RESILIENCE
AND
STABILITY OF ECOLOGICAL SYSTEMS
C.
S. Holling
September
1973
Research Reports are publications reporting
on the work of the author. Any views or
conclusions are those of the author, and do
not necessarily reflect those of IIASA.
Copyright
1973.
All nghts
mrved
RESILIENCE
tth'l)
S'~AI31IJIrl1Y
OF
L(;OLO(:I(;AL
SYSrl'ki\lS*
C
S.
Holling
Institute of Resource Ecology. University of British Columbia. Vancouver. Canada
INTRODUCTION
Individuals die, populations disappear, and species become extinct. That is one view
of the world. But
ar~other view of the world concentrates not so niuch on presence
or absence as upon the nunibers of
organisms and the degree of constancy of their
numbers. These are two very different ways of viewing the behavior of systems and
the usefulness of the
view depends very much on the properties of the system
concerned. If we are
examining a particular device designed by the engineer to
perform specific tasks under a rather narrow range of predictable external condi-
tions, we are likely to be more concerned with consistent
non\,ariable performarlce
in which slight departures from the performance goal are
immediately
counteracted.
A quantitative view of the behavior of the system is, therefore, essential. With
attention focused upon achieving constancy, the critical events
seen1 to be the
amplitude and frequency of oscillations. But if we are dealing with a system pro-
foundly affected by changes external to it, and
contillually confronted by the unex-
pected, the constancy of its behavior becomes less important than the persistence
of the relationships. Attention shifts, therefore, to the qualitative and to questions
of existence or not.
Our traditions of analysis
in theoretical and empirical ecology have been largely
inherited
froni developments in classical physics and its applied variants. Inevitably,
there has
been a tendency to emphasize the quantitative rather than the qualitative,
for it is important in this tradition to know not just that a
quantity is larger than
another quantity, but precisely how much larger. It is similarly important, if a
quantity fluctuates, to know its amplitude and period of fluctuation. But this orienta-
tion may simply reflect an analytic approach developed in one area because it was
useful and then transferred to another
where it may not bs.
Our traditional view of natural systems,
tllerefore, might well be less a meaningful
reality
thau a perceptual convenience. There can in sonie years be more owls arid
fewer
mice and in others, the reverse. Fish populatiol~s wax and wane as a natural
condition, and insect populations can range over
extremes that only logarithmic
*
Reprinted with permission from "Resilience
and Stability of Ecological
Systems," Annual
Review of
Ecology and Ssstematics, Volume
4,
pp. 1-23. copyright
@
1973 by Annual Reviews
Inc.
All
rights reserved.
2
HOUING
transformations can easily illustrate. Moreover, over distinct areas, during long or
short periods of time,
speties can completely disappear and then reappear. Different
and useful insight might be obtained, therefore, by viewing the behavior ofecological
systems in terms of the probability of extinction of their elements, and by
shifting
emphasis from the equilibrium states to the conditions for persistence.
An equilibriuni centered view is essentially static and provides little insight into
the transient behavior of systems that are not near the equilibrium. Natural, undis-
turbed systems are likely to be
conti~iually in a transient state; they will be equally
so under the influence of man. As man's numbers and economic demands increase,
his use of resources shifts equilibrium states and moves populations away from
equilibria. The
prescnt concerns for pollution and endangered species are specific
signals that the well-being of the world is not adequately described by concentrating
on equilibria and conditions near them. Moreover, strategies based upon these two
different views of the world might well be antagonistic. It is at least conceivable
chat
the effective and responsible effort to provide a maximum sustained yield from a fish
population or a nonfluctuating supply of water from a watershed (both equilibrium-
centered views) might paradoxically increase the chance for extinctions.
The purpose of this review is to explore both ecological theory and the behavior
of natural systems to see if different perspectives of their behavior can yield different
insights useful for both theory and practice.
Some Theory
Let us first consider the behavior of two interacting populations: a predator and its
prey, a herbivore and its resource, or two competitors. If the interrelations are at
"11
regulated we might expect a disturbance of one or both populations in a constant
environment to be followed by fluctuations that gradually decrease in
aniplitude.
They might be represented as in Figure 1, where the fluctuations of each population
over time are shown as the sides of a box. In this
example the two populations in
some
sense are regulating each other, but the lags in the response generate a series
of oscillations whose amplitude gradually reduces to a constant and sustained value
for each population. But if we are also
concenled with persistence we would like
to know not just how the populations behave from one particular pair of starting
values, but from all possible pairs since there might well be combinations of starting
populations for which ultimately the fate of one or other of the populations is
extinction. It becomes very difficult on time plots to show the full variety of re-
sponses possible, and it proves convenient to plot a trajectory in a phase plane. This
is shown by the end of the box in Figure 1 where the two axes represent the density
of the two populations.
The trajectory shown on that plane represents the sequential change of the two
populations at
colistar~t time intervals. Each point represents the unique density of
each population at a particular point in time and the arrows indicate the direction
of change over time. If oscillations are damped, as in the case shown, then the
trajectory is represented as a closed spiral that eventually reaches a stable equilib-
rium.
RESILIENCE
AND
STABILITY
OF
ECOLOGICAL
SYSTEMS
3
Figure
I
Derivation of
a
phase plane showing the changes in numbers of two
populations over
time.
We can imagine a number of different forms for trajectories in the phase plane
(Figure 2).
Figurc 2a shows an open spiral which would represent sittlaiions where
fluctuations gradually
increasc in amplitude. The small arroivs are addtd to suggest
that this condition holds no
matter what corrlbination of popi~latlor~s ~niriates the
trajectory.
In
Figure 2b the trajectories are closed and given any starting point
eventually return to that
point. It is particularly significant that each starting point
generates a unique cycle and
there is no tende~~cy for points to convergz to a singlc
cycle or poi~rt. This can be termed "neutral stability" and
it
is the
k~nd
of stability
achievcd by an imaginary frictionless pendulunl.
Figure 2c
represents
a stable system similar to that of Figure I, in which all
possible
trajcctories in the phase plane spiral into an eq\~ilibriun~. These three
examples are relatively simple and, however relcvant for classical stability analysis,
may well be theoretical
curiosities
in ecology. Figures 2d-2i add sorne co~nplexities.
In
a sense Figure 2d represents a combination of a and c, with a region
i~r
the center
of the phase plane within which all possible trajectories spiral
illwards to equilib-
rium.
Those outside this rcgion spiral outwards and lead eventually to extinction
of one or the other populations. This is an example of local stability
ill
contrast to
the global stability of Figure
2c. I designate the region within which stability occurs
as the domain of attraction, and the line that contains this
domain as the boundary
of the attraction domain.
The trajectories in Figure
2e behave in just the opposite way. There is an internal
region within which the trajectories spiral out to
a
stable limit cycle
and
beyond