Title: Ecological Interaction as a Source of Economic Irreversibility




James R. Kahn (corresponding author)

Department of Economics

534 Stokely Management Center

University of Tennessee

Knoxville, TN 37996-0550



Robert V. O’Neill

Environmental Sciences Division


Oak Ridge National Laboratory 


Proposed Running Head: Ecological Interaction & Irreversibility


JEL codes:Q2, Q3


Acknowledgment Footnote: This research was funded by the U. S. Department of Energy, Office of Energy Research. Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research, Inc., under contract DE-AC05-84OR21400 for the Department of Energy.  Appreciation is expressed to Dina Franceschi, Jonathan Hamilton, and anonymous reviewers for helpful comments.




Irreversibility can be either physical or economic in origin. For example, the extinction of a species is physically irreversible. On the other hand, contamination of lake-bottom sediments by mercury is not physically irreversible (the mercury and/or sediments can be physically removed), but the cost is so high that it can be said to be economically irreversible. This paper argues that economic irreversibility associated with environmental change is much more common than typically discussed in the economics literature. The source of the problem is the inherent complexity of ecological relationships. The paper discusses the origin and policy importance of these indirect irreversibilities.

1. Introduction


In a series of articles during the 1970s, Arrow, Fisher and Krutilla (Arrow and Fisher 1974; Krutilla and Fisher 1975)  discuss the importance of environmental irreversibility. Some economic actions, such as damming a river, producing nuclear waste, emitting CO2 into the atmosphere, or releasing heavy metals, cause damage that simply cannot be repaired by the ecosystem.  In addition, ecological interactions may amplify the damage and transform seemingly reversible economic action into irreversible alterations.  For example, competitive interactions may prevent a valuable wildlife population from recovering, even after the damaging economic activity ceases.

 These effects are generated because the direct impacts of economic activity can cause indirect nonlinear changes in ecological, social, and physical systems.  Nordhaus (1994), for example, suggests that irreversible thresholds will determine the socio-economic impacts of global climate change.  In fact, it may be that “...low probability catastrophic events...should be our main concern” (IPCC 1996). Thus, commonplace non-linear interactions have important implications for economic activity and economic policy. This paper argues that economic irreversibility is much more common than typically discussed in the economics literature. The source of the problem is the inherent complexity of ecological relationships. Of course, uncertainty regarding irreversibility complicates the decision making process and generates the need for greater prudence in policy. (Arrow and Fisher 1974; Krutilla and Fisher 1975; Weisbrod 1964; Dixit and Pindyk 1994)



2. Economic Analysis of Environmental Change

The economics literature has shown a relatively narrow focus when measuring the changes in social welfare associated with improvements or declines in  environmental quality. Most of the literature has focused on either direct use values or existence values.1   Other important values associated with environmental change include the value of changes in ecological services. Ecological services include attributes and outputs of ecosystems, including nutrient cycling, hydrological cycling, maintenance of atmospheric chemistry and global climate, biodiversity, soil formation and primary productivity. While these ecological services generally do not directly enter utility functions in a fashion which is perceivable by the individual, they do contribute greatly to utility either directly through their life support functions, or indirectly through their impact on production and consumption activities.

The early contingent valuation studies (such as Knetsch and Davis 1966) and the early travel cost studies (such as Clawson 1959) focused on measuring the recreational benefits associated with environmental resources. The focus of the valuation literature expanded to include aesthetic benefits of environmental change (such as the visibility benefits or air pollution reductions (such as Randall, Ives and Eastman et al 1974) and the morbidity and mortality benefits of environmental change (see Berger et al. 1987). In fact, both the Clean Air Act and the Clean Water Act specifically discuss human health benefits as the primary benefit of environmental improvement. In addition, valuation studies have tended to focus on existence values, measuring the willingness to pay to protect individual endangered species, environmental quality in natural parks, and unique natural environments such as the Grand Canyon or Chesapeake Bay. It is interesting to note that the studies that come the closest to measuring the value of ecological services have really only focused on existence values or direct use values. For example, the study by Rubin, Helfand, and Loomis (1991) looks at the willingness to pay to preserve the presence of an indicator species, the spotted owl, rather than the value of the ecological services of the spotted owl’s’s habitat, the ancient growth forests of the Pacific Northwest. In fact, the public debate on the question of harvesting wood in ancient growth forests tends to focus on the prevention of the extinction of the spotted owl, rather than the total value of the ecological services which are provided by these forests. Similarly, studies of the value of biodiversity, such as the study by Simpson, Sedjo, and Reid (1996), focus on the value of potential medicinal uses of the species, rather than the total ecological and social benefit provided by the biodiversity.

If one has a relatively narrow perspective on what constitutes the benefits associated with environmental quality, then one will have a correspondingly limited perspective on what constitutes the optimal level of pollution, which constitutes the basis for environmental policy goals. The purpose of this paper is to attempt to broaden economists’ viewpoints on the benefits of environmental improvement, to focus on the value of ecological services and to show the potential interruption (and diminution) of these ecological services through irreversible environmental change. This paper also contributes to our understanding of environmental change by extending the concept of irreversibility to examine indirect irreversibilities, which are introduced and defined in the following section.


3. Nonlinearities and irreversibilities

Irreversibility can be either physical or economic. For example, the extinction of a species is physically irreversible. On the other hand, contamination of lake-bottom sediments by mercury is not physically irreversible (the mercury and/or sediments can be physically removed), but the cost is so high that it can be said to be economically irreversible.

Figure 1 presents a schematic of a damage function, which constitutes a functional relationship between the anthropogenic activity that modifies both the ecological and socio-economic systems, and resulting change in social welfare. Irreversibilities can occur at any stage of the process. For example, slash and burn clearing of tropical forests may result in irreversible (depending on soil type) loss of forests. Emissions of heavy metals into the environment are irreversible, since no natural processes exist to decompose the heavy metals. Carbon dioxide, once emitted into the atmosphere has a residence time of approximately 500 years.

These types of irreversibilities can be characterized as direct irreversibilities, as the original environmental modification (the direct result of the anthropogenic activity) can not be

reversed. This is the type of irreversibility that has generally been examined by the environmental economics literature. For example, Krutilla and Fisher (1975) focus on land use decisions, and the irreversible decision to allow development in wilderness areas.

Although direct irreversibility is important, this paper focuses on what can be termed indirect irreversibility. Indirect irreversibility does not occur through a direct impact, but through a behavioral response to a direct impact. In other words, direct irreversibility refers to the irreversibility of the processes modeled in the small boxes of Figure 1. Indirect irreversibilities occur as a result of the impact of these processes on behavioral relationships within the ecologic or economic system. These ecological and social responses are generated and  exacerbated by the complexity and nonlinearity of behavioral relationships.

Our objective in this paper is to demonstrate that this type of indirect irreversibility is pervasive in both ecological and social systems. This implies that irreversibility is inherently more common than implied by the direct irreversibility discussed in Krutilla and Fisher (1975), Porter (1982), and Arrow and Fisher (1974), which would imply that environmental policy should be correspondingly more cautious.

Ecological systems are fundamentally nonlinear and display complex behavior in response to disturbance.  Ecosystems are ordinarily stable, i.e., when they are disturbed, they recover back toward a stable equilibrium.  Naively considered, an environmental irreversibility only occurs when a catastrophic disturbance drives the ecological system beyond its ability to survive or recover. But viewed at a larger scale, the equilibrium itself is not constant and shifts in response to changes in background environmental conditions. It is critically important  to realize that irreversible ecological thresholds can be crossed even with small, gradual changes in the environment.

 As the environment slowly changes, the local system can enter a region of "metastability".  In response to even a minor disturbance, the local system no longer recovers to the old equilibrium, but moves rapidly to a new state.  The local system now responds to further disturbances by recovering to the new equilibrium.  For example, throughout the world, deserts are encroaching on grasslands, because of the overgrazing of livestock. This overgrazing gives a competitive advantage to desert scrub. However, if the animals are removed from the landscape, it does not return the competitive advantage to the grasses. The established desert scrub will continue to out-compete the original vegetation, preventing it from becoming re-established.

The phenomenon  can be explained  relatively simply in mathematical theory (Tikhonov 1950).  A model is solved for equilibrium by setting the differential equations to zero.  Under conditions of metastability, the system has moved into a region of parameter space where setting the equations equal to zero yields a higher order equation. That is, the equations are quadratic or higher in the state variables and there is more than one possible equilibrium state.  Empirically, one often observes a stable system moving rapidly to a new stable state, without the intervention of a major external disturbance.

An Example

It is important to emphasize that nonlinear phenomena can occur even in very simple environmental systems, without the complexities associate with order state equations.  Consider the dynamics of a population, N1, valued as a food resource, and N2, an inedible competitor.  Their dynamics are expressed as:


dN1/dt = r1N1 - bN1N2


dN2/dt = r2N2 - bN1N2


where ri is the potential rate of increase in the population and b represents a competition coefficient.  For simplicity, we will consider the rates of increase to be equal, that is, r1 = r2 = 1.  The two populations are competing for a common resource that supports a total combined equilibrium of K = N1 + N2.  At this equilibrium, Nj = K - Ni ,  further growth is impossible and


dNi/dt = Ni - bNi(K - Ni) = 0, so that

b = 1 / (K - Ni)                                                                                                                   (2)


Substituting the equilibrium expression for b (Eqn. 2) back into Equations 1 yields,


dN1/dt = N1 (1- N2 / (K - N1))


dN2/dt = N2 (1- N1 / (K - N2))


The reason for deriving Equations 3 is to illustrate a counterintuitive response one often gets from an ecological system.  The system is asymptotically stable to the equilibrium point, K.  That is, if we harvest a few of the food organisms, the system replaces the harvest by growing back to N1 + N2 = K.  However, the system is neutrally stable in the sense that the new equilibrium will have a different proportion of N1 and N2.

Consider the simple case in which initially N1 = N2 = 50, so that K = 100.  Now we will harvest a given number, H, of the food organism at a single point in time and allow the system to asymptotically approach a new equilibrium of K = N1 (¥) + N2 (¥) = 100.  To simplify the presentation, we will stop the simulation of Eqs 3 when N1 + N2 > 99.5.  The resulting equilibria for different levels of harvest are shown in Table 1. 

Simply explained, what happens is that the harvest of the food organism reduces the system below its carrying capacity and both edible and inedible populations grow back in response to this opportunity.  But the result is that the system does not have any single equilibrium value for the edible population.  The populations grow at the same rate and the final ratio N1(¥) / N2(¥) is sensitive to the initial conditions and, therefore, to the harvest.  Because of the nonlinear response, each harvest leads to a new equilibrium value for N1.

At first thought, it may seem that the dilemma of harvesting the food organism is simply resolved by applying some pest or weed control to the inedible population.  However, the underlying nonlinear dynamics make this strategy difficult.  Consider the situation in which K = 100 and N1 (0) = N2 (0) = 50.  Assume that one  would like to harvest H individuals of the food organism and allow 10 years for the system to recover before another H individuals are harvested.  What percentage of the inedible population would one then have to kill each year in order to ensure that N1 = 50 after 10 years?  The results are given in Table 2.  The results show that there is a maximum harvest of about 30 food organisms every 10 years, even if the competitor is almost completely killed back each year.

Thus, even though Equations 3 are a trivial representation of an ecological system, the nonlinear dynamics leads to important differences in the response of the system to human impact.  We have developed this example for competing fish, but readers will readily see the analogy with more complex situations such as the clear-cutting of forests, modification of the pH of an aquatic system, destruction of habitat, global climate change or introduction of non-native species. We have chosen a simple model of species interaction to illustrate that nonlinearities and indirect irreversibilities can arise from even a simple nonlinear dynamic model. As the system becomes more realistic and more complex, as the number of species and the number of interactions increase, the potential for the generation of  indirect irreversibilities also increases.


Nonlinear Irreversibilities

 So much for theory. Is there any reason to believe that such nonlinear phenomena occur in biological and environmental systems (O'Neill, Gardner, and Weiler 1982; O’Neill, Johnson and King 1989)?  At the smallest scale, it is generally accepted that this type of response causes periodic bursting in nerve cells (Plant and Kim 1975) and rapid transients in microbial colonies (Rozich and Gaudy 1985; Worden and Donaldson 1987).  At the ecosystem scale, Jones (1975) argues that outbreaks of pests follow these dynamics.  At the global scale, Crowley and North (1988) show that in very simple models of ice cap dynamics; that the system can jump from one stable state to another. They argue that this accounts for rapid climate changes in glacial‑interglacial transitions.

The most convincing evidence for nonlinear behavior in the global system is provided by mass faunal extinctions (Donovan 1989).  The fossil record documents nine major extinction events with climate change and/or sea level change implicated in eight.  The ninth event was probably precipitated by an asteroid which, in turn, created climate change.  However, the other eight extinctions were not simply caused by a major abiotic event.  Internal dynamics, i.e., biotic interactions, were also involved.  For example, the evolution of biomineralized (bony) jaws changed the efficiency of predators.  Land bridges caused faunal exchanges and extinctions of less efficient fauna.  These internal dynamics moved the ecological system to a new stable state, exactly as predicted by nonlinear theory.  While there appears to be little risk of mass extinctions due to projected CO2 increases, many candidates for nonlinear responses appear at the landscape, ecosystem, and population scales.  The criteria include: (1) systems near the limits of their geographic range, (2) systems already under severe stress, (3) systems that have impaired recovery ability due to other impacts.

The most conspicuous threshold at the landscape scale occurs at the ecotone, the tension zone where one vegetation type changes suddenly into another, e.g., grassland into forest (Hansen, di Castri and Naiman 1994).  These sharp transitions have long attracted the attention of ecologists (e.g., Clements 1897, 1905; Livingston 1903; Griggs 1914). Changes occur as disturbances destroy the existing vegetation and open the opportunity for new vegetation to take over the site.

As with other threshold phenomena, some ecotones are simply explained by sharp discontinuities in the abiotic environment.  The simplest example is seen on mountains in the northern hemisphere where the northern (colder) slope differs in vegetation from the adjacent south-facing (warmer) slope, yielding a sharp ecotone along the ridgeline.  But as with other nonlinear threshold phenomena, some ecotones occur as sharp transitions even along gentle gradients in abiotic factors (Hobbs 1986).  These ecotones are sharp because of competitive interactions within the system (Daubenmire 1968) and a small change in environment causes the system to move to a new stable state.  As environmental changes occur through time, the ecotone responds by moving in space (Boaler and Hodge 1962; Spugel 1976; Delcourt and Delcourt 1987).  Pollen records indicate that past climate changes have caused a slow (5 - 200 km per century) migration of ecotones.  The IPCC (1996) reports a consensus that biomes may migrate 150-500 km north due to global warming.

The concern for nonlinear responses is also motivated by the broad spectrum of stresses being imposed by society (Goodland 1991).   Average temperature is increasing faster than it has in the last 10,000 years (Arrhenius and Waltz 1990).   The human economy uses 40% of net primary production (Vitousek et al. 1986).  Natural vegetation has been fragmented, making it more difficult to recover from natural disturbances (Gardner , O’Neill and Turner 1993).  The ozone shield has been damaged.  Soil erosion is nearly universal, with soil losses exceeding soil formation rates by at least 10-fold (Pimentel et al. 1987).  More than 50% of the tropical forests have been cut with the current rate of deforestation exceeding 168,000 square kilometers per year (Goodland 1991).  Some impacts, such as species loss, are irreversible (Krutilla and Fisher 1975) and technology is not available to repair large-scale damage (Norton 1991).

Phillips (1995) discusses the importance of the time interval between successive disturbances and its implications for the time required to recover from a disturbance.  The multiple stresses currently being imposed on the global system are both increasing the frequency and intensity of disturbances and decreasing the ability of ecosystems to recover.  This twofold impact increases the risk of threshold phenomena and irreversibility.

4. Policy Implications of Ecological Irreversibilities

Nonlinearities and irreversibilities have long been recognized as having important implications for policy.  In the past, ecological and economic models have incorporated thresholds, but as discrete and isolated phenomena. The present study points out that these nonlinearities and indirect irreversibilities may result from common place, but complex interaction among ecologic and economic variables. The potential existence of these nonlinearities and indirect irreversibilities has important implications for policy.

One set of policy implications arises from nonlinear thresholds associated with renewable resources within the ecological system.   Nonlinear thresholds, for example, appear to be a reasonable explanation for the global collapse of fisheries which has been occurring during the last decade.  This is important to emphasize, because the existence of indirect irreversibilities implies that increasing the demand will eventually cause the collapse of the fishery. While increasing fishery effort will initially lead to a new equilibria associated with a smaller stock and smaller populations, indirect irreversibilities can prevent the return to the old equilibrium. These indirect irreversibilities may also trigger the crossing of a threshold, implying the collapse of the fishery. There are further implications for fishery and renewable resource management. For example, “pulse fishing” is often suggested as an appropriate management strategy for some fisheries (see Clark 1985 for a discussion of pulse fishing.) Following this policy, a species is fished extremely hard for several periods and then allowed to recover.  During this recovery period, attention moves to a different species which is fished extremely hard and then allowed to recover, and son on. However, in the population growth models which underlie the potential efficiency of pulse fishing, each species is assumed to be independent with no nonlinear competitive interactions and conventional management.   More complex models have been developed which focus on inter-species interaction, but fishery management policy continues to operate as if species were independent and as if it were feasible to restore collapsed species simply with a cessation of fishing effort.

 Analogous examples can be constructed for forests and other renewable resources.  Shortsighted fire-prevention policies, for example, simply stop small fires.  These small fires are a normal part of the evolutionary history of the forest and not only do not kill mature trees but aid in the dispersion and germination of the seeds of the climax trees.  The small fires also act to decrease the fuel level of dead wood and form natural fire-breaks.  Without the small fires, a threshold is reached where fuel accumulation permits hotter fires that can spread over large continuous regions and create vast stretches where the forest is completely decimated. Thus,  inevitable fires associated with a fire prevention policy are larger and far more costly.

Policy must also consider irreversibilities when setting standards for pollutants that affect a renewable resource.  The direct impact may be acceptable in itself, but may move the renewable resource across a threshold.  This occurs, for example, when a pollutant impacts the competitive interactions between species.  If a fish species, valued for its recreational potential,  is more sensitive than its competitors, then acid precipitation may have a large indirect impact.  As sulfur dioxide emissions increase the acidity of the system, other fish are given a competitive advantage and displace the valued species.  Our analysis of even the very simple interactions of Equations 3  suggests that even if the original pH of the system were restored, the valuable species may not recover because of the nonlinearities generated by competitive interaction

A similar scenario appears to be occurring in the coniferous forests of the southern Appalachian mountains.  Although acid precipitation has not directly killed the ridge-top spruce forests, the sublethal impact has weakened the trees and made them susceptible to attacks of a pest, the balsam wooly adelgid.  The mature trees are dying and other species, unable to compete under normal conditions,  are growing into the gaps created by the dead trees.  The sublethal impact, combined with an irreversibility due to competition, may eliminate this forest type from the region.  It is important to recognize that many other types of environmental impacts, such as nutrient enrichment, conversion of wetlands, introduction of non-native species and global warming also have the potential to cause such disruptions and associated indirect irreversibilities.

The implication of these phenomena is that even pollutants with short environmental residence times may create damage over very long periods. This creates a very different optimization problem for these short-lived pollutants than traditionally utilized. For example, the typical optimization problem for short-lived pollutants such as sulfur dioxide is to minimize



where the total social cost (TSC(t)) of sulfur dioxide emissions (E(t)) in period t is  the sum of the total cost of abatement and the damages from the pollution that remains. In this example, TSC is a function of emissions, and TSD is directly a function of emissions and indirectly a function of emissions through its affect on the fish stock (N1). The first order conditions indicate that the optimal level of emissions in each period is independent of the level of emissions in other periods.

Nonlinearities change the nature of the optimization, because emissions in period t also affect a stock through the state equations which govern the competitive interactions. Hence the problem shifts from a simple static optimization problem to a dynamic problem.  The optimal control problem becomes



Thus, the policy decision no longer involves simply choosing today’s optimal level of emissions.  The policy must consider the optimal time path of emissions, taking into account the interdependencies among time periods. The necessity to determine an optimal time path of emissions has long been recognized for persistent pollutants which accumulate in the environment (such as heavy metals, DDT, or chlorflourmethanes) but has not been discussed for short-lived pollutants such as sulfur dioxide.2


5. Policy Implications of Economic Irreversibilities

The complex competitive interactions of ecological systems also occur in economic systems. This has many implications for economic policy, such as anti-trust and trade policy,  but it also has specific implications for environmental policy. Environmental change may alter the competitive relationship among economic activities, such as production of specific agricultural crops.  Nonlinearities may allow new activities to keep a competitive advantage despite amelioration of the environmental problem.  Assume, for example, that cotton is particularly sensitive to tropospheric ozone. As tropospheric ozone increases, cotton yields fall which simultaneously causes cotton farming profits to fall while cotton price increases. Two types of adaptive reactions take place in the economy. Garment manufacturers switch to other fabrics and cotton farmers switch to other crops which are less sensitive. Although a series of adjustments has been made, the level of social welfare falls because the environmental change distorted economic activity.

Moreover, a whole set of indirect reactions take place. Fashion designers develop styles more suited to the new fabrics. Department store buyers begin to think in terms of the new fabrics and fashions. Farmers redesign their farms towards the new crops, changing cropping schemes and capital equipment. Some farmers may even invest in perennial crops, such as pecan trees, to replace the cotton. All these reactions create barriers to the economy returning to its original position, once tropospheric ozone is reduced and cotton grows more prolifically. Hence, there is a legacy of damages even after the environmental problem is eliminated.

Many economists argue that these adaptations are good because they ameliorate the damages associated with environmental change. At one level of analysis, this is certainly true and this point is made persuasively in the global climate change literature (NAS 1991). However, if  tropospheric ozone levels dropped so that cotton again became the most efficient fabric, the altered state of the economy has restructured the market and created barriers to reintroducing cotton. In short, the reaction to the environmental change limits future options, as economic conditions adapt to environmental conditions. Again, this argues that intertemporal dependencies must be explicitly considered when developing environmental standards.  Comparing present period marginal damages and abatement costs is insufficient to maximize social welfare.

6. Conclusions

This paper argues that environmental systems are far more complex systems than traditionally perceived in economic analysis. This complexity can be measured both in terms of the diversity of ecological services that the ecological systems provide, and in terms of the nonlinearity of ecological interactions and interactions between the economic and environmental systems. This complexity and nonlinearity can lead to indirect irreversibilities, where seemingly small and inconsequential actions have very large and irreversible impacts.

The implications of this different conception of ecological processes for environmental policies follow in a relatively straightforward fashion following Krutilla and Fisher’s (1975) approaches to direct irreversibility. The potential for indirect irreversibilities and the uncertainty associated with their trigger points implies an additional need to be cautious with regard to environmental degradation. Instead of adopting a “wait and see” attitude towards measuring the costs of environmental degradation, the importance of ecological services and the existence of indirect irreversibilities implies that proactive policy is necessary and that environmental quality goals should be more stringent than traditionally conceived. This is true with respect to all environmental policy, but particularly true with environmental problems that have the greatest potential for system-wide change, such as policy towards non-native species introductions, global climate change, tropical deforestation, desert encroachment and loss of habitat in general.


1. Direct use values arise when environmental quality is directly used in activities such as water quality for swimming. Existence values occur when the knowledge of the existence of an environmental resource increases an individual’s utility, such as people gaining utility from the presence of whales in the ocean.


2. An exception is Farmer, et al. (1998) who examine the abatement cost side of the pollution problem and show how intertemporal dependencies related to technological innovation in abatement technology generate a dynamic optimization problem for short-lived pollutants.



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Figure Captions:


Figure 1: Schematic of Marginal Damage Function



Table 1.  Results of harvesting a food fish, N1, that shares resources with an inedible competitor, N2.  Shown are the equilibria (Eqs 3) achieved after a single harvest.


Harvest                      N1 (¥)                        N2 (¥)

1                                  49.5                             50.5

2                                  49                                51

4                                  47.8                             52.2

8                                  45.3                             54.7

16                                39.1                             60.9

20                                35.4                             68.6

30                                24.6                             75.4

40                                12.5                             87.5

42                                10.0                             90.0

44                                7.5                              92.5

46                                5.0                              95.0

48                                2.8                              97.9




Table 2.  The percentage of the inedible fish, N2, that must be killed each year to ensure that the food fish, N1, recovers fully from a harvest, H, after 10 years.


H, harvest of N1 every 10 years         % of N2 that must be killed each year

1                                                                                              0.5

5                                                                                                 3

10                                                                                               6

15                                                                                            10

20                                                                                            20

25                                                                                            30

29                                                                                            100