Population Ecology

Population Ecology

(for S. Sarkar and A. Plutynski (eds.), A Companion to the Philosophy of Biology,
Blackwell, forthcoming.)



1. Introduction.
A population is a collection of individuals of the same species that live together in a
region. Population ecology is the study of populations (especially population abundance)
and how they change over time. Crucial to this study are the various interactions between
a population and its resources. A population can decline because it lacks resources or it
can decline because it is prey to another species that is increasing in numbers.
Populations are limited by their resources in their capacity to grow; the maximum
population abundance (for a given species) an environment can sustain is called the
carrying capacity. As a population approaches its carrying capacity, overcrowding means
that there are less resources for the individuals in the population and this results in a
reduction in the birth rate. A population with these features is said to be density
dependent. Of course most populations are density dependent to some extent, but some
grow (almost) exponentially and these are, in effect, density independent. Ecological
models that focus on a single species and the relevant carrying capacity are single species
models. Alternatively, multi-species or community models focus on the interactions of
specific species.
The discipline of population ecology holds a great deal of philosophical interest.
For a start, we find all the usual problems in philosophy of science, often with new and
interesting twists, as well as other problems that seem peculiar to ecology. Some of the
former, familiar problems from philosophy of science include the nature of explanation
and its relationship to laws, and whether higher-level sciences (like ecology) are
reducible to lower-level sciences (like biochemistry). Some of the philosophical problems
that arise from within population ecology include whether there is a balance of nature and
how the uneasy relationship between the mathematical and empirical sides of the

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discipline might be understood. As we shall see, many of these questions are intricately
linked, and providing satisfactory answers is no easy matter. But there is no doubt that
there are important lessons for philosophy of science to be gleaned from the study of
population ecology.
In what follows I will focus on some of the central questions that are prominent in
the recent philosophy of population ecology literature. There are, of course, other
questions and problems, some of which the interested reader may pursue in the works
listed in the references and further reading. But despite this admittedly less than
comprehensive treatment of the philosophical issues in population ecology, those I
address will give a sense of the flavor of the philosophical issues that arise in population
ecology.

It is worth mentioning that many of the philosophical problems in population
ecology are of great importance to working ecologists. For example, the issue of whether
there are laws in ecology is seen by many ecologists as an important internal question to
their discipline and one that has immediate methodological implications. (If there are no
laws, ecologists might settle for a more pragmatic and even pluralist attitude towards
their models.) Philosophers have been a little slow to turn their attention to ecology and
so working ecologists have had to tackle many of the philosophical issues themselves. As
a result a great deal of the philosophical ground work has been carried out (for the most
part, with a high degree of philosophical sophistication) by working ecologists. (See, for
example, Ginzburg, 1986; Pimm, 1991; and Turchin, 2001) But the philosophical
problems in population ecology are important in another way. Population ecology itself
has a great deal of social and political significance. Conservation management strategies
often depend on predictions of population ecology. Where population ecology meets
conservation management we find that philosophy of science meets ethics. Typically a
great deal more than scientific or philosophical curiosity hangs on the answers to the
philosophical and scientific problems faced by population ecology. For example,
scientific issues about burden of proof in hypothesis testing have a distinctly ethical
dimension. I will say more about such matters in section 6.

2. Laws in Ecology

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It has been claimed that ecology is not law governed (Murray, 1999; O’Hara, 2005) The
reasons for denying the existence of laws in ecology is not always clear. Often appeals
are made to lack of generality and lack of predictive success, but the complicated nature
of ecology seems to feature especially prominently in this debate. We need to be careful
not to set the bar too high for lawhood though. Consider the claim that ecology is too
complex to submit to general laws. This may well be true but it is not obviously true, and
it is certainly not something we can determine a priori. After all, we take celestial
mechanics to be law governed, even though every massive body in the universe interacts
gravitationally with every other massive object. It does not get much more complicated
than that! While it is true that populations are affected by a great deal around them—the
weather, predators, parasites, resources, fertility, and so on—considerations elsewhere in
science show that complexity alone does not disqualify a discipline from being law
governed. The complexity might “wash out”, (Strevens, 2003), or much of the
complexity might be properly ignored in many situations (as we can properly ignore the
gravitational influence of Sirius on the earth when we consider the Earth’s orbit around
the sun).
A case can be made for accepting that ecology has laws, albeit laws with
exceptions. There is a very natural way to think of a highly simplistic and idealized
equation like Malthus's equation, N(t) = N ert (where, N is the population abundance, t is
0
time, N is the initial abundance, and r is the population growth rate), as a fundamental
0
law of ecology. After all, this equation can be thought of as analogous to Newton’s first
law. Each describes what the respective system does in the absence of disturbing
influences. In the ecological case, Malthus’s law tells us that populations tend to grow
exponentially unless interfered with. Interference can come in the form of density
dependence, predators, and so on. Of course there always are disturbing influences, so no
population grows exponentially for any significant period of time. But why should this
disqualify Malthus’s equation from being a law? After all, no massive body in the
universe moves with uniform motion, but this does not disqualify Newton’s first law. If it
is good enough for celestial mechanics, it is good enough for ecology. Malthus’s equation
can be thought of as a fundamental law of population growth—it describes the default
case from which departures are to be explained. Moreover, like Newton’s first law,

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Malthus’s equation has considerable empirical support (e.g., the approximate exponential
growth of microbial populations in laboratory situations). If we do treat Malthus’s
equation as a law, analogous to Newton’s first law, we are then faced with the project of
identifying the “ecological forces” that result in such departures from exponential growth
(Ginzburg and Colyvan, 2004).
What of explanation in ecology? On traditional accounts of explanation (e.g.,
Hempel, 1965), laws are required for explanation. So if ecology does not have laws, there
can be no ecological explanation. One response is to deny the traditional account of
explanation: ecology has explanations but not laws (Cooper, 2003). Though if what I
have suggested above is correct and ecology does have laws, then even on the traditional
account of explanation there can be genuinely ecological explanations. Let us focus on
the latter response. That is, let us assume that ecology does have laws and ask after the
nature of the explanations delivered. There is still a problem for ecological explanation.
The laws we are talking about are population-level laws; they are not about the
individuals that constitute the populations in question. Consider Malthus’s law. It has
only initial abundance and the growth rate as parameters, and these both concern
properties of the population, not the individual. But now here’s the problem. Surely the
real explanation for why a population has the abundance it does will be about births,
deaths, immigrations, and emigrations of individual members. The law seems to ignore
the individual events and the latter are what are causally relevant. How can such a law be
genuinely explanatory?
I think this argument against ecological laws being explanatory fails. First, note
that the argument is very general and, as stated, it would tell against any macro-level
explanations of micro-level phenomenon. For example, the ideal gas law has only macro-
level parameters—the individual properties of gas molecules do not feature in this law—
so it would seem that the ideal gas law also falls foul of this line of attack on ecological
laws. But, any statistical law—by its very nature—is at the level of ensembles not of
individuals. It would seem that all statistical laws stand or fall together: the ideal gas law,
ecological laws and many others. Surely the argument against ecological laws being
explanatory is misguided. I will return to the issue of explanation in ecology in the next
section, when I look at mathematical models in ecology.

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3. Mathematical Models
Despite being a highly mathematical discipline, ecology has an uneasy relationship with
the mathematics it employs. We have already seen that ecology is about assemblages of
living organisms and a population grows or declines by adding or subtracting individuals.
The details of the population growth or decline will depend entirely on what happens to
the individuals that constitute the population in question. But the typical mathematical
models of a population ignore the details of individuals. Or rather, all the details about
the individuals are packed into a few population-level parameters such as growth rate,
carrying capacity and the like.

In order to focus the discussion, let us consider a couple of simple mathematical
models. Recall Malthus’s law from the previous section. This states that the rate of
change of population abundance, with respect to time, is proportional to population
abundance. Represented mathematically, this becomes the following simple first-order
differential equation:

dN/dt = rN,

where r is the population growth rate, t is time, and N is the population abundance.
Solving this equation yields the familiar exponential growth equation (which we also
refer to as Malthus’s law):

N(t) = N ert,
0

where N is the initial population abundance. Of course populations do not grow
0
exponentially for long (if at all)—eventually their growth is limited by resources.
Introducing such considerations into the mathematical model yields the logistic equation:

dN/dt = rN(1 − N/K),

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where r, t, and N are the same as before, and K is the carrying capacity for the population
in question. The logistic equation is, arguably, the simplest useful model in population
ecology. Despite a number of idealizations (such as ignoring age structure and genetic
variation in the population, and treating that carrying capacity as constant) it is a very
good description of many populations. Of course there are other refinements one can
make but we wont bother here. The logistic equation will serve as our canonical example
of a mathematical model in population ecology.
Now let us turn to the question of the use of mathematical models of population
growth. These models are put to at least two different purposes: prediction and
explanation. I will return to explanation shortly but for now let us focus on prediction.
Most mathematical models are notoriously poor predictors. Of course they can be made
to match existing data by suitably adjusting free parameters, but this gives one little
confidence in the predictive accuracy of such models. Indeed, models whose parameters
are too finely tuned are treated with considerable suspicion. Such models are
(pejoratively) called “over fitted” and are thought to be unrealistically complicated and
thus unreliable predictors. So an important question about the predictive reliability of
models needs to be addressed: what means are available for guaranteeing that the model
will give us the right answers? Or failing such guarantees, how do we go about specifying
the degree of confidence in the model?
The kind of uncertainty we are dealing with here is called “model uncertainty”
and is notoriously difficult to quantify (Regan et al., 2002). But while a mathematical
model may not predict the details, it may preserve gross trends. So, for example, we
might find that under any reasonable value of the free parameters (or less commonly,
under any reasonable model design) the model gives more or less the same answer. The
model thus exhibits a certain robustness, and testing models in this way is called
sensitivity analysis (Levins, 1966; Morgan and Henrion, 1990, pp.39–40; Wimsatt, 1987).
Of course, a great deal hangs on how “reasonable values of the free parameters” is
understood, but in practice, and in at least some cases, ecological theory provides
guidance.
One interesting feature of sensitivity analysis, is that it gives rise to a
supervaluational logic (admittedly, under a non-standard epistemic interpretation of the

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logic in question). If the population p is deemed to have property Q on all reasonable
values of the parameters, then we are confident that p has Q. If p fails to have Q on all
reasonable values of the parameters, then we are confident that p does not have Q. But
what of the indeterminate cases, where on some reasonable values of the parameters p
has Q, while on others p does not have Q? Here it would seem that the right thing to say
is that we are neither confident that p has Q nor are we confident that p does not have Q.
In short, we assert that p has Q if and only if p has Q on all valuations. The resulting logic
is a supervaluational logic and is familiar in the philosophical logic literature as the tool
of choice in dealing with vagueness. This logic has interesting features such as being
non-bivalent while preserving the classical law of excluded middle (van Fraassen, 1966;
Beall and van Fraassen 2003). (Strictly speaking we are talking about the logic of the
modal operator “confident that …” but I will not explore such complications here.)
Validation studies are another way to test a model. Here, one uses part of a data
set to construct the model, including the fixing of all free parameters, while withholding
another part of the data set. The second, withheld part of the data set is then used to test
the model. If the model predicts the withheld data, the model is said to be validated. The
problem with such an approach is that it requires large data sets—typically long time
series data of a population—and such data is rarely available. Indeed, the absence of such
data is often the motivation for constructing a model in the first place.
The problems concerning model uncertainty are deep and philosophically rich.
For a start, such uncertainty does not readily submit to probabilistic treatment (Regan et
al., 2002). After all, it is very often impossible to assign values to the probability that the
model is correct in every detail. Or at least on standard methods of assigning such
probabilities, they will come out to be zero. New methods for dealing with such
uncertainty are required. One such approach is non-classical logic. For in the face of
serious uncertainty, it is necessary to entertain at least three categories: definitely true,
definitely false, and indeterminate. Multi-valued and modal logics may prove fruitful in
dealing with uncertainty that resists probabilistic treatment (Regan et al., 2002). There
are various questions about the relationship between simplicity and predictive success of
models. Can we be more confident in a simple model? This is an old chestnut in the
philosophy of science. On the one hand, there are good pragmatic arguments for insisting

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on simplicity in the models or laws of ecology; thus formulated, the relevant theory will
be easier to work with, and generally more tractable. But, on the other hand, what do
pragmatic virtues of a theory have to do with truth or even predictive success? Put
another way, what is so bad about complex (or overfitted models)? Interesting work on
this problem has been carried out by Forster and Sober (1994). Forster and Sober use a
theorem due to Akaike to forge a link between simplicity and predictive success.
Mikkelson (2001) applies these ideas specifically to ecology. (See also Colyvan and
Ginzburg, 2003 for discussion of possible limitations of this approach to simplicity.)
Thus far, I have been focusing on the typical population models that employ
population-level properties like carrying capacity, growth rate, and the like. There are
extensions that relax some of the assumptions of single aggregated population dynamics.
Age- and stage-based models (also known as matrix models; Caswell, 2001) are models
in which organisms are differentiated based on their age or morphological features such
as size. Each age or stage class then has its own population growth equation that is
coupled with other age or stage classes in the model. Meta-population models incorporate
space through a population of sub-populations which are separated by a distance (Gotelli,
2001).
These are all population-level models, though, and it is worth saying a little about
another kind of model: individual-based models. The latter are models that focus on the
properties and behavior of the individuals of a population. The global population-level
properties are then derived from the local interactions. Unlike the global population-level
models, individual-based models keep track of individual properties and behaviors
(DeAngelis and Rose, 1992). They incorporate diversity amongst individuals by
representing each individual separately and explicitly specifying attributes such as the
individual’s age, size, spatial location, gender, energy reserves etc. Sometimes
individual-based models are used to estimate or model population-level parameters
(McCauley et al., 1990 and Gurney et al., 1990). In a sense, such individual-based
models take a bottom-up approach to determining global population-level properties. A
familiar example of an individual-based approach is found in various simulations such as
“the game of life” and spatialized prisoner’s dilemmas. In such simulations, individuals
are located in an environment consisting of cells. Individuals are able to take one of a

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number of states and there are rules about the interactions between neighboring cells (or
individuals). Such approaches have been put to good use in shedding light on altruism in
populations (Sober and Wilson, 1998) and the evolution of various social structures
(Skyrms, 2004).
In population ecology, individual-based models are becoming more widely used.
Typically such models are spatially explicit. That is, they associate a spatial location with
each individual. Such spatially-explicit individual-based models are especially useful in
modeling species that aren’t terribly mobile—otherwise movement rules need to be
included and these present serious difficulties. But if the species in question is reasonably
sedentary, each individual in the population can be associated with a particular fixed
spatial region. These models are particularly suited to plant populations (see, for
example, Regan et al., 2003). But with some additional complications individual-based
models are also able to be used for animal populations where individuals are allowed to
roam over more than one spatial region. Individual-based models are often employed
when information about the structure of the population is required. So, for example,
spatially-explicit individual-based models are very useful for determining forestation
patterns—not just the number of individual trees (Deutschman et al., 1997). To some
extent at least, individual based models and the more traditional population-level models
are not direct competitors. Very often they are used to answer different questions (Regan,
2002).
Some ecologists take individual-based models to be less problematic than the
usual population-level models. For example, individual-based models cannot be accused
of ignoring the properties and behavior of the individual members of a population while
focusing only on averaged population-level properties. There are still idealizations
though. The behavior and properties of the individuals in individual-based models will be
highly idealized and often reduced to one of a small number of states. Moreover, the
individuals will be restricted to a small number of possible actions. As with other models,
the devil is in the details. There is nothing inherently wrong with such idealizations; the
question is whether the idealizations at issue are theoretically well motivated and whether
they are useful. These are important questions for ecology but they are not, it would
seem, questions that will submit to general answers; they must be answered on a case-by-

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case basis. And it would seem that these questions must be answered for both individual-
based models and population-level models.
Another application of mathematical models is to provide understanding and
explanation of certain features of the population in question. Here there is less emphasis
on getting detailed predictions and instead the focus is on gaining insights into general
population trends and the reasons behind them. Such models are rather controversial in
ecology. It is thought by some that mathematical models cannot be explanatory, for they
either obscure the underlying biological mechanisms or, worse still, they ignore the
biological mechanisms. After all, if a population is exhibiting periodic behavior, say, the
reason for this behavior must have something to do with births, deaths, immigration, and
emigration of individual members of the population. The mathematical model, however,
typically employs population-level parameters like carrying capacity and growth rate. A
mathematical model thus cannot provide explanation because it is not couched in the
right terms (or so the argument goes).
The first thing to stress here is that very often the mathematics is just representing
the biological facts in a mathematical way. Properly understood, the mathematics neither
ignores nor obscures the underlying biological causal mechanisms. Instead of listing all
the individuals in a population at different times, for instance, we can summarize this
information in terms of equations for the population abundance. The individual
organisms might seem to have dropped out of the picture but they have not. All that is
relevant about them is represented mathematically in the equation of growth. Consider
another example. The constant K in the logistic equation is not just an uninterpreted
constant introduced purely for mathematical convenience. As I have already pointed out,
K has a very natural ecological interpretation as the carrying capacity. (Though, it might
be argued that this interpretation is rather abstract and it is mathematically convenient in
that the constant K is just a crude summary of the interactions of a population with its
environment.)
Next I note that some explanations are more readily drawn from the model than
from the biology. For example, the mathematical model may focus attention away from
confusing local-level causal interactions and towards higher-level population trends. We
see this in the mathematical explanation of why certain populations undergo specific

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