 β B (3.2) minimize W L B + R K B subject to T = ϕ B [ δ B L B ρ B + ( 1 − δ B ) K B ρ B ] 1 / ρ B

Equation (3.1) introduces aggregate harvests H_B as a function of fishing season length T, the aggregate (non-spatially differentiated) blue crab population n₇, and parameters d_B, a_B, and β_B. The season length is simply an aggregate measure of effort (given by capital and labor employed in the fishery) translated into the time (days) needed to land H_B given the blue crab stock. The industry is assumed to minimize the cost of harvesting according to Equation (3.2) by employing capital and labor to work time T, at wage W and rental rate of capital R subject to the constant returns to scale aggregation function. ϕ_B and δ_B are parameters and σ_B =1/(1 − ρ_B) is the elasticity of substitution between capital and labor in the fishery. The associated cost function is linearly homogenous in time, allowing the total costs of harvesting to be written as C(W, R)T.

Spatial targeting by harvesters is introduced by defining harvests as a function of spatially delineated stocks and seasons, that balance aggregate harvest and seasons, and exhaust all rents under open access. Space in the fishery is defined by the populations of blue crab (n^d₇ and n^s₇) in the deep and shallow channels, and season lengths (T^d and T^s) required to land harvests (H^d_B and H^s_B) in either channel. Harvests and time spent harvesting in each region are given by expressions (3.3).

(3.3) H B d = d B T d α B n 7 d β B and H B s = d B T s α B n 7 s β B H B = H B s + H B d and T = T s + T d

Given aggregate harvests and season lengths, spatial targeting is defined by adjustments in channel specific seasons so that there are zero net returns at the aggregate (fishery) level.

Fishery rents are driven to zero in the long-run through entry and exit of firms (in this representation given by changes in the season length). Each firm minimizes costs and applying Shepard's Lemma yields factor demands. Industry equilibrium is given by rent exhaustion: (3.4) π B = P B ( H B d + H B s ) - C ( W , R ) T = 0

The total factor payments over the season equal the total revenue divided by the season length, or average revenue per time. Harvesters, therefore, hire capital and labor optimally but under conditions of open access will continue to harvest (i.e., spend time harvesting) until all rents are exhausted (there is not an optimization problem for T, it is determined by rent exhaustion). We do not consider what factors employed in the fishery do during the off-season as in [58].

Standard methods are employed for agriculture, composite goods production and households, documented in the Appendix. Only the treatment of consequences from N reduction on agriculture is mentioned here. While the direct consequences on agricultural production from policies of N reductions are complex and beyond the scope of this analysis, a brute force tact is followed herein, where N reduction policies serve to increase producers' costs. This simplistic restriction allows a menu of potential cost scenarios to be seamlessly compared without having to change the technological specification of the sector. The addition of agricultural cost “shifters” modifies the industry's cost function: (3.5) C A = ( φ A N ) - 1 Q A [ δ A σ A W A 1 - σ A + ( 1 - δ A ) σ A R A 1 - σ A ] 1 / ( 1 - σ A )N reduction policies increase agriculture's cost function through the specification of the parameter ( ϕ A N ) - 1 = Δ N ( ϕ A ) - 1 where Δ^N is the percentage change in agricultural costs induced by the policy and ϕ_A is the sector's efficiency parameter in the absence of any cost impacts.

Regional households derive their income from sales of labor and capital endowments and consume regional agricultural goods, composite goods and blue crab harvests. Non-market linkages between households and the ecosystem are not considered herein but remain a focus of future work. Welfare impacts of alternative policies are evaluated in terms of modified Hicksian equivalent variational measures similar to those developed in [56]. Each policy change leads to changes across prices and income in relation to a reference/benchmark sequence of business as usual. Let the Hicksian expenditure function associated with consumption in period t be given by M_t(·). Vectors of prices in any period t of the reference scenario b or policy alternate a are given by P̄^b_t and P̄^a_t, with corresponding indirect utility functions V t b and V t a both a function of the croaker population in that period. In the results we employ annual equivalent variations E V t = M t ( P ¯ t b , V t a ) - M t ( P ¯ t b , V t b ) (see [61]) to calculate welfare changes for every period across policy scenarios. Cumulative aggregate welfare measures are found using discounted summations of EV_t which is possible as the measure is based upon a common baseline price vector. Also, given the exogenous time horizon a termination term is added to account for welfare impacts after the final period T. In this we assume that by T the economy is close to a steady state.

Time is defined in annual increments, and given the small share of the North Carolina economy comprised by Neuse agriculture and blue crab harvests (less than 0.1% of state gross product), capital and labor stocks are taken as constant over time. While lacking in detail, this format allows a representation of the relative importance to the North Carolina economy of those sectors and linkages with direct contact to the Neuse.

Human generated N flows in the deep and shallow channels are spatially differentiated, distributed randomly, and taken as exogenous to the ecological model. Changes in these inputs impact the resource competition between dinoflagellates and diatoms, with resulting energy transfer impacts up the food web. As described below, dinoflagellates are assumed to prosper at higher levels of N, while diatoms prosper at lower levels.

Ecological data for the Neuse estuary were obtained for plant and animal populations, benchmark plant biomasses and animal biomass demands, and parameters that include embodied energies, basal metabolisms, and plant and animal weights and lifespans and shown in Table 1. Species (1–5) are immobile and common to both deep and shallow channels; species (6) and (7) migrate between the two regions. Published network analyses of the estuary were used to glean the balance of the data [26,27].

We assume the average of the annual data is an approximation of a long-run equilibrium in the ecosystem, and we assume N levels are such that both dinoflagellates and diatoms coexist in both the deep and shallow channels. The equilibrium data provides a benchmark dataset that is employed in calibration to determine parameter estimates in the plant and animal respiration and supply functions [62]. Calibration consists of simultaneously solving for each individual the net energy expressions set to zero, first-order conditions or the derivatives of the net energy expressions set to zero, and the demand/supply clearing conditions. In the benchmark, there are several critical assumptions. The annual average is taken to be an approximation of an intervened (due to blue crab harvests) long-run ecosystem equilibrium in the absence of hypoxia. N levels are such that both dinoflagellates and diatoms coexist in both channels [63]. Blue crab harvests are assumed to be sustainable at an average of the 1994 through 2002 levels [64] and all other populations are not directly impacted by human contact (although indirectly impacted through the food web harvests).

In a fashion similar to the ecosystem modeling, the economic specification is based on a chosen benchmark year, and the data were used in calibrations to estimate parameters. The benchmark dataset constructed in the analysis is shown in Table 2 where all values are in millions of dollars. In this version of the model all North Carolina economic activity is produced and consumed within the state (i.e., there are no imports or exports) and all levels of government are omitted from the model (other than the regulator governing the nitrogen policy). These “closed economy” assumptions allow a focus on the impacts of the policy throughout the specific economic and ecological systems affected, but has consequences on the results as it neglects the response of the greater economic system surrounding North Carolina, just as the ecosystem model neglects the response of the greater ecological system that surrounds the Neuse. Details of the economic data and calibration follow standard methods and are presented in the appendix.

The linked models can be used to evaluate the welfare impacts of N reductions, although our main focus is on the advantages of using the linked approach as opposed to a standard bioeconomic model. The standard bioeconomic model we have in mind would formulate the problem from the perspective of an isolated fishery sector harvesting an isolated blue crab population. In the economic component of the analysis, all input and output prices would be assumed constant over time, with perfectly inelastic input supply and output demand (i.e., the fishery can hire all the factors of production they wish at a fixed cost per unit, and they can sell whatever they harvest at a fixed price). The ecology component would be a logistic growth curve of the blue crab population in which N loading would change the carrying capacity for the species. A functional relation between N loading and carrying capacity might be estimated from ecological data. The combined components would then determine the time paths of effort, harvests, and harvested stock for alternative N concentrations. Everything else in the economy and ecosystem would not be accounted for.

Although ecosystems provide myriad services to economies, only one service is considered in most economic renewable resource models. The more complete bioeconomic model introduced here makes clear that economic policies and activities influence myriad services. We demonstrate that N reduction in the Neuse has consequences throughout the ecosystem and economy owing to the joint determination of important variables. The reduction altered levels of all ecosystem populations, economic factor reallocation, changes in all regional prices, incomes, demands, outputs and both ecological welfare (in terms of species populations) and economic welfare (in terms of equivalent variations).

Inserting ecological detail into economic models is a promising new approach that raises numerous research issues. We will briefly discuss three issues that fall out of our linked Neuse models. First, the models reveal linked economic inefficiencies that suggest coordination in correcting the inefficiencies may be important. Agricultural runoff into the Neuse is a negative externality imposed on the blue crab industry, and the lack of property rights for blue crabs creates familiar open access harvesting problems. Finding an optimum level of runoff requires knowing its damage costs, and these will depend on the property rights regime in the fishery. Introducing mechanisms such as a transferable runoff permit system into agriculture and an individual transferable quota system in the fishery would work to establish property rights over the two externalities. To establish an efficient outcome requires linking the systems as any change in either property right has indirect consequences on the other.

The second issue that falls out of the analysis is how boundaries of the systems are defined. Whether to use partial or general equilibrium analysis is a common question in economics that carries over to ecosystems. In the Neuse the economics could be confined to the crab fishery, or broadened to include other estuary fisheries, or further to include agriculture, to include North Carolina, the Southeast region, and so on. Similarly, the ecosystem could be confined to crabs, or to include crabs and their prey in the estuary, to their competitor croakers in the estuary, to the croakers adult stage in the ocean and ocean going species, and so on. Regardless of where the boundaries are drawn around the systems there are going to be leakages to and from outside the systems, and this requires judicious selection of those variables that will significantly impact the results but not unduly complicate the model.

Thirdly, the linked approach incorporates the economic value of “non-economic” species. The linkages between most species and humans are not direct, but they are indirect through ecosystem services and food web linkages. The systems approach of the ecological and economic systems accounts for these indirect linkages by providing some interpretation of welfare changes owing to changes in non-economic species populations. For example, zooplankton are not directly linked to humans, but in the ecosystem they are an intermediate good in that they are prey for jellyfish and croakers. Since croakers have direct economic value to humans, a positive imputed value can be assigned to zooplankton. At the same time, overabundant jellyfish can hamper recreational activities such as swimming and boating implying that there may be a negative imputed value to zooplankton. Further, the disaggregated nature of the modeling approach provides a foundation easily adaptable to incorporate numerous other linkages through production processes and the specification of utility functions.

In sum, the CGE/GEEM linked modeling approach is flexible and can be applied to numerous other conflicts that arise when economic development and environmental conservation appear at odds. Three links between the Neuse economy and ecosystem were explored, but others could be added to the analysis. For example, including the croaker populations and their ecosystem outside the estuary would expand the economic model to include commercial and recreational croaker harvests. Additionally, existence values or other use values such as birding in the estuary are presumably significant (evidenced in the vast research dedicated towards the Neuse estuary), and incorporating them could result in different welfare impacts.