1
FISHERIES MANAGEMENT AND COMPLEX DYNAMICS
J. Barkley Rosser, Jr.
Professor of Economics and Kirby L. Kramer, Jr. Professor
MSC 0204
James Madison University
Harrisonburg, VA 22807 USA
Tel: 001-540-568-3212
Fax: 001-540-568-3010
Email: rosserjb@jmu.edu
Website: http://cob.jmu.edu/rosserjb
September, 2000
Paper to be presented at PRSCO and GERT conference, Nihon University,
Tokyo, Japan, October 1-3, 2000
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Abstract
Fishery dynamics are considered within the context of an integrated ecologiceconomic, or bioeconomic, approach. The possibility of complex dynamics is
examined, both of the chaotic as well as the catastrophic variety. Issues
involving learning and convergence by fishers are considered. Complications
arising from multi-species interactions are considered as are complications
arising from the hierarchical nature of fisheries. Policy responses to these
problems are seen to involve the precautionary principle to mitigate the threat of
catastrophic discontinuities and the scale-matching principle to ensure that
management and property rights system are properly implemented. Dynamic
policy approaches are discussed for certain special situations.
Introduction
Most discussions of environmental problems have presumed a certain degree
of simplicity of dynamical relationships that implies the existence of unique
steady-state equilibria for given parameter values, with continuous variation of
such equilibria as functions of the relevant parameter values. This has implied a
degree of simplicity of analysis of the possible set of policy solutions, even as the
difficulty of implementing any of these possible solutions remains very great in
the real world with conflicting interests with regard to such possible policies.
Thus, the possibility that these dynamical relationships may exhibit various forms
of complexity of a nonlinear sort presents a serious additional challenge to
policymakers who already face serious difficulties.
These nonlinearities can present themselves at multiple levels and in multiple
ways. Although the initial impression may be that the existence of possible
nonlinearities in subsystems merely serves to complicate policymaking in a
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complex world, in some cases we shall see that it may offer possible solutions
that might not initially seem to be available. However, in other cases the
complications are such as to call for greater precautions than would be the case
otherwise in a simpler linear world. In particular, it is the case that chaotic
systems tend to remain bounded and thus may represent sustainable solutions
despite that apparently erratic nature of the dynamics associated with them. On
the other hand, systems in which catastrophic discontinuities can arise present
especial dangers and call for greater precautions and investigation to determine
the critical boundaries within which the system must be kept in order to maintain
sustainability. In effect, we see a conflict between chaos and catastrophe in
which the former represents possible sustainability whereas the latter represents
the threat of its loss. This conflict rather resembles the conflict between stability
and resilience posed by Holling (1973).
In this paper we shall broadly consider the systems of fisheries. We shall
consider in more detail questions of possible chaotic and catastrophic dynamics
within fisheries. These will be considered in the broader context of multi-species
systems with possible complications arising from the emergence of higher-order
structures of system dynamics within ecologic-economic hierarchies.
This paper will review broad approaches to fishery management within the
context of complex dynamics, as well as certain specific policy proposals. Within
such broadly accepted approaches as the Lisbon Principles on oceanic fisheries
(Costanza, Andrade, Antunes, van den Belt, Boesch, Boersma, Catarino, Hanna,
Limburg, Low, Molitor, Pereira, Rayner, Santos, Wilson, & Young, 1999), certain
4
policies will be emphasized, especially those that provide protection against
catastrophic collapse in line with the precautionary principle. This will include
certain dynamics approaches to management as well as proposals for the
establishment of reserves for endangered species. It will also be emphasized
that both property rights regimes and more specific management policies
regarding harvest rates must be appropriate to the scale and level of the
appropriate ecological hierarchy.
Chaotic Fishery Dynamics
We shall now consider a model of fishery dynamics studied by Hommes &
Rosser (2000) and Rosser (2000a). Its basic bioeconomics follow Clark (1990)
who shows that backward-bending supply curves can arise even in optimally
managed fisheries for sufficiently high discount rates. Following Schaefer (1957),
for x = fish biomass, r = intrinsic growth rate, k = ecological carrying capacity, t =
time, h = harvest, and F(x) = dx/dt growth of fish without harvest, sustained yield
is given by
h = F(x) = rx(1 - x/k).
(1)
Following Gordon (1954), for E = catch effort in standardized vessel time, q =
catchability per vessel per day, a cost function of c = c/qx, p = price of fish, and 
= time discount rate, then
h(x) = qEx.
(2)
From this Hommes & Rosser (2000) show that the optimal control solution gives
a discounted supply curve of fish of
5
x(p) = k/4{1+(c/pqk)-(/r)+[(1+(c/pqk)-(/r))2+(8c/pqkr)]1/2}.
(3)
The system is shown in Figure 1, a diagram first shown by Copes (1970),
albeit without formal derivation. For  = 0 the supply curve will be upward-sloping
while if it is infinite, the case of myopia, it will coincide with the open access
solution derived by Gordon (1954) of
S(p) = rc/pq(1 - c/pqk).
(4)
[ insert Figure 1]
The supply curve will bend backwards at very low discount rates and will
generate multiple equilibria of the sort shown in Figure 1 for a discount rate of
8%1 for a linear demand curve
D(p) = A - Bp,
(5)
with B = 0.25 and A = 5240.5 at which value the minimum possible price will yield
a consumer demand exactly equal to the maximum sustained yield.2 Assuming
that agents expect prices to be the same next period as the current period,
cobweb adjustment dynamics occur such that
pt = D-1S(pt-1) = [A - S(pt-1)]/B.
(6)
Hommes & Rosser (2000) show for this system with these parameter values that
as the discount rises above 2% period-doubling bifurcations will occur with
1
This is much lower than the minimum discount rate for which chaotic dynamics emerge in
golden rule neoclassical growth models as shown by Nishimura & Yano (1996).
2 Conklin & Kolberg (1994) show the possibility of chaotic dynamics in the halibut fishery with a
more elastic demand curve that generates only one equilibrium, given certain discrete adjustment
dynamics and a backward-bending supply curve. Doveri, Scheffer, Rinaldi, Muratori, &
Kuznetsov (1993) find chaotic dynamics in multi-species aquatic ecosystems. May (1974)
initiated study of chaotic dynamics in ecological populations, and indeed introduced the term
"chaos" to dynamical systems prior to the famous "period three equals chaos" theorem of Li &
Yorke (1975).
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chaotic dynamics occurring at around 8%.3 For a discount rate greater than 10%
the system converges on the "bad" equilibrium of high price and low fish stock.
Grandmont (1998) pointed out that when the true dynamic for such systems
is chaotic it may be possible for agents to mimic it by using a simple one-period
autoregressive expectational system. Hommes & Sorger (1998) followed this
idea to introduce the concept of consistent expectations equilibria (CEE) in which
agents generate sample means and autocorrelations that mimic an underlying
process even though they do not actually know what that process is. They show
for the one-period autoregressive case that such CEE can exist and that they
may either be a steady state, a two-period cycle, or a chaotic dynamic.
Furthermore, they show that even when the agents do not begin with
parameters for the autoregressive expectational system that will mimic the
underlying system, that for fairly simple kinds of learning patterns they can learn
to adjust the parameters so that they mimic the true underlying dynamic.
Following Sorger (1998) this is called learning to believe in chaos. Hommes &
Rosser (2000) show that such learning can take place even in the presence of
noise. Such a learning process is shown in Figure 2 (from Hommes & Sorger,
1998) in which the agents start out assuming very simple behavior and then pass
through periodic behavior to converge on a chaotic dynamic. Given that this
chaotic dynamic is bounded, this can be viewed as provisionally optimistic.4
[insert Figure 2]
3
Chiarella (1988) and Matsumoto (1997) show possible chaotic dynamics in more generalized
cobweb models.
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However, we must note that this is almost certainly far too optimistic for the
conditions that obtain in real world fisheries. As we shall see in the next section,
fisheries are subject to catastrophic dynamics which are implicit already in Figure
1 for the case where demand continuously increases. Furthermore, whereas this
model shows noise not interfering with learning and convergence to a bounded
outcome, Conrad, Lopez, & Bjrndal (1998) show that observational errors can
combine with biological stochasticity to generate a nonlinear increase in risk, and
Zimmer (1999) shows that environmental noise can interact with endogenous
chaotic population dynamics to generate fluctuations of greater variance. That
such extreme uncertainty and risk are endemic in fisheries can be seen by the
sudden and unforecast collapse of the cod fishery off Newfoundland in 1992
(Ruitenback, 1996). This led Lauck, Clark, Mangel, & Munro (1998) to propose
the establishment of reserves to reduce such risks and possible outcomes.
Another possibility that might beckon is that of "controlling chaos." A local
such method was developed by Ott, Grebogi, & Yorke (1990) and a global
method is due to Shinbrot, Ott, Gregogi, & Yorke (1990). The local method was
first applied in economics by Holyst, Hagel, Haag, & Weidlich (1996) and the
global method was first applied in economics by Kopel (1997), with Kaas (1998)
suggesting the use of both in succession for full and exact macroeconomic
stabilization. A variation on the global method due to Pan & Yin (1997) involves
merely reducing the bounds of the chaotic dynamics without eliminating chaos as
such. It is even possible to induce chaos where none exists for cases where it
4
Clearly there are serious philosophical and psychological issues involved regarding the nature
of illusion and reality in this case, where people are tracking an underlying complex reality without
8
might be desirable as in a variety of contexts (Schwarz & Triandaf, 1996).5
However, all of these techniques involve a far greater knowledge of both the data
and the underlying dynamical systems than we realistically possess in either
ecological or economic systems, much less in the difficult bioeconomic cases
involving fishery dynamics (Sissenwine, 1984).
Catastrophic Discontinuities in Fisheries
Examination of Figure 1 shows how easily larger scale discontinuities can
arise in the sorts of nonlinear dynamical systems that underlie real ecologicaleconomic systems. Even in a simple non-chaotic situation, as demand shifts
outwards due to rising income, population, or increasing focus on the health
advantages of eating fish, a discontinuity in the equilibria can arise in which the
system suddenly jumps from a low price-high fish stock situation to a high pricelow fish stock one. This example has long attracted attention and been used to
explain the numerous actually observed sudden collapses of fisheries around the
world (Clark, 1985). Such outcomes become more clear with the possibility of
full collapse and outright extinction when such phenomena as the possibility of
critical depensation in the yield curve is allowed as shown in Figure 3 (Clark,
1990), or the very real world problem of capital stock inertia arising from the
unwillingness of fishers to give up their boats even as the fishery they operate in
is collapsing (Clark, Clarke, & Munro, 1979).
realizing what they are really doing. We shall not attempt to resolve these in this paper.
5 An example in ecology is provided by Allen, Schaffer, & Rosko (1993) who argue that chaotic
population dynamics may reduce the threat of extinction sometimes, although Zimmer (1999)
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[insert Figure 3]
The most developed mathematical approach to modeling such dynamic
discontinuities has been catastrophe theory, developed by Thom (1975) and
Zeeman (1977). It has been applied specifically to the problem of the collapse of
fisheries, initially to that of the collapse of the blue whale population (Jones &
Walters, 1976) and to the problem of predatory depensation by Clark and Mangel
(1979) in the context of critical depensation discussed above. This theory arises
from studying the structural stability of singularities of certain kinds of nonlinear
dynamical systems, especially those with gradient dynamics. It has been applied
in many contexts, including some for which the proper mathematical conditions
do not hold.6 Figure 4 shows the equilibrium manifold for the simplest of all
catastrophe models, the fold catastrophe, which could arise from the system
shown in Figure 1 if demand were to increase and decrease in succession. Such
a situation is relevant to many contexts involving multiple equilibria with
hysteresis, even when the precise mathematical conditions required for the
application of catastrophe theory do not hold. A variety of such situations have
been observed in ecology, including the hysteretic cycle of spruce-budworm
outbreaks (May, 1977; Ludwig, Jones, and Holling, 1978) and the eutrophication
and recovery of freshwater lakes (Carpenter, Ludwig, & Brock, 1998).7
questions this result. Matsumoto (1999) shows that chaotic disequilibrium dynamics may lead to
outcomes Pareto superior to market equilibria.
6 For reviews of applications in economics and related disciplines see Rosser (2000b), Guastello
(1995), and Puu (2000). For a more complete discussion of underlying mathematical issues see
Arnol'd (1992).
7 Such situations can be magnified in certain cases where an external forcer interacts with the
system, as has been argued by Johnston & Suitinen (1996) with regard to the impact of climatic
change on the collapse of the Peruvian anchoveta fishery in 1972, a case they label catastrophic
harmony.
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[insert Figure 4]
Now a problem with both the chaos and catastrophe models presented above
is their essentially aggregated nature. There is no modeling of emergent
dynamics or structure arising from lower level phenomena in them. Everything is
on the surface at the same level. However, an alternative approach to modeling
discontinuous dynamics that has attracted attention from complexity modelers
that offers a partial response to this problem has been that of mean-field
dynamics drawn from the study of phase transitions in interacting particle
systems of statistical mechanics (Kac, 1968; Spitzer, 1971). Originally applied in
economics by Föllmer (1974), this approach has received further development by
Brock (1993) and Brock & Durlauf (1995) with numerous applications following in
economics (Arthur, Durlauf, & Lane, 1997). It appears to offer real possibilities
for modeling ecologic-economic systems.
A simple case considered by Brock & Durlauf (1995) involves a set of n
agents who might be humans but might also be individuals of other species who
face two alternative choices (-1,1), usually interpreted as being pessimistic and
optimistic, with m representing the average of their choices, the mean field. The
agents interact with each other with the strength of that interaction being given by
J and they also possess an "intensity of choice," equal to , interpreted in the
original statistical mechanics literature as being temperature. The gain from
switching choices equals h, which shows the general stochastic state of the
system, along with an exogenous stochastic process. Optimal behavior is given
by
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m = tanh(J + h)
(7)
with tanh being the hypertangent function. Brock & Durlauf (1995) show that a
critical value for this system occurs at J = 1. The case for which h = 0 is
depicted in Figure 5 which is from Rosser (1999, p. 179), and which shows a
bifurcation with two stable but distinct equilibria for cases where either the
strength of interaction or the intensity of choice are sufficiently high. Such
outcomes can be manifested by agents clustering to act together in some
coherent manner, a case of emergent structure. In the original statistical
mechanics literature such bifurcations were seen as indicators of phase
transitions between states of matter such as the boiling or freezing of water.8
[insert Figure 5]
Multi-Species Complications
Gause (1935) developed a Lotka-Volterra model of two competitive species:
dx/dt = rx(1 - x/k) - xy
(8)
dy/dt = sy(1 - y/L) - xy
(9)
where s is the intrinsic growth rate of the y species, L is its carrying capacity, and
all other variables are defined as above. This model admits either coexistence or
competitive exclusion under different conditions. Gause considered cases where
x has excluded y, but y still exists nearby as a "refugee," capable of returning if
8
This example was a favorite for dialectical theorists when contemplating the nature of qualitative
change arising from quantitative change. Rosser (2000c) discusses this in the context of
nonlinear dynamics, and Georgescu-Roegen (1971) has applied the dialectical approach to
ecological economics.
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anything should happen to x. Clark (1990) argues that if x is harvested by an
amount = qEx, its x = 0 isocline will be given by
y = (r/)(1 - x/k) - (q/)E.
(10)
As E increases the system will bifurcate and a collapse of x can occur as it is
competitively replaced by y at a value of E^ = s/. This might occur if fishery
managers are unaware of the threat posed by the competitor species. Murphy
(1967) analyzed the collapse of the Pacific sardine fishery in the late 1940s and
its replacement by the anchoveta in a manner that suggests the above outcome
as a possibility, although the event may also have been due to exogenous
environmental shocks.
If E^ < r/2q, the value of E associated with maximum sustained yield of x
without y, such a mistake could easily occur. The collapse of x could occur while
its yield-effort curve is still increasing, as depicted in Figure 6.
[insert Figure 6]
Brauer and Soudack (1979) derive a similar result for a Lotka-Volterra
predator-prey model in which the predator is harvested. For harvest levels below
the maximum for which an equilibrium might exist, two equilibria will exist: one a
saddle point, the other either locally stable, unstable, or a limit cycle, with Dávila
and Martín-González (1997) showing backward-bending supply curves for both
predators and prey under harvesting of either with realistic discount rates. Under
certain conditions the predator population may collapse at a harvest level less
than the apparent maximum sustained yield. This occurs as the non-saddle
equilibrium suddenly goes from being stable to being unstable, depending on a
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change in the behavior of the separatrices emanating from the saddle point. This
is depicted in Figure 7 with (a) being the stable situation and (b) being the
unstable collapse situation that emerges as the harvest rate increases, with x the
prey and y the predator. The predator's isocline includes the effect of harvesting.
In (a) any initial point inside the hatched zone will asymptotically approach the
long-run equilibrium.
[insert Figure 7]
Brauer and Soudack (1985) show that in the "fragile" case above, an optimal
harvesting strategy that can approach the maximum sustained yield is a bangbang harvest cycle. In the predator-prey case such a strategy may also be
optimal in the non-fragile case. They also show that if the harvest thresholds are
sufficiently high, period-doubling and chaotic dynamics may emerge along the
optimal trajectory of the two populations, with Rosser (1991) discussing a series
of other cases.
A dramatic example of difficulties in managing predator-prey systems with
catastrophic dynamics in fisheries has involved the difficult example of trout in
the Great Lakes of the U.S., which were nearly wiped out by an invasion of
lampreys. Managers have stocked trout, but Mehra (1981) and Walters (1986)
have argued that this has simply fed the catastrophic dynamics along lines
suggested by Ludwig, Jones, and Holling (1978).
A particularly difficult problem in such situations is gaining adequate
information regarding the thresholds of the system while avoiding triggering the
catastrophic collapse. Walters (1986) suggests "surfing" to investigate "Koonce's
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doughnut" as seen in Figure 8. The approach is to vary harvest rates so as to
both maximize yields while determining the critical threshold. This is shown by
the circle labeled (a) in Figure 8. The circle labeled (b) shows "pathological
surfing" in which a collapse of the wild trout stocks could occur, which reflects too
great a variation of the harvest rates. On the other hand the strategy indicated
by (c) in Figure 8 shows the low-yield strategy that obtains no information.
[insert Figure 8]
The Hierarchy Complication
The above discussion leads us to a more difficult source of complexity, the
problem of levels of hierarchy interacting with each other. It has been widely
argued that lower hierarchical levels are nested within higher ones and are
constrained by them in a variety of ways. Nevertheless, it appears that there are
cases where events at a lower level of hierarchy can impact those at a higher
level.
The question of how to model hierarchical systems has been a matter of
greater attention in ecology than in economics, with Simon (1962) providing an
initial framework used by many in different fields. Among those developing
approaches in ecology are Allen & Starr (1982), O'Neill, De Angelis, Waide, &
Allen (1986), and Holling (1992). Efforts to model dynamics within hierarchical
systems have used a variety of approaches including the synergetics model of
Haken (1983)9 and associated models of entrainment at different levels of
hierarchy (Nicolis, 1986). Following this approach, Rosser, Folke, Günther,
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Isomäki, Perrings, & Puu (1994) model the possible emergence of new levels of
hierarchy, the anagenetic moment.
Aoki (1996) provides an intriguing approach that allows draws on the
synergetics-derived master equation model of Weidlich & Braun (1992). This
approach allows for the introduction of mean-field dynamics as described in the
previous section. In his work the mean field effects are seen as due to
externalities that bring about higher level coherences and emergent structures.
Sudden structural changes in dynamical hierarchical systems are associated with
fixed points in the coarse graining or aggregation of microunits (Dyson, 1969). A
sequence of phase transitions can arise as a sequence of clusters of equilibria
(Rose, Gurewitz, & Fox, 1990). Development of such an approach within a
system of coupled logistic maps in a hierarchical framework has been carried out
by Kaneko (1990).
In many of these models of hierarchy it is assumed that higher levels
constrain lower level dynamics, or "slave" them to use the terminology of
synergetics. However, the possibility arises again in association with the
existence of certain critical points of a "revolt of the slaved variables" (Diener &
Poston, 1984) in which a change in lower level variables can destabilize the
higher levels and bring about changes at those levels. Holling (1986)
characterizes such cases as ones of "local surprise and global change."
It can be argued that in such cases there may exist critical levels whose stability
must be ensured in order to maintain the stability of the larger hierarchical
system at both higher and lower levels. Such a level may operate much like a
9
For general applications of synergetics to economics, see Zhang (1991).
16
"keystone species" within more general ecosystems (Vandermeer & Maruca,
1998).
The problem of appropriate levels is a crucial one for policy. Wilson, Low,
Costanza, & Ostrom (1999) demonstrate that for fisheries managing at too high a
scale can lead to unexpected levels of overfishing as crucial local stocks may be
destroyed. This problem is closely linked with the issue of assigning property
rights, or to be more precise, rights to control access to biotic resources. Rosser
(1995) emphasizes particularly that such rights must correspond to the
appropriate level of the relevant combined ecologic-economic system.
Management Approaches in Complex Fisheries
There is little doubt that the possible existence of such nonlinear complexities
in global ecologic-economic systems severely complicates the difficulties facing
policymakers. The obvious issue that must be dealt with is a greater focus on
determining critical boundaries and threshold levels for systems that must be
kept within in order to avoid catastrophic collapses. This is easier said than
done, needless to say. Beyond this a number of points can be made for the two
cases we have discussed in this paper.
With regard to fisheries, it is useful to reiterate the Lisbon Principles
(Costanza, Andrade, Artunes, van den Belt, Boesch, Boersma, Catarino, Hanna,
Limburg, Low, Molitor, Pereira, Rayner, Santos, Wilson, & Young, 1999) and to
reemphasize their usefulness. These include the Responsibility Principle, the
Scale-Matching Principle, the Precautionary Principle, the Adaptive Management
17
Principle, the Cost Allocation Principle, and the Full Participation Principle. When
taking into account the kinds of problems associated with nonlinear complex
dynamics in fishery systems, it would seem that the second and third of these
may be especially important.
As noted above, the Scale-Matching Principle is fundamental for successfully
assigning property rights or rights to control access to a fishery. Dynamics in
hierarchies present special problems and mistakes in operating at the wrong
level can lead to unfortunate outcomes. These issues become heightened when
policymakers are perceived by the often insular fishing communities as outsiders
not sympathetic to their social and economic problems (Charles, 1988).
Unpopular efforts by outsiders to restrict fishing effort can lead to poaching which
can heighten the problem of uncertainty (Milliman, 1986). It has been argued
that informal practices of traditional communities may offer superior and more
cooperative outcomes (Johnson and Libecap, 1980; Ostrom, 1990). However,
they may over or underfish depending on their management policies (Stollery,
1987), and the intrusion of market economies into such economies has
historicallly undermined their traditional management practices (Lawson, 1984;
Bromley, 1991; Rosser, 1995).
Certainly the Precautionary Principle is crucial in situations with critical
threshold levels or effects as seems to be the case in many fisheries. Ongoing
uncertainty about what those levels are of course bedevils actual policymaking,
but this may be the most important of all of these for fisheries, especially in
comparison with some others that seem much vaguer, such as the last one
18
where it is very unclear who stakeholders are and who should have more say
than whom about outcomes and policies. Whatever the determination of such
issues, it is clear that more innovative policies and mutually agreed upon
interventions may be needed to deal with some of the special problems
associated with fisheries, such as overcoming the difficult capital stock inertia
issue. The proposals by Walters (1986) for careful variations of harvest rates
("surfing Koonce's doughnut") and by Lauck, Clark, Mangel, and Munro (1998)
for establishment of reserves for endangered species offer possibilities for such
innovative policies that are consistent with the Precautionary Principle.
We note that the old problem of the appropriate discount rate is a serious
problem here. In the fisheries models we can see that higher discount rates
increase the likelihood of "bad" equilibria arising. This is not a new issue for
environmental or ecological economics. A further complication arises when there
are delayed costs that can lead to capital theoretic paradoxes in the form of
reswitching between alternatives, where one alternative is favored at low and
high discount rates but not at intermediate ones. That this can arise in
environmental systems and can complicate analysis has been argued by Porter
(1982) and by Prince and Rosser (1985). With respect to fisheries this interacts
with issue of uncertainty, with Plourde and Bodell (1984) arguing that threats to
population stocks due to exogenous risks might imply higher discount rates and
efforts to "harvest while we can before the species is wiped out," while risks
relating to species growth may argue for lower discount rates to preserve future
generations.
19
We note the recent discussions involving efforts to balance off the present
and the future through such ideas as the green golden rule (Chichilnisky, Heal, &
Beltratti, 1995) which seem to lead to ideas of using higher discount rates in the
near term but lower ones for evaluating outcomes farther in the future. We note
that the formal models of this rule involve imposing constraints on future
outcomes that suggest again the need for being concerned with critical
boundaries and thresholds that the global system must be kept within. We also
note that there are potential problems of time inconsistency if one is operating
within a system in which the agents or policymakers possess an infinite horizon
perspective, although this may not be a problem if one is considering multiple
finitely lived generations, exactly the context in which the ethical issues arise that
the green golden rule is supposed to resolve.
Finally we must deal with the crucial and unresolved institutional issue. In
contrast to world trade and world peace, there is no accepted global entity
designated to deal with environmental issues in general. What we have are a
series of ad hoc treaties, accords, protocols, and partial arrangements that deal
with a variety of issues separately. There is no general global accord or
agreement with regard to fisheries, although some aspects of fisheries are
affected by some other agreements, notably those relating to endangered
species and especially the restrictions upon whaling that have been widely
agreed upon, despite ongoing disputes about actual implementation with certain
nations insisting on hunting certain whale species in the face of widespread
global disapproval.
20
Thus, it must be recognized that the existence of such a global institution or
body is no guarantee that treaties or accords or protocols or agreements will be
obeyed or followed. The existence of the World Trade Organization has not
ended disagreements and conflicts over trade, including violations of existing
agreements by individual countries. Likewise, the existence of the United
Nations most certainly has not guaranteed the existence of world peace. Many
of the global environmental agreements that have been reached have worked
well and been widely accepted. Others have not. The ultimate dependence for
agreements to work upon their genuine acceptance by the nations involved
remains an argument for seeking out flexible and innovative approaches to these
difficult policy issues.
Perhaps the world political economic system will evolve to a point where a
genuine global environmental agency will emerge. But until that time, and even
perhaps after such a time, we must work to convince nations and groups within
nations that it is in their own ultimate best interest to accept and obey the
agreements that have been reached for dealing with global environmental
problems.
Conclusions
Fisheries systems can exhibit complex nonlinear dynamics that complicate
policymaking efforts. Chaotic dynamics and catastrophic discontinuities can
arise. These can be exacerbated in hierarchical systems with evolving meanfield dynamics and in complicated multi-species systems such as predator-prey
21
relationships. These difficulties have been quite evident in fisheries, thus
presenting severe challenges to policymakers.
Such difficulties tend to emphasize the need to put in place safeguards about
remaining within critical boundaries or thresholds, in short a serious application of
the Precautionary Principle. They also emphasize the need to clearly identify
relevant scale levels in hierarchical systems at which policies and access
controls should be implemented, in short the Scale-Matching Principle. Flexibility
of policies in an adaptive framework would seem to be appropriate as well. But
these efforts are all contingent on the emergence of appropriate institutions and
arrangements for dealing with these policy problems. This is an evolutionary
process that has yet to achieve a critical anagenetic moment.
Let us conclude by contrasting again chaotic and catastrophic dynamics in
these models. Contrary to many expectations, chaotic dynamics may actually be
a desirable outcome for sustainability of systems, as long as the bounds of those
dynamics remain within sustainable levels. Agents may even be able to learn to
believe and follow such dynamics through simple boundedly rational rules of
thumb. The greater threat comes from catastrophic discontinuities associated
with crossing critical threshold levels or from non-chaotic oscillations of much
greater amplitude that can emerge in coupled systems out of chaotic underlying
subsystems. Thus, it is catastrophe rather than chaos that appears to be the
greater threat to the sustainability of fisheries in a world of complex dynamics.
22
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