ECOSYSTEMS
Ecosystems (2000) 3: 451– 471
DOI: 10.1007/s100210000040
                                                        © 2000 Springer-Verlag




         Socioeconomic Mechanisms
         Preventing Optimum Use of
          Ecosystem Services: An
        Interdisciplinary Theoretical
             Analysis
         Marten Scheffer,1* William Brock,2 and Frances Westley3

 1
  Aquatic Ecology and Water Quality Management Group, Wageningen University, P.O. Box 8080, 6700DD Wageningen, The
Netherlands; 2Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, Wisconsin 53706, USA; and
      3
       Faculty of Management, McGill University, 1001 Sherbrooke St. West, Montreal P.Q. H3A 1G5, Canada


ABSTRACT
Ecosystems provide a wide range of services to so-           and data indicate that this type of concentrated
ciety. Some forms of use affect the quality of the           group is systematically better at mustering political
ecosystem, reducing its value for other users. This           power than large groups, which find it difficult to
leads to a conflict of interest that is often settled          realize collective action due to what is known in
through political processes, resulting in some form           game theory as “free-rider problems.”
of regulation. We link theory on ecosystem re-               Our analysis suggests that the following three key
sponse to theories from the socioeconomic                ingredients are needed to correct the problems of
branches of science to analyze the mechanisms be-            bias and compromise: (a) clear insight into ecosys-
hind two widespread problems associated with such            tem dynamic responses to human use, (b) a broad
political solutions. First, they often represent a com-         inventory of credible measurements of ecosystem
promise rather than an integrative solution. We             utilities, (c) avoidance of bias due to differences in
demonstrate that, particularly in sensitive ecosys-           the organizational power of groups of stakeholders.
tems, integrative solutions yield a higher average           We argue that good ecosystem models, institution-
social utility and imply a higher ecosystem quality.          alized ecosystem valuation, and innovative tax-set-
Integrative solutions require insight into ecosys-           ting schedules are essential to achieving a socially
tems responses to different forms of use and a com-           fair and sustainable use of ecosystems by societies.
plete overview of ecosystem services to society. Sec-          In addition, we highlight the fact that many envi-
ond, there is a systematic bias away from optimal            ronmental problems remain unresolved for a long
shared use toward activities that are detrimental to          time and briefly identify the social mechanisms re-
ecosystem quality. This bias arises from the fact that
                                    sponsible for this delay.
utilities depending on ecosystem quality are often
                                    Key words: ecosystem; utility; tax; model; wel-
shared by large diffuse groups, whereas pollution
                                    fare; stakeholders; lake; resilience; collective action;
and harvesting activities can usually be traced to
relatively small and well-organized groups. Theory           hysteresis.




Received 10 November 1999; accepted 28 April 2000.
*Corresponding author; e-mail: marten.scheffer@aqec.wkao.wau.nl



                                 451
452    M. Scheffer and others


INTRODUCTION                       berger 1974). In practice, this is a formidable task
                             with many difficulties. Indeed, the best minds in
Ecosystems are usually of importance to several      social science have struggled with this problem (Sen
different groups in human societies (“stakehold-     1999). We have nothing to add to this discussion
ers”). Lakes, for instance, can be used by industries   and will take a utilitarian approach here. Even
to get rid of waste water, but they can also be used   more complex, however, than solving the question
by swimmers who want clean water and by fisher-      of what should be done is the problem of unravel-
men who prefer certain kinds of fish. Also, the lake    ing the mechanisms that determine what actually is
water may pass through rivers and other lakes be-     done. The dynamics of societies depend on eco-
fore ending up in the ocean, affecting many more     nomic and political interactions, and ultimately on
distant stakeholders along the way. Since some      the behavior of individuals who respond to their
ways of using the ecosystem services tend to lower    environment in much more complex ways than can
the quality of the system for other users, there is    be captured by the basic rules of economy and
often a conflict of interests. If one regards human    politics. The literature on this problem covers a
interests as paramount, policy makers would ideally    wide range, from plain economic motives to beliefs
strive to maximize the total utility obtained from a   and ethics.
given ecosystem to serve society as a whole. In this    In the third section, we review the theory on the
paper, we explore that idea and analyze the influ-     economic aspects of this range, known as “positive
ence of socioeconomic dynamics on the outcome of     economics” or “political economics.” In this ap-
attempts to achieve this theoretical optimum. Ob-     proach, economic analysis is used to measure and
viously, any analysis of this problem requires an     predict the political strength of a coalition of com-
insight into the response of ecosystems to different   mon-interest stakeholders.
types of human use, as well as an understanding of     In our final discussion, we reflect on the main
socioeconomic dynamics and their effect on the      conclusion and the limitations of the approach.
ecosystem.
  One widely recognized barrier to the develop-     ECOSYSTEMS RESPONSE         HUMAN USE
                                             TO
ment of an integrative theory is the current segre-
gation of the scientific disciplines that analyze eco-   Ecosystems are tremendously complex and quite
systems dynamics from those that analyze         unpredictable in their response to human activities.
economics and social interactions. Indeed, in our     Furthermore, they differ widely in terms of species
experience, it is not only the jargon and methods,    composition, potential services to society, and
but even the perception of “what drives this world”    threats to their resilience. In view of this idiosyn-
that divides these disciplines. This paper is the prod-  crasy and complexity, any attempt to review their
uct of the cooperation of scientists working in three   potential response to human use in a single section
different disciplines: ecology (M.S.), economy      of a paper may seem futile. However, we think that
(W.B.), and sociology (F.W.). We have attempted to    with respect to the search for strategies for sustain-
link the insights from each of these branches of     able use, there is at least one aspect that deserves
science that we consider essential for an under-     special attention because it is very important and
standing of the problem of the shared use of eco-     can be treated in a rather generic way—namely,
systems by various societal groups. The results high-   irreversibility and hysteresis in the response of eco-
light various aspects that have been largely ignored   systems.
by both economists and ecologists (for example,       Early work showing how fisheries and grazing
Clark 1990, and many others) in the existing liter-    systems may collapse when they are overexploited
ature on dynamic ecosystem management.          has become well known. However, ecologists in
  In the first section, we note that various ecosys-   different fields are gradually discovering that a mul-
tems tend to respond nonlinearly to stress increases   tiplicity of stable states and the resulting nonlinear-
resulting from human use, a fact that has important    ity of responses to change in conditions may be the
implications for the interaction of ecosystems with    rule rather than the exception in a wide class of
socioeconomic systems.                  ecosystems (for example, DeAngelis and others
  In the next section, we address the theoretical    1989; Holling 1973; Ludwig and others 1997; Riet-
question of how to use ecosystems to maximize       kerk and others 1997; Walker and others 1981;
benefits for all different users. This type of problem   Hanski and others 1995; Carpenter and Pace 1997;
is addressed by normative economics, a version of     Case 1991; Lertzman and others 1994; Scheffer and
which assumes that all kinds of interests can be     others 1993; Tilman 1982). It is important to note
usefully expressed in a common currency (Har-       that catastrophic response in a certain class of eco-
                                                      453
                             Socioeconomics and Ecosystem Services

                                          Figure 1. Schematic repre-
                                          sentation of possible re-
                                          sponses of ecosystems to
                                          stress imposed by human
                                          use. The lines represent equi-
                                          librium states. The arrows
                                          indicate the direction of
                                          change when the system is
                                          out of equilibrium.




systems is usually due to a single dominant feed-    can represent the response in simple graphs that
back mechanism. As a result, we believe that, in     plot the ecosystem state as a function of the stress
addition to being highly relevant, catastrophic     imposed by human use (Figure 1). For simplicity’s
change is often relatively easy to understand and    sake, these hypothetical graphs consider only one
predict, unlike gradual changes in structure, com-    state variable and one stress factor. Obviously, this
position, and biodiversity. In this section, we briefly  is a rather minimal representation of the response
sketch the range from smooth to catastrophic re-     of ecosystems to human impact. Nonetheless, it
sponses that can be found in ecosystems, focusing    serves to illustrate the points we want to make in
on the latter in view of the thorny consequences for   our analysis.
sustainable use. The case of shallow lake eutrophi-     The unidimensional representation of state seems
cation serves as an example. This simple model will   a strong simplification at first sight. However, much
be used in the subsequent sections to discuss the    of the essence can often be captured by a single
implications of such nonlinearities for human–na-    variable, because in a given type of ecosystem,
ture interactions.                    many aspects of the system’s state tend to shift in
                             concert with a few important key state variables.
Irreversibilities and Hysteresis in           Examples of such key state variables that could be
Ecosystems                        represented by the vertical axis are total plant bio-
                             mass per unit area or turbidity of lake water.
It is often assumed that impact will tend to increase
                             Clearly, many more aspects of ecosystem state are
more or less smoothly with intensity of use. How-
                             of importance to human users, and even more fac-
ever, accumulating evidence indicates that the re-
                             tors are essential for the functioning of the systems.
sponse to increasing stress is frequently far from
                             For instance, in shallow lakes, quality of the fish
smooth. Indeed, the ecosystem may often appear to
                             stock, occurrence of toxic algae blooms, biodiver-
be untouched by increasing stress until it suddenly
                             sity, and turbidity may all be of interest to different
collapses when certain threshold values are sur-
                             groups of users; in addition, zooplankton biomass
passed. To clarify differences in the way in which an
ecosystem may respond to changing conditions, we     and species composition may be essential to the
454    M. Scheffer and others

ecosystem’s functioning. A stress to the system,     areas is an example (Rietkerk and Van de Koppel
such as overloading the lake with phosphorus, will    1997). An increase in grazing intensity can destroy
affect all of those characteristics, but changes tend   vegetation; but when conditions are sufficiently
to follow the same coherent pattern in most lakes.    dry, erosion, sunburning of seedlings, and lack of
Therefore, the value of one key variable, such as     capacity to retain soil water may prevent recoloni-
turbidity or phosphorus sequestered in algae (Car-    zation by plants even if all grazers are removed.
penter and others 1999), may be used to roughly       Since catastrophic changes from one stable state
reflect the general state.                 to another have serious implications for the dynam-
  “Stress” is the general term we will use here to    ics of ecosystem use, we pay extra attention to
describe the effect of human use. The human use of    systems with this property in our review. The the-
nature can be through harvesting or destroying bio-    oretical possibility of catastrophic switches in eco-
mass (for examples, rainforest harvest, fisheries,     logical systems has long been a topic of interest
cattle ranching), but much of the impact may also     (May 1977). Examples include lakes (Carpenter
be due to stressing the system by affecting its abiotic  and Pace 1997; Scheffer and Jeppesen 1998) des-
conditions (eutrophication, groundwater level re-     sertification (Noy-Meir 1975; Walker and others
duction, climate change). The horizontal axis of the   1981), and various grazing systems (Van de Koppel
figures may be thought of as representing any of      and others 1997). A simple mathematical model for
these stress factors.                   the behavior of systems with catastrophic shifts be-
  The state of some ecosystems may respond in a     tween alternative stable states is presented in Ap-
smooth, continuous way to increasing stress (Figure    pendix 1. Here we briefly describe the insights ob-
1a), but more often the system remains relatively     tained from studies of shallow lakes in The
inert over certain ranges of conditions and then     Netherlands, which will serve as the main example
responds more dramatically when that stress ap-      throughout the paper.
proaches a critical level (Figure 1b). A crucially
different situation arises when the response line is   Shallow Lakes
folded backward (Figure 1c, d). This is known as a
                             Many of the shallow lakes and ponds situated near
“catastrophe fold” and implies that the ecosystem
                             populated areas have become murky as a conse-
has two alternative stable states over a range of
                             quence of eutrophication resulting from the use of
environmental conditions. The explanations and
                             fertilizers on the surrounding land and an increased
consequences of this scenario are discussed more
                             inflow of waste water from human settlements and
extensively in the next section, but in short it im-
                             industries. Although some deeper lakes have recov-
plies that when the ecosystem is in a state on the
                             ered quite well in response to eutrophication con-
upper branch of the sigmoid response curve, it will
                             trol programs, many shallow lakes have shown lit-
not pass to the lower branch smoothly. Instead,
                             tle improvement despite large investments. In fact,
when increasing human use has altered the condi-
                             even when the nutrient load is reduced to values
tions sufficiently to pass the threshold (F2), what
                             well below those at which the collapse of the clear
follows is a “catastrophic” transition to the lower
                             and vegetated state occurred, shallow lakes tend to
branch (vertical line with double arrow). Note that
                             remain in a highly turbid eutrophic state. A positive
when one monitors the system prior to this switch,
                             feedback in the development of submerged vegeta-
little change in its state is observed. Indeed, such
                             tion is probably the main explanation. In most
catastrophic shifts typically occur quite unan-
                             lakes, light is likely to be a primary factor in limiting
nounced, and early warning signals of approaching
                             the colonization by submerged plants (Hutchinson
catastrophic change are difficult to obtain.
                             1975; Chambers and Kalff 1985; Vant and others
  Another important feature of the response of
                             1986; Skubinna and others 1995). On the other
such catastrophic systems is that in order to induce
                             hand, water clarity tends to increase in the presence
a switch back to the alternative state on the upper
                             of plants (Schreiter 1928; Canfield and others 1984;
branch, it is not sufficient to restore the stress level
                             Jeppesen and others 1990; Pokorny and others
that occurred before the collapse (F2). Instead, one
                             1984). As a result there can be two alternative
needs to go back much further, beyond the other
                             stable states. In very turbid water, light conditions
switch point (F1), where the system recovers by
                             are insufficient for vegetation development; but
shifting back to the upper branch. It may be possible
                             once vegetation is present, the water clears up and
that the threshold level for a forward switch, but
                             the improved light conditions allow the persistence
not that for the backward switch, is within the
                             of a lush vegetation (Scheffer 1989; Scheffer 1998;
range of conditions that may be easily influenced by
humans (Figure 1d). Desertification in some xeric     Scheffer 1990).
                                                        455
                              Socioeconomics and Ecosystem Services

                              bidity for plant survival is reached (horizontal line).
                              At this point, vegetation collapses and the lake
                              “jumps” to the turbid upper branch. Reduction of
                              nutrients after this catastrophic transition does not
                              result in a return of plants until the critical turbidity
                              is reached again.
                               However, note that this backward switch hap-
                              pens at a much lower nutrient level than the for-
                              ward switch. Thus, often, reduction of the nutrient
                              level to values at which the lake used to be clear
                              and vegetated will not lead to restoration of that
                              state. This is indeed the experience of many lake
                              managers. The essence of the explanation is that in
                              the absence of the clearing effect of vegetation, the
                              water remains too turbid for vegetation to return.
                              This simple graphic model is analogous to the
                              smooth sigmoidal catastrophe fold shown in Figure
Figure 2. Graphic model for alternative stable states in  1c. The intuitively traceable lake example allows
shallow lakes.
                              one to get a feel for the way in which such cata-
                              strophic responses may arise. Clearly, the graphic
                              model is a rather extreme simplification of the func-
  At first, the argument that lake ecosystems will     tioning of lake ecosystems. However, more elabo-
have alternative equilibrium states may be convinc-
                              rate mathematical models and analysis of the be-
ing. However, demonstration of stabilizing mecha-
                              havior of many lakes confirm the main result:
nisms per se is not sufficient to conclude that a lake
                              shallow lakes may have alternative stable states
has alternative stable states. Although relatively
                              over a certain range of nutrient levels (Scheffer and
complex mathematical models are needed to cap-
                              Jeppesen 1998).
ture the dominant mechanisms that are involved, a
                               One may get a better intuitive feel for the impli-
very simple graphic approach suffices to illustrate
                              cations of such alternative stable states from stabil-
the main point in the shallow lakes case (Figure 2).
                              ity landscapes of the system (Figure 3). The bottom
The graph is based on three assumptions: (a) tur-
                              plane of this composed figure shows a line that
bidity increases with the nutrient level; (b) vegeta-
                              indicates how turbidity increases with the nutrient
tion reduces turbidity, and (c) vegetation disappears
                              level. The interpretation is analogous to that of the
when a critical turbidity is exceeded.
                              main sections of the previous graph (Figure 2). The
  In view of the first two assumptions, equilibrium
                              middle part of the folded line represents the critical
turbidity can be drawn as two different functions of
                              turbidity for plant survival. The two outer sections
the nutrient level: one for a plant dominated situ-
                              represent the clear and the turbid state. The five
ation, and one with a systematically higher turbid-
                              subsequent hilly landscapes in the figure represent-
ity for an unvegetated situation. The third assump-
                              ing stability landscapes show the equilibria and
tion translates into a horizontal line representing
                              their stability at five different nutrient levels. The
the critical turbidity for vegetation survival. Above
                              system, like a rolling ball, will be attracted to the
this line, vegetation will be absent, in which case
                              valleys. These correspond to stable parts of the
the upper equilibrium line is the relevant one; be-
                              folded curve on the bottom plane, whereas the
low this turbidity, the lower equilibrium curve ap-
                              hilltops represent the threshold turbidity corre-
plies. The emerging picture shows that over a range
                              sponding to the dashed middle section of the curve.
of intermediate nutrient levels, two alternative
                              The front landscape represents a situation with
equilibria exist: one with clear water and aquatic
                              heavy nutrient loading in which just one equilib-
plants, and a more turbid one without vegetation.
                              rium exists, a turbid one, whereas the rear picture
At lower nutrient levels, however, only the macro-
                              represents the pristine state of a lake, a low-nutri-
phyte-dominated equilibrium exists; whereas at the
                              ent situation in which a clear water equilibrium is
highest nutrient levels, there is only the turbid
                              the only possible stable state. Between these two
equilibrium without vegetation. If the lake is in a
                              extremes, there is a range of nutrient levels over
clear state (on the lower branch of the graph), an
                              which two valleys, and hence two alternative stable
increase of the nutrient level will lead to a gradual
and moderate rise in turbidity until the critical tur-   states, exist.
456    M. Scheffer and others


                                 Social Optimum in the Shared Use of
                                 Ecosystems
                                  Stakeholders and Their Welfare. One approach in
                                 economics to finding the best solution for society as
                                 a whole is to express all interests in a common
                                 currency (in practice, money) reflecting something
                                 termed “welfare” or “utility,” which is measured
                                 using principles expressed in Harberger (1974) and
                                 Wilson (1992). In the case of lakes, stakeholders
                                 whose welfare is related to use of the ecosystem
                                 may be:
                                 ●  Farmers who allow nutrients from cattle dung
                                   and fertilizers to pollute the water in the catch-
                                   ment area of the lake. Reducing such diffuse
                                   pollution has a cost for the farmers. Thus, this
                                   use of the lake has an economic benefit for
                                   them.
                                 ●  Households (or municipalities) and industries
                                   that drain their waste water into the lake. Re-
                                   duction of pollution from such point sources
                                   also has a cost that increases with the required
                                   level of cleaning.
                                 ●  Recreational fishermen, swimmers, boaters, bird
                                   watchers, owners of homes bordering on the
                                   lake. These users require that a certain basic
                                   quality be maintained for the water and its as-
                                   sociated ecosystem.
                                 ●  Hotels, campgrounds, restaurants, and so on,
                                   that serve recreational users. Their income in-
Figure 3. “Marble-in-a-cup” representation of the sta-
                                   creases with the number of recreational users
bility properties of lakes at five different levels of nutrient
                                   attracted by the lake.
loading.
                                 ●  Drinking water companies that use lake water as
                                   a source. Cleaner water is cheaper to process
                                   than polluted water with toxic cyanobacteria.
  The response of a lake with such properties to
                                 ●  Users of the chain of rivers, lakes, and oceans
eutrophication and subsequent restoration efforts
                                   that receive water from the outflow of the lake.
can be easily understood from this representation.
Starting from the pristine state, a moderate increase      Obviously, estimating the welfare functions that
in nutrient level gives rise to an alternative turbid      describe how the welfare of each stakeholder
valley, but if no large perturbations occur, the lake      changes with its use of the lake is not simple. Al-
will stay in the clear state. Continuing enrichment,       though there are various techniques that yield re-
however, gradually causes the size of the clear val-       producible results for valuating different ecosystem
ley to shrink to nil, making the lake more and more       services, the topic is still controversial (Portney and
vulnerable to perturbations, such as storms or plant       others 1994). It will probably always be difficult to
kills, which can bring the system across the hill to       express the value of these highly diverse aspects in
the valley of the turbid state. However, even in the       a common currency. Also, one may argue whether
absence of perturbations, the period in which the        the maximization of the value for human use,
lake stays relatively clear despite nutrient loading       rather than other ethical standards, should be the
will finally end with a catastrophic transition into a      criterion of choice. Nonetheless, the valuation ap-
turbid state as the valley around the clear water        proach is, in our opinion, a great step forward com-
state disappears. Attempts to restore such lakes by       pared to the current practice, in which many obvi-
reduction of the nutrient level often have little ef-      ously important values of ecosystems are simply not
fect, since the system tends to stay in the turbid        considered in the policy-making process.
valley of attraction.                        To clarify, and to avoid a long debate on this
                                                      457
                              Socioeconomics and Ecosystem Services

controversy, imagine that the lake and its water-     RASP needs to take into account how some uses of
shed are owned by a single entity (for example, a     the system affect the value for others (for example,
monopolist) and operated like a park or a public     swimming is incompatible with algae bloom).
utility where the objective is to design pricing     Therefore, it is crucial that the RASP also knows
schemes (Wilson 1992) that maximize every possi-     how the system changes in response to its exploi-
ble dollar of value that can be squeezed out of the    tation. Thus, it is the combination of the ecosystem
variety of services provided by the lake and its     response with the welfare functions that serves as a
watershed. For example, potable water could be      basis for the RASP to find the integrated use that
sold to cities from the watershed itself, provided    yields the highest welfare for society. To illustrate
that the watershed was kept clean enough for hu-     the principle of maximizing welfare using knowl-
man consumption. Recreational, scenic, boating,      edge of the constraints imposed by the functioning
fishing, and other services could be packaged in this   of the ecosystem, we will return to the response
imaginary world, much like the packaging of park     graphs (Figure 1) presented in the previous section.
rides or services offered by a public utility. Admis-   In these figures, the horizontal axes represent con-
sion fees could be charged to visitors to the area,    ditions, such as nutrient loading, that are affected
and rental fees could be levied on living units      by human use. There is usually a clear economic
within the area. The monopolistic owner would       benefit related to such use. If we assume that the
have an incentive to maintain the lake and its wa-    intensity of human use increases along the horizon-
tershed in such a way as to maximize the total sum    tal axis, the economic benefit, and hence the wel-
of these values and might not sell any loading ser-    fare of the users, will increase along this gradient.
vices at all to agriculture, developers, leaking septic  The precise relationship will depend on the specific
systems from cottages, and so on. The owner would     situation, but the increase of welfare will usually
charge leakage fees to any cottage owner whose      diminish at very intense use. In the following dis-
septic tank leaked into the lake, as well as loading   cussion, we will call users that significantly affect
fees to the farmers.                   the state of the ecosystem “Affectors” for short.
  The park or public utility paradigm can help to      The vertical axes represent an aspect of the state
clarify our thinking about the myriad of services     of the ecosystem, such as plant biomass. Most com-
that a lake and its watershed generates and the      ponents of the ecosystem tend to change in concert,
skills that a monopolistic operator needs to extract   and the variable depicted on the vertical axis merely
the maximal value from the spectrum of services.     serves as an indicator of the overall state. There can
This way of seeing the problem might help to avoid    be many uses of an ecosystem that depend on its
nonproductive debates about the merits of utilitar-    state but have little effect on it. For instance, swim-
ianism and problems with benefit/cost analysis, and    ming and bird watching are better in clear lakes and
to focus the discussion on how society might mea-     have little effect on lake ecology. Also, ecosystems
sure and extract all potential values out of the bun-   may provide services to a wide group of more dis-
dle of resources comprised by a lake and its water-    tant stakeholders that depend on the state. For in-
shed. The practical problem of delivering clean      stance, in shallow lakes, vegetation helps to purify
water to New York City is discussed by Chichlinisky    the water through natural processes such as deni-
and Heal (1998). We urge the reader to look at this    trification. Many downstream inhabitants will en-
case as a prototype for the design of a watershed     joy the benefits of the clean water that flows from
clean-up program and an institutional framework      the lake into the river system and eventually into
that can get the job done.                the ocean. In the following discussion, we will call
  A Graphic Theory of Ecological Limitations to Shared  users that benefit from the system but do not sig-
Use. In a society comprised of different interest     nificantly affect the state of the ecosystem “Enjoy-
groups, the situation is obviously more complex. As    ers” for short.
a first approach, we introduce the concept of a        In most cases, the ecosystem’s value for Enjoyers
hypothetical Rational Social Planner (RASP), which    will diminish with increasing exploitation by Affec-
replaces the monopolistic park owner of the previ-    tors. Thus, in the graphs (Figure 1), the low level of
ous example. We will use this concept to show       the system’s state indicator at high exploitation will
more specifically how the trade-off of different lake   correspond to the lowest value for Enjoyers, and
uses might work. Our hypothetical RASP knows       the welfare that Enjoyers can obtain from their use
how the welfare of each stakeholder is related to its   of the ecosystem will increase systematically with
use of the lake and therefore should be able to      the level of the state indicator represented by the
decide what combination of uses would yield the      vertical axis.
highest per capita welfare. However, to do this, the     Obviously, many more groups of stakeholders
458    M. Scheffer and others

exist in practice, and their interests are often over-
lapping rather than strictly complementary as in
this Affectors–Enjoyers model. However, this dis-
tinction is useful for a first exposition of the ideas.
We thus assume that overall community welfare
obtained from the ecosystem is simply that of the
Affectors plus that of the Enjoyers. Total welfare
will therefore increase along both axes used in the
ecological response graphs (Figure 4). If nature im-
posed no restrictions, the highest welfare could be
obtained by combining maximum exploitation with
a maximum value of the ecosystems state indicator.
However, the state is a function of the exploitation.
Hence, the response of the ecosystems limits the
possible combinations of use by Affectors and En-
joyers to points on the stable equilibrium lines in
the response graphs (Figure 1). Projection of these
lines on the welfare plane (Figure 4) shows in one
picture what stable combinations of use by Affec-
tors and Enjoyers are possible, as well as depicting
their associated welfare (see Appendix 2).
  Bad Compromises and Risky Optimum Solutions. This
information allows the hypothetical RASP to guide
society in its use of the ecosystem. The highest point
on such graphs represents the maximum overall
welfare that a society of stakeholders can achieve.
Mostly, it will be good for society to move as close
as possible to such a maximum. Depending on the
precise shape of the ecosystem response curve,
there may be a single optimum (Figure 4a, curve I)
at an intermediate stress level indicating that a com-
promise between Affectors and Enjoyers yields the
highest overall welfare, or two local optimum
points (Figure 4a, curve II) representing biased sit-
uations that maximize the welfare of either Affec-
tors or Enjoyers. The latter observation is impor-
tant because it shows that a compromise (which is    Figure 4. Graphic model showing how a theoretical
often the outcome of sociopolitical processes) may    society of Enjoyers and Affectors may obtain optimal
                             welfare from use of an ecosystem. The welfare of Enjoy-
well be a bad solution, because it represents a situ-
                             ers increases with the ecosystem state indicator, whereas
ation with low overall utility. Curve II in our ex-
                             the welfare of Affectors increases with the level of stress
ample, which results in this situation represents the
                             imposed on the system by their activity. Thus, total wel-
response of a sensitive ecosystem. Even low levels
                             fare will increase as indicated by the plane. The curves on
of stress result in extensive deterioration of the    the plane indicate how the ecosystem state responds to
state. The reason that a simple compromise yields    the imposed stress (as in Figure 1). The optimum social
low overall welfare in such situations is intuitively  welfare compatible with ecosystems dynamics is there-
straightforward. Even a low stress level (yielding    fore obtained at the highest point of each curve.
low gains for Affectors) produces a large loss for
Enjoyers. If the ecosystem can be treated in separate
spatial units (for example, if many lakes exist in an  desired feature of lakes by some users but regarded
area), the obvious solution may be to assign some    as a nuisance by others (Van Nes and others 1999).
units entirely to Enjoyers and others entirely to     Figure 4b shows what happens if the response of
Affectors. This kind of compromise problem has      the ecosystem is catastrophic (Figure 1c, d). In this
been worked out in more detail for the manage-      case, the maximum utility tends to be close to the
ment of aquatic vegetation, which is considered a    threshold at which the system collapses. The reason
                                                       459
                              Socioeconomics and Ecosystem Services

is that in such ecosystems, stress typically has little  ecosystems. A formal mathematical framework of
effect due to the stabilizing feedbacks that tend to   these theories is presented in the appendices.
keep the system in the same state, until stress has     Naive and Smart Ways for Approaching Optimum
increased enough to bring the system close to the     Utility. Obviously, in reality, an ideal RASP does not
border of collapse. Therefore, Enjoyers will be well   exist to oversee the entire system. In the worst case,
off until quite high levels of stress are imposed on   a management authority that tries to maximize
the system. This implies that aiming for the maxi-    community utility from the ecosystem may actually
mum welfare may be a hazardous strategy, because     know nothing about the dynamics of the overall
a slight miscalculation of the RASP or some envi-     system. In that case, one might imagine that the
ronmental variability (for instance, an exception-    authority would follow a simple iterative “hill-
ally hot year) may easily induce a switch to the     climbing” strategy to optimize overall utility. The
lower branch of the curve representing an alterna-    minimum requirement is that the authority can
tive stable state with a low overall utility. In order  somehow measure the utility that different groups
to restore the system, the stress level has to be     (Affectors and Enjoyers) obtain from the lake.
reduced to quite low values (at the cost of a con-    This can be done, for instance, by measuring the
siderable further loss of total welfare) before a     “willingness to pay” for different aspects. If the au-
switch back to the other branch occurs. This implies   thority continuously monitors the rise and fall of
that for societies that use ecosystems with multiple   utility for different groups, it can iteratively adjust
stable states, it may pay in the long run to be      regulations on pollution in such a way that total
conservative in their ecosystem management strat-     utility increases (see Appendix 2). For instance, if a
egy. This aspect is analyzed in some depth by Car-    small increase in the pollution load results in an
penter and others (1999).                 increase of total utility, the regulating authority will
  Note that the total welfare of a group depends on   allow a small further increase; whereas in the case
the welfare of individuals in that group multiplied    of an observed decrease in utility, it will reduce the
by the number of individuals in that group. Thus, if,   allowance a bit. This hill-climbing strategy results in
for instance, the proportion of Affectors decreases    a gradual iterative movement to increasingly higher
relative to that of Enjoyers, the stress-dependent    utility and can thus guide society to an optimum
welfare should be down-weighted. In terms of Fig-     utility, as indicated in Figure 4.
ure 4, this would imply that the welfare plane is      Apart from the question of whether this ap-
tilted, and the optimum welfare will be further      proach is feasible in any practical situation, there
away from the critical threshold. Indeed, in societ-   are several fundamental caveats to this approach to
ies where the enjoyment type of nature use be-      finding optimal utility. First, in a system with alter-
comes more important, overall utility will benefit     native stable states, the optimum tends to be close
from an even more careful use of its surrounding     to the threshold at which the system collapses.
ecosystems.                        Since in reality the authority will never be abso-
  However, a regulating authority will usually re-    lutely accurate, it may well accidentally allow the
spond to political pressure from Enjoyers and Af-     system to go beyond the “flip,” which is a little
fectors rather than seek the real social welfare op-   beyond “Optimum” on the diagram, causing the
timum. The nature of the political pressure depends    lake to switch to the “bad” state. Second, after this
not only on potential individual welfare gains and    crash, the hill-climbing method guides the author-
the size of different interest groups, but also on    ity further up along the lower branch, allowing
other socioeconomic aspects that determine the po-    progressively higher pollution to the advantage of
litical power of groups. Industries and other types of  the Affectors but not that of overall welfare. In
Affectors are often more effective in exerting polit-   order to move to the more desirable utility opti-
ical pressure than Enjoyers, among other reasons     mum on the “good” branch of the curve, after the
because the latter tend to be more widely scattered.   crash, society would need to move temporarily
As a result, politics tend to distort the picture, and  “downhill” (that is, to a further decrease in overall
an authority seeking to balance political pressure    welfare) until it reaches the point where the lake
from Enjoyers and Affectors will be biased away      recovers to the upper branch to come back to the
from the social optimum in the direction of further    optimum.
deterioration of an ecosystem.                Obviously, it would be much better if the author-
  In the following sections, we use the lake exam-    ity had some insight into the rules that govern the
ple to highlight several socioeconomic theories      ecosystem dynamics and adjusted its policy in a
about the factors that facilitate or prohibit societies  cautious way so as to minimize the chance of letting
from obtaining the theoretical optimal utility from    the ecosystem and its utility for society collapse.
460    M. Scheffer and others

                               general theory of mechanism design (Wilson 1992;
                               McAfee and Reny 1992) should be useful for the
                               design of more elaborate regulatory mechanisms
                               that have good incentive properties and minimize
                               costs of implementation and administration (see
                               also Brock and Evans 1986).
                               Mechanisms Preventing Optimum Use
                               In practice, the forces that drive societies do not
                               naturally approach an optimum welfare situation.
                               Positive economics, as opposed to normative eco-
                               nomics, deals with the problem of analyzing these
                               forces. The basic assumption is that each individual
                               will try to maximize its welfare by “playing its cards
Figure 5. Tax as a way to reduce stress (a) imposed on
                               in the smartest way.” Game theory is the standard
the ecosystem by the activity of Affectors to a desired
                               tool used for computing strategies that individuals
level a*. If the Affector optimizes his/her net benefit
(U(a)–Ta), he/she will tune his/her activities to the point  (or groups) would choose on the basis of their prior
where the first derivative of the utility curve equals the   assumptions on how other individuals (or groups)
tax rate U (a) T.                       will respond to problems. Quite often, the tendency
                               to tune behavior to such prior assumptions results
                               in suboptimal situations from the viewpoint of so-
  There are many ways in which authorities can        cial welfare. As an environmental example, con-
regulate, but in practice, taxation or some kind of      sider the case in which two individuals (or cities or
user charge is a popular instrument. The idea be-       countries) use the same lake (or ocean or atmo-
hind taxation as an incentive is that given the tax      sphere). Each one expects that the other will adjust
rate Affectors will choose their pollution load in      its behavior to prevent the ecosystem from deteri-
such a way that they maximize their individual net      orating. However, precisely for that reason, each
benefit, taking both tax and gains into account.        one will have less incentive to adjust its own be-
Since the gains usually will not keep increasing at a     havior, and the system is more likely to deteriorate.
constant rate with the intensity of the Affectors        In the following discussion, we will further elab-
activities and the resulting pollution, a fixed tax rate    orate our Affector vs Enjoyer example to show how
per unit of pollution will lead a rational Affector to    this type of theory can be applied to the analysis of
keep its pollution activities to a certain predictable    forces that determine which interest groups are
level (Figure 5). Theoretically, an authority with a     more powerful in forcing policy in a desired direc-
sufficient understanding of the system can thus set      tion.
the tax rate in such a way that Affectors realize        Pollution Is Profitable: The CCPP Phenomenon. One
precisely the level of pollution that leads to the      well-known problem in environmental protection
social welfare optimum (see Appendix 3).           is known as the “CCPP phenomenon” (Communize
  One can easily derive a tax-setting scheme that      the Cost, Privatize the Profit) (Hardin 1993). In an
would allow a society to follow the hill-climbing       unregulated situation, Affectors benefit from their
procedure described in the previous section (see       activities while the costs resulting from a deterio-
Appendix 3). However, this hill-climbing approach       rated ecosystem state are carried by the Enjoyers. In
is rather limited. If the system has multiple equilib-    the common situation where Affectors are also
ria or several local welfare maxima, one needs a       partly Enjoyers of the same ecosystem, the costs of
deeper insight into the ecosystems dynamics. Using      the activities may be considered to be borne by to
this insight, the authority may want to levy a tem-      the community as a whole, whereas the profit from
porary surtax to lower pollution for a long enough      the affecting activity goes exclusively to the Affec-
period of time to allow the lake to flip to the “good”     tors. This imbalance is at the core of many environ-
branch. The surtax could then be lifted. This is       mental problems. In the absence of any feedback,
something like placing a quantity control on the       Affectors may keep increasing the stress on ecosys-
Affectors to guide them toward the right basin of       tems, even if the profit associated with further in-
attraction, and then imposing a tax to guide them       crease is very small. In this type of saturated utility
toward the right level for that basin. It is beyond the    situation, even a slight tax on stress-inducing activ-
scope of this paper to discuss the design of such       ities could have a large effect. A fair tax system as
elaborate decentralized regulation schemes. The        sketched earlier would ideally force Affectors to
                                                        461
                                Socioeconomics and Ecosystem Services

                               tend to be much more complicated than those in-
take real environmental costs into account, typi-
                               corporated in such models.
cally inducing a large reduction in the stress im-
                                 Total political pressure from an interest group
posed on the ecosystem. However, if there is no
                               depends, among other things, on the tendency of
RASP and there are no regulations yet for this par-
                               their members to free-ride on the efforts of other
ticular Affectors activity, the first step toward estab-
                               group members and their belief in the effectiveness
lishing a more fair situation from a social point of
                               of the overall pressure. Political-pressure supply
view is to mobilize the forces of the Enjoyers in
                               functions may be derived as Nash equilibria from a
order to change the policy. Game theory models
                               noncooperative game model following Magee and
suggest that the political pressure mounted by
                               others (1989, Appendix A.6.5, p 287). Their analy-
groups such as Enjoyers and Affectors depends
                               sis suggests that the resources invested by an indi-
strongly on their ability to overcome so-called col-
                               vidual to exert political pressure depend on the
lective action problems.
                               interest at stake, but also on what has been termed
  The Collective Action Problem and its Effect on Politics
                               “perceived effectiveness and noticeability” (Magee
The essence of models that address collective action
                               and others 1989). A mathematical treatment can be
problems is easy to understand. Suppose a tax T on
                               found in Appendix 4, but the idea is intuitively
pollution is proposed by the regulatory authority as
                               straightforward. The perceived effectiveness de-
a trial balloon. Affectors will want to invest their
                               pends on the strength of beliefs in the power of the
resources to exert political pressure against this pol-
                               sum of contributions to move policy in the direction
icy. The amount of effort will depend on their be-
                               desired by the Enjoyers. This will increase along
liefs about the impact of their total contributions on
                               with the merit of the Enjoyers’ case. However, no-
the chances of this policy actually being imple-
                               ticeability, and hence the eventual individual effort,
mented. However, each Affector also has an incen-
                               decreases along with group size due to the free-
tive to free-ride on the contributions of his com-
                               rider problem (Figure 6). This is because, all else
rades in the common effort to stop passage of T by
                               remaining equal, the larger a group, the more
the authority. In practice, an Affector will tend to
                               anonymous each member tends to feel. Hence, self-
contribute less than he/she should if he/she be-
                               interest is likely to lead each individual in a large
lieves that his/her comrades will invest properly.
                               group to shirk the duty of contributing a fair share
  We can model this specific case as a simple non-
                               to the group effort.
cooperative game where each Affector forms his/
                                 The decrease in individual effort with group size
her beliefs based on the actions of the other Affec-
                               depends upon how effective the group is in making
tors and chooses his/her contribution level in such
                               each member feel “noticeable,” so that he/she pulls
a way that it maximizes his/her expected gain given      his/her own weight in the joint effort of exerting
his/her prior beliefs. It is easy to show that in such    pressure. Its efficacy depends on the forces that
models contributions in equilibrium increase as the      determine how well a group can muster a collective
stakes are less evenly distributed over the players      effort in a situation such as mustering political pres-
(Magee and others 1989, Appendix to Chapter 6, p.       sure that serves its common good (Ostrom and
278 –90). This makes sense because if the losses       others 1994; Putnam 1995).
were all concentrated on one large Affector, he/she       For example, if the Enjoyers are dominated by
would not face a free-rider problem and would         recreational businesses and these businesses have a
optimize his/her effort against the policy, whereas if    formal organization of longstanding tradition, such
there were two even-sized Affectors, each would        as a recreational businessmen’s association, then
tend to free-ride on the other’s efforts. A similar      the noticeability would be quite large. Each busi-
free-rider analysis can be applied to the Enjoyer side    nessman will be monitored by the association and
of the political struggle.                  may be punished for contributing less than the
  In some situations, if the regulator is a manage-     standard expected level of effort. The businessmen’s
ment agency, a pressure analysis using game theory      association may have built up a relationship with
may approximate what actually goes on in practice.      the authority over the years, which might show up
However, it should be stressed that such noncoop-       in an increase in the perceived effectiveness that
erative Nash equilibrium modeling is not always        each unit of contribution has on policymaking.
appropriate. In a repeated situation where the Af-        Other forces that might act to increase noticeabil-
fectors are interacting on a face-to-face basis, other    ity include the necessity for each member of the
more adequate models have been proposed (Os-         group to have access to a commonly shared factor of
trom and others 1994; Frank’s 1992 review of         production (for example, operating room access for
Coleman 1990). Still, in practice, social interactions    a surgeon, access to the common milk distribution
462    M. Scheffer and others




Figure 6. Game theory predicts that an individual’s ef-
fort invested in political pressure to reach the goal of a
political interest group depends on the “noticeability” felt
by the group member and the “perceived effectiveness” of
the pressure on changing policy in the desired direction.
The individual contributions decrease with group size due
to an increasing incentive to free-ride on the efforts of
others in larger groups, where each member feels more
anonymous. Notice that small groups that have a clear
case and a social system that reduces free-riding will be
politically more powerful than expected from their mere
numbers and the welfare at stake.



network for a dairy farmer, access to the docks for a
stevedore, access to the multiple listing service for a
real estate agent, access to the informal multiple-
listing service network based on the goodwill of
fellow real estate agents above and beyond access to
the formal multiple-listing service for these agents,
access to a referral network for a doctor, and so on).
                                Figure 7. Differences in efficiency at mobilizing political
The necessity of access to such a factor of produc-
                                pressure (see Figure 5) distort the process of optimization
tion may give a group leverage over the tendency of
                                of social welfare depicted in Figure 4b. The system will
its members to shirk their responsibility and free-ride.    tend to an equilibrium in which political pressure from
  The repeatability of interactions and density of      different interest different groups is in balance. If Enjoy-
the communications network within a group           ers are more efficient (a), that equilibrium will be on a
(Coleman 1990; Putnam 1995) are key factors that        more resilient part of the branch representing the desired
determine the strength of the group to prevent         ecosystem state. However, typically, Affectors are more
free-riders on collective efforts. Further discussion     efficient at mustering political pressure, resulting in a
                                situation (b) where the system tends to increasing stress
of the forces relating to the relative efficiency of
                                on the ecosystem, even after it has collapsed to the lower
resolving collective action problems is beyond the
                                branch of the curve.
scope of this paper.
  The graphic models that show how social welfare
can be maximized (Figure 4) can be modified to
produce graphs that show the expected outcome of        interest group to mobilize forces, which depends on
political pressure (Figure 7). A formal treatment of      aspects such as noticeability and effectiveness per-
the relationship between the two sets of graphs can      ceived by the members (Figure 6). Therefore, we
be found in Appendix 4, but the interpretation is       can obtain a graph that represents the political force
intuitively straightforward. The change of focus is      that can be applied by Affectors and Enjoyers to
that, rather than seeking the social welfare opti-       obtain a certain utility from the ecosystem by mul-
mum, the authority that regulates the system is        tiplying that utility with a factor that represents the
responding to political pressure. Political pressure      ability of the group to mobilize forces (Figure 7).
depends on the interest at stake (that is, the welfare      In a situation where the Enjoyers are a more
in Figure 4), but also on the effectiveness of the       coherent and concentrated group than the Affec-
                                                        463
                               Socioeconomics and Ecosystem Services

tors, the Enjoyers’ political power will be relatively   good idea of the range of different functions the
strong. In the case of our example of ecosystems      ecosystem offers for society and the dependence of
with alternative stable states, this will tend to lead   utilities on the state of the ecosystem. The general
to an equilibrium that is on a relatively safe part of   observation that better solutions of a conflict of
the “good” branch of the equilibrium curve (Figure     interest often require more effort to analyze and
7a). The resilience of this situation is relatively high.  communicate the problem has already been dis-
However, as we have seen, Affectors tend to be       cussed by Mary Parker Follett (1924), who drew the
better organized than Enjoyers, who are often a       distinction between integrative and compromise so-
large but diffuse group. As a result, the political     lutions. When two people/parties fundamentally
power of the Affectors is relatively high, resulting in   disagree as to outcomes, they have a number of
a situation in which there is no local optimum       options. One can force his/her position and the
representing a power equilibrium on the “good”       other accommodate. Both parties can simply walk
branch of the curve (Figure 7b). Instead, the polit-    away from the issue. Or the two parties can seek a
ical pressure will drive society further and further    way to come to terms. The classic way to do this,
up along the branch with low Enjoyer value, due to     according to Follett, is the compromise.
the high pressure produced for even slight gains of      For example, two people in a room are arguing
Affector utility.                      about whether the window should be opened or
                              closed. The compromise is to leave it half open.
                              Compromises have the advantage of seeming fair,
DISCUSSION                         but they leave neither party satisfied and so do not
                              generally represent long-term solutions. Integrative
Our analysis of the interactive dynamics of ecosys-
                              solutions are those that go beyond superficial trade-
tems and societies has revealed two types of prob-
                              offs and issues of fairness and seek to find innova-
lems that may be crucial to the sustainable and
                              tive and more longlasting solutions. This is more
socially fair use of ecosystem utilities. First, ecosys-
                              difficult, because it requires greater patience and
tem responses to stress can complicate the choice of
                              deeper understanding of the interests or concerns
management targets and allocation of ecosystem
                              that both parties bring to the table. Continuing with
services in complex ways. Second, differences in the
                              the example of the window, further exploration of
ability of social groups to muster political power
                              the motives and concerns of both parties may reveal
tend to cause a power bias that results in subopti-
                              that the conflicting positions (window shut or win-
mal overall utility obtained from the system and a
                              dow open) are due to one person wanting to have
drop in ecosystem quality. Here we review the main
                              air while the other wants to avoid a draft. An inte-
points and discuss some complications that could be
                              grative solution might be to open a window in an
addressed in further studies.
                              adjacent room. That way both of their basic needs
                              or concerns are met. An integrated solution is better
Compromise vs Integrative Solutions             than a compromise, but it takes more work, a
A first observation from our simple graphic model      greater understanding of the needs of all parties,
of the shared use of ecosystems by contrasting       and more creativity.
groups labeled “Affectors” and “Enjoyers’” (Figure       Another major conclusion from the graphic
4) is that sensitive ecosystems may often have two     model is that in ecosystems with alternative stable
alternative optima for social use. In one optimum,     states, the optimum shared use from a short-sighted
the quality of the ecosystem for Enjoyers is low,      economic point of view tends to be at the border of
whereas the utility from activity that negatively      collapse of the ecosystem. In fact, ecosystem col-
affects its quality is high. In the alternative opti-    lapse is quite likely to occur in such situations, for a
mum, quality-affecting activities (and their reve-     number of reasons. Stochastic variation in environ-
nues) are very low, whereas the resulting quality of    mental conditions and imperfect information about
the ecosystem and hence its utility for Enjoyer       the state of the ecosystem are major risk factors in
groups is high. In such ecosystems, compromise       the vicinity of the theoretical social optimum (Car-
solutions are bad from a overall social point of view;   penter and others 1999). Importantly, our analyses
often, a better strategy is to preserve some ecosys-    also indicate a systematic bias away from the opti-
tems while offering others for intense Affector ac-     mum toward increasing intensity of uses that affect
tivities.                          the ecosystem quality. This bias is detrimental for
  To see and realize such solutions, it is obviously    social welfare and ecosystem quality in general, but
essential to understand the response of the ecosys-     its effects can be especially dramatic in ecosystems
tem to increasing stress, but one must also have a     with alternative stability domains, where it easily
464    M. Scheffer and others

results in collapse of the system to a state with low   bring the pressures on regulators and politicians
overall social utility.                  into balance with the overall social interest. Our
                              model is meant to illustrate this problem and to
Toward Solution of the Power Bias             prompt discussion about mechanisms that might
Our analysis of the power bias suggests that the      help balance equilibrium pressures on politicians
differential organizational efficacy of Affectors rel-   and produce the overall social optimum.
ative to Enjoyers at mustering political power is a      Another logical approach to addressing the power
key problem. The ultimate roots of this differential    bias and pushing the political balance back in the
ability lies not in corruption but in the superiority of  direction of the social welfare optimum would be to
Affectors in overcoming collective action problems.    institutionalize the search for integrative solutions,
Enough is known now about what kinds of forces       as advocated by Mary Parker Follet (1924). Obvi-
determine the relative efficacy of collective action    ously, it is vital to integrate a broad form of benefit/
that one could imagine designing policies that       cost analysis into public policy making (“broad” in
would level the collective-action organizational      the sense that a wider spectrum of values is consid-
playing field across the two groups. An ideal solu-     ered, rather than just the narrower monetary val-
tion would be a surrogate for a tax levied on the     ues addressed by traditional benefit/cost analysis).
negative externalities that the Affectors load onto    Given that the current policy-making process tends
the Enjoyers through their relative efficiency at      to select a far worse alternative, this form of benefit/
using the political system. The relative efficiency of   cost analysis seems preferable, despite the concerns
the Affectors may have nothing at all to do with      expressed by critics such as Bromley (1990).
things like bribery, which capture the attention of      Bromley argues that efficiency measures used in
the news media and the public imagination while      benefit/cost analysis, such as the potential Pareto
generating general outrage. The real culprit is the    improvement criterion, do not “pass the test of
slow, subtle “education” of the politicians and reg-    consistency and coherence within economic the-
ulatory authorities imposed by steady daily contact    ory, nor do such measures accord with what public
with agents of the Affectors, who are better fi-      decision makers seek in policy advice from econo-
nanced due to their superiority at mustering more     mists” (Bromley 1990, p 86). If we assume that (a)
resources per unit of stakeholder interest than the    our ecosystem is small relative to the economy as a
poorly organized Enjoyers.                 whole, so that general equilibrium feedbacks may
  For example, an association of real estate agents    be ignored, and (b) income effects are small and
in the US can be much more effective with legisla-     may be ignored, then treating the objective of man-
tors than a collection of individual homeowners,      agement of the lake ecosystem in the manner of a
because real estate agents must interact intensely     public utility manager gets around some of the crit-
with each other in order to match up buyers and      icisms of the operationalized utilitarianism that we
sellers. This intense social networking of real estate   are using here. See Bromley’s critique of Harberg-
agents produces collective action for other objec-     er’s (1974) attempt at an operationalized utilitari-
tives such as “informing” legislators as a by-product   anism, and see Sen (1999) for the general difficul-
of the microeconomics of their professional prac-     ties in social choice and various approaches for
tice. In theory, some kind of tax could be levied on    dealing with them. However, Frank provides a spir-
such effective associations in order to correct the    ited counterargument to some of these objections to
resulting bias in pressure on politicians. Indeed, this  benefit/cost analysis. For example, he argues that if
is an example of a situation where the social capital   a benefit/cost criterion “is employed as a policy for
created by intense, repeated networking (which is     resolving large numbers of social decision, what is
created, perhaps, as a by-product of particular busi-   relevant is the pattern of decisions it produces”
ness activities or cultural connections)—as has been    (Frank 1992, p 160, where “policy” and “pattern”
stressed by writers such as Coleman (1990), Frank     are in italics). Frank’s argument probably explains
(1992), and Putnam (1995)— can lead to a loss for     why there seems to be a rough consensus in how to
the economy as a whole. Indeed, a major cause of      deal with this problem in those small parts of the
poor allocations such as those associated with the     economy called “public utilities.”
environmental problem is differential social capital     Hence, we take a benefit/cost posture in formu-
across different stakeholders. Differential social cap-  lating the social objective here in order to get on
ital leads to differential creation of political pres-   with what we have to offer the reader. We assume
sure, which in turn leads to an overall outcome that    that the RASP operates our “environmental public
is not in the social interest. Once a correct diagnosis  utility” to optimize the total value computed from
of the problem is made, remedies can be sought that    willingness-to-pay (or willingness-to-accept) sched-
                                                       465
                              Socioeconomics and Ecosystem Services

ules over all the services provided, in order to max-   Gray and others 2000; Nahapiet and Ghoshal
imize the “size of the pie.” Then we assume that the   1998), social groups and systems vary enormously
RASP redistributes the proceeds to different users to   in the degree and kind of reciprocity that is built
balance political pressures, such as, for example,    across and between formal organizations. Social
delivering “basic needs” services to the poor at less   capital represents a repository of good will, energy,
than cost. We shall assume that the RASP effects     and effort that can be mobilized rapidly around a
this redistribution in such a way as not to distort    given social cause (Fukuyama 1995). It is key in
any of the efficiency incentives to optimize the total   early domain formation and in breaking gridlock
value. For example, this could be accomplished by     situations in later stages of domain formation. As
lump-sum subsidies to favored groups financed by      Burt (1992; 1997) has pointed out, bridges across
revenues collected from efficient (nonlinear) pric-    “structural holes” (linking two individuals whose
ing schedules (Wilson 1992) imposed on all services.   primary networks are linked in no other way) rep-
                             resent the greatest increase in resources for the
The Problem of Slow Social Dynamics            individual, but such links also bring new groups of
In the current analysis, we focused on mechanisms     stakeholders into exchange relationships and so
that determine the equilibrium use of ecosystems     may be of key importance.
by society; however, in many situations, the trajec-     Common culture is another crucial factor that
tory toward that state of equilibrium is of particular  can facilitate the process of finding a solution to an
interest because it may be very long. Indeed, it may   environmental problem. Particularly in the absence
take a long time before an environmental problem     of a long history of reciprocity and the trust that it
is even recognized, if it becomes recognized at all. In  engenders, stakeholders often decide to enter into
addition, the process of reaching a solution that     the initial reciprocities based on the belief that they
reflects the balance of political power may be very    share “representations, interpretations, and systems
slow. Since the cost for society of the many unset-    of meaning with the other party or parties” (Na-
tled spillover problems is obviously huge, an under-   hapiet and Ghoshal 1998). This, in part, explains
standing of the mechanisms governing these dy-      the key role of “domain entrepreneurs” or visionary
namics is essential if one wants to reduce the      leaders in domain organization. They among oth-
overall social cost of environmental problems. We     ers, have the ability to “tell a story” (create a struc-
address this dynamic multiproblem dimension in      ture of signification) that appeals to many different
some detail in a separate paper (Scheffer and others   stakeholders (Gardner 1995) or tailor the story so as
forthcoming) and merely touch upon the main        to secure the cooperation of key stakeholders
mechanisms of delay here.                 (Westley 1992).
  Among the key factors determining the time        Furthermore, the relative strength of incentives
needed to solve an environmental issue are social     of organized private profit-seeking corporate or
network structure, culture, and the role of particu-   commercial groups tends to be much greater.
lar key individuals. A first delay can be caused by    Hence, these groups are quicker to move toward
the fact that in the early stages, many involved     opportunity than governments or regulators, as
stakeholders may not even recognize that they have    well as more diffuse and hence loosely organized
a stake (Westley and Vredenburg 1991). For in-      groups. This imbalance can cause a disconnect be-
stance, a chemical firm may be unaware that their     tween time scales of action on the part of, say,
operations will be impacted by the efforts of an     private profit agricultural firms acting as Affectors
environmental group concerned about the water       and sluggishly responding regulators or sluggishly
quality in a nearby town. At the same time, many     responding, loosely organized Enjoyer groups. Cor-
citizens may be unaware that their health has al-     recting the response disconnect caused by dispari-
ready been affected. Another significant delay may     ties in incentive strength is part of the remedy
come in a later phase of the conflict at very high     needed to synchronize the response times of the
levels of organization. All stakeholders may find     different interest groups.
themselves entrenched in conflicting positions,
making negotiations and coordination almost im-      CONCLUSION
possible (Lee 1993).
  Social networks can play a decisive role in pre-    The analyses presented here are admittedly rather
venting or solving such conflicting gridlock situa-    stylized and do not take much of the dazzling com-
tions if they represent repositories of social capital  plexity of ecosystems and human societies into ac-
that can be mobilized. As Putnam and others have     count. Nonetheless, they comprise a simple diagno-
noted (Putnam 1993a, 1993b, 1995; Coleman 1990;      sis of some of the major barriers to a sustainable and
466    M. Scheffer and others

                                  Case TJ (1991) Invasion resistance, species build-up and com-
fair shared use of ecosystem services and suggest
                                   munity collapse in metapopulation models with interspecies
some possibilities for their solution. A tendency
                                   competition. Biol J Linnean Soc 42:239 –266
toward suboptimal compromises, systematic bias in
                                  Chambers PA, Kalff J (1985) The influence of sediment compo-
mustering political power, and slow social response         sition and irradiance on the growth and morphology of Myri-
to environmental problems emerge as key prob-            ophyllum spicatum. Aquat Bot 22:253–264
lems. Obviously, amelioration of the detrimental          Chichilnisky G, Heal G (1998) Economic returns from the bio-
effect of common practices in ecosystem use on            sphere. Nature 12:629 – 630
society and the environment require that strategies        Clark C (1990) Mathematical bioeconomics: the optimal man-
be tailored to the specific case. Our analysis suggests        agement of renewable resources. 2nd ed. New York: Wiley
that such strategies would need to include at least        Coleman J (1990) Foundations of social theory. Cambridge, MA:
                                   Harvard University Press
the following key ingredients:
                                  DeAngelis DL, Bartell SM, Brenkert AL (1989) Effects of nutrient
●  A reliable model of the ecosystem’s response to         recycling and food-chain length on resilience. Am Nat 134:
  different forms of use                      778 – 805
                                  Follett MP (1924) Creative experience. New York: Longmans
●  An overview and valuation of the range of eco-
                                   Green
  system services to society
                                  Frank R (1992) Melding sociology and economics: James
●  Correction of political bias due to differences in        Coleman’s foundations of social theory. J Econ Lit, 30:147–
  the organizational power of groups of stakehold-         170
  ers                              Fukuyama F (1995) Social capital and the global economy. For-
                                   eign Affairs 74:89 –103
In addition, smart facilitative management of the
                                  Gardner H (1995) Leading minds. New York: Basic Books
social process could help to reduce the delay in
                                  Gray B, Westley F, Brown D (2000) The transformation of vol-
settling environmental disputes.                   atile, interorganizational domains. Working paper. Pennsylva-
                                   nia State University
ACKNOWLEDGMENTS
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The ideas presented in this paper originated at           libria in metapopulation dynamics. Nature 377:618 – 621
workshops of the Resilience Network. We are grate-         Harberger A (1974) Taxation and welfare. Boston: Little, Brown
ful to Buzz Holling for creating and inspiring this        Hardin G (1993) Living within limits. Oxford: Oxford University
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network, which was funded by the MacArthur
                                  Holling CS (1973) Resilience and stability of ecological systems.
Foundation, and to three anonymous reviewers
                                   Annu Rev Ecol Syst 4:1–23
whose comments helped to improve the clarity of
                                  Hutchinson GE (1975) A treatise on limnology. Volume 3. Lim-
the manuscript.
                                  nological botany. New York: Wiley
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                  ¨
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                                  Suppose the lake is affected by n Affectors, and each
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                                  Affector i loads a(i) nutrients into the lake. Then,
of business and environmentalists. J Appl Behav Sci 27:65–90
468    M. Scheffer and others

the dynamics of the lake in response to the Affec-    governs the ecosystem. Let the set S of steady states
tors action can be characterized by substituting a    be defined by S    {(a, x) 0   Na–bx   rf( x)}. It
with A   Sum[a(i)] in Eq. (1).             may then operate in an iterative way, simply re-
 Now let the Affector utility be given by        sponding to short-term changes in utility perceived
                             by Affectors and Enjoyers in its attempts to regulate
        UA   Sum u a i , i ,       (2)  Na so as to increase Nu(a)    Mv( x). For instance,
                             if the authority starts at a very low level of “a” and
and the utility to Enjoyers be given by
                             gradually increases “a,” continuously trading off the
                             measured willingness to pay of Affectors against the
         UE    Sum v x, k        (3)
                             measured value of quality loss from the Enjoyers, it
where u, v are concave functions, and where u is     will eventually reach a point indicated as “Opti-
assumed to increase in a(i), and v is assumed to     mum” in Figure 4b. Notice that this point does not
decrease in x. Here the index k denotes the index of   have to be a global maximum. It may be a local
Enjoyer k, and the Sum in Eq. (3) is taken over all    maximum.
Enjoyers while the Sum in Eq. (2) is taken over all
Affectors. Carpenter and others (1999) treat this
                             Appendix 3 Tax as a Way to Direct Society
problem in some detail.
 In the “normative” case, where the future is
weighted equal to the present (that is, there is no    Following Brock and Evans (1986), let a tax T on
discounting), we would optimize welfare by solving    loadings be proposed as the regulatory instrument.
the problem                        The idea behind tax as an incentive is that given the
                             tax rate T, Affectors will choose their loading “a” in
        Maximize UA     UE ,      (4)
                             such a way that they maximize their individual net
                             benefit. Thus they solve:
subject to the constraint that the ecosystem equi-
librium state responds to the stress imposed by the
                                     Maximize u a –Ta ,         (6)
total load A imposed by the Affectors. Note that we
have assumed that once A is set and fixed, the
                             which causes each Affector to choose a(T) to solve
ecosystem has relaxed to a steady state given by
                             (Figure 5),
       dx/dt  0   A–bx    rf x    (5)
                                        ua    T,          (7)
Figure 4 captures the solution to this kind of prob-
lem for the special case in which all Affectors and all  where u (a) is the derivative of u with respect to a,
Enjoyers are identical. In the figure, we plotted the   and we assume that there is a unique solution to
value of the objective Eq. (4) on the vertical axis, A  Eq. (7) for each positive T. If a* is the social opti-
on the stress axis, and a desirable aspect of ecosys-   mum from the problem in Eqs. (4), (5), then we can
tem state such as vegetation biomass on the third     choose T T* by setting T* u (a*) such that Eq.
axis. Note that, since x represents an unwanted      (7) yields the choice a  a*. That is, just put T*
aspect (for example, turbidity or barren soil), x     u (a*). This is the simplest story told in decentral-
would increase from left to right along this axis.    ized regulation of the negative externalities spilling
 In the special case where there are n identical     over from the Affectors onto the Enjoyers.
Affectors and M identical Enjoyers, with utilities      Turn now to a slightly different type of tax-set-
u(a), v( x) respectively the problem in Eqs. (4), (5)   ting scheme that will serve as a foundation for the
becomes                          political economy model. Suppose a tax T is levied
                             on Affectors’ activities and the proceeds a(T)T are
       Maximize Nu a     Mv x     (4 )  redistributed in a lump sum to the Affectors in such
                             a way that Eq. (7) still holds. This can happen, for
subject to
                             example, when there are a large number of Affec-
                             tors and each ignores his actions’ impact on the
       dx/dt  0   Na–bx   rf x    (5 )
                             total tax take. For each T, social welfare W(T) is
One can now imagine a management authority        then given by
(compare the RASP) that defines the public interest
as the total sum of Affector and Enjoyer utility as         WT    Nu a T     Mv x T ,    (8)
defined above. Suppose now that the authority
does not know the law of motion Eq. (5 ), which      where the ecosystem state experienced by the En-
                                                        469
                              Socioeconomics and Ecosystem Services

joyers for given tax level, x(T), is found by solving   get stuck on a local maximum when there are mul-
the ecosystem’s equilibrium condition:          tiple local maxima.

        0  Na T –bx   rf x       (9)
                             Appendix 4 Collective Action Problems
                             and their Effect on Political Power
Notice that for a given a(T) there may be more than
one solution to Eq. (9), which depends on the his-
tory of the tax T. Suppose, for example, the tax is    Political-pressure supply functions may be derived
very low to start. Then a(T) is initially very high,   as Nash equilibria from a noncooperative game
and there is only one solution, which is very high.    model following Magee and others (1989, Appen-
As T increases, a(T) falls and the ecosystem “slides”   dix A.6.5, p 287). Their analysis suggests that the
down the upper branch of the catastrophe fold until    resources invested by an individual to exert political
it reaches the lower “critical point”, where there is   pressure depends positively on the expected effec-
a sharp drop in x(T) that solves Eq. (9). For lower    tiveness of its individual contribution and its inter-
values of a(T), there is now only one solution x(T)    est at stake. For a very special case, Magee and
to Eq. (9). We see that the tax T can be used to trace  others derive the following formulas for Nash equi-
out the same hysteresis cycle depicted in Figure 4.    librium contributions for both sides of the conflict:
  Now in the case where there is only one global
welfare optimum (which is often not the case, as          cx T   A/N    B U 0 –U T ,    (12)
argued above), we can adjust T in the direction of
increasing welfare on a slow scale of time relative to       cy T   C/M   D V T –V 0 ,    (13)
the time of relaxation of the ecosystem dynamics to
                             where cx(T) and cy(T) represent the pressure from
a steady state given the loading by the hill-climbing
                             individual Affectors and Enjoyers respectively
procedure:
                             against and in favor of raising the pollution tax from
dT/dt  WT    Nu a T   Mv x x T          0 to T;
              b–rf u    vMx,  (10)   UT   Affectors’ utility  u a T –a T T,
                                which is assumed to fall as T increases
where denotes derivative. The right hand side of
Eq. (10) is obtained by differentiating equation (5)
                                from zero; and V T     Enjoyers’ utility
with respect to T at the solution Na(T)     bx(T)–
rf( x(T)). Eq. (10) is intuitive. As the tax increases,          vxT     1/M Na T T ,
a(T) falls. Hence, x(T) falls as long as the solution
                              where x T solves Eq. (9) for a      aT.  (14)
x(T) is located on a rising part of the function
bx–rf( x), which will be the case when there is only
                             In this model, the terms [A/N B] and [C/M D]
one global welfare optimum (which we assume).
                             represent the power attained by mustering collec-
Hence, Eq. (10) instructs the RASP to keep increas-
                             tive effort for the Affectors and Enjoyers, respec-
ing the tax, provided that the marginal benefit to
                             tively (Figure 6). The coefficients C, D for the En-
the Affectors is less than the marginal cost to the
                             joyers (likewise A, B for the Affectors) capture
Enjoyers. Hence, we see that at a rest point of Eq.
                             Mancur Olson’s notions of “perceived effective-
(10) we have:
                             ness” and “noticeability,” respectively (Magee and
                             others 1989). The perceived effectiveness (C) de-
        0   b–rf u   vM,       (11)
                             pends on the strength of beliefs on the power of the
provided that x (T) is not zero (which we assume).    sum of contributions to move policy in the direction
Notice that, indeed, Eq. (11) is the first-order nec-   desired by the Enjoyers. The size of C would tend to
essary condition for a maximum for the welfare      increase along with the merit of the Enjoyers’ case.
problem in Eqs. (4 ), (5 ). Thus, such an iterative    Notice that the free-rider effect is captured by the
tax setting procedure may result in reaching the     term C/M, so that if each Enjoyer does not feel
welfare optimum. We shall think of Eq. (10) as a     “noticeable” (that is, D 0), then the contribution
model for a regulator (a RASP) who is guided by      of each, cy(T), will fall to zero as the number of
normative analysis. This regulator adapts the in-     Enjoyers (M) increases. Notice however, that when
strument T toward the direction of increased wel-     D is zero, the total contribution is C, so depending
fare where all interests are equally weighted. Since   on how C depends on M, this may rise with M or fall
Eq. (10) is a local hill-climbing procedure, it may    with M when D is zero.
470    M. Scheffer and others

  Let us give a brief explanation of the derivation   (C/M   D) in order for the system to deliver the
of, for example, Eq. (12). Suppose the net utility    same marginal conditions as maximization of the
that an individual i gets from giving contribution cx   social objective
is {A log(Sum cx( j))     Blog(cx(i))}S(i)–cx(i)},
                                Nu a   Mv x , subject to a, x in S    (16)
where the sum is over all j in i’s lobbying group and
S(i) is the stake that i has in the outcome.       Any difference in power at mustering political pres-
  Notice that here A denotes a weight in the utility   sure results in a deviation of the realized situation
function, not the total load on the lake, as in Eq. (5)  from welfare optimum, as discussed in the section
above. The formulation is just a mathematical met-    on normative economics.
aphor (with a convenient illustrative functional       Generalizations of this simple model can be done
form) to capture the idea that i believes that the    to accommodate other, more realistic distribution
total contributions Sum cx( j) help to achieve the    formulas for the proceeds of the taxes. Indeed, one
desired goal, the contribution gives i “warm glow”    can imagine designing the distribution scheme to
(Andreoni 1998), or i feels “noticeable” by the      mobilize support for the program. For example, in
group if he/she does not contribute (Magee and      practice, it is common to observe that it is a few
others 1989, p 287), and that the value of the goal    Affectors who are at the root of the problem. This
to i increases with his/her stake in the group goal    suggests that a redistribution scheme might be de-
S(i). Maximize this function w.r.t. cx(i) and solve    signed to mobilize most of the Affectors (who
to obtain Eq. (12) after putting the stake S(i)      would like to run cleaner operations if they could
{U(0)–U(T)}.                       afford it) against these few dirty players. One way of
  Recent work by Andreoni (1998) gives us an-      doing this that is consistent with a more complete
other useful interpretation of the coefficients B and   concept of efficiency, which takes into account ad-
D besides that of Magee and others (1989). These     ministrative costs and compliance costs of any reg-
terms are an attempt to capture the “warm glow”      ulatory scheme, is to use regulatory tiering (Brock
that the individual on each side of the conflict gets   and Evans 1985). This concept is based upon using
from giving and fighting for the cause that he/she     empirical evidence on the distribution of problem
believes in. See Andreoni’s work (1998) for a view    sizes (which tends to be highly skewed, with a few
of group effort to promote a cause that focuses on    of the players causing the bulk of the damages) to
developing a theory where people appear to be       argue that overall efficiency is served by either ex-
going against their individual self-interest in favor   empting or lightly taxing most of the smaller prob-
of the collective interests of their group. Andreoni’s  lem causers. Basically, one uses data to estimate a
“supply functions” of the effort exerted by both     “scaling law” of damages (Brock 1999). This scaling
sides of a conflict turn out to be closely related to   law is then used to design a tax schedule that taxes
those of Magee and others when terms playing       the big problem causers at a higher rate than the
similar roles to B and D are present.           smallest ones. Indeed, the smallest problem causers
  Suppose that there is a regulator who continually   may even be exempt from the tax. Regulatory tier-
adjusts the pollution tax T in such a way that the    ing is attractive not only from the viewpoint of
marginal pressures from the different interest      overall efficiency, but it also blunts political oppo-
groups is equalized. That is,               sition emerging from small Affectors (of which
                             there are typically many more than large Affectors),
        dT/dt   Y T –X T ,       (15)
                             because they are exempted or, at most, lightly
                             taxed. Hence, regulatory tiering is a valuable tool in
where Y(T)    Mcy(T)   Na(T)T equals total pres-
                             putting together effective programs for environ-
sure supplied by Enjoyers in favor of the tax move
                             mental cleanup in practice. Indeed, there is evi-
from zero to T, and X(T)      Ncx(T) equals the
                             dence that the US political system acts “as if” it is
Affectors’ pressure against the move. Notice that we
                             tiering in many cases (Brock and Evans 1986). No-
have assumed that the proceeds of the taxes
                             tice that tiering can be predicted to blunt opposition
Na(T)T effectively go to the Enjoyers. The condi-
                             from the Affector sector in political models such as
tions for a rest point of Eq. (15) are identical to the
                             the median voter model, as well as political models
first-order conditions for a maximum of the
                             like ours that focus on balancing political pressures.
weighted sum
                             A review of many kinds of political science models
A  BN u a    C  DM v x ,              can be found in Magee and others (1989).
                               The graphic models that show how social welfare
            subject to a, x in S   (15 )
                             could be maximized (Figure 4) can be modified to
Thus, we need the power terms ( A/N    B) equal to  produce graphs that show where the respective po-
                                                     471
                             Socioeconomics and Ecosystem Services

litical power of the Affectors and the Enjoyers will    Now consider the pair of socially optimal utility
be in balance (Figure 7). To see this, first consider   directional “arrows” (Nu , Mv ). Politics distorts
the precise meaning of the figure in terms of our     these arrows by changing them into ([A/N
models. If one plots the ordered pair (Nu , Mv ) on   B]Nu , [C/M    D]Mv ). A political force graph
the surface of Figure 4b at each point (a, x) in the   would thus be obtained by plotting ([A/N
floor of the diagram, one gets the “flux” of local     B]Nu   [C/M  D]Mv) rather than (Nu    Mv) as
utility. That is, if one moves in the direction (da,   the objective function. This implies that differences
dx) at (a, x) the flux of incremental social welfare is  in political power will tilt the depicted welfare
given by Nu da    Mv dx   (Nu , Mv ).(da, dx),   plane, downweighting the interests of the less pow-
where “.” denotes “vector dot product”. Thus, wel-    erful group. Since, in the most egregious cases,
fare increases locally when Nu da      Mv dx    there are typically a small number of highly orga-
(Nu , Mv ).(da, dx)     0 for a proposed policy   nized large Affectors and a large number of tiny
move (da, dx). Since each level of a needs to be a    diffuse Enjoyers, we have C and D at approximately
steady state x(a) of the ecosystem, we must restrain   zero, so the objective function increases with stress
proposed differential policy movements (da, dx) to    (a) imposed by Affectors but becomes almost inde-
be compatible with the ecosystem equilibrium set S.   pendent of the ecosystem state ( x). Thus the hill-
That is,                         climbing political system will myopically move to
                             higher stress levels, as it simply keeps looking for
     0  da–bdx a   f x a dx a     (17)
                             incremental moves (da, dx(a)) such that ([A/N
                             B]Nu , [C/M    D]Mv ).(da, dx(a)) is approxi-
In other words, the system guided by our RASP will
                             mately equal to ([A/N      B]Nu , 0.Mv ).(da,
move uphill in the direction of increasing social
                             dx(a)) ([A/N B]Nu )da 0, and a just keeps
welfare (the plane) following the ecosystem equi-
librium state.                      tending to increase (Figure 7b).