Biology and Philosophy 18: 529–552, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
The plaza and the pendulum:
Two concepts of ecological science
MARK SAGOFF
Institute for Philosophy and Public Policy
University of Maryland
College Park, MD 20742
U.S.A.
E-mail: [email protected]
Key words: Ecology, Ecosystem, Philosophy of science, Theory
Abstract. This essay explores two strategies of inquiry in ecological science. Ecologists may
regard the sites they study either as contingent collections of plants and animals, the relations
of which are place-specific and idiosyncratic, or as structured systems and communities that
are governed by general rules, forces, or principles. Ecologists who take the first approach
rely on observation, induction, and experiment – a case-study or historical method – to
determine the causes of particular events. Ecologists who take the second approach, seeking
to explain by inferring events from general patterns or principles, confront four conceptual
obstacles which this essay describes. Theory in ecology must (1) define and classify the object
it studies, e.g., the ecosystem, and thus determine the conditions under which it remains the
“same” system through time and change. Ecologists must (2) find ways to reject as well as to
create mathematical models of the ecosystem, possibly by (3) identifying efficient causes of
ecosystem organization or design. Finally, ecologists will (4) show ecological theory can help
solve environmental problems both in pristine and in human-dominated systems. A failure to
solve – or even to address – these obstacles suggests that theoretical ecology may become a
formal science that studies the mathematical consequences of assumptions without regard to
the relation of these assumptions to the world.
Introduction
Last summer, I walked through the Luxembourg Gardens on a fine June
day. The complexity and diversity of activity in that plaza reminded me
of phenomena ecologists study. Competition, often important in natural
communities, could be observed in the boisterous contests at the tennis courts
and – next to them – in the quiet concentration at the chess tables. Tourists
wary of pickpockets resembled prey alert to predators. Concepts ecologists use – such as “disturbance,” “heterogeneity,” “density-dependence,” and
“patch dynamics” – might describe the motions of people as they swirl and
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eddy in crowds about hawkers of trinkets, food vendors, street singers, and
shops. The “discordant harmonies” (Botkin 1990) that attract ecologists to
the places they investigate – savannas, forests, lakes, estuaries – may likewise
attract tourists to places like the Luxembourg Gardens that similarly reflect
free beauty and constrained variety.
If you walk up residential streets a few minutes from the Luxembourg
Gardens, as I did, you can visit the Pantheon, where in 1851, Jean Bernard
Foucault hung a pendulum from the dome to demonstrate the rotation of the
earth. A similar pendulum today metes out the hours by swinging straight
back and forth as the floor – and the earth – rotate beneath it. Someone
uninformed of the diurnal rotation of the earth and of the Newtonian principle
of inertia might not discern the pattern but attribute the elliptical vagaries of
the pendulum to contingent, historical, or haphazard events. We know that
inertial forces that govern the largest phenomena also shape the behavior of
smaller systems such as the path of a Foucault’s pendulum. Mathematicians
can model the motion of the pendulum, predict its behavior, and make its
patterns intelligible and explicit.
Two kinds of research
In this essay, I want to use the analogy of the plaza and the pendulum to
distinguish between two kinds of inquiry in ecology. One kind of inquiry
uses experimental, empirical, and inductive research – the same kinds of
methods detectives like Sherlock Holmes rely upon – to identify the causes
of particular phenomena in particular places. Research of this kind, which
explores causal relations and processes at specific sites, may describe how
each species responds idiosyncratically to the activities of its neighbors and
to the properties of a place. This kind of research, which relies on the
methods of observation, comparison, and experiment, often suggests solutions to environmental problems, for example, by identifying the causes of
the decline of a species or by predicting how a population will respond to
specific changes in environmental conditions.
The second kind of research emphasizes theoretical principles, metaphorical analogies, and mathematical models to examine “higher levels of
biological organization,” that is, “the properties of large-scale, integrated
systems” (Odum 1977). Research of the second kind seeks to identify general
rules or principles that govern the assembly, structure, and emergent properties of ecological systems. For example, in the early days of ecology,
Clements (1916) proposed that the natural community constitutes a “complex
organism” governed by laws of development. Ecologists since then have
offered a succession of theoretical models to provide a mathematical basis
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for understanding how natural communities or systems develop and function
(Simberloff 1980).
While theoretical ecologists attend to the task of creating and elaborating
mathematical models of ecosystem structure or function, they often leave it to
others to see if these models represent reality. “I am not going to discuss much
data in this book,” writes the author of one introduction to theoretical ecology.
“I am just going to discuss theory . . . and will leave it to each reader to fill in
examples from his or her other studies in biology and ecology” (Yodzis 1989:
3). Another primer in ecological theory states, “We will not be concerned
very much with testing whether the assumptions or predictions of a model
are true. Instead, we will test, so to speak, whether the predictions of a model
follow from the assumptions . . .” (Roughgarden 1998: xi).
How can one tell whether the ecological goings-on in a lake, forest, or
estuary exhibit the kinds of patterns or processes that warrant a theoretical
top-down mathematical approach as contrasted with a case-based bottom-up
inductive inquiry? The patterns and processes that govern ecosystem structure and function may be so hidden that one cannot infer them directly
from the behavior of ecosystems; one may need a mathematical model to
reveal them. Without the theory of the motion of the earth, one might not
identify the pattern meted out by Foucault’s pendulum. It may be the same
with ecosystems. Princeton ecologist Simon Levin (1981: 866) makes this
point. “In studying the logical consequences of assumptions, the theoretician
is discovering, not inventing, . . . .” He adds: “To the theoretician, models are
a part of the real world.”
Case-study vs. top-down explanation
Commentators often refer to the difference between “case study” and “top
down” explanation in ecology. The case-study approach, as Shrader-Frechette
and McCoy (1994) argue, employs “informal causal, inductive, retrodictive,
or consequentialist inferences in order to ‘make sense’ of a particular example
or situation.” This method explains a given event by referring to other events
that are its causes. A case-study, historical, or bottom up account might
describe the circumstances that brought Jean Bernard Leon Foucault and, a
century and a half later, me to the Pantheon. The occasion of a Paris exhibition
led Foucault, after accidentally discovering the gyroscopic behavior of a free
swinging pendulum, to suspend a 62-pound cannonball from a 220-foot long
steel wire attached to the Pantheon dome. A strike at the Louvre led me and
my family to visit the Luxembourg Gardens instead of that museum and then
the nearby Pantheon.
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While only an historical account will explain the sequence of events that
led to the presence of Foucault’s pendulum in the Pantheon, a mathematical
theory or model – that of a harmonic oscillator – is needed explain the
motions characteristic of any Foucault pendulum, wherever it is found. To
be sure, the motions of a particular pendulum in a particular place, because
of wind, for example, may differ slightly from what the model predicts. A
general mathematical theory or model not only explains by predicting the
events that follow from it (the signal) but also, in doing so, helps to identify
aberrations to be accounted for on other grounds (the noise). A mathematical
model should allow us, in other words, to distinguish motions that represent
the behavior of objects of the kind, e.g., Foucault’s pendulum, from the noise
or deviation that is to be explained in terms of contingent or local conditions
or events. An idealization should correspond to observation well enough that
one can distinguish the signal from the noise.
Many ecologists search for idealizations – mathematical theories or
models of ecological systems – because they regard a case-study approach
as an inadequate basis for their science. These ecologists take as the ideal
of scientific research the development of general mathematical patterns and
principles. Robert MacArthur began Geographical Ecology (1972: 1) by
stating, “Not all naturalists want to do science; many take refuge in nature’s
complexity as a justification to oppose any search for patterns. This book
is addressed to those who wish to do science.” The top-down or theoretical
approach MacArthur recommended explains a phenomenon by deducing (and
thus predicting) it by applying a general mathematical model to the relevant
kind of object in the context of a statement of initial conditions. According
to this prominent Popperian or Hempelian view in the philosophy of science,
“only understanding based on covering laws” or general mathematical models
“can provide explanations that invoke standards consistent with the need for
predictive power in science” (Peters 1991: 177).
Led by this philosophy of science, ecologists have created mathematical models and theories that seek to reveal or discover general rules and
principles that govern ecological phenomena. That ecological phenomena
reflect the behavior of orderly albeit complex systems is assumed. Ecological phenomena “can be analyzed using the concepts of a system, since this
approach provides definitions and general rules which allow very complex
structures to be understood and predicted. When allied to mathematical
modelling techniques, system theory provides the best conceptual framework
for a highly effective general approach to the study of ecosystems” (Franzle
2000: 94).
The belief that ecological phenomena represent the behavior of organized complex systems that can be represented mathematically – albeit
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by formulae far more complex than those that explain the behavior of a
Foucault’s pendulum – has been central to the pursuit of a unifying theory
in ecology (Jorgensen 2002: 13–18). Ecologists caution against “resorting to
telling stories about special cases instead of rigorously defining the general
condition . . . so that order can emerge from a wide-ranging pattern” (Allen
and Hoekstra 1992: 9). The goal of mathematical modeling, on this view,
is not to simulate, map, or represent the goings-on at a particular site but
to show “that ecosystems function in accordance to some overarching rules
that control structure and/or function” (Shugart 2000: 383). For MacArthur,
as Donald Worster (1994: 398) observes, “Species swung back and forth as
on a fixed pendulum, and the motion of their competitive action was exactly
predictable.”
Theory in ecology
Case study or inductive research, which emphasizes observation, comparison,
and experiment at particular sites, has produced a vast amount of useful
and reliable knowledge in ecology (NRC 1986). With respect to “top-down”
approaches, however, some ecologists agree with Simberloff (1980) that the
theoretical focus on ecosystems has failed “to add substantially to our understanding of the workings of nature.” Drake et al. (1999: 241) caution that “the
relationship between self-organization, natural selection, and the mechanisms
and assembly operators of ecology are simply unknown despite a growing
theoretical effort.” Despite “continuous efforts, ecology has not been able to
offer universal laws or precise ubiquitous principles” (Brecking and Dong
2000: 51).
One might speculate that if mathematical theorizing in ecology has been
less than a success, the reason is that ecological phenomena are more like the
swirl of activity at the Luxembourg Gardens than like the patterned motions
of Foucault’s pendulum. In other words, “The absence of a unifying theory
may . . . be simply inherent in the subject” (Pahl-Wostle 1995: 6). Gilbert
and Owen (1990: 33) wrote that their observations provide no evidence of
“an ontological emergence of a community level of biotic organization.” Any
suggestion of pattern or structure in ecological phenomena “is a biological
epiphenomenon, a statistical abstraction, a descriptive convention without
true emergent properties but only collective ones, wholly referable in its
properties to those of its constituent species, populations, and individuals.”
In the same vein, Ernst Mayr (1959) wrote, “The more I study evolution the more I am impressed by the uniqueness, by the unpredictability,
and by the unrepeatability of events.” He asked, “Is it not perhaps a basic
error of methodology to apply such a generalizing technique as mathematics
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to a field of unique events?” William Drury (1998: 23) inveighed against
the “strong tendency to accept the existence of self-organizing principles as
inherent in natural systems.” He wrote, “I feel that ecosystems are largely
extemporaneous and that most species (in what we often call a community)
are superfluous to the operation of those sets of species between which
we can clearly identify important interactions . . . . Once seen, most of the
interactions are simple and direct. Complexity seems to be a figment of our
imaginations driven by taking the ‘holistic’ view.”
Other ecologists present at least four reasons to believe that it would be
a mistake to give up on the ‘holistic view,’ that is, the idea “that ecosystems
are integrated, interconnected systems with their own laws and organizational
principles” (Pahl-Wostle 1995, paraphrasing Loehle 1988). First, ecology is
a young science, and as it matures, laws and organizing principles may be
discovered. Second, many ecologists agree with Peters that “covering laws”
are essential to scientific as distinct from historical inquiry. For ecology to
progress as a science, as J. B. Wade (1995) wrote, it has to develop “a
comprehensive synthetic theory of the ecosystem.” K. E. Watt (1971: 569)
wrote earlier that unless ecologists develop “a strong theoretical core that
will bring all parts of [ecology] back together . . . we shall all be washed out
to sea in an immense tide of unrelated information.”
Third, as Jorgensen (2002: 14) among many others points out, “We are
facing complex, global problems which cannot be analysed, explained or
predicted without a new holistic science.” A. O. Hirschman (1979: 164)
noted in another context that power comes with understanding the basic
laws of change. He wrote “the quick theoretical fix has taken its place in
our culture alongside the quick technical fix.” In response to the need for
sweeping theoretical approaches to environmental problems, the International
Biology Program became in the 1970s “the most massively supported American ecological effort and one wholly conceived in a holistic, ecosystem
vein” (Simberloff 1980). This was followed by a another program, Ecosystem
Studies, in the National Science Foundation. In addition, NSF through its
program on Biocomplexity and the Environment now offers $36 million each
year to support integrated research in environmental systems. “To the extent
that grant funding is an important determinant of academic advancement, and
economic well-being a general goal, one might reasonably argue that the
ecosystem paradigm is seductive on economic grounds alone, independent
of either philosophical or biological considerations” (Simberloff 1980).
Fourth, “In the academy, the prestige of the theorist is towering”
(Hirschman 1979: 163). Ecology could greatly enhance its prestige if it had a
solid mathematical foundation. A survey of ecologists concluded that “there
is an unease that we still do not have the equivalent to the Newtonian Laws
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of Physics, or even a generally accepted classificatory framework” (Cherrett 1989). Roughgarden and co-authors (1989: 9) argue that mathematical
theory in ecology “provides an antidote to the helpless feeling engendered
by the view that nature is so complicated, and evolutionary processes so
contingent on accident and history, that all we can ever hope to achieve is
detailed understanding of specific situations . . . rather than any general rules
and patterns.”
Not all ecologists who achieve a “detailed understanding of specific situations,” however, may experience a “helpless feeling;” indeed, case-by-case
understanding is hard to accomplish, and it provides the kind of site-specific
knowledge which public policy – attempts to protect or restore a species
in decline, for example – often requires. Nevertheless, the four reasons
described above show it makes sense for ecologists to pursue the mathematical basis of ecosystem structure, function, or behavior rather than to
surrender to skeptics who cavil that an organizing mathematical principle is
absent from the science because it is absent from the subject – the phenomena
– the science studies.
Four conceptual obstacles to a theoretical ecology
The general question I raise – how ecology may develop as a theoretical topdown science as distinct from a bottom-up inductive one – is the subject of a
large literature ably reviewed by others (Golley 1993; Hagen 1992; Kingsland
1995; McIntosh 1985). I will not comment on this literature. Instead, I want to
describe four hurdles ecology will overcome if it is to emerge as a theoretical
and mathematical science. In this section, I characterize these four obstacles;
in succeeding sections, I elaborate them. Philosophical problems of these
kinds confront theory-building in any science, not just ecology.
First, no theory can be tested unless it defines the class of objects the
behavior of which it seeks to understand. For example, a Foucault’s pendulum
can be defined as a free-swinging bob on a string, cord, or wire. The behavior
of objects that do not meet this definition – for example, a decaying carcass
of a beached whale – would not provide tests to confirm hypotheses about
the Foucault’s pendulum. Similarly, ecological theory must define the kind
of object it studies, e.g., the class ecosystem or ecological community. Does
a rotting carcass of a beached whale count as an example of an ecosystem?
Only a definition of the class ecosystem can determine what observations
about which objects will help to confirm or disconfirm general statements
about members of that class.
A definition also allows one to distinguish tautologies from empirical and
therefore testable hypotheses. For example, the sentence, “The period of a
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Foucault’s pendulum is independent of its mass,” states a testable hypothesis.
The sentence, “The bob of a Foucault’s pendulum swings freely,” in contrast
can be deduced from the definition and so states a truth by stipulation not
discovery.
Criteria that determine what kinds of things count as ecosystems – or as
certain types of ecosystems – would allow ecological science not only to state
and test falsifiable hypotheses but also to identify and reidentify the objects
it studies through time and change. One cannot bathe in the same river twice,
if by “same” one means the same in all details and qualities. If a river is
deprived of half its species – or if it takes on as many again “invaders” –
does it remain the “same” system? If so, the system shows its persistence,
resilience, stability, etc.; if not, its fragility. The concept ecosystem should
provide criteria for telling if the system (1) persists in spite of a change by
adapting to perturbation or (2) collapses in the face of that change and segues
into a different system.
Theories of ecosystem structure and function confront a second problem
simply because there are so many of them. The abundance of untested mathematical theory threatens to turn ecology into formal rather than an empirical
science – as some critics believe mathematization has formalized such disciplines as political science and economics (Porter 1995). A formal science
studies the logical consequences of assumptions with little or no concern
about how or whether these assumptions correspond to reality.
Third, theory could better succeed if it identified an efficient cause of
ecosystem pattern or structure. Scientists have discovered the forces of nature
– e.g., inertia and gravitation – that account for the patterns they attribute to
Foucault pendulums. What forces explain patterns or regularities ecologists
attribute to ecosystems? Evolutionary forces – genetic mutation and natural
selection – shape organisms. If ecosystems are not organisms – if they are not
units of selection – what forces of nature shape them, causing them to exhibit
a design or to behave in orderly ways?
The problem of identifying the efficient cause of ecosystem structure
or organization appears particularly vexing because sites that have radically different histories – and thus have presumably have responded to
very different forces – may not differ with respect to their emergent or
organizational properties. Consider, for example, (1) a recently created lake
comprising only exotic species, and (2) a pristine lake that has not been
disturbed for centuries. These places may differ so little with respect to
ecosystem structure, function, and pattern that observation will not reveal
which is which. Yet it would be hard to claim that the same evolutionary
forces shaped them both.
Fourth, ecology strives not only to be a theoretical but also an applied
science. A century ago, William James (1990: 10) pointed out that usefulness
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in solving real world problems “distinguishes statements that can be true or
false from metaphysical disputes that are empty and interminable.” During
the Clinton Administration, the White House established an Interagency
Ecosystem Management Task Force to introduce the ecosystem concept as
the basic unit of environmental policy (Fitzsimmons 1999: 6). Ecologists may
vindicate ecosystem theory by showing it can apply usefully in public policy.
First obstacle: What kinds of objects count as ecosystems?
A general scientific hypothesis typically asserts of some class of objects
A a correlation (either general or probable) with some pattern or property
P. To avoid tautology, the definition of the subject term A cannot refer to
the predicate concept P. The Archimedean principle, “All objects that float
displace their weight,” passes this test because one can tell whether or not
an object floats without knowing its weight or how much water it displaces.
Similarly, one can define a Foucault pendulum – “a free-swinging bob on
a string” – without referring to its period or mass. Thus, one can test the
empirical hypothesis that the period of the pendulum is independent of its
mass.
MacArthur (1972: 257) understood that no one could meaningfully test
any hypothesis of the form “All A is (or tends to be) P” except in relation to
a classificatory system that defines objects of kind A without referring to the
property P. He wrote that attempts to establish a classificatory system would
consume “most of the creative energy of ecologists.” MacArthur argued that
ecology must establish general statements “of the form ‘for organisms of type
A, in environments of structure B, such and such relations will hold.’ ” The
principal obstacle to a theoretical ecology, as he correctly thought, lay in its
lack of a classificatory system and thus in its inability to identify the kinds
of objects in terms of which it may confirm hypotheses. In thirty years, this
situation has not changed. The National Research Council (1993: 75) has
stated that “no broadly accepted classification schemes” exist for “ecological
units above the level of species.”
Definitions of the class ecosystem found in the literature are either overor under-inclusive. In 1942, Lindeman defined an ecosystem as a “system
composed of physical-chemical-biological processes active within a spacetime unit of any magnitude.” Similarly, a Report by the Ecological Society
of America (ESA) (Christensen et al. 1996, quoting Likens 1992), defines
an ecosystem as “a spatially explicit unit of the Earth that includes all of
the organisms, along with all components of the abiotic environment within
its boundaries.” This kind of definition is over-inclusive because it takes in
everything from a kitchen sink, a head full of lice, a yeast infection, an
orchard, and an aquarium, to a transportation, education, or sewage system.
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Indeed, the ESA (p. 13) states, “a dung pile or whale carcass are (sic)
ecosystems as much as a watershed or a lake.”
Under-inclusive definitions build into the ecosystem concept the very
property – e.g., self-organization, autocatalysis, complex adaptiveness – that
is then predicated of it. Consider, for example, the statement, “Ecosystems are
dynamic assemblages of interacting components, self-organized into evanescent patterns of interaction on multiple scales of space and time” (Levin
1999b: 6). An opposing definition might hold that ecosystems are not selforganizing but adapt to outside forces. In that case, ecosystems could be
“complex adaptive systems assembled from sets of available components as
one would assemble a new computer system” (Levin 1999: 101). Neither of
these definitions allows one to test whether ecosystems are self-assembled or
adaptive because each lays down the quality in question – self-organization,
adaptive complexity – as a necessary condition for membership in the class
that is otherwise undefined.
To test whether a kind of system possesses an emergent quality such as
organization, one could rely on the most inclusive definition. If the class
ecosystem includes whale carcasses, kitchen sinks, and dung piles, and if
these are not, e.g., self-organizing (as my sink is not), the hypothesis is
disconfirmed. A statement that characterizes the concept ecosystem in terms
of self-organization constitutes stipulation not discovery. Order in nature
should not be taken for granted; it must be demonstrated, not assumed. “The
method of ‘postulating’ what we want has many advantages; they are the
same as the advantages of theft over honest toil” (Russell 1919: 71).
The problem of definition at issue here is a logical not just a spatial one.
Many ecologists have observed that the spatial contours of an ecosystem are
difficult to draw, e.g., because the “boundaries of the component populations may be much larger than the ecosystem boundaries” (O’Neill 2001:
3277). I am not referring to the problem of setting geographical boundaries.
A more important challenge, I believe, is to define conditions even a bounded
collection of trees, for example, must satisfy to be a “forest” for purposes
of ecological theory. One may ask if a Christmas tree farm is a “forest,”
an impoundment behind a dam, a “lake,” a field of Roundup-Ready grain
a “savanna,” and so on. A sewage treatment lagoon is well bounded; is it
a member of the class “lake,” “community,” “ecosystem”? The first step
in a theoretical science is taxonomy. Daniel Simberloff (1998: 253) wrote,
“whereas a species is usually easy enough to define . . . which ecosystems
are so similar as to be representative of the same type is often not a trivial
question.”
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Is it the same ecosystem?
A statement of the criteria that define membership in the class ecosystem,
ecological community, etc. would help to solve a related problem – that of
reidentifying the “same” system through time and change. When pendulums
break, they cease to swing, so one knows that they cease to be. When ecological assemblages pass, in contrast, other assemblages replace them, often
gradually (Simberloff 1998: 253). Ecologists do not yet have the conceptual
resources to decide whether or when an ecosystem has changed or whether
and when it has collapsed and been replaced by a different kind of system.
In a famous experiment, David Schindler and colleagues (1980, 1985)
perturbed a lake by pouring sulfuric acid into it. They observed that certain
qualities changed, such as the species ratios, while other qualities, such
as energy flows and productivity stayed the same. University of Georgia
ecologist Frank Golley (1993: 195) concluded that “the genuine properties
of the lake . . . are more robust and vary much less with an environmental
change.” But how did Golley – or how would anyone – know which qualities to count as the “genuine” properties of the lake? If you consider energy
flow to be “genuine,” the experiment confirms the hypothesis that lakes are
robust against perturbation. If you think species ratios are constitutive, the
experiment disconfirms that hypothesis.
O’Neill (2001: 3277) adds that the way one classifies ecosystems –
whether by species lists or by functional systems – will determine if an
ecosystem is stable or not. As a functional system, the perturbed lake
remained a going concern and thus would be considered stable. “The
ecosystem defined by a species list is almost always unstable because it rarely,
if ever, recovers to the identical list of species” (O’Neill 2001).
A science must provide criteria that not only identify a collection of things
as constituting, e.g., a “lake,” but also as “the same lake” though its properties
differ over time. Without criteria for identifying and reidentifying membership in the class ecosystem of kind A ecologists would study a Heraclitean
flux in which they cannot step even once. “Despite the importance of selfidentity,” Kurt Jax and colleagues (1998: 253) have written, “there is no
consensus on how to define and measure it.” These authors decry the assumption that ecosystems are “given as such in nature” and “therefore have to
be found and identified instead of being defined and delimited.” There is no
entity without identity. There are no ecological units – such as ecosystems –
without criteria for identifying those objects and reidentifying them through
time and change.
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Human-dominated ecosystems
In setting criteria for including some sites but not others in the class
community or ecosystem, ecologists will address a perplexing question,
namely, whether places that human beings dominate can belong to that
class. According to O’Neill (2001: 3279), “The ecosystem concept typically considers human activities as external disturbances . . . Homo sapiens
is the only important species that is considered external from its ecosystem,
deriving goods and services rather than participating in ecosystem dynamics.”
Others agree that humanity is only a disruptive force. “Ecologists traditionally have sought to study pristine ecosystems to try to get at the workings
of nature without the confounding influences of human activity” (Gallagher
and Carpenter 1997). “Ecologists’ preoccupation with the pristine reflects a
long tradition in western culture and a philosophy of separating humanity and
nature” (Western 2001: 5458).
The question whether to include human-dominated sites in the extension
of the class ecosystem creates a dilemma. One the one hand, one encounters at
least two difficulties if one argues that sites humans dominate are not ecosystems of the kinds to which ecological theories and models apply. First, it may
be difficult to find phenomena that exemplify forces that govern nature free
of human influence. “Many ecosystems are dominated directly by humanity,
and no ecosystem on Earth’s surface is free of pervasive human influence”
(Vitousek et al. 1997). Accordingly, “Drawing a sharp line between the
human and natural realms serves no purpose when our imprint is as ancient
as it is pervasive” (Western 2001).
Second, by separating humanity from the rest of nature, ecology would
become a unique science. An ethical, spiritual, and metaphysical divide separates humanity from other creatures because human beings have free will and
moral responsibility, while other creatures, as far as we know, do not. Yet
no natural science besides ecology adopts this moral division between nature
and humanity as part of its conceptual framework. All the forces other natural
sciences study – e.g., the Newtonian forces that govern Foucault’s pendulum
– apply indifferently to artifacts and natural objects, indoors and out. In the
comic strip Calvin and Hobbes, Hobbes, a tiger, turns into a limp doll if
humans are present. Do ecological principles likewise lose efficacy when
people enter the picture?
On the other hand, to include human-dominated sites in the extension of
the class ecosystem is to suggest that one might most easily discover and
test the rules or forces that govern ecosystems by studying not wild areas
but intensely managed ones, such as factory farms, waste treatment plants,
and golf courses. Just as Darwin explained the concept of selection in terms
of its artificial application in pigeons, so ecologists could identify, explain,
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and test the principles they study in relation to their application to largescale vertically-integrated technology-driven aquacultural, silvicultural, and
agricultural operations. Indeed, some ecologists argue that the test of their
science lies in its ability to create and control ecosystems – just as any natural
science has engineering applications. Bioengineering, according to this view,
is the future of ecology (Forcella 1984).
Second obstacle: Pluralism or promiscuity?
A second kind of difficulty mathematical models of the ecosystem have to
overcome is that there are so many of them. In the Handbook of Ecosystem
Theories and Management (Jorgensen and Muller 2000), for example,
one finds chapters that describe ecosystems as “Functional Entities,” as
“Self-Organizing Holarchic Open Systems,” as “Subjects of Self-Organizing
Processes,” as “Information Systems,” as “Network Environs,” as “Cybernetic
Systems,” as “Dynamic Networks,” as “Hierarchical Systems,” as “Chaotic
Systems;” as “States of Ecological Successions,” and so on. As these chapter
titles suggest, theorists seek to shed light on the structure and function
of ecosystems by borrowing concepts and assumptions from the study of
information systems, cybernetic systems, equilibrial systems, non-equilibrial
systems, thermodynamic systems, turbulent systems, stochastic systems,
optimization systems, catastrophic systems, complex adaptive systems, and
many more. Ecosystem modelers have borrowed from game theory, hierarchy
theory, chaos theory, statistical mechanics, network theory, probability theory,
and even the theory of oscillators. Platt and Denman (1975: 189) have urged
“the nonlinear oscillator representation of living systems” as a foundation for
theoretical biology.
Sven Jorgensen and Felix Muller, the editors of the Handbook, helpfully
ask how ecologists can cope with “approaches as varied as thermodynamics,
cybernetics, information theory, network theories, utility theory, hierarchy
theory, chaos and catastrophe theories, the theories about ecological stability,
buffer capacities and resilience of ecosystems, and the theory of ecosystems
as self-organizing critical systems” (p. 465). The answer they offer, I believe,
presents an important obstacle to progress in theoretical ecology.
“We need them all, if we want to get a comprehensive, pluralistic view
of the ecosystem,” Jorgensen and Muller (p. 6) state. Other sciences tend to
replace one theory with another, for example, the phlogiston with the oxidation theory of combustion. Ecology, in contrast, seeks to add one theory to
another. With ecology, the challenge is often described not as one of falsification but of integration into a holistic perspective. Ecological theory may
practice a kind of competitive inclusion. Metaphors, models, and paradigms
542
do not crowd each other out; they congregate into a deeper truth. To alter
a phrase from a Buffalo Springfield song, “Nobody’s wrong if everybody’s
right.”
To explain how all these disparate research programs could all be right –
how they add up to a larger truth – Jorgensen and Muller (p. 466) refer to “the
well-known elephant parable.” They compare their colleagues to zoologists
who unknowingly study different parts of the same animal. These scientists
“don’t realise that these parts form an elephant because this holistic view is
only possible by taking a step backwards and discussing ones (sic) own observations with those of their colleagues.” Zoologists who did not know they
were studying parts of the same elephant, however, would not benefit from
sophisticated mathematical models. They must deal instead with elementary
taxonomy – problems of classification that were resolved in zoology by the
time of Aristotle.
To be sure, many different kinds of ecosystems may exhibit many different
kinds of dynamics; a pluralistic approach is justified. Since the 1960s,
however, ecologists have worried that they played the role of the Sorcerer’s
Apprentice in creating an immense tide of untested theories; they inveighed
not against pluralism but against promiscuity. Of a collection of theoretical
models in ecology, E. O. Wilson (1969) commented, “[O]ne gets the feeling
he is receiving secrets of the universe from a space visitor anxious to be on his
way.” Many other biologists agreed. “Theoretical ecology is a major growth
industry, and the pages of ecological . . . journals are littered with theory”
(Levin 1981: 865).
For decades ecologists have expressed dismay at the unconstrained
production of theory that lacks relevance to empirical puzzles or problems.
“No single model dominates, none is clearly preferred, even by ecologists.
And the credentials of paradigm spinners all look pretty much the same,”
George Woodwell (1976) said in a presidential speech to the Ecological
Society of America. “[M]uch mathematical ecology is simply mathematics
dressed up as biology, and is dismissed by field biologists as being of no
relevance to their interests” (Levin 1980). Ecology continues to confront a
“constipating accumulation of untested models” (Schoener 1972) after indulging in “a feast of theory [that ecology] isn’t quite ready to digest” (Futuyma
1975). On the other hand, the sheer amount of mathematical theory in ecology
may attest to its importance. There must be an elephant in there somewhere.
Third obstacle: Finding a cause of ecosystem organization
If ecologists succeed in establishing a general theory to describe the design,
function, structure, organization, etc. of ecosystems, they must identify the
543
force, power, or agency that constitutes the efficient cause of that design or
order. If you found, for example, a watch or a piano in a forest, you would
not say that it organized itself; rather, you would posit the existence of a
watchmaker or a piano maker. Similarly, if the forest itself displayed a design
that suited it for some function, you would similarly try to identify the agent
or power that provides the efficient cause of that organization.
One might reply that ecosystems organize themselves, but this is problematic. There are objects, such as crystals, that may be said to be self-organizing,
but they have no obvious similarity with ecosystems. The mathematician Per
Bak (1996) identified what he called self-organized criticality in the way piles
form when sand is dripped on a plate. One cannot think of two items more
unlike, however, than, say, a forest and a dribbled pile of sand. That some
objects, such as Foucault’s pendulum, toll the hours tells us nothing about
places like forests, rivers, or coral reefs. That dribbled sand piles display
self-organized criticality suggests nothing whatsoever about pendulums or
ecosystems.
It is easiest to understand such terms as “structure” or “function” when
they are applied to objects that are designed for a purpose. The structure and
function of a kidney, for example, can be understood in relation to the purpose
of cleansing the blood. Similarly organisms are organized by evolutionary
forces to enjoy relative reproductive success. If ecosystems had a purpose
– if God created them for the benefit and support of humanity – one could
identify the properties of design, organization, and function by which they
serve that end. Absent such a theological assumption, however, it is difficult
to say that ecosystems serve any purpose. Accordingly, to study the structure
and function of ecosystems, as ecologists do, is to accept a logical challenge.
What kinds of things other than ecosystems have structure and function but
not purpose? There are ways to answer this question – for example, a snowflake has a structure but not a purpose. Snowflakes, however, do not seem to
provide an analogy for understanding ecosystems.
Ecologists recognize the need to identify the forces that give ecosystems
the structure, design, or functions they are said to possess. Levin (1999b: 6)
points out, “one must recognize the powerful adaptive and self-organizing
forces that shape ecosystems.” What force, power, or agency assembles
ecosystems and causes them to have the organization that theorists attribute to
them? Levin explains that what is required besides a diversity of components,
e.g., species, and interactions among them, is an autonomous process, such as
natural selection, “that uses the outcomes of those local interactions to select
a subset of those components for replication or enhancement” (1999: 12).
He concludes, “Large-scale patterns primarily result from, rather than drive,
evolution at lower levels” (p. 104).
544
Recent vs. heirloom ecosystems: A paradox
Is natural selection the “autonomous process” that results in ecosystem structure and function? It is hard to see how it can be. Ecosystems have no
genomes; they “do not represent evolutionary units” (Levin 1997). If evolutionary forces, which work slowly, build up ecosystems, this process would
take time to accomplish. Evolutionary forces, then, would not appear to
be responsible for organizing recently created ecosystems and those that
comprise mostly exotic species. These systems appear, however, to be as well
organized as ancient ecosystems that contain only indigenous organisms.
Consider an example. The State of Maryland has no naturally occurring
but only man-made lakes. The largest, Deep Creek Lake, was created in
the 1920s by a hydroelectric dam. People who settled around the flooded
valley introduced whatever species they thought desirable, and fishing is
good there to this day. Ecologists (Howell et al. 1978) inventoried the new
lake and diagrammed its ecological processes. Their surveys, models, energy
budgets, etc. suggest that no structural differences distinguish this lake,
created recently by a corporation, from one that “evolved” or self-assembled
over millennia. The youthfulness of the lake did not detract from its dynamic
properties.
Consider another example. Researchers who studied the San Francisco
Bay determined that in many places “exotic organisms typically account for
40 to 100% of the common species, up to 97 percent of the total number of
organisms, and up to 99% of the biomass.” Of the roughly 400 species found
in Bay waters, 234 are known to be exotic and another 125 are “cryptogenic”,
i.e., of unknown origin (Cohen and Carleton 1998). If large-scale patterns
result from evolution at lower levels, the presence or absence of these patterns
would indicate whether a site is free of or full of introduced species. Yet, no
one can tell whether or which species are exotic except by consulting the
historical record.
Ecologists might be able to test the hypothesis that natural selection operates, however indirectly, to bring into existence the properties of organization
or structure that ecosystems are thought to possess. Consider a place such as
Deep Creek Lake created in the last century. There, species brought together
at random, some from the four corners of the earth, have “naturalized”
– i.e., have formed relatively stable populations – to make an ecosystem.
One could investigate these creatures to see whether they have, indeed,
evolved over a century or whether they are more or less the same genetically and phenotypically as members of the populations from which they were
obtained.
If the organisms that inhabit Deep Creek Lake have evolved into unique
and endemic forms over the past decades, this would provide evidence of
545
the powerful adaptive and self-organizing forces that shape ecosystems. One
would have reason to agree that evolution at lower levels shapes ecosystem
structure and function. If these organisms are unchanged in genotype and
phenotype, however, this finding would be consistent with two different
possibilities. On the one hand, the lake may lack the unifying properties –
the organization, structure, or large-scale patterns – that ecological theory
attributes to ecosystems in general. This would present a paradox, however,
because there seems no way to distinguish the dynamic or organizational
properties of this ecosystem from those of an heirloom lake. Thus, if the
kind of system-level organization mathematicians study is absent from an
impoundment created by a corporation less than a century ago, one has to
infer it is absent from all ecosystems, and thus that there is no design in
ecological systems.
On the other hand, one could conclude that “the ecosystem is not an
organism and has not been shaped by evolution to perform particular functions” (Levin 2001). This possibility suggests that if ecosystems are organized
in mathematically intelligible ways, it is not evolution but some independent
Force that accounts for design in ecology.
Fourth obstacle: Can ecosystem theory be applied?
Perhaps the most convincing way to demonstrate the legitimacy of mathematical ecosystem theory is to show how it can be applied to help solve
problems of environmental policy. Unfortunately, as a National Research
Council Report found, “ ‘Ecological theory,’ as described in standard textbooks on ecology, is seldom applied directly to environmental problems”
(NRC 1986: 1–2). Sarkar (1996) observed in a paper titled “Ecological
Theory and Anuran Declines” that no theoretical model of ecosystem structure or function can assist policy makers by explaining the cause of any
problem, e.g., “drastic declines in amphibian, particularly anuran, populations
throughout the world.” The inability of ecosystem theory to tell, for example,
that UV radiation may be killing certain toads supports Sakar’s contention
that theoretical and mathematical ecology is of limited or perhaps of no use
to conservation biology. The failure of theoretical or mathematical models to
explain particular losses “shows that, if conservation is a goal, generality is a
poor desideratum in ecology” (Sakar 1996).
Daniel Simberloff and co-authors (1999) have described difficulties
involved in applying general concepts of ecosystem theory to determine the
causes of phenomena at particular sites. With enormous amounts of sitespecific information, they say, it may be possible “to predict which species
will be found at which site and which species will not coexist. The necessary
546
research . . . generally falls under the rubric of natural history.” The subtle
responses of species “suggest that assembly rules, if they exist, will be quite
local. Not only will assembly rules not be simple, they will not be very
general.”
Perhaps mathematical theory in ecology will make its greatest contribution to society by clarifying ecosystem-level properties, such as ecosystem
integrity, health, development, or sustainability that can guide environmental
policy at a greater level of generality and at a more inclusive scale than sitespecific studies. Yet the absence of any definition of the class ecosystem – the
lack of a classificatory system, criteria of identification and reidentification,
rules for spatial limitation, agreement about the meaning and measurement of
emergent properties, and so on – has kept ecologists from defining normative
terms by which society may gauge the well-being of the environment.
Although ecosystem theory has been a burgeoning academic industry
since the 1950s (Jorgensen 2002: 1), many ecologists believe it has failed to
provide any basis or guidance for management. In many instances, the application of mathematical theory has proven counter-productive because “the
crucial detailed natural history and autecology were ignored” (Simberloff
1997: 276; see also Gilbert 1980; Williamson 1981, 1989). In spite of a vast
social investment in mathematical modeling, “the new approach of ecosystem
management does not have a foundation of well-developed theory to guide
it” (Ostfeld et al. 1997: 4). Indeed, public officials and environmental and
industry groups express exasperation at the futility of applying in management contexts the concept ecosystem and related normative notions such
as ecosystem health, integrity, and stability (Fitzsimmons 1999). Michael
Bean (1997: 23) of the Environmental Defense Fund has redirected to the
concept ecosystem management what a former Labor Secretary said about
the concept of competitiveness. “Rarely has a term of public discourse gone
so directly from obscurity to meaninglessness without any intervening period
of coherence.”
A group of ecologists, assessing the progress of research on ecosystem
theory in relation to environmental policy, have endorsed a judgment that
Christensen (1988) adapted from Mark Twain. Twain said in another context,
“The researches of many commentators have already shed considerable darkness on the subject, and it is probable that, if they continue, we shall soon
know nothing about it” (Fiedler et al. 1997: 86).
Conclusion
I have proposed in this essay that theoretical and mathematical ecology
will succeed not by advancing more complex theories or by deepening the
547
mathematical sophistication of models but by attending to the basic conceptual conditions on which theories and models can be tested and applied.
First, to secure ecology as a science of ecosystems, ecologists will define
the object they study, e.g., the concept or class ecosystem or community;
otherwise, general hypotheses that predicate properties to ecosystems cannot
meaningfully be confirmed. Criteria that allow ecologists to classify their
objects of study should also allow them to identify and reidentify those
objects through time and change. Only in relation to established criteria for
classifying ecosystems may emergent qualities, such as stability, resilience,
and continuity, be treated as empirical properties rather than as conceptual consequences of an arbitrary way – species lists, productivity, materials
cycling, etc. – by which “sameness” is defined.
Second, ecologists will find ways to test and reject mathematical models,
theoretical paradigms, and the like. If ecologists continue to propose theoretical frameworks and models without providing crucial experiments to test
them, pluralism in ecology will appear to be promiscuity. As G. W. Salt
(1983: 699) has lamented, “thanks to the dubious but nonetheless popular
cachet of legitimacy provided by mathematics to an idea, a theoretician’s
hypotheses were likely to be accepted until demonstrated false.” Few if any
mathematical theories are tested empirically. Outsiders to ecology might get
the impression that anyone with a metaphor and some mathematics can model
the ecosystem.
Third, ecologists will identify the causes – the forces of nature – that
explain the structure, function, order, or design they predicate of ecosystems. The thesis that ecosystems are self-organizing because, say, sand piles
exhibit that quality constitutes a non sequitur of laughable proportions. To
argue that ecosystems display “chaotic” behavior, moreover, does not justify
a complex mathematical approach to modeling their structure or function.
Chaotic behavior is precisely the condition that makes a site an appropriate
subject of historical and inductive rather than of deductive and theoretical
science.
Fourth, ecologists will show that mathematical theory – as distinct from a
case-study approach that reveals the particular causes of specific events – can
usefully be employed in environmental policy. No one would suppose that
mathematical theory could help a detective like Sherlock Holmes to identify
who is responsible for a crime. To what extent will mathematical theory assist
in the detective work the public often asks ecologists to undertake to identify
the causes of an untoward environmental change?
Philosophers of science have suggested that questions about the organization of ecosystems “are at bottom empirical questions to be settled by
empirical study rather than conceptual argument” (Cooper 2001: 482). If so,
548
ecology could succeed along with other biological sciences as an essentially
inductive, empirical, and historical discipline in relation to which mathematical theory appears pretentious and largely irrelevant. Stephen Jay Gould
(1985: 18) argued for a historical approach in evolutionary biology. Historical
narratives “explain, but do not usually try to predict; they recognize the irreducible quirkiness that history entails, and acknowledge the limited power of
present circumstances to impose or elicit optimal solutions; the queen among
their disciplines is taxonomy, the Cinderella of the sciences.”
Taxonomy, however, is not a path to fame and glory; one can easily locate
academic centers of excellence in mathematical ecology and biocomplexity,
but one would be hard pressed to find professional training in taxonomy.
Ecologist Paul Dayton wrote in 1979, “Ecology often seems dominated
by theoretical bandwagons driven by charismatic mathematicians, lost to
the realization that good ecology rests on foundations of natural history
and progresses by the use of proper scientific methods.” Gould adds that
biological science has “tended to denigrate history, when forced into a
confrontation, by regarding any invocation of contingency as less elegant
or less meaningful than explanations based directly on the timeless ‘laws of
nature’ ” (Gould 1989: 51).
No one knows where the future of ecology lies. If the sites that ecologists
study are like the swirl of activity at the Luxembourg Gardens, the properties
of which are historically contingent, ecology may mature into an inductive
and experimental science like medicine. To be sure, statistical analysis is
useful in testing empirical hypotheses; nevertheless advances in medicine,
like those in the life sciences generally, appear to be more dependent on
empirical and inductive methods of comparison, observation, and experiment
than on advances in mathematics. Something of this sort may also be true
of a science that seeks to protect and restore environmental health. On the
other hand, if ecosystems, once defined and delimited, turn out to be regulated systems like Foucault’s pendulum, ecology may become a mathematical
and deductive science like physics. Progress depends on whether and when
ecologists address conceptual and logical problems of the sort described here
– problems that they have ignored to the detriment of their science.
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