OIKOS 94: 17–26. Copenhagen 2001
Does population ecology have general laws?
Peter Turchin
Turchin, P. 2001. Does population ecology have general laws? – Oikos 94: 17–26.
There is a widespread opinion among ecologists that ecology lacks general laws. In
this paper I argue that this opinion is mistaken. Taking the case of population
dynamics, I point out that there are several very general law-like propositions that
provide the theoretical basis for most population dynamics models that were devel-
oped to address specific issues. Some of these foundational principles, like the law of
exponential growth, are logically very similar to certain laws of physics (Newton’s
law of inertia, for example, is almost a direct analogue of exponential growth). I
discuss two other principles (population self-limitation and resource-consumer oscil-
lations), as well as the more elementary postulates that underlie them. None of the
‘‘laws’’ that I propose for population ecology are new. Collectively ecologists have
been using these general principles in guiding development of their models and
experiments since the days of Lotka, Volterra, and Gause.
P. Turchin, Dept of Ecology and E
olutionary Biology, Uni
. of Connecticut, Storrs,
CT 06269-3043, USA (peter.turchin@uconn.edu).
Like many scientists who are not physicists, ecologists
have been unable to resist unfavorable comparisons
between their science and physics. Some argue that
ecologists do not think like physicists, and that is why
there is little progress in ecology (Murray 1992). Others
reply that biologists should not think like physicists
because of the nature of biological science (Quenette
and Gerard 1993, Aarssen 1997). On both sides of the
debate, there is a widespread belief that ecology is
different from physics because (1) it lacks general laws,
and (2) it is not a predictive (and, therefore, not a
‘‘hard’’) science. For example, Cherrett (1988) com-
mented that ‘‘there is unease that we still do not have
an equivalent to the Newtonian Laws of Physics, or
even a generally accepted classificatory framework’’ (see
Kingsland 1995: 222–223 for a commentary). ‘‘Parts of
science, areas of physics in particular, have deep univer-
sal laws, and ecology is deeply envious because it does
not’’ (Lawton 1999). Even eminent theoretical ecolo-
gists appear to subscribe to this view: ecology, appar-
ently, is different from physics because one of its
distinguishing features is the near absence of universal
facts and theories (Roughgarden 1998: xi). As to ecolo-
gy’s ability to generate testable theories, Aarssen (1997:
177) thinks that ‘‘On this scale, ecology admittedly has
a weak record’’ (see also Weiner 1995). ‘‘Ecology was
not and is not a predictive science’’ (McIntosh 1985).
Much can be said to counter these arguments. First,
physics is not a monolithic science. In certain highly
respectable subfields, like astrophysics, it is not possible
to test theoretical predictions with manipulative experi-
ments. Does it mean that there is no progress in astro-
physics? No, because astrophysicists can still make
predictions about yet unobserved phenomena. A true
experiment can be conducted without actively messing
with nature. Second, it is a gross exaggeration to claim
that physics is a predictive science in all its aspects.
Physicists assure us, on one hand, that they have a
complete understanding of the laws of fluid dynamics
that govern atmospheric movements. On the other
hand, neither they nor anybody else can accurately
predict weather more than 5–7 days in advance. I could
go on, but I do not think that trying to counter each
charge of the critics is what is needed. A more produc-
tive approach is to simply do ecology and eventually
show that it is a vigorous, theoretical, and, yes, predic-
tive science. In fact, we may not need to wait very long
to demonstrate this, because, in my opinion, at least the
Accepted 14 February 2001
Copyright © OIKOS 2001
ISSN 0030-1299
Printed in Ireland – all rights reserved
OIKOS 94:1 (2001) 17

population dynamics branch of ecology is on the verge
of a major synthesis (Turchin unpubl.).
Furthermore, I think that population ecology has
general laws resembling laws characterizing certain
fields of physics (e.g., classical mechanics, or thermody-
namics). In particular, population dynamics appears to
have a set of foundational principles which are very
similar, in spirit and in logic, to Newton’s laws
(Ginzburg 1972, 1986). In the rest of this paper, I will
sketch out what I think these foundational principles
are, and discuss the similarities between the logical
foundations of population dynamics and Newtonian
mechanics. I should warn you right away, however, not
to expect any deep and novel insights. My main argu-
ment will essentially be that we had, and used these
principles all along (at least since the 1920s), but simply
did not call them ‘‘laws’’.
Exponential growth – the first law of
population dynamics
Practically all ecological textbooks start exposition of
population ecology with the exponential law of popula-
tion growth (Malthus 1798). There is a reasonable
consensus among ecologists that the exponential law is
a good candidate for the first principle of population
dynamics (e.g., Ginzburg 1986, Brown 1997, Berryman
1999). My formulation of this principle is as follows: ‘‘a
population will grow (or decline) exponentially as long
as the environment experienced by all individuals in the
population remains constant’’. Environment here refers
to all environmental influences affecting vital rates of
individuals, including abiotic factors, the degree of
intraspecific crowding, and density of all species in the
community that could interact with the focal species.
Most elementary textbooks give the derivation of the
exponential law for the case when all individuals in the
population are absolutely identical (in particular, there
is no age, sex, size, or genetic structure) and reproduce
continuously. We start by writing the law of conserva-
tion (the number of individuals can only change as a
result of birth, death, emigration, and immigration),
and then change to per capita rates:
dN
dt
=B−D=bN−dN= (b−d)N=rN (1)
where B and D are the total birth and death rates, b
and d are the per capita rates, N is the total number of
individuals in the population, and r is the per capita
rate of population change. There are no immigration/
emigration terms because I assumed that the popula-
tion is closed. This elementary derivation readily
generalizes to more realistic settings:

For semelparous organisms (such as annual grasses
or insects) we obtain the discrete form of the expo-
nential law: Nt+1=
Nt

Adding age or stage structure is also relatively
straightforward. However, we now have to wait for
the population to achieve a stable age distribution,
after which all age classes (as well as total number of
individuals) begin to grow according to the exponen-
tial law.

The general pattern of growth is still exponential
when we consider finite populations and add demo-
graphic stochasticity. For example, Bartlett (1966)
shows that the expected population size in a stochas-
tic birth process is the same as in the deterministic
model.

The environment does not have to be constant. If the
environment varies in such a way that the per capita
rates b and d have stationary probability distribu-
tions, then we obtain a model of stochastic exponen-
tial growth/decline (Maynard Smith 1974: 14–15).
The expected population density is again described
by the exponential equation (but see e.g. Lande 1998
for a caveat).

Finally, adding space and diffusive movements leads
to a simple partial differential equation model, ana-
lyzed by Fisher (1937) and Skellam (1951). In this
model, the total number of individuals continues to
grow exponentially, even as they diffuse out from the
initial center.
In short, as long as the environmental influences do not
change in a systematic manner, we end up with one or
another version of the exponential law. In fact, we can
formulate it even more generally by substituting ‘‘con-
stant environment’’ with ‘‘stationary environment’’ (en-
vironmental influences on vital rates fluctuate with a
constant mean and variance) in the definition given
above. The exponential law is a very robust statement.
But is it a law? Let us compare it to something about
which there is no argument that it is a law – Newton’s
First Law, or the law of inertia. The similarity between
the exponential law and the law of inertia is striking.
First, both statements specify the state of the system in
the absence of any ‘‘influences’’ acting on it. The law of
inertia says how a body will move in the absence of
forces exerted on it; exponential law specifies how a
population will grow/decline in the absence of system-
atic changes in the environmental factors influencing
reproduction and mortality.
Second, the action of both laws in real life is ob-
scured by complexities characterizing real-life motions
of bodies, or population fluctuations. As a result, nei-
ther statement can be subjected to a direct empirical
test. Just as we cannot observe a body on which no
forces are acting, we cannot observe a population grow-
ing exponentially (at least, not for long), because we
cannot indefinitely keep its environment stationary. In-
18 OIKOS 94:1 (2001)