Theor Ecol (2012) 5:433–444
DOI 10.1007/s12080-011-0134-0
ORIGINAL PAPER
Mechanistic analogy: how microcosms explain nature
John M. Drake & Andrew M. Kramer
Received: 15 March 2011 / Accepted: 12 July 2011 / Published online: 4 August 2011
# Springer Science+Business Media B.V. 2011
Abstract Microcosm studies of ecological processes
have been criticized for being unrealistic. However, since
lack of realism is inherent to all experimental science, if
lack of realism invalidates microcosm models of ecological processes, then such lack of realism must either also
invalidate much of the rest of experimental ecology or its
force with respect to microcosm studies must derive from
some other limitation of microcosm apparatus. We
believe that the logic of the microcosm program for
ecological research has been misunderstood. Here, we
respond to the criticism that microcosm studies play at
most a heuristic role in ecology with a new account of
scientific experimentation developed specifically with
ecology and other environmental sciences in mind.
Central to our account are the concepts of model-based
reasoning and analogical inference. We find that microcosm studies are sound when they serve as models for
nature and when certain properties, referred to as the
essential properties, are in positive analogy. By extension, our account also justifies numerous other kinds of
ecological experimentation. These results are important
because reliable causal accounts of ecological processes
are necessary for sound application of ecological theory
to conservation and environmental science. A severe
sensitivity to reliable representation of causes is the chief
virtue of the microcosm approach.
Keywords Microcosm . Mechanism . Analogy . Inference .
Daphnia
J. M. Drake (*) : A. M. Kramer
Odum School of Ecology, University of Georgia,
Athens, GA 30602-2202, USA
e-mail: [email protected]
Introduction
Ecological microcosms are miniature constructed ecosystems in which physical and biological constraints are
imposed to enable the controlled study of ecological
processes. The use of microcosms in ecological research
has been criticized for a variety of reasons (King 1980;
Carpenter 1996; Schindler 1998; Carpenter 1999) and
rebuttals have been mounted by a number of groups (Fraser
and Keddy 1997; Morin 1998; Lawler 1998; Drenner and
Mazumder 1999; Huston 1999; Cadotte et al. 2005; Benton
et al. 2007). While the rebuttals have largely consisted of
empirical and practical arguments, we focus on the logic
that enables one to use microcosms to understand ecological phenomena. Whereas most writings in this genre are
focused on if microcosms can tell us something about
nature, we explore how microcosms tell us about nature.
Our thesis has three parts:
1. That microcosms enable one to explore the processes
by which nature can work;
2. That this is part of a mechanistic program in science;
and
3. That this mechanistic program is key to an understanding of nature that supports counterfactual predictions or
subjunctive conditional assertions, i.e., conditional
statements of the form “if it were the case that X, then
it would be the case that Y”, indicating what would be
the case if the antecedent X were true. Typically, we will
think of X as some unobserved state of nature, perhaps
one that has not ever been realized, but might be in the
future.
To start, we clarify these three claims. First, concerning
(1), we point out that this is an explicitly modal claim,
where the modality of possibility (implied by the auxiliary
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verb can) is the weakest of the three modalities (possibility,
probability, necessity). That is, microcosms tell one how
nature can work, not how it frequently works nor how it
must work. Further, what we mean when we say that nature
can work in such and such a way is contextualized to the
real world. That is, microcosms go beyond showing what is
merely logically possible (this can be done with a
mathematical model) to show what is possible in the real
world, complete with all its known and unknown constraints. Second, concerning (2), we mean that the aims of
microcosm research are to elucidate specific classes of
interactions that together, in some context, give rise to a
phenomenon (Glennan 1996; Machamer et al. 2000). This
is a kind of weak reductionism, which we think is important
if ecological research is to be successfully applied, for
instance to conservation. Notably, this kind of science goes
beyond statistical generalizations (Hempel 1965; Peters
1991; Werner 1998). Finally, in (3) when we claim that this
mechanistic program is key to an understanding of nature
that supports counterfactual predictions, we mean that it is
impossible to say what might happen under some future
conditions if we do not first know what possibilities there
are in nature (1) and how these possibilities may manifest
as some phenomenon in a new context (2). We note
specifically that this is a counterfactual aim, not a simple
material conditional “if X, then Y” because the material
conditional is true in the case that the antecedent X is false.
In phrasing our thesis in this way, we are aiming to indicate
what we believe to be its generality. Concretely, we are
saying that if we do not know what mechanisms can be at
work in population dynamics (e.g., Allee effects, demographic stochasticity) or how those mechanisms interact to
give rise to some set of phenomena (e.g., fluctuations of a
certain variance or autocorrelation), then we will be at a
loss to predict how extinction risk will change as habitats
are fragmented, sea level rises, atmospheric CO2 increases
in concentration, or actions are taken to conserve species.
All of these are material antecedents that are anticipated but
have not yet been observed in nature in a way that allows
inferences to be made from statistical characterization.
In our research, we use microcosms to understand the
process of population extinction. Our goal in this paper is to
spell out the logic of this research program. The scientific
soul searching that gave rise to the arguments advanced
here was motivated by skepticism on the part of many
ecologists concerning what can be learned about nature
from microcosm studies. In our experience, the overarching
cause for this skepticism is that microcosms are not
realistic. This, of itself, is a slightly curious criticism, since
most scientific apparatus pokes and prods nature under
conditions that are not realistic. Viruses replicate in all
kinds of animal tissues, but African green monkey kidney
cells have become standard to measure replication rates
Theor Ecol (2012) 5:433–444
under alternative pharmaceutical manipulations. Counterexamples such as this blunt, but do not remove, the force of
the critique. To understand how we learn about nature from
microcosms, we undertook first to try and understand why
the nonrealism critique is so compelling.
Critics argue that the lack of realism in microcosms
limits their scope of application, resulting in studies that can
be “irrelevant and diversionary”, “a very indirect way of
learning” (Carpenter 1996), and/or “often yield erroneous
conclusions” (Schindler 1998). A survey of the ecological
literature yielded three broad ways in which microcosm
studies are commonly perceived to be unrealistic (Lawton
1996; Jessup et al. 2004; Cadotte et al. 2005):
Criticism 1: Microcosms are ecologically simplistic.
One of the most obvious simplifications in microcosms
is the subset of species included. This arises from both
the goals of tractability and control and the exclusion of
large-bodied species from small enclosures (Schindler
1998). A view common to many criticisms is that
because properties of natural systems can arise from
their complexity, a reduction in complexity from the full
ecosystem eliminates the capacity of an experiment to
provide reliable predictions about the ecosystem for
which it is a model. Carpenter (1996) and Schindler
(1998) call attention to failed attempts to extrapolate
from the results of aquatic microcosm experiments to
lakes and attribute this to the absence in microcosms of
important features of natural systems such as the water–
sediment interface and wind-driven mixing.
Criticism 2: Because of their small size and short
duration, microcosms do not exhibit natural quantities
of spatial and temporal variation. We mean to include
in this category both temporal changes (e.g., diurnal
and seasonal periodicities, environmental stochasticity)
and physical heterogeneity. The small size of microcosms substantially limits physical environmental
heterogeneity to characteristic scales smaller than the
extent of the microcosm and excludes processes
occurring at large spatial extents altogether, such as
migration (Diamond 1986; Ricklefs 2004). The lack of
environmental variation in controlled microcosms is
also perceived to be a weakness, since natural
ecosystems generally undergo variable conditions
(Bulling et al. 2006). Similarly, because microcosm
experiments typically last less than a year (Diamond
1986; Ricklefs 2004), the time scales over which
observations are made are considered to be short
relative to the intervals over which natural phenomena
are exhibited. The use of mesocosms, essentially larger
microcosms exposed to more environmental variation,
often has the goal of partially including these sources
of variation (e.g., Relyea 2005).
Theor Ecol (2012) 5:433–444
Criticism 3: The microcosm apparatus gives rise to
artifacts. For instance, some critics argue that findings
from microcosms are dominated by their construction
(e.g., edge effects; Schindler 1998) or inhabitants
(which may be highly domesticated or otherwise
unique in their affinity for microcosms; Lawton 1996)
and primarily provide information only about these
idiosyncrasies (King 1980; Schindler 1998). Carpenter (1996) sees “cognitive danger that the microcosm
(rather than the ecological system) will become the
object of study.”
Broadly speaking, these criticisms comprise the argument that, because microcosms are simple, they are
insufficiently generalizable and therefore inapplicable to
understanding other, less simple parts of nature (Carpenter
1996; Schindler 1998), except in a “supportive and
heuristic” role (Carpenter 1996). At an equally broad level,
our counter argument is that the generality we seek in
microcosm studies comes not from some statistical relationship between microcosm and nature (“scaling up”), but
through the identification of ecological mechanisms and
qualitative and quantitative determination of the phenomena
such mechanisms give rise to. Indeed, field experiments and
microcosm studies share the conceit that often their objective
is to identify generalities that apply more generally than to the
particular actors under study. That is, both field experiments
and microcosm studies are performed in the hope of
extrapolation.
We observe, moreover, that lack of realism is not limited
to ecological microcosms, but is an attribute, at some level,
of all scientific experiments, even field experiments and
whole ecosystem manipulations (Crowder et al. 1988; Fee
and Hecky 1992; Beier and Rasmussen 1994; Werner
1998). Thus, realism is not a binary true/false attribute of
a study, but a matter of degree (Morin 1998). Indeed, in the
biological sciences, virtually all major research programs
have some version of in vitro experimentation, i.e.,
experimentation under highly constructed and artificial
conditions. Further, experimentation works. Experimentation gives rise to deeper understanding of nature. Thus, we
are led to ask how it is that experimentation works to
establish theories when the objects of manipulation in
experiments are clearly not realistic representations of
nature’s counterparts? To further underscore the lack of
realism that can be tolerated (when a mechanistic understanding of nature is the goal), we consider briefly a famous
piece of scientific apparatus, the cloud chamber, and then
go on to consider the logic that underwrites the use of
apparatus in science in general.
The cloud chamber is a device that was invented by
Charles Thomas Rees Wilson in 1911 to study cloud
formation (DasGupta and Ghosh 1946). Subsequently,
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cloud chambers became famous as an instrument for
visualizing ionizing radiation and detecting the presence
of theoretical particles. Cloud chambers (and their descendants, diffusion chambers, bubble chambers, wire chambers,
and spark chambers) are favorite devices of historians and
philosophers of science, at least partly because they are the
archetype of a scientific instrument insofar as they provide
the material trace of unobservable objects or processes
(when water vapor condenses on the resulting ions, leaving
a trail). Like microcosms, cloud chambers create in the
laboratory a set of conditions that are not anywhere realized
in nature. Nonetheless, because the phenomena they exhibit
may be related to processes and entities in nature via a
causal theory, they are taken to provide evidence for those
theories as applied to nature. Cloud chambers, of course,
are not unique as scientific objects that create conditions
not realized in nature. Super cool Bose–Einstein condensates, high energy plasma soup, and transgenic mice are
other examples. Indeed, in all these cases it is precisely
because they are non-natural constructions that scientists
are able to use them to test their theories.
A logic for microcosm research: measurement
and demonstration
A deeper appreciation of the importance of non-realism in
science can be obtained by considering the various ends to
which scientific apparatus is put. We will make a distinction
between apparatus used as instruments and apparatus used
as models. The distinction is determined by the goals of a
scientific study. Here, we are concerned with goals as
candidate intellectual outcomes that are envisioned when
the study is designed.
Outcome 1. A piece of apparatus (i.e., a microcosm)
enables the measurement of a quantity in
nature.
An example of such a measurement is decline in somatic
growth rate of prey in the presence of predators. Numerous
observations suggest that prey increase their predator
avoidance behaviors in the presence of predators even if
encounters are not typically lethal (reviewed in Werner and
Peacor 2003; Cresswell 2008). For zooplankton, limnological theory predicts that this change of behavior will result
in modified patterns of vertical migration, which in turn
expose animals to time-averaged temperature regimes that
are colder, reducing individual growth. The standard
method for quantifying this reduction in growth is to
expose laboratory animals to different concentrations of
kairomones (waterborne chemicals produced by predators)
and to calculate the difference in average growth across the
gradient (e.g., Loose and Dawidowicz 1994; Pangle and
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Theor Ecol (2012) 5:433–444
60
50
40
30
20
10
0
Fig. 1 Observed differences in
specific growth rate of Daphnia
mendotae. D. mendotae in
microcosms containing predator
(Bythotrephes longimanus) kairomone grew slower than in
controls (modified from Pangle
and Peacor 2006)
Specific growth rate (% d−1)
For an example of such a demonstration, we turn to our
own experimental observation of a predation-induced Allee
effect in a model Daphnia–Chaoborus system. It has
recently been observed that predators with a saturating
functional response (i.e., Holling type II response) can,
under conditions elaborated by Kramer and Drake (2010),
give rise to an unstable equilibrium in the prey population
density. Observationally, such a phenomenon meets the
demographic definition of an Allee effect—a critical
population size below which population decline accelerates
to extinction—and has therefore come to be called a
“predation-induced Allee effect” (Gascoigne and
Lipcius 2004). Since the mechanism is different than that
envisioned by the classical theory of Allee effects, it has
been suggested that this be considered a new class of
phenomena. To empirically demonstrate the predator-driven
Allee effect, we set up experimental conditions which were
minimally restrictive but aimed to induce the phenomenon
(Kramer and Drake 2010; Fig. 2). Of course, the theory is
deterministic and real populations exhibit demographic
fluctuations. Therefore, we developed a model extending
the theory to include the conditions exhibited in the
experiment, which ultimately showed evidence that the
predator–prey interaction did indeed affect extinction rate in
the hypothesized way. The point is that the development of
some auxiliary theory (i.e., the addition of fluctuations due
to demographic stochasticity) enabled the separation of
artifacts due to the small size of the microcosm and the
demonstration of the predator-driven Allee effect that is
predicted to occur in all populations that exhibit the
Control
Bytho.
Per capita growth rate (r)
4
2
0
−2
−4
−6
b) 120
Extinction time (days)
Outcome 2. A piece of apparatus (i.e., a microcosm)
enables the demonstration of a class of
phenomena.
a)
c)
Proportion extinct (day 99)
Peacor 2006). When the goal of this procedure is to
quantify the effects of predators on zooplankton production
in nature, this procedure provides a measurement, as when
Pangle and Peacor (2006) investigated the effect of the
invasive predatory cladoceran Bythotrephes longimanus on
the native herbivorous cladoceran Daphnia mendotae
(Fig. 1).
By contrast,
100
80
60
40
20
0
1.0
Predator
No predator
Population
Mean
0.8
0.6
0.4
0.2
0.0
0
10
20
30
40
50
60
Initial population size
Fig. 2 Microcosm populations of Daphnia magna exposed to Chaoborus predation (in red) exhibited an Allee effect. This is evident in the
positive density dependence of per capita growth rate (a) and the
sigmoidal distribution of extinction time (b) and probability (c; adapted
from Kramer and Drake 2010). These results constitute the first
mechanistic test of this phenomenon that had previously been proposed
to explain observation in natural populations (Wittmer et al. 2005)
appropriate antecedent conditions (i.e., saturating functional
response), even numerically large (but sparsely distributed)
populations in nature.
We underscore that the two outcomes of measurement
and demonstration are not accidental. They are not just two
instances of many possible uses of microcosms. Rather,
they are central to the way that empirical investigations
inform us about nature. This centrality is reinforced by
observing the different ways we refer to apparatus in
practice. Following Harré (2003), we make these distinctions more precise by using the word instrument to refer to
apparatus when it is used to obtain measurements, and the
word model to refer to apparatus when it is used for
demonstration. The main difference between our view and
that of Harré is that we do not think that whether a
Theor Ecol (2012) 5:433–444
particular piece of equipment is an instrument or a model
depends on what it is, but what it is used for, in any
particular instance.
Why does the distinction matter? Because different kinds
of realism are needed to derive correct conclusions about
nature, depending on whether the apparatus (microcosm) is
used as an instrument or as a model. Neither critics nor
advocates of microcosm research have distinguished these
uses. Defenses of the microcosm approach have argued that
because of their unrealism (i.e., simplicity), microcosms are
indispensable for testing ecological theory (Morin 1998;
Lawler 1998). We think the critics have sometimes
misunderstood this point because they considered microcosms to be used as instruments. In what follows, we
extend and clarify these arguments by exploring what kinds
of realism must hold for a microcosm to be useful as a
model. In our view, the justification for the use of
microcosms as instruments is considerably trickier and we
defer consideration of microcosms as instruments to a
future analysis.
Microcosms and model-based reasoning
We start by observing that drawing inferences from microcosms (when used as models) requires using what cognitive
scientist Nancy Nersessian (2008) calls model-based reasoning. Model-based reasoning refers to the construction
and manipulation of qualitative, quantitative, and/or simulative representations of nature, a class which should be
construed to include diagrams, mathematical expressions,
physical constructions, and virtual systems simulated on
computers. In our view, model-based reasoning works
together with the hypothetico-deductive model of scientific
reasoning popularized by Karl Popper (1963), for instance
in our experiment on predation-induced Allee effects,
where a stochastic population growth model (a mathematical representation, solved by simulation on a computer)
was studied to deduce consequences of the hypothesized
interaction when instantiated in a stochastic context (a
physical–biological model—a population of Daphnia in a
microcosm). Even together, model-based reasoning and
hypothetico-deductive reasoning do not exhaust the kinds of
scientific reasoning, but these are enough to elucidate the
reasoning process when applied to microcosms and to answer
our central question, “How do microcosms explain nature?”.
One of the chief virtues of model-based reasoning is that
the criteria for evaluation of scientific theories are more like
those used in actual scientific practice than the confirmation/falsification dichotomy of Popper and his predecessors.
For instance, models can identify fruitful directions for
further investigation. Further, and again true-to-practice,
model-based reasoning supposes that the objects scientists
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deal with on a regular basis are more often models than
networks of syllogisms and propositions. Regardless of how
much or little deduction from theory is used in the prediction
of the outcomes of microcosm experiments, the application of
any findings in microcosm studies is clearly also an exercise
in model-based reasoning. A key difference between
hypothetico-deductive reasoning and model-based reasoning
is a change from purely deductive/inductive reasoning to
reasoning by analogy. Specifically, model-based reasoning
supposes that some phenomenon or process that may be
directly inspected in the model is within the model as its
counterpart is in nature. In microcosm experiments, we
presume that the (typically quantifiable) biological property
or process in the microcosm is to the microcosm system as its
counterpart is to the ecosystem. Representing such properties
with variables X and Y, we express this in terms of the
fundamental analogical premise:
Fundamental analogical premise :
X in microcosm
Y in microcosm
::
X in nature
Y in nature
To understand inferences about nature derived from
microcosm studies, it will aid us to understand a bit more
about analogical reasoning in science in general.
Model-based reasoning is analogical reasoning
In trying to determine how analogical reasoning in science
works, we are in the fortunate position that this question
has been studied at relative length. Important for understanding the validity of analogical arguments is the
trichotomy of positive analogies, negative analogies, and
neutral analogies first developed by Mary Hesse in Models
and Analogies in Science (Hesse 1966). In our consideration of microcosm studies, the analogy will almost always
be between the microcosm system (sometimes called the
source in analogical analysis) and nature (the target, using
the analogical terminology; more precisely, some system in
nature that is an instance of the class of systems to which
the theory we are testing is intended to apply). As we read it,
the trichotomy concerns not just the relation between the two
analogs, but also the state of our understanding of the analogy.
Every analogy consists of three parts: positive analogies,
which are properties known to be held in common between
the two analogs; negative analogies, which are properties
known not to be held in common between the two analogs;
and neutral analogies, for which the true relation is unknown.
According to Hesse, the neutral analogies are the crucial
ones:
The important thing about this kind of model-thinking
in science is that there will generally be some
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Theor Ecol (2012) 5:433–444
properties of the model about which we do not yet
know whether they are positive or negative analogies;
these are the interesting properties, because, as I shall
argue, they allow us to make new predictions. Let us
call this third set of properties the neutral analogy. If
gases are really like collections of billiard balls,
except in regard to the known negative analogy, then
from our knowledge of the mechanics of billiard balls
we may be able to make new predictions about the
expected behavior of gases. Of course, the predictions
may be wrong, but then we shall be led to conclude
that we have the wrong model. (p. 8–9)
In what follows, we will see that the neutral analogies
are also the crucial ones when it comes to properly making
inferences from microcosm studies in ecology. But, first, we
must understand better the properties of an analogical
argument.
Valid analogical arguments depend on causal relations
On the basis of this conceptual framework for understanding analogies, Hesse is in a good position to tackle her main
question, “When is an argument from analogy valid?” For,
of course, there are many analogical arguments that are not
valid, at least not with respect to science. Not surprisingly,
it turns out that the role of causality is one key difference
between (scientifically) valid analogical arguments and
(scientifically) nonvalid analogical arguments. Equally
important, however, is that the assumption about causality
is not strong. According to Hesse, “The use of analogical
argument presupposes a stronger causal relation than mere
co-occurrence, … but it does not presuppose that the actual
causal relation is known” (Hesse 1966, p. 84).
How, then, does causality enter the construction of valid
analogies? Hesse suggests that we view an analogy
according to a table of properties. Consider the following
analogy concerning two familiar scientific objects, the earth
and the moon (modified from Hesse, page 59).
Property
Earth
Moon
Shape
Atmosphere
Life
Spherical
Present
Present
Spherical
Absent
?
Evidently, there is a positive analogy with respect to shape
and a negative analogy with respect to atmosphere. At one time,
anyway, whether or not there was life on the moon was a neutral
analogy, which could be addressed by considering the known
positive and negative analogies and reasoning accordingly.
What is important about this table is that it signifies two kinds
of relations. First, each line of this table represents some
property, which we can recognize as belonging to each analog.
These horizontal relations represent instances of identity or
difference, or, more generally, similarity. Second, each column
of the table contains the vertical relations, the collection of
properties together with their various causal relations. Because
we believe (possibly incorrectly) on the basis of our
experience of life on earth that an atmosphere is necessary
for life, we may conclude that there is no life on the moon.
For concreteness, the following table depicts another
analogy, represented by some of its positive and negative
components, that might hold for some ecological microcosm studies, where the population of zooplankton in a
microcosm is an analogy for a population of zooplankton in
a natural aquatic ecosystem (e.g., Drake and Griffen 2010;
Griffen and Drake 2008, 2009).
Property
Reproductive
mode
Open/Closed
Competitive
species
Food supply
Habitat
boundaries
Habitat size
Carrying
capacity
Microcosm
Asexual
Natural population
Asexual
Closed
Absent
Closed
Present
ad libitum (0.1 g C d-1)
Plexiglass
Abundant (1.0 g C d-1)
Sediment/Air
Small
Small
Small
?
In this case, the microcosm is not a realistic model of the
natural population because although some properties are
identical (both populations are of asexually reproducing
organisms), other properties are different (presence of
competitors) and some properties are only similar (food
supply is not identical but is similar in another sense,
namely that in both cases all organisms are expected to be
satiated; habitat size is small). Thus, the model comprises a
mix of positive analogies (reproductive mode, openness to
immigration, and habitat size), negative analogies (presence
of competitive species, habitat boundaries), and one neutral
analogy (carrying capacity). Importantly, these are just the
kind of negative analogies that critics of microcosm
research in ecology advance as being devastating to the
microcosm program of research.
As above with the earth/moon example, population
ecologists will recognize within the columns (the vertical
relations in Hesse’s terminology) causal relations implied
by well-established theories. Not all relations are causal,
however, particularly with respect to the neutral analogy of
carrying capacity. These relations, together with the aid of
some causal theories, enable one to reason analogically. For
concreteness, consider the following example.
Theor Ecol (2012) 5:433–444
439
First, we define a few propositions, which may be true or
false:
A Habitat size determines carrying capacity
B Food supply determines carrying capacity
C Food supply is limiting
D Habitat size is small
Next, we assert the following premises based on our
causal theory:
Causal Premise I (CP-I): Habitat size determines
carrying capacity or food supply determines carrying
capacity ðA _ BÞ
Causal Premise II (CP-II): Food supply determines
carrying capacity if and only if food supply is limiting
(B↔C)
Empirical Premise I (EP-I): Food supply is abundant in
microcosm populations ð:C Þ
Empirical Premise II (EP-II): Food supply is abundant
in natural populations ð:C Þ
Empirical Premise III (EP-III): Carrying capacity is
small in microcosm populations (D)
Finally, we sketch an outline of a proof (since our purpose
is illustrative, we combine some steps and quantification, over
microcosm and natural systems, is understood implicitly) (See
Table 1).
By deduction, we conclude that two important positive
analogies hold (steps 3 and 5): that food supply does not
determine carrying capacity in microcosm populations or
natural populations and that habitat size determines carrying capacity in both. We further confirm that within the
scope of our knowledge there are no remaining causal
negative analogies and proceed to the analogical step.
Expressing our inference in terms of the fundamental
analogical premise, underwritten by the table of positive,
negative, and neutral analogies above,
Habitat size in microcosm
Carrying capacity in microcosm
::
Habitat size in nature
Carrying capacity in nature
to which we add the EP-III that carrying capacity is small in
microcosm populations, we conclude (by analogy) that
carrying capacity in nature will be small.
Obviously, this reasoning is not fool proof (it is not
deductive). For instance, it involves a premise that cannot be
absolutely confirmed (CP-I), and thus step 2 might be viewed
as an instance of abductive inference, i.e., inference to the best
explanation, with its known problems (i.e., committing the
fallacy of affirming the consequent). Further, just because we
do not know them does not mean we can rule out absolutely
the existence of important negative analogies. It is for these
reasons, in our view, that a research program based on
analogical model-based reasoning cannot be divorced from
either field trials or hypothetico-deductive reasoning (perhaps
to bring to light negative analogies that have not yet been
considered). Nonetheless, it appears that our analogy is valid
so far as it goes.
How far does it go? The answer is that it depends on how
accurate our causal theory is. Particularly, we notice that
because some of the properties of the model do not enter our
causal theory (e.g., mode of reproduction, kind of habitat
boundaries), not all properties must be similar for an analogical
argument to be valid. But surely some properties must exhibit
positive analogy. Which properties are these? In the theory of
analogical reasoning, these are referred to as the essential
properties. A critical issue is how to identify which properties
are essential and which are not. Here, there is a central role
for theory. For instance, in the theory of population
extinction, the intrinsic rate of increase figures prominently
in the causal conditions envisioned by the theory to be
important (e.g., Lande and Orzack 1988). We therefore
suspect that it belongs to the class of essential properties.
By contrast, we do not expect the kind of habitat boundary to
have an effect on the carrying capacity and this difference
may be ignored. We may be wrong about this, but that is a
deficit of our theory, not of the model system in virtue of its
ability to test the theory. Of course, a final determination
about this property must be made empirically but this is one
of the aims of analogical reasoning—to arrive at predictions
about nature that can be tested empirically there. Further, if
there are good reasons to believe that the causal relations
holding in the microcosm would not hold in nature, then the
analogy would not be valid. Thus, analogical reasoning is of
use particularly in situations where our knowledge of the
Table 1
Step
1
2
3
4
5
Statement
Food supply determines carrying capacity if and only if food supply
is limiting
Food supply is abundant in microcosm and natural populations
Food supply does not determine carrying capacity in microcosm
populations or natural populations (establishing positive analogy)
Habitat size determines carrying capacity or food supply determines
carrying capacity
Habitat size determines carrying capacity
Formula
(B↔C)
Reason
Causal premise (CP-II)
ð:C Þ
ðB $ C Þ ^ :C ! :B
Empirical premise (EP-I/EP-II)
From (1) and (2) by biconditional
elimination and modus tollens
Causal premise (CP-I)
A_B
ðA _ BÞ ^ :B ! A
From (3) and (4) by disjunctive
syllogism
440
Theor Ecol (2012) 5:433–444
causal processes at work in the target is so incomplete that we
cannot reason from our information in that context alone.
Unsurprisingly, there are some subtleties to determining
which are the essential properties when reasoning about
microcosms. Recalling that microcosms are models (in Harré’s
sense), we note that while not all analogies are models (in the
material sense that microcosms are), all models presuppose
analogies. Special considerations apply to what Hesse calls
“analog machines”, objects that have been constructed to
simulate the behavior of the target. Microcosms are prime
examples of such analog machines. The potentially tricky part
in considering analog machines is that it may be unclear when
it is the material constituents of the machine that must be in
positive analogy (i.e., the material of the habitat boundaries)
or the mutual relations of the parts (i.e., the relation between
food supply and successful reproduction). The determination
depends not on the thing itself, but the theory for which it is a
model system. In such cases, where we are interested in the
mutual relations of the parts, we allow for material negative
analogies because the material substance is not essential. By
contrast, it is expected that the laws of behavior, i.e.,
biological processes such as the kinetics of predators and
prey, consist of neutral and positive analogies only. This point
can be brought out by examining an important difference
between microcosms (at least as we use them, as models) and
cloud chambers. Cloud chambers are used to establish the
existence of a class of objects. Microcosms, by contrast,
establish the conditions under which a class of processes can
occur. Objects and processes are, of course, very different.
Objects are things while processes are things in motion, or
things transformed. In population ecology, our interest
typically is in the class of behaviors exhibited by such things
in motion, that is dynamics. Thus, what is required is that the
mutual relations giving rise to population dynamics are
similar in microcosm and nature. Where they are not, the
microcosm will be a poor model.
In summary, then, there are two conditions for a material
analogy to be valid (modified from Hesse 1966, p. 87):
1. The horizontal relations between essential properties
are relations of similarity. In our zooplankton example,
we had that food supply was ad libitum in microcosm
and abundant in nature. Of course, a relation of identity
is the extreme case of similarity.
Analogy I:
Analogy II:
2. The vertical relations are causal relations in some
acceptable scientific sense, where there are no compelling a priori reasons for denying that causal relations of
the same kind may hold in the target. For us, the causal
relations are typically given by some theory.
How to use analogies in science
Supposing our view that microcosm studies may be
reasonably interpreted through the analogical inferences
afforded by model-based reasoning is accepted, it
remains still to establish the relative value of this
research program to conservation science. In our view,
microcosm studies complement and do not replace field
trials. We therefore do not need to prove that they are
always and in every way superior, only to show (1) how
they are useful in some respects and (2) that they meet
the same evidentiary criteria as other kinds of ecological
studies.
To establish these claims, we point out first that
analogical arguments are not unique to microcosm
studies. There are many ways that one can approach
the scientific question of extinction, for instance. Many
of these are analogical; none that we know of are
replicated experimental manipulations of populations of
threatened and endangered species in the field, both
because the logistic obstacles are insurmountable and
because such experiments would be viewed widely to
be unethical. To develop this example further, we note
that in standard presentations of extinction theory, the
extinction time is a random variable. Since it is difficult
to study the statistics of extinction time in nature, two
different approaches that have been taken are to study
the distributions of extinction time in microcosms
(Drake 2006; Drake and Griffen 2009) and the distributions of quasi-extinction time in nature, where quasiextinction times are the times a population declines to an
arbitrary threshold but not complete extirpation (Brook et
al. 2000; Fagan and Holmes 2006). Reasoning from quasiextinction to extinction is also analogical reasoning. The
only difference is that the source of the analogy is
different.
Distribution of extinction time Distribution of extinction time
::
Microcosm conditions
Conditions in nature
Distribution of quasiextinction time Distribution of extinction time
::
Conditions in nature
Conditions in nature
Theor Ecol (2012) 5:433–444
Thus, microcosm studies can have the same intellectual
standing as other forms of extinction study. Our point here is
not to make a definitive judgment about the value of either of
these analogies but to highlight that each is in fact an analogy.
We can take this argument further, however, and make an
additional positive case for microcosm studies in ecology.
Namely, since analogical reasoning is so deeply a part of
research of many (all?) kinds, it follows that combinations
of positive and negative analogies are similarly ubiquitous.
Such negative analogies are everywhere a vulnerability. In
this respect, however, microcosm studies are indeed
privileged because their simplicity and low cost means that
a wide variety of model systems can be constructed that
differ from each other in a variety of minor and major ways.
By manipulating permutations of these variations so that
they also differ in their positive and negative analogies, the
clever experimentalist can identify the essential properties
within a class of systems. For example, if the shape or
material of constructed habitats is shown not to have a large
effect on extinction across multiple microcosm systems,
this is warrant for supposing these properties to be
inessential. We note that in many cases the most concerning
neutral analogies will be the biological composition of
experimental models (species, genotypes, etc.). In our view,
this provides a strong rationale for devoting more effort to
the development of new model organisms, especially in
cases where there is scope to develop models from a suite
of closely related species differing from each other only
slightly in their properties and thereby in the collections of
positive and negative analogies that may be constructed
from them.
When analogical reasoning misleads
Analogical reasoning can also mislead, of course. To
responsibly use analogical reasoning to draw scientific
inferences therefore requires understanding the conditions
under which analogical reasoning fails. Curiously, it
appears that models in which the analogy is most suspect
may be the best for identifying the causal failures of theory.
Given the patent lack of realism in microcosm studies, it
follows that in some cases such experiments may actually
be especially suited to conservation practice. To illustrate,
we develop this counter-intuitive relation between model
and nature with an example.
We start with an ordinary scientific theory relevant to
conservation, the diffusion model for population dynamics
in a fluctuating environment (Richter-Dyn and Goel 1972).
A prediction of this theory is that the duration of the final
decline to extinction decreases with the intrinsic rate of
increase (Lande et al. 2003). This is, in principle, an
observable quantity and has in fact been quantified in
441
Drake and Griffen (2009) in an experimental Daphnia
system. We point out that it is a prediction that derives from
the causal theory, not an empirical generalization from
experience. To be specific, we can envision lots of
populations each with their own intrinsic rate of increase
and duration of final decline. We represent these two
quantities as an ordered pair (x, y). The theory predicts that
the rank-correlation of the vectors x and y will be positive,
in any system, either microcosm or natural.
Prior to the experiment (Drake and Griffen 2009), and
not knowing whether this theory would hold in the
microcosm system (much less in nature), one is presented
with the following set of possibilities. At this point, in
virtue of the theoretical prediction that the duration of final
decline decreases with intrinsic rate of increase, the relation
between microcosm and nature is a neutral analogy. There
are four possibilities:
Theory matches
microcosm
Theory does not match
microcosm
Theory matches
nature
A
Theory does not match
nature
B
C
D
If the unknown real relation between microcosm and
nature is either A or D, then we have a positive analogy
between microcosm and nature. Only if B or C holds do we
have a negative analogy. Before we perform the microcosm
experiment, we do not know which of these relations
between microcosm and nature holds. After we perform the
experiment, we are in a slightly better position because we
know that the theory either did hold for the microcosm, in
which case C and D are excluded, or that the theory did not
hold for the microcosm, in which case A and B are
excluded. Now, suppose the theory did hold. We would like
to take this to be good news for the theory. But of course, it
is good news only if the analogy between microcosm and
nature is positive, that is if we are in position A. However,
to be in position B means that the theory only accidentally
held in the microcosm and for microcosm-specific reasons.
This requires a double coincidence: the overlooked features
of the system that actually determines the duration of final
decline to extinction (the cause) must not be present in
nature and coincidentally must be present in the microcosm.
Alternatively, one may perform the microcosm experiment and make findings that are inconsistent with the
theory. In this case, we are in either position C or position
D. But we are only misled if we are in position C, that is if
the theory is correct in nature and does not hold in the
model because of some model-specific property. In contrast
to the positive finding in the microcosm, this way of being
misled requires only a single coincidence, that some model-
442
specific feature of the experiment (an artifact of being a
microcosm) overrides the correct prediction of the theory,
destroying the relation between x and y. As a not-toofanciful example (but contrary to our actual findings),
consider if the habitat size of the microcosm was such that
the carrying capacity was of the same order of magnitude as
the mean of the offspring distribution. In this case, the
population would be strongly regulated at all population
sizes and the estimated population growth rate would
effectively be just noise (in theory, anyway), in which case
there would be no correlation.
This shows that successful prediction by a theory of
observations in a microcosm is actually a low bar. If the
theory fails to hold under controlled circumstances, what
chance is there that it holds in nature? But how often is this
bar met? In fact, microcosm experiments often show us
ways that our theories fail because they are causally
incorrect. Moreover, it is much faster and less costly to
learn of these failures in microcosm experiments than from
the same experiments performed in the field.
Of course, there is a final class of possible errors. It
could be that we are in position A or position D, but not for
the reasons we think. In this case, our causal interpretation
of the experiment will be mistaken, but the analogy
between nature and microcosm will still hold. Of course,
the accidental alignment of theory and data is a risk taken
by causal inference of any kind, and it not special to
microcosm experiments. That is, this third kind of failure is
not due to the fact that we are using a model system or
reasoning by analogy. A corollary of this conclusion is that
understanding “model-specific properties”, edge effects,
and similar artifacts is important to not being misled by
microcosm studies. We believe that microcosm experimenters are in fact quite aware of this point and indeed are
therefore themselves in the best position to evaluate what
causal inferences are warranted from microcosm studies. It
is the experimenters themselves therefore that are also in
the best position to spell out the terms of the analogy—the
positive analogies, negative analogies, and neutral analogies—as is required to properly draw correct inferences in
specific cases.
Causality: the chief virtue of microcosmology
The main positive argument for the use of microcosms in
research, then, is that microcosms-as-models offer decided
advantages for developing a causal understanding of how
nature works by enabling tests of causal theory and
identifying causal relationships. The control over experimental conditions allows selection of the positive and
negative analogies present between the model and nature
and isolation of the neutral analogy of interest. As a result,
Theor Ecol (2012) 5:433–444
microcosms can provide evidence for or against mechanistic predictions that are difficult to test in nature. Indeed, the
biological or physical simplicity that is often criticized for
being ecologically unrealistic is precisely what is required
for an experiment to meet the assumptions of some theory
that is typically advanced with respect to uncontrolled
nature only under some large set of ceteris paribus restrictions
(Lawler 1998; Petchey et al. 2002; Cadotte et al. 2005).
Indeed, criticism 1 is basically the empirical claim (possibly
unwarranted by evidence) that the complexity required to
understand ecological phenomena exceeds that which can be
investigated via microcosm experiments—and that this is so
widely true among ecological phenomena that it may be
generally presumed. At “medium” levels of complexity,
however, such as is typical of much modern ecological
theory, microcosms may well be most suitable because of
their openness to manipulation along multiple dimensions
simultaneously. Low cost and small size enables construction
of replicate microcosms or repeat runs of an experiment,
increasing statistical power, and enabling tests of theories
represented as stochastic processes (e.g., genetic evolution,
demographic fluctuation).
Thus, the perceived weaknesses of microcosms actually
provide the very advantages that make them useful for
isolating mechanisms. Because the organisms used have
short generation times, microcosms often last much longer
than other experiments when time is considered relative to
an ecological scale (see Morin 1998; Lawler 1998; Petchey
et al. 2002; Cadotte et al. 2005, and Bulling et al. 2006 for
further discussion on this point). Further, as Cadotte et al.
(2005) point out, not only can environmental variation be
minimized, but it can also be induced in a controlled
fashion (Petchey et al. 1999; Drake and Lodge 2004). To
us, this defeats criticism 2, that because of their small size
and short duration, microcosms do not exhibit natural
quantities of spatial and temporal variation, at least in cases
where variability is the focus of the experiment. Finally, the
closed nature of microcosms allows processes that occur
over large spatial scales, such as long distance dispersal, to
be emulated by manual introductions or transfers (Srivastava et al. 2004). Indeed, as with any other hypothesized
mechanism, it would seem that the contribution of
environmental stochasticity or spatial heterogeneity to a
directly observable phenomenon can only be conclusively
determined by inducing environmental variation at different
levels holding other properties constant. This is a possibility
provided only in constructed systems.
Of course, this positive argument for the use of microcosms in ecological research goes hand in hand with the
negative argument that experiments in natural systems are
difficult to interpret because nature is so uncontrollable. Put
simply, testing mechanisms in natural systems is difficult
because it is impossible to control confounding variables.
Theor Ecol (2012) 5:433–444
This precludes replication and isolation of specific causal
factors. In order to make predictions and generalizations,
natural ecosystems must be understood mechanistically, and
microcosms provide a tractable way to test mechanistic
models (Morin 1998; Huston 1999). These mechanistic
models can then be treated as hypotheses relevant to larger
systems and tested against observations and results from
field studies and natural ecosystems (Werner 1998; Drenner
and Mazumder 1999).
443
&
What will be the trajectory of our system if we
reintroduce a top predator?
Concrete examples of (b) are:
&
&
What will be the trajectory of our system if we
supplement the population with a captive breeding
program at the rate of one breeding pair per year?
What will be the trajectory of our system if we increase
the harvesting rate by 20%?
Concrete example of (c) are:
Models and the subjunctive conditional in conservation
biology
In conclusion, our aim throughout this paper has been to
examine how it is that microcosms, which are thoroughly
artificial constructed systems, tell us about nature and to relate
this to research priorities in conservation science. Our first
claim was that microcosms tell us about what is possible. By
pushing nature into regions of parameter space that do not
occur naturally, one can draw inferences about the kinds of
mechanisms that may be at work. We then turned our attention
to the kind of reasoning supported by microcosms and
concluded that, in addition to the hypothetico-deductive
reasoning emphasized by Popper and his followers, much of
science and all microcosm studies require an additional
model-based reasoning. We argued that model-based reasoning is a kind of analogical reasoning and investigated the
conditions under which analogical arguments are valid. We
found analogical arguments to be scientifically valid when
there were positive analogies between the essential properties
of the source and target and where the vertical relations among
properties were causal in some suitably scientific sense. In this
final section, we want to explore what these conclusions imply
for conservation practice.
In our introduction, we argued that conservation science
requires of its models that they are able to support
counterfactual predictions. Perhaps somewhat provocatively,
we claimed that this occurs through (and only through)
mechanistic understanding, what we called a “mechanistic
program for science”. Here, we wrap up our argument by
bringing together our reflections on the logic of analogical
arguments and the goals of conservation science.
When we say that conservation science requires its models
to support counterfactual predictions, what we mean is that
they give answers to questions of the form, “What will be the
future trajectory of our system if we change some antecedent
condition which might be (a) a state variable, (b) a process
rate, or (c) a system constraint?”
Concrete examples of (a) are:
&
What will be the trajectory of our system if we remove
an invasive species?
&
&
What will the trajectory of our system if we switch from
fixed effort harvesting to fixed quota harvesting?
What will be the trajectory of our system if we set aside
two additional nature reserves?
These are standard questions for theoretical conservation
biology. Importantly, for any applied system of interest, we
will not be in a position to empirically determine the
answer prior to implementation of the new antecedent
condition. Answering the subjunctive conditional what-if
will require a model that gives (approximately) the right
answer. To give the right answer when there is no
possibility of mere statistical extrapolation requires a model
that is correct with respect to its causal relations. We have
argued above that microcosms are ideal for examining such
causal relations. Indeed, Cadotte et al. (2005) have gone
further and argued that natural experimental systems cannot
adequately disentangle the set of possible causal relations
because of the nature’s uncontrollable complexity. It
follows, we believe, that the mechanistic program of study
exhibited by microcosm studies is indeed a key stage in the
development of a scientific understanding of nature that
supports the counterfactual predictions necessary for a
successful science of conservation.
Acknowledgments We thank participants of the Sustainable conservation: Bridging the gap between disciplines conference held in
Trondheim, Norway (March 15–18, 2010) for criticisms of these ideas
which were first presented there and for conversations that helped us to
develop them more fully. C. Brassil, M. Cadotte, J. Chase, and J. Shurin
kindly provided many useful comments on an earlier version of this
paper, which was further improved by the comments of three reviewers.
A. Silletti and A. Janda assisted with the preparation of the manuscript.
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