Commentary
Good Models and Immature Theories
David W. Onstad
NHIS FORUM COLUMN, which appeared in the Fall 1991 American Entomologist, Alan Berryman expresses his
opinions about management modeling based
on ecological theory. I support his efforts to
use logical and cost-effective models, bm I
disagree with his arguments about theory and
his disparagement of complex numerical
modeling. I believe that population-dynamics "theory" cannot be used as a foundation
to ensure the accuracy of models. The value
of management models must still be judged
according to their predictions, the quality of
the calibration data, and the costs of development.
The problem with most ecological theories, and the reason they often are ignored,
is that most are immature and should really
be considered hypotheses or speculation (Salt
1983, Loehle 1987, Onstad 1988, Onstad et
al. 1990, Price 1991). While stressing the need
for theory maturation in ecology, Loehle
I
(1987) stated, "The vagueness of much theory in ecology makes it difficult to derive
explicit hypotheses or predictions." Creating
mathematical formulations is one step in theory maturation, bl.:tentomologists should be
aware that a concept is more than a mathematical equation or formula (McIntosh 1985).
They also should realize that vague definitions of variables or vague concepts have no
place in ecological theory (MacArthur 1972).
As Loehle (1987) and Peters (1988) point om,
variables in equations and terms in theories
must be operationally defined. For example,
general temporal and spatial scales must be
included in all theories if they are to be tested
in scientific studies or implemented in pest
management. Most population-dynamics
theories based on mathematical models lack
spatial scale and ignore temporal scale by
describing temporal equilibria.
As many ecologists, entomologists, and
modelers have done before him (Kingsland
1985), Berryman compares entomology to
physics. The mission to the moon was a very
simple problem primarily involving only three
objects: the moon, the Earth, and a spaceship. Although engineering the spaceship was
difficult, the overall physics of the Right was
simple, as are most traditional problems in
physics (Smarr 1985, Onstad 1988). When
astrophysicists tackle a more complex system
such as the universe, they must work with
large numerical models (Smarr 1985). For example, many astrophysicists have decided
that, because their models and theories based
on observed matter cannot explain the temporal and spatial dynamics of stars within
galaxies, up to 90 percent of the universe
must consist of dark matter that cannot be
directly observed (Horgan 1990). This dark
matter exists, they say, but they do not know
what it is or how much exists. One result of
this confusion is that the theorists must insert
their simple physical theories into larger and
Good Theories and Premature Models
Alan A. Berryman
T
NHE FALL 1991 issue of the American
Entomologist (Berryman 1991a), I argued
that simple theoretical models with parameter values estimated from real data generally will have greater practical utility in
management situations because they are
cheaper to build, easier to understand and
operate, and often more accurate than large
biologically explicit models. David Onstad
disagrees, arguing that population dynamics
theory is too immature, vague, and ill-defined
to provide a sound conceptual framework
for building predictive models.
Onstad's main contention, that population
dynamics theory is immature, is a matter of
opinion rather than fact. Population dynamics theory originated in the 1930s with the
pioneering work of Lotka, Volterra, Pearl,
and Thompson (an entomologist), among
others. It then temporarily got bogged down
in the acrimonious debate between the entomologists Nicholson and Andrewartha, and
I
202
their adherents, over the theory of density
dependence. Disenchanted with this confusion, other entomologists began initiating
long-term intensive field studies on the population dynamics of several important insect
pests (some familiar names are Morris, Stark,
Madden, Geri, Holling, Varley, Baltensweiler, Isaev, Klomp; see Berryman 1988 for reviews of some of the insect populations studied). At the same time, mathematical ecology
was being consolidated and publicized (Pielou 1969, May 1973); ideas from general systems theory, nonlinear dynamics, and control
theory were penetrating ecological thought
(Milsum 1968, Berryman 1981, DeAngelis et
al. 1986); and powerful analytical tools were
being applied to ecological problems (May
1973, Royama 1977, 1981, Svirezhev & Logofet 1983, Berryman & Millstein 1990, Turchin 1990). Out of these developments has
emerged a synthetic theory of single-species
population dynam,ics that seems to account
for the accumulated empirical data (Isaev &
Khlebopros 1977, Berryman 1987, Berryman
et al. 1987). Therefore, in my mind and probably in many of those mentioned above, population dynamics theory has grown up and
matured in the last two decades, and is now
up to the task of describing and explaining
the complex dynamics observed in real populations.
Onstad goes on to claim that population
dynamics theory is vague and ill-defined. Yet
in my previous article I explicitly presented
the general synthetic theory of single-species
population dynamics as a simple mathematical generalization of Verhulst's "logistic"
equation. This interpretation may be wrong
(although Onstad does not claim this) but it
certainly is not vague or ill-defined! In the
end, a theory must stand or fall on the logic
of its underlying assumptions and derivation,
and also must weather the assaults of empirical evidence. When it fails, the theory
AMERICAN ENTOMOLOGIST
more complex models in anempts to match
what lin]e they do observe (Horgan 1990).
Thus, ecologists and entomologists
should
not justify the use of simple models by referring to physics. Furthermore, are we bold
enough to support our immature hypotheses
about population
dynamics
by claiming
unobserved organisms are influencing each
system?
Most of my arguments in support of large
theoretical models and my criticisms of small
analytical models have been published elsewhere (Onstad 1988). Berryman's criticisms
of detailed models were not and cannot be
supported by current evidence. If ecological
models are expensive and time consuming,
so are astrophysical models and the models
used by engineers to build spaceships. Onstad
(1988) directly questioned the heuristic qualities of small ana]ytical models. For instance,
when an age-structured population is distributed heterogeneously in space, how heuristic
is a model that ignores these characteristics?
Berryman claims that parsimony is important. The limits of parsimony and the
challenge of realism were acknowledged
by
MacArthur (1972), who concluded that more
complexity would be needed in models to
study spatia] and temporal variability. Onstad
and Maddox (1990) and Onstad et al. (1990)
have discovered that hypotheses about insect
population
dynamics that fail to consider
chronic diseases or spatia] dynamics may be
inadequate for prediction. Diseases, insect
movement and spatial heterogeneity may not
be important in Berryman's forest communities, but they are important in many other
systems.
For management purposes, the size of the
model should be independent of theory but
dependent on the quality of the calibration
and validarion data. As the quality and appropriateness of the data increase, so do the
options availab]e for mode] building. Certainly, the costs of model development and
computation should be weighed against the
need for realism, but the balance of these
two factors is different for each project. If a
simple model can provide 50 percent greater
efficiency in pest management over the short
term compared to traditional approaches,
then perhaps a simple model should be implemented and a separate decision be made
about creating a more realistic model for the
long term.
I support the effort to use appropriate
models based on ecology, and Berryman does
a good job of this. However, I believe that
he demonstrates
only that a good modeler
can use simple models to investigate specific
problems. He did not provide evidence that
his models are more theoretical than larger
models. In fact, his approach appears to be
a hybrid of empirical and "theoretical" modeling. He logically considers a few equations
and then fits the equations to field data. Pure
statistical modelers would choose equations
with the best fit no maner what their form.
This commentary should not be used as
an excuse to avoid logic, eco]ogical knowledge, and hard work in model development.
Ultimate]y, good modelers will make good
models if they have good data. Some modelers may be better at creating managementoriented models, whereas others may be more
prepared to investigate theory. At times,
however, good modelers also may make a
few unsatisfactory models, especially when
models and decisions must be based on equal
parts of good data, inappropriate or unreliable data, and vague theories.
0
should be replaced by a new one or a modification of the old one. Onstad offers us no
factual or logical evidence to abandon the
synthetic theory of population dynamics, nor
does he provide us with an alternative (better)
theory. Thus, I find no compelling reason to
abandon my contention that contemporary
population dynamics theory offers a firm conceptual foundation for building single-species population dynamics models.
And so to the question of detailed versus
simple models and their usefulness in practice. Holling et al. (1977) listed ten fables and
counterfables about systems models and their
application to management situations. I repeat just two of them:
Fable 2. A complex system must be described by a complex model in order to respond to complex policies.
Counterfable 2. A simple but well-understood model is the best interface between a
complex system and a complex range of policies.
Fable 5. The descriptive phase of applied
systems analysis ends with the systems mod-
complex models are premature and should
be boiled down to their essentials before they
are used for management purposes.
I agree with Onstad that the value (usefulness) of management
models must be
judged by the accuracy of their predictions
and the costs of their development (I'm not
sure how one judges the "quality of validation data"). I also would include the cost of
collecting data to initialize the model and the
cost of running it. Obviously, large, detailed
models stack up poorly in the cost department! So the justification for building detailed management models must be that their
predictions are much more accurate than
simple models. But this generally does not
seem to be true for reasons stated in my
article (where I actually gave examples of
large expensive models that are much less
useful for prediction than cheap theoretical
models). Onstad presents no hard evidence
to force me to reconsider this position.
Finally, I would like to draw anention to
a new approach (or more correctly, to the
revival of a old one) in applied ecology. There
are two basic ways to model insect populations. The first and most commonly employed is to construct a model from known
information or assumptions about the biology or ecology, or both, of the species in
question and then to check (validate?) the
model by comparing its output to observed
data. Let us call this the a priori approach
because the model is built before the population data are used. The problem with the
a priori approach is that validation virtually
is impossible because all reasonable population models can be "tuned" (by changing
their parameter values) to produce any behavior one desires; stable points, periodic cycles or even seemingly random chaos. Although the modeler may insist that the model
was not tuned to get the desired behavior, a
lurking suspicion must always remain in the
mind of the user.
The second approach can be called a posteriori or diagnostic. Here the modeler analyzes the data using statistical procedures
like time-series analysis, in an attempt to diagnose the underlying causal process(es) and
to build predictive models (Royama 1977,
1981, Berryman & Millstein 1990, Turchin
1990). This is the approach I advocated in
my article, with the added proviso that the
underlying model should have a sound theoretical structure, an ecological rather than
statistical theory, because we are building an
ecological model. The a posteriori approach
treats data as symptoms of some underlying
ecological process(es) that can be described
by a theoretical model. The trick is to deduce
which of the many possible processes are the
el.
Counterfable 5. The descriptive phase of
applied systems analysis does not end until
the model has been simplified for understanding.
Hence, according to Holling et al. (1977),
Winter 1991
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Price, P. W. 1991. Darwinian methodology and
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Once this has been done, the data can be fit
by statistical procedures to the correct theoretical model.
The problem with a posteriori analysis is
that diagnosis is always, to a certain extent,
subjective and dependent on the experience
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diagnostic tests (the available statistical methods). The same can be said for medical diagnosis, and the answer is to seek a second
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article: I do not denigrate the large behavioral, spatially defined, supercomputer
models that Onstad loves so much, but merely
try to put them in their right place. They will
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David W. Onstad is associate professor
of Agricultural Entomology at the University
of Illinois and Illinois Natural History Survey and research professor at the National
Center for Supercomputing Applications,
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Alan A. Berryman is professor of entomology and Natural Resource Sciences,
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AMERICAN ENTOMOLOGIST