Human–ecosystem interactions: a dynamic integrated

Ecological Economics 31 (1999) 227 – 242
Human – ecosystem interactions: a dynamic integrated model
Bobbi Low a,*, Robert Costanza b, Elinor Ostrom c, James Wilson d,
Carl P. Simon e
School of Natural Resources and En6ironment, Uni6ersity of Michigan, Dana Building, 430 East Uni6ersity, Ann Arbor,
MI 48109 -1115, USA
Uni6ersity of Maryland Institute for Ecological Economics, Center for En6ironmental Science, Uni6ersity of Maryland, Box 38,
Solomons, MD 20688 -0038, USA
Workshop in Political Theory and Policy Analysis, Indiana Uni6ersity, 513 North Park, Bloomington, IN 47408 -3895, USA
School of Marine Sciences, Uni6ersity of Maine, 5782 Winslow Hall, Orono, ME 04469 -5782, USA
Mathematics, Economics, and Public Policy, Uni6ersity of Michigan, 412 Lorch Hall, Ann Arbor, MI 48109 -1220, USA
We develop an interactive simulation model that links ecological and economic systems, and explore the dynamics
of harvest patterns as they simultaneously affect natural and human capital. Our models represent both single and
multiple systems. The level of natural capital is influenced by interactions of (1) natural capital growth and
(non-human influenced) depletion, (2) ecological fluctuations, (3) harvest rules, and (4) biological transfers from one
ecological system to another. We focus first on isolated systems in which there are no biological transfers between
units and humans rely for subsistence on the resource; thus both the economic and ecological portions of the system
are relatively independent of other systems. In this case, the maximum sustainable harvest rate depends on the local
carrying capacity, the stock growth rate, and fluctuations in such ecological variables as rainfall and temperature,
which are ‘extrinsic’ to the stock–human harvest, but nonetheless affect stock levels. Next, we address spatially
complex situations in which biological resources move from one spatial unit to others. In these models, the greater
the potential movement of stocks across ecosystems, the more any particular human sub-system can increase its
harvesting rate without danger of its own collapse — although at a cost to neighboring subsystems. © 1999 Elsevier
Science B.V. All rights reserved.
1. Introduction
Managing human use of important ecosystem
resources to be sustainable can clearly be problematic (McCay and Acheson, 1987; Ludwig et
* Corresponding author.
al., 1993; Jansson et al., 1994). We mine ocean
and coastal ecosystems to provide important biological resources — fish, whales, and lobsters, for
example — yet these ecosystems remain particularly intractable for sustainable resource management. Both resource stocks and harvesters may
cross boundaries; it is difficult-to-impossible to
0921-8009/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 8 0 0 9 ( 9 9 ) 0 0 0 8 1 - 6
B. Low et al. / Ecological Economics 31 (1999) 227–242
Fig. 1. Ecosystems and human social systems may be structured in parallel ways to facilitate analysis of interactions. Both systems
have ‘stocks’ (resource stocks, human-made capital) that result from ‘flows’ (births, deaths, harvests of resource stocks; interests,
taxes, and expenditures of human-made capital). ‘Controls’ (physical, behavioral, and legal laws) influence these flows. ‘Attributes’
of stocks and flows include predictability, resilience, efficiency, and extent in time and space.
Fig. 2. A simplified model of an isolated ecosystem in which some resource stock is harvested by humans.
census many resource stocks accurately; numerous and varied actors have conflicts over resource
use, and may find it difficult to agree on rules.
Even when formal agreement exists, if actors exceed quotas, it can be extremely difficult both to
monitor (because of physical scope) and to sanction (because agreements are frequently international and interests differ greatly). Many fisheries
resources are common-pool resources, with all the
attendant difficulties in resource management (Ostrom et al., 1994).
Almost all scholars agree that sustainability is
enhanced when human-designed rules are ‘welltailored’ to the realities of the exploited resource.
But what does that mean? Many factors contribute to the problem: carrying capacity, growth
rate of populations over time, the extent to which
an ecosystem is isolated or connected to adjacent
B. Low et al. / Ecological Economics 31 (1999) 227–242
Fig. 3. Up to the sustainable harvest limit (here, 24% of carrying capacity), profit (human capital at the end of the 200-year
simulation) increases as the harvest limit increases; the effect on natural capital is less dramatic. When sustainable limits are
exceeded, the collapse in this model is relatively dramatic; there is little ‘early warning’ that sustainable limits are being approached.
ecosystems, and the impacts of ecological influences such as rainfall or temperature, to name
only a few. The relationships among these variables are frequently non-linear. Interactions between human systems and ecosystems also vary
along many dimensions — the wealth and power
of users, their harvesting strategies, whether any
rules exist to limit use of an ecosystem, and the
impact of population growth on resource demand,
among others.
Such complex, non-linear, interactive systems
present challenges. Empirical tests are difficult
because field data may not include all variables
(particularly those considered external to the system). Thus, field studies of ecosystems may of
necessity ignore important economic, social, and
political variables; and studies of human institutions and decision-making systems frequently ignore important ecological variables. Yet if
ecological and economic realities interact, both
approaches will miss patterns, and make unreliable predictions.
Because ecosystems are complex, dynamic, and
non-linear, no single model is appropriate to all
systems. Here we apply a flexible framework,
within which we can construct diverse worlds by
specifying five variables:
1. The carrying capacity of the resource system;
2. The regeneration rate at which the stock of a
system can grow;
3. The natural mortality rate of the resource
4. The predictability of external influences on
stock growth and mortality; and
5. The natural transfer rate from one spatial unit
to another.
The resulting compartmental dynamic model of
fisheries structures ecological and economic components in precisely parallel ways (Cleveland et al.
1996). It links human decision systems and
ecosystems, measuring outcomes directly in each.
Initially, the model is extremely simple; we establish its basic behavior as an isolated system, and
analyze the interactions of harvest rates (maximum sustained yield rule), resource growth rate,
and external stochastic fluctuations as they affect
natural capital and fishermen’s profit. We then
model a three-unit system — like a series of
B. Low et al. / Ecological Economics 31 (1999) 227–242
Fig. 4. (a) The sustainable harvest limit in any system will be influenced not only by the growth rate of the resource stock, but by
fluctuations in the extrinsic ecological factors that influence the stock level (e.g. any fluctuation causing deaths or heightened
recruitment of the stock). With a harvest limit of 24% of carrying capacity, sustainable if there are no extrinsic fluctuations, some
systems fail. Failure is more frequent when extrinsic fluctuations are of greater magnitude (here, extrinsic factors affect the
population causing fluctuations from 50 to 150%, average effect, 100%) than when fluctuations are more limited (90% – 110%,
average, 100%). (b) The four harvest rules tested are differentially vulnerable to extrinsic fluctuations in stock populations of 950%:
‘per cent stock’ and ‘sole owner’ systems proved more robust than ‘% carrying capacity’ and open access. Note, however, that
complications such as mis-counts of stock populations and lags in effect of fluctuations are not included, so all systems here perform
better than is likely in real-world systems.
B. Low et al. / Ecological Economics 31 (1999) 227–242
Fig. 5. When resource systems are not isolated, both resource stocks and resource users may move among systems. Here, movement
of natural capital is shown.
coastal fisheries — in which the independent actions of fishers in any subsystem can affect the
harvests of fishers in other units, and fish can
move from one harvesting region to another. In
this three-unit system we compare the robustness
of additional harvest rules. Wilson et al. (1999)
add reality to test effects in structured metapopulations versus large single populations.
We focus on how natural capital and human
profit are affected by: carrying capacity; stock
growth rate; range of variation in ‘extrinsic’ ecological variables such as rainfall and temperature (‘extrinsic’ to the stock-human harvest,
but nonetheless affecting stock levels); harvest
rules; and rates of movement of stocks such as
fish across both ecosystem and political system
B. Low et al. / Ecological Economics 31 (1999) 227–242
Fig. 6. Transfer rates of natural capital and harvesting rates of all units interact. Here, combined harvest rates are reflected by the
‘harvest pressure bias’ ([exploiter rate − MSYe] − [MSYc − conserver rate]). This number increases as all harvest rates increase in any
system. When natural capital transfer rates are low, the failure of the highest-harvesting unit is relatively independent of the total
harvesting bias, and ‘exploiters’ fail at approximately the same harvest levels as for isolated systems. At higher transfer rates, units
that harvest heavily can be protected and persist throughout the run (200 years), up to some harvest bias (e.g. when other units
harvest near the MSY, or the exploiter takes ] 26% of the carrying capacity). This is shown by the flat portion of the high transfer
rate curves.
boundaries. We examine the interactions of these
as they affect the robustness of a system.
2. Structure of an ecosystem – human system
Fig. 1 represents a general scheme of parallels
between human and ecological systems, and the
nature of their interactions (Cleveland et al.,
1996). Both ecological and social systems have
‘stocks,’ ‘flows’, and ‘controls’ of those flows. All
stocks, flows, and controls have attributes (e.g.
richness, predictability). The interaction sector,
where human decisions affect resources in ecosystems, lacks stocks; it has flows, controls, and
‘Stocks,’ in both human and ecological sub-systems, are materials whose basic unit of measure
does not involve time; they can accumulate or
decline. In the ecosystem sector, stocks are natural
capital of one of two broad types: (1) renewable
(biotic) natural capital, and (2) non-renewable
(abiotic) natural capital. Here we focus entirely on
one renewable stock: the biomass of one species of
fish. Additional complexities will arise when more
than one species is modeled (Clark 1990; Hilborn
and Walters 1992). In the human system, humanmade capital (typically renewable), is the monetary
stock upon which actors can draw. Human capital
assets, including boats and fishing equipment as
well as the knowledge and skills of the fishers,
comprise additional stocks.
B. Low et al. / Ecological Economics 31 (1999) 227–242
Fig. 7. The interactions of transfer rates, total harvest pressure bias, and extrinsic ecological uncertainties mean that high transfer
rates alone cannot protect exploiters. In all cases here, the total harvest pressure is 720( =3 ×240, or the sustainable harvest as per
cent of carrying capacity if all units acted identically); the exploiting unit takes 250, and the two conservative units each take 235.
At both transfer rates (0.1 and 0.2), higher extrinsic fluctuations cause more failures of the exploiter. (a) When the transfer rate is
0.1 (10% of stock differential can move between units in a time period), \30% of exploiters fail by year 40 (extrinsic fluctuations
0.5–1.5), or by year 80 (fluctuations 0.9–1.1), as opposed to persisting 150 years, the case if there were no extrinsic fluctuations. (b)
The pattern is different for higher transfer rates (0.2): moderate (0.9 – 1.1) fluctuations and high transfer rates allow \20% of
exploiters to persist for the full 200-year run (as would be the case with no extrinsic fluctuations). However, in the face of both high
fluctuations and high transfer rates, \ 60% of exploiters fail by year 40 — and in contrast to low transfer rate conditions, these
failures have also destroyed the neighboring conservative units.
B. Low et al. / Ecological Economics 31 (1999) 227–242
All systems involve controls that regulate flows
(Fig. 1). In ecosystems, physical and behavioral
laws control many processes (e.g. temperature
controls the speed at which many reactions can
occur). Natural selection, the rules governing the
existence and reproduction of all living things,
interacts with physical laws to constrain the life
histories and behavior of living components of
ecosystems. Ecological relationships (competition,
predator–prey, mutualism) result from the interaction of physical laws and natural selection, and
further constrain the type of interactions possible
in ecosystems. In human systems, controls include
not only the same physical and behavioral laws
that influence other species but also cultural rules
(mores, laws). In the first model, the principal
control in the human sector is simply the harvest
rule; later, higher-order political controls will be
In interactions between humans and ecosystems, two controls, production and consumption,
represent major transformations (physical changes
of inputs into outputs). In addition, there are
transactions: the transfers from one party to another, in exchange relationships, of rights to inputs, outputs, and assets. Harvesting rules affect
both transformations (how much of the stock is
removed) and transactions (who receives the distributions of benefits from productive activities).
Here we focus on the effects of rules on
Attributes are the characteristics of stocks,
flows, controls, and the relationships among these
(Fig. 1). The number of attributes that potentially
affect the capacity of human actors to manage
resources sustainably is very large, including at
least: heterogeneity, predictability, resilience, decomposability, range of variation, extremeness,
extent in space and time, and productivity (Cleveland et al., 1996). All of these attributes can be
measured in ecosystems as well. Here we concentrate on a limited number of attributes: range of
variation (e.g. in ecological fluctuations affecting
resources), and extremeness (of growth rates of
stock), for example. Because this model includes
human and ecosystems interactions, an additional
set of attributes can be modeled in this framework: excludability, observability, enforceability,
divisibility, and sustainability (Ostrom et al.,
1994). Here, we focus on sustainability.
3. A single-unit model
Using this framework, we construct as simple
an initial model as possible while retaining the
crucial aspects of these complex systems (Fig. 2).
We use STELLA, a dynamic programming software
(Hannon and Ruth, 1994). This first model represents an isolated fishery, and (like our general
framework) has three sectors: ecosystem, human
system, and interactions.
3.1. Ecosystem
The ecosystem sector contains one state variable, labeled natural capital, that here represents
the biomass of fish. Natural capital (NC) grows
over time at a rate determined by the carrying
capacity of the area, some intrinsic growth or
recruitment rate (births, immigration of animal
stocks), and a set of external influences. The
growth of natural capital is represented by:
NCgrowth = NC× ExtInfl× NCgrowth rate[1-NC/K]
This formulation reflects logistic stock growth
(including ‘r,’ the intrinsic growth rate) as it is
influenced by ‘K,’ the carrying capacity, and external influences (e.g. weather, rainfall, and natural
disasters) that can influence this growth rate. We
reflect the fact that stocks are reduced by harvesting, death, emigration, etc., by the natural capital
depreciation rate. We represent human harvest
separately from other natural capital depreciation,
as harvest strategy, defined in the interactions
sector (below), rather than the ecosystem sector.
The overall equation for natural capital is:
= NCgrowth − NCdepreciation − Transfer−NCharvest
where NCdepreciation = (NCdepreciation rate)*NC. We
set the initial value of natural capital at the start
of the simulation to equal the long-term carrying
capacity. The transfer value is only operative
when multiple socio-ecosystems are connected. In
B. Low et al. / Ecological Economics 31 (1999) 227–242
our initial analyses of a single system, transfer is
The logistic growth curve for dynamic Eq. (2),
with NC harvest and Transfer set to 0, produces
the standard parabolic recruitment curve of most
bioeconomic models (Hilborn and Walters 1992).
Under these assumptions the actual carrying capacity is x*= K(1−(D/Er)), and the maximum
sustained yield — the maximum value of the
growth curve — is:
xmsy = (KrE/4)(1− (D/Er))2
where K is the carrying capacity, r is the growth
rate, D is the depreciation rate, and E is the
external stochastic influences.
3.2. Human system
In the simplest model, the human system sector
also has a single state variable, human made
capital (HMC), representing the assets that humans are able to amass to carry out the harvest.
Human-made capital fluctuates as a result of its
growth rate (e.g. interest), depreciation, and in
some cases, taxes (we do not model taxation in
this set of models). Depreciation and taxes are set
at a value by the researcher to represent particular
environments of interest. Here, the growth rate of
human capital is simply revenues minus costs,
where revenue is (price per unit of NC) ×(amount
of NC harvested) and cost is (cost per unit of
HMC)×(HMC used for harvesting). In these
simulations, we set the (price/unit NC)= 10 and
the (cost/unit HMC) = 500. As is true for biological stocks Eq. (2), the stock of human-made capital is a function of prior human-made capital, and
the growth and depreciation rates for humanmade capital:
dHMC/dt = HMCgrowth −HMCdepreciation −Tax
3.3. Human–ecosystem interaction sector
The interaction sector has no state variables,
but two-way flows between ecosystems and human systems. In this initial application we focus
on two relationships: harvest efficiency and har-
vest strategy. We assume in these first models that
the amount harvested is proportional to both the
harvest factors (i.e. HMC) and the size of the
resource population (NC). We call this proportionality factor the total efficiency (TE) and set it
equal to 0.007 in these simulations. In later explorations, we will explore the effects of increased
Thus the amount harvested in the absence of
any externally imposed limits is HMC× NC×
TE. We call the multiplier (NC × TE) of HMC
the Harvest Efficiency, HE. For resources for
which there is no search problem (i.e. when harvest success is unrelated to resource abundance),
we would use a constant HE, independent of NC.
Harvest rules can now be chosen. In these
initial models we do not allow for harvests above
harvest limits (there is no cheating). Four harvest
rules are compared: ‘per cent carrying capacity’
(maximum sustained yield), per cent population,
open access, and sole owner profit maximizer.
The ‘per cent carrying capacity’ harvest strategy
rule sets the harvest limit, HL, at a constant
percentage of the carrying capacity K. The harvest
is then given by:
HS1 = min{HMC× HE, HL}
Thus if the potential harvest, HMC× HE, is less
than the harvest limit, then the potential harvest is
taken; otherwise, the harvest limit HL is taken.
In the ‘per cent population’ rule, harvest (HL)
is simply a specified per cent of the current population of fish. This rule requires absolutely accurate censoring of the stock at the appropriate
times to predict sustainable harvest (including effects of ‘lag’ related to seasonality of stock reproduction and growth, for example). In these
simulations, harvesting 28.5% of the existing population maximized HMC under this rule.
In the ‘open access’ regime, each actor responds
to his/her current revenues minus costs, and keeps
harvesting so long as profit is non-negative; entry
continues in this regime until total profits are
zero. Actors do not behave as if they could predict a trend; they are short-term profit maximizers
with no incentives for restraint.
Under the ‘sole owner profit maximizer’ rule,
the sole owner controls access to natural capital
B. Low et al. / Ecological Economics 31 (1999) 227–242
and harvests it at a rate that maximizes longterm profit. In these simulations, the sole owner’s decisions are based on the 5-year trend
(slope) of profits instead of the most recent
profits, because delays in feedback from the biological sector can cause the most recent profit
level to produce a false signal. A 5-year trend
generates a slower response but tends to find the
sustainable profit-maximizing harvest level more
reliably. The time horizon for sole owner’s decisions is thus longer than for fishers under the
open access rule.
4. Rules and sustainability in a single-unit model
For convenience in the STELLA runs that
follow, K is set to 1000; the initial value of
natural capital is set to 10. We allow the system
to run to a maximum of 200 periods (e.g.
years), and unless otherwise specified, do 100
runs (equivalent to gathering empirical data on
100 fisheries for 200 years each). For such systems, we explore how:
1. Harvest limits influence the stock levels of
natural and human-made capital. When the
system is not sustained (where ‘sustained’ is
defined as having natural capital in excess of
20 units at the end of a 200-year run), we track
the number of years until collapse of the
2. The growth rate of natural capital influences
the sustainability of different harvest limits.
3. (1) and (2) interact, and finally,
4. Stochastic fluctuations in extrinsic ecological
influences affect the resource stock (and thus
sustainability). In all runs, fluctuations are
randomly generated, so we explore the effects
of range of variation, rather than temporal
In the first three analyses, we focus on deterministic relationships to explore the underlying curvilinear structure affecting long-term survival of the
natural capital. We then model stochastic environmental fluctuations that affect growth of natural capital, mimicking the complexities of
empirical data.
4.1. Har6est rules and stock growth rate in a
single-unit deterministic model
Local, regional, or national authorities frequently impose an upper bound on the quantity
of ecosystem flow, such as fish, that can legally be
harvested during a defined time period. One type
of harvesting rule assigns an upper limit on the
quantity harvested based on a judgment made of
the carrying capacity K of the ecosystem. We can
see in Eq. (3) that if one assumes a constant
harvest rate, the maximum sustainable yield
(MSY) is the maximum reasonable harvest (as we
note below, in actual practice, MSY is problematic). One computes easily that xmsy = 0.2401K
under our initial conditions of growth rate r= l,
death rate= 0.2, and no external pertubations
(E= 1). For a series of growth rates (0.9–1.1), we
varied the authorized harvesting rate from 15 to
30% of K. One can see in Eq. (3) that the maximum sustained yield is an increasing function of
growth rate r: (xmsy/(r =E× K/4(1−(D/Er)2)\
0. That is, rapidly growing stocks can sustain
heavier exploitation. In all systems, exceeding
MSY caused the collapse of a system; the greater
the excess, the more rapid was the collapse of the
4.2. Growth and har6est rates with ecological
The intrinsic growth rate of an exploited stock
can have a great impact on the sustainability and
effectiveness of management strategies. Extrinsic
fluctuations (mimicked here by stochastic shifts
affecting stock levels by 9 10%) also affect sustainability. In a series of runs tracking natural
capital and human made capital in a single-unit
system with stochastic perturbation, the strongest
predictor of the amount of natural capital at the
end of a run (200 years, or whenever natural
capital was exhausted) was harvest limits (d.f.=
2.98, r 2 = 0.63, PB 0.00001), although the growth
rate of natural capital was also highly significant
(PB 0.000l). When human-made capital was the
dependent variable (d.f. = 2.98, r 2 = 0.27), harvest
limits were again most significant (PB 0.00001);
the growth rate of natural capital, while signifi-
B. Low et al. / Ecological Economics 31 (1999) 227–242
cant, contributed less to the model (P B 0.032).
The strongest predictor of years until collapse of
the system (d.f.= 2,98, r 2 =0.49) was harvest limits (PB 0.00001), though growth rate of natural
capital is more influential in this case than it was
in predicting human capital (P B 0.009).
This analysis highlights some of the difficulties
in using the concepts of K (carrying capacity) and
MSY (Conrad and Clark 1987; Clark 1990). In
real-world situations, using carrying capacity estimates to set harvest limits ignores information.
Fig. 3 reflects an additional management problem.
Up to the sustainable harvest limit, human capital
increases in a linear fashion as the harvest limit is
increased; the decline in natural capital (biomass
of the resource) is less dramatic. Up to the point
of collapse, there is a relatively great increase in
human capital for a relatively small decrease in
natural capital. This concern is further heightened
by the fact that most resource users are able to
measure the change in human capital (the accumulation of assets such as buildings, boats, harvesting equipment) more reliably than the change
in natural capital.
When sustainable limits are exceeded even
slightly, the collapse of both forms of capital is
relatively dramatic. Thus, in this model, there is
little ‘early warning’ that sustainable limits are
being approached (Gulland, 1977). Nor is there
any feedback that allows regulators to react to
changes in stock size or growth. The pattern we
uncover here may be related to the empirical
observation that many resource-use systems fail
relatively abruptly.
Unless we have chosen wildly inappropriate
numbers, these results, combined with the information in Fig. 3, suggest precisely the sorts of
difficulties actually encountered in the field. That
is, high harvest limits, even when no cheaters
exist, can build human capital at the expense of
natural capital. Further, the level of human capital gives little prior warning of impending system
collapse. In fact, since all human capital is plowed
back into harvesting capacity in this set of runs,
the growth of human capital accelerates the rate
at which the system approaches collapse. If other
opportunities existed for the use of human capital
or if the investment in harvesting capacity were
sensitive to the state of natural capital, the probable collapse of the system might vary. We will
explore these possibilities in future papers.
4.3. Har6est rules and stochastic extrinsic factors
In the real world, extrinsic ecological events
affect the level of natural capital, and thus the
outcomes of harvest rules, even in isolated systems. Consider Eq. (3): with our values of r and
D, if no extrinsic fluctuations exist and the regeneration rate is held constant at 1, a harvest rate of
24% of carrying capacity generates the maximum
sustained yield. This rule is not responsive to
ecological fluctuations: stochastic extrinsic factors
influence resource stock levels, and the probability
of an ecosystem remaining active to year 200 is
reduced in the face of environmental fluctuations
(Fig. 4). When the rule was ‘24% of carrying
capacity’ and stochastic fluctuations occurred at
910%, approximately 15% of systems retained
some natural capital by year 200; most survived
up to 100 years (Fig. 4a). At 910% stochastic
fluctuations in stock, systems using more conservative rules uniformly persisted to 200 years.
Wealth accumulation under stochastic fluctuations differed with harvest rule (maximum about
$500,000 per actor for sole owner and per cent
stock rules; about $22,000 for open access).
When extrinsic fluctuations were more severe,
harvest rules were still differentially sensitive (Fig.
4b). With extrinsic fluctuations causing stock to
fluctuate 950%, 57% of ‘24% carrying capacity’
systems failed by 40 years; only eight systems (of
100) persisted beyond 120 years. No sole owner
system failed within 40 years; 57% of sole-owner
systems lasted more than 120 years, and nine of
these were functioning at 200 years when the
experimental runs were terminated. The rule ‘50%
of stock’ lasted to 200 years in all tests, reflecting
the buffering effect of harvesting according to
existing stock population levels. Note, however,
that this rule still retains unrealistic assumptions.
Among the principle assumptions are: that we
fully understand and have captured in the model
the essence of the population dynamics, that stock
populations can be sampled and the data analyzed with absolute accuracy, that there are no
B. Low et al. / Ecological Economics 31 (1999) 227–242
delays due to measurement, analysis or any other
reason. These and other complications are introduced in later versions of the models.
5. Spatial heterogeneity
These results appear to be reasonably consistent
with the expected behavior of a single exploited
population. However, the ‘reasonable’ behavior
explicitly assumes no significant interactions with
other populations.
But populations are rarely isolated in this way.
We now explore a series of coastal fisheries, in
which the fish can move (‘transfer’) from one
system to another along the coast (Fig. 5). Allowing harvesters to move across the limits of a
system generates a similar transfer (Wilson et al.,
1999). Maine lobster fisheries represent such complex conditions, and both political and biological
difficulties arise from this fact. Although only
older, mature (marketable) lobsters migrate, migration can create significant biological transfers
when mature lobsters move across human
boundaries, as from inshore waters where one set
of local rules obtains, to offshore waters where
different rules exist. Inshore Maine fishermen may
only retain lobsters above a minimum, and below
a maximum, size. They are required to return to
the sea lobsters outside this range. The (local)
conservation idea behind the rule is to maintain a
size/age distribution in the wild population, to
minimize the risk of recruitment failure. However,
because animals at and above the maximum permissible size tend to migrate outside the area
where the rule applies, boats from other areas
(New Hampshire and Massachusetts) line up each
fall at the Maine boundary to catch the migrating
lobsters (Carl Wilson, personal communication).
This creates a variety of problems. It does not
simply mean a more compressed size/age distribution in all areas (and thus greater risk of recruitment failure), but Maine fishermen see outside
lobstermen as free riders and question the collective wisdom of their restraint — why should we
restrain ourselves, for others to reap the benefits?
At a larger scale, eliminating restraint for Maine
fishermen would simply mean higher takes in all
areas — and likely overexploitation typical of
open-access resources. Yet to ask Maine fishermen to restrain themselves so that outsiders can
profit seems illogical. In this example, there is
high biological transfer across governance units,
local harvest rules, low or no higher-level control;
that is, human rules and ecological realities do not
appear to match.1
5.1. Spatial representation of multiple ecosystems
Here we explore how, and at what levels, biological transfers between non-isolated systems affect situations such as the Maine lobster fishery;
we reserve exploration of the governance rules for
a later paper. Each of the spatially identifiable
systems in Fig. 5 has three compartments: ecosystem, human system, and interactions (Sanchiro
and Wilen, 1999, who have developed a remarkably parallel system independently). To represent
three spatial areas, all equations for a unit model
are appended with a suffix to indicate the appropriate unit. In the ecosystem portion of each
spatial unit, initial values of variables such as
natural capital, natural capital growth rate, and
carrying capacity can be set independently, mimicking spatial ecological variation. Local ecological areas, then, can differ from one another in
terms of the stock-carrying capacity and the incidence of ecological fluctuations. In the human
systems of each model unit, decision rules (e.g.
harvest limits, effort) can also vary.
The natural transfer of natural capital between
units (T) is here assumed to be proportional to
the biomass differential in the two units. If the
natural transfer rate is 0, the three spatial units
are ecologically isolated from each other, as in the
single-unit analyses above. A transfer rate of 50%
between adjacent units will equalize the stock
population in the two units. The higher the natural transfer rate, the more biological transfer exists between adjacent units.
As the reader might imagine, this situation has created
political conflict between Maine fishermen and those from
Massachusetts and New Hampshire. At the present time, it
appears that the conflict will be resolved by applying the
Maine inshore rules to offshore areas.
B. Low et al. / Ecological Economics 31 (1999) 227–242
5.2. Questions explored
In this series of experimental runs, we ask the
following questions:
1. In the absence of extrinsic ecological fluctuations, by how much can people in one unit
exceed the ‘normal’ maximum sustained yield
(here 24% of carrying capacity) if there is a
small (e.g. 1%) level of biological transfer and
other units have conservative harvesting rules?
2. When a moderate (here 9 10%) level of extrinsic fluctuations exists, how are these parameters shifted?
When no external ecological fluctuations exist,
the amount that can be sustainably taken in any
unit depends on the carrying capacity, the natural
capital growth rate, and the transfer rate. If the
transfer rate equalized all differences, then the
sustainable total harvest pressure for a three-unit
set of ecosystems, with the settings we have explored here, would be 24% of the initial carrying
capacity for all three units (here, 24× 3000). In
such a case, the three systems would be totally
interdependent with regard to harvest limits. Most
systems, while not completely isolated, do not
have full movement of stocks throughout all subsystems. When this incomplete flow of stocks
occurs, what any unit can take sustainably is a
complex function of its own harvest, the harvests
of other units, and the transfer rate.
What happens when the central unit of the
three-unit system receives flows from the first and
third units, and adopts a harvesting rate above
24% of the initial carrying capacity of the linked
systems? In other words, what happens when the
two outer units are conservative (take less than
the amount determined to be locally sustainable)
in their harvesting practices, while fishers in the
central unit exploit their conservative strategies by
harvesting at a rate that would not be independently sustainable? When the transfer rate is very
low (e.g. 1%), any single unit will be unsustainable
if its harvest rules exceed 24% by even a small
When transfer rates are higher and the harvest
rules in neighboring ‘conserving’ units are low, a
highly exploitative harvesting unit, one that harvests more than would be sustainable, receives
some protection from the combination of high
transfer rates and low exploitation by its neighbors. But how conserving must other units be to
sustain an over-exploiting unit? For very low
transfer rates, an exploiting unit’s persistence was
not related to harvest pressure bias (Fig. 6), but
behaved as an isolated system. However, even at
quite low rates of natural capital movement
across systems, a complex interaction occurred
among the transfer rate, the harvest rates of the
exploiter and the conservators. To reflect this
complexity, we constructed a ‘harvest pressure
bias’ index:
HPB= ([exploiter rate− MSYe]
− [MSYc-conserver rate])
to represent the range of conservator-versus-exploiter harvest limits that will leave the entire
system’s natural capital sustainable. In our runs,
this measure ranged from − 20 to + 15, depending on the natural capital transfer rate. The effects
of any level of harvest pressure bias differ, depending on the transfer rate of natural capital.
For natural capital transfer rates as low as 5%,
when the harvest pressure bias was low (−5 for
5% transfer rate; 5 for transfers rates ]1), even
quite high harvest rates could be sustained in a
single unit — if the other units were sufficiently
conservative. When the limits are exceeded, the
time an exploiting unit can be sustained declines
precipitously (Fig. 6).
Although a combination of high transfer rates
and conservative neighbors could theoretically
shield an exploitative unit, it is likely in most
circumstances that people in conserving units will
learn of the situation (as in the Maine lobster
example above). If ‘conserving’ units respond by
raising their harvests, the entire system collapses.
Thus, a real problem exists in matching local and
supra-local rules to the ecological realities of
transfer rates, as well as to more obvious phenomena such as carrying capacity and intrinsic growth
rate (not varied in this set of runs).
The combination of high transfer rates and
conservative neighbors affords protection for exploiters in the absence of extrinsic unpredictable
fluctuations — but almost all ecological systems
are subject to extrinsic fluctuations, which have
B. Low et al. / Ecological Economics 31 (1999) 227–242
the potential, at least, to interact with harvest
limits and transfer rates. To explore these problems (Fig. 7), we modeled four conditions:
1. Transfer rate, 0.1; range of stochastic fluctuations, 0.9–1.1. (Stochastic extrinsic fluctuations on a6erage have no effect on natural
capital level, but in any one year randomly
influence population numbers from 90 to
110%.) An ‘exploiter’ in such systems with no
extrinsic fluctuations would persist 150 years.
2. Transfer rate, 0. 1; range of stochastic fluctuations, 0.5–1.5. An exploiter in such systems
with no extrinsic fluctuations would persist
150 years.
3. Transfer rate, 0.2, range of stochastic fluctuations, 0.9–1.1 An exploiter in such systems
with no extrinsic fluctuations would persist
200 years.
4. Transfer rate, 0.2; range of stochastic fluctuations, 0.5–1.5. An exploiter in such systems
with no extrinsic fluctuations would persist
200 years.
Fig. 7 shows that the presence of any fluctuations reduces the probable persistence of the exploiter — even when protected by conservative
neighbors and a 10% natural capital transfer rate.
The greater the range of unpredictable fluctuation, the more persistence is lowered (Fig. 7a).
When fluctuations are moderate (0.9 – 1.1), a
higher transfer rate affords greater protection to
an exploiter with conservative neighbors. When
transfer rates are higher, the non-linear interaction changes the response. With a 20% transfer
rate, 28% of exploiters survive more than 180
years (Fig. 7b), versus only 4% (Fig. 7a) when the
transfer rate is 0.1. At the low transfer rate, 33%
of exploiters fail before year 80. Thus, in the face
of moderate extrinsic fluctuations, high transfer
rates and conservative neighbors can protect exploiters. In contrast, when both extrinsic fluctuations and transfer rates are high (Fig. 7b), the
exploiter is likely to cause the entire system to
crash relatively earlier; this is reflected in Fig. 7b
by the fact that more than 60% of exploiters fail
by year 40 under these conditions. Short-term
gains by exploiters from exceeding ‘baseline’ sustainable harvest rates are reduced by external
fluctuations as well as by (above) any response
managers in nearby units might make.
6. Discussion and conclusions
These dynamic models are extremely simple,
compared to many fisheries models. Nonetheless,
their linking of human and ecosystems demonstrates that human resource–use systems interact
non-linearly with ecosystem parameters.
The growth rate of natural capital interacts
strongly with the harvest limits to affect the sustainability of systems. These variables are difficult
to measure and frequently are only loosely incorporated in current efforts to manage resources
sustainably. Further, some variables that are
rarely measured and analyzed by natural resource
managers have a major impact on the sustainability of ecosystems. Many models of sustainable
yield are based on averages over a long time
period, and information about the quantity of a
stock removed is recorded. The degree of exogenous variation — here a strong influence on
long-term sustainability — is rarely measured or
taken into account in textbooks, yet its effect
argues that variance, not simply the long-term
mean, in resources should be considered.
The sustainable management of complex ecological economic systems can be a tricky thing
indeed, especially when incentives to maximize
short-term economic gain are strong, as is typical.
Even the relatively simple models we show here
demonstrate complex behaviors and subtle
thresholds that are difficult to foresee. The real
world is much less tractable; perhaps it is not
surprising that many resource systems, even relatively isolated ones, have collapsed in recent
In isolated ecosystem models, the sustainability
of stock depended on the harvesting rule as this
interacted with the stock regeneration rate and
extrinsic ecological fluctuations. In the second set
of simulations, spatially discrete ecosystems were
linked, and the possibility of free-rider behavior
by some sub-unit managers was possible (as in the
Maine fisheries example above). Even if outsiders
can be excluded, if one fishery limits harvest in a
conservative way, while another sets limits at or
above sustainability, and fish can move between
the fisheries, we have a spatially dispersed freerider system, in which one fishery’s restraint simply subsidizes another fishery’s harvest.
B. Low et al. / Ecological Economics 31 (1999) 227–242
With others, we have argued that many resource-management failures arise from problems
of ‘scale mismatch’ between human rules and
ecological realities (Cleveland et al., 1996). Modeling additional forms of spatial heterogeneity will
allow us to explore the effects of match or mismatch between the scale of interrelationships in
an ecosystem and the scale of decision making
about the governance and management of that
system (Wilson et al., 1999). Large-scale ecosystems are not simply small-scale systems writ large,
nor are small ecosystems mere microcosms of
large-scale systems. Thus, we suggest that management systems that produce perfectly acceptable
outcomes in ecosystems at one level can produce
disruptive or destructive results when applied to
higher-level or lower-level systems. The importance of scale depends greatly upon the structure
of both human systems and ecosystems, and the
geographical range over which ecological interactions occur in that system. No wonder sustainable
management of ocean fisheries is problematic!
When the scale of ecological interactions and
human rules for their governance are appropriately matched, we suggest that governance systems can be responsive and appropriate; whether
a local or larger-scale rule is appropriate depends
on the scale at which the relevant interactions
take place. For example, if small coastal villages,
spatially isolated from each other, take fish from
independent populations of fish, to what extent
are higher-level rules helpful in creating sustainable use? In contrast, if, as in the lobster fisheries
(above), certain age classes of lobster move across
political boundaries, other problems arise. In future work we need to explore further what that
If one management goal is sustainability, then
managers might consider some notion of invoking
‘safe minimum standards’ (Bishop, 1993) or the
‘precautionary principle’ (Low and Berlin, 1984;
Costanza and Cornwell, 1992; Costanza et al.,
1998) to ensure that harvest limits and other
environmental thresholds are not exceeded. These
are difficult to impose or get agreement on in
most systems, because ‘safe’ levels may be difficult
to determine, particularly when significant exogenous fluctuations exist. They are particularly
difficult in systems in which significant conflicts of
interest exist among actors — most resource systems. Dynamic modeling may help us resolve
some conflicts, in part by helping actors with
opposing views appreciate the sensitivity and
complexity of the system about which they are
making decisions.
This is a report of the Social and Ecological
System Linkages Project of the Property Rights
and the Performance of Natural Resource Systems Workshop, The Beijer International Institute
of Ecological Economics, The Royal Swedish
Academy of Sciences B 29–30 August 1994, and
28 May–3 June 1995, Stockholm, Sweden). We
appreciate the support provided our project by
the Beijer Institute and by the Workshop in Political Theory and Policy Analysis at Indiana
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