AMER. ZOOL., 32:674-682 (1992)
Thresholds and Multiple Stable States in
Coral Reef Community Dynamics1
NANCY KNOWLTON2
Smithsonian Tropical Research Institute, Apartado 2072,
Balboa, Ancon, Republic of Panama
Multiple stable states occur when more than one type of community can stably persist in a single environmental regime. Simple theoretical analyses predict multiple stable states for (1) single species dynamics via the Allee effect, (2) two-species competitive interactions
characterized by unstable coexistence, (3) some predator-prey interactions, and (4) some systems combining predation and competition. Potential examples of transitions between stable states on reefs include the
failure of Diadema antillarum and Acropora cervicornis to recover following catastrophic mortality, and the replacement of microalgal turf by
unpalatable macroalgae after rapid increase in the amount of substratum
available for colonization by algae. Subtidal marine ecosystems in general,
and reefs in particular, have several attributes which favor the existence
of multiple stable states. Studies of transitions between states often need
to rely upon poorly controlled, unreplicated natural "experiments," as
transitions typically require pulses of disturbance over very large spatial
scales. The stability of a state must often be inferred from analyses of the
dynamics of participants at that state, as generation times and the potential
for further extrinsic disturbance preclude the use of persistence as an
indicator of stability. The potential for multiple stable states strongly
influences our interpretation of variability in space and time and our
ability to predict reef responses to natural and man-made environmental
change.
SYNOPSIS.
ration of nutrient input does not result in
recovery of the macrophytes (Scheffer,
1990). Thus a lake with a particular nutrient
regime may be dominated by phytoplankton or
macrophytes. More generally, the
potential for multiple stable states exists
w h e n a sin
gle environment can stably supP o r t t w 0 o r more communities. Sudden and
difficult to reverse change is typical of transitions between alternative stable states,
The
existence of multiple stable states has
been a
source of considerable interest and
argument for over two decades (Lewontin,
!969; Sutherland, 1974, 1990; Noy-Meir,
1975; May, 1977;ConnellandSousa, 1983;
Drake, 1990), and much recent debate has
• From the Symposium on Long-Term Dynamics of focused on whether proposed examples of
Coral Reefs presented at the Annual Meeting of the the phenomenon are legitimate. Here I wish
American Society of Zoologists, 27-30 December 1991, t o consider instead a more general question
a t
^ S a S S n g address: Smithsonian Tropical < D ?* e > 1 9 9 0 ) : w h a t features make multiple
Research Institute, Unit 0948, APO AA 34002-0948, s t a b l e s t a tes more Or less likely? I dlSCUSS
U.S.A.
previously proposed examples of alterna674
INTRODUCTION
"The straw that broke the camel's back"
describes the discontinuous response to
continuous change which is a denning characteristic of thresholds. Moreover, it portrays a kind of threshold of particular interest to ecologists, for if you remove the last
straw, the camel does not regain its original
state. Analogous phenomena have been
described in biological communities. For
example, gradual increases in nutrient input
to lakes can lead to sudden collapse of the
macrophyte community and domination by
phytoplankton, while subsequent amelio-
MULTIPLE STABLE STATES IN REEF DYNAMICS
tive stable states for reefs using simple
graphical analyses (Rosenzweig and MacArthur, 1963; Vandermeer, 1973), ignoring
the problem of whether the stability of the
alternative states is proven in the field. My
approach focuses on the biological correlates of theoretical assumptions which
increase the likelihood of multiple stable
states, drawing on previous empirical work
for examples of issues posed by theory.
675
Stable cqumbrtum
Unstable equilibrium
Perturbation
PROPOSED EXAMPLES OF MULTIPLE
STABLE STATES
FIG. 1. Dynamics for a single population showing an
Single species interactions
effect, combined with some recruitment from
Diadema antillarum was once the most Allee
external sources (Yodzis, 1989). Two stable equilibria
abundant and important generalized grazer are indicated: carrying capacity and a low abundance
on many Caribbean reefs. In 1983-84 it suf- maintained by recruitment from elsewhere. In the
fered catastrophic mortality throughout absence of external recruitment, the low abundance
most of its range, with reductions in some equilibrium would be at the origin. The dotted line
how catastrophic mortality, such as that suffered
areas exceeding two orders of magnitude. shows
by D. antillarum, could result in a transition from a
Since then in most places recovery has not high to low abundance state.
occurred, although limited recruitment persists (Lessios, 1988, and references therein).
An Allee effect (Allee, 1931) is the sim- fertilization studies alone (Levitan, 1991).
plest way to model these events in the con- Thus individuals could be approximately
text of multiple stable states (Yodzis, 1989). replacing themselves at both high and low
Allee effects occur when reproduction shows densities. Compensation between fertilizainverse density dependence (i.e., declining tion success and gamete production as
per capita reproduction with declining described for D. antillarum implies a near
abundance) below a critical density. The zero growth rate for most population sizes
result is two stable states, high density and below the threshold population size (unstazero density, or as modelled in Figure 1, ble equilibrium of Fig. 1). Alternatively,
high density and very low density main- decimated populations may be recruitmenttained by recruitment from elsewhere. The limited (Karlson and Levitan, 1990), with
two states are separated by a threshold den- most new recruits coming from a few source
sity; populations just above the threshold populations (sensu Pulliam, 1988). Barbawill increase to carrying capacity, while those dos is one possible source population, as
just below will decrease to low abundance urchins were more abundant there both
or extinction.
before and after the epidemic, and the popExperimental work on fertilization at ulation appears able to "reseed" itself via
varying densities in D. antillarum (Levitan, larvae trapped in local eddies (Lessios,
1991) supports the suggestion (Lessios, 1988; 1988). Such a model implies that D. antilLevitan, 1991) that reduced fertilization larum would go extinct throughout most of
success at current low densities could pro- its range in the absence of larval leakage
duce an Allee effect in this species and from source to sink populations (Pulliam,
thereby prevent recovery. There are, how- 1988).
ever, many empirical uncertainties, even in
In general, Allee effects seem to require
this comparatively simple situation. Urchins several conditions in order to produce mulat low density are larger and produce more tiple stable states. First, nearly complete
gametes, so that per capita reproductive rates regional elimination is needed, where region
at high and low densities are much more is denned by the limits of routine larval dissimilar than would be predicted based on persal. This is because Allee effects do not
676
NANCY KNOWLTON
•
•
^. .
—
__
Stable equilibrium
Unstable equilibrium
Perturbation
Competitor 1
Competitor 2
COMPETITOR 1
FIG. 2. Dynamics for two competitors exhibiting
unstable coexistence, with two alternative stable states
consisting of one or the other of the competitors. Isoclines show those combinations of abundance for the
two species leading to zero population growth for each
species. For each species, populations decline beyond
the isocline and increase inside it. The separatrix divides
the domains of attraction for the two equilibria; its
linear form implies that the two species have equal
intrinsic rates of natural increase (Dorschner et at.,
1987). (A) Linear isoclines, whose shape implies that
interspecific competition is more intense than intraspecific competition for both species. The dotted line
indicates how catastrophic mortality of competitor 1
followed by modest recruitment from elsewhere of
competitor 2 could lead to a transition between states.
(B) Non-linear isocline for competitor 2, showing the
case where its competitive ability declines after competitor 1 becomes sufficiently abundant. The production of debris by algae could cause such a decline in
the competitive ability of corals (see text).
usually operate until populations are reduced
far below normal densities. Second, reproductive success must decrease or mortality
increase at these very low densities for reasons apart from competition or predation
(which are discussed below). Finally, if
extinction is not to occur, there must be
surviving source populations which both
sustain themselves and export recruits to
sink populations. For marine organisms this
implies a mixed pattern of local and longdistance larval dispersal.
Of course, extinction versus survival are
two alternative states in their own right.
Extinction mediated by Allee effects may
have major effects on species distributions.
For example, the 1982-83 El Nino event
resulted in several immediate extinctions
on eastern Pacific reefs (Glynn and de
Weerdt, 1991; Glynn and Colgan, 1992),
but some species with only widely scattered
survivors may subsequently go extinct if they
are sessile, dependent on external cross-fertilization for reproduction, and have propagules that are widely dispersed. Similarly,
western Pacific species are occasionally
recorded on eastern Pacific reefs (Colgan,
1990). In some cases their failure to become
established may be due to low reproductive
success when rare rather than persistent or
periodic unsuitability of the exotic habitat.
Competition
I am unaware of any proposed examples
of multiple stable states in reef composition
explained purely in terms of competition.
Nevertheless, competitive interactions on
reefs have received considerable attention
(see Lang and Chornesky, 1990, for corals),
and a discussion of the general features of
such systems is warranted.
The theory predicting multiple stable
states via competition is simply the case of
unstable coexistence (Fig. 2), with stable
existence of either one or the other species
but not both. A separatrix divides the
domains of attraction of the two stable states,
whose shapes and sizes depend on details
of parameters in the equations (Dorschner
etai, 1987).
Competitive multiple stable states require
that the alternative dominant species have
broadly similar ecological requirements, for
MULTIPLE STABLE STATES IN REEF DYNAMICS
if they do not, the isoclines are so far apart
that intersection at any point is unlikely.
Given that isoclines cross, species 1 must
do better than species 2 when species 1 is
abundant, and species 2 must do better than
species 1 when species 2 is abundant. Otherwise, stable coexistence instead of multiple stable states occurs.
There are two general ways for this to
happen. One is when interspecific competition is more damaging for both species
than intraspecific competition (Fig. 2A), as
for example, if both produced allelochemicals to which the competitor was more sensitive than the producer. Kin recognition
mechanisms might also result in more highly
escalated aggressive interactions between
closely related species than between conspecifics, leading to more intense interspecific than intraspecific competition. A second way for this to occur is if competitive
ability is positively density dependent. Social
effects (Hutchinson, 1947) produce such
non-linear isoclines (Fig. 2B) when, for
example, competitive ability is greater in
groups than in isolated individuals. More
generally, species when abundant may modify the environment in such a way as to
render it inhospitable for other species
(Peterson, 1984). This process, an extreme
form of inhibitory succession (Connell and
Slatyer, 1977), may contribute to the permanence of phase shifts between coraldominated and algal-dominated communities (Done, 1992 a, b). Areas which favor
the growth of corals over algae when algae
are uncommon may change in their physical
characteristics once algae pass a threshold
of abundance to favor algae over corals via
the detrimental effects for corals of algal
debris on water clarity and nutrients.
Predation
The failure of staghorn coral to recover
following damage caused by Hurricane Allen
in Jamaica has been interpreted as an example of multiple stable states mediated by
predation (Knowlton et ai, 1990). This species was a competitive dominant by virtue
of its rapid growth rate, and was predicted
to return to its prestorm densities within a
decade (Graus et ai, 1984). Instead, it continued to decline, with substantial mortality
•
•
<. .
—
_
677
Stable equfflbrtum
Unstable equUJhrtuoi
Perturbation
Prey isocline
Predator isocline
PREY
FIG. 3. Dynamics of prey and predator showing alternative stable states of low prey and predator abundance
versus high prey and moderate predator abundance.
One possible separatrix divides the two domains of
attraction. The dotted line shows how substantial mortality of prey coupled with more modest mortality of
the predator, as was seen in staghorn and staghorn
predator populations following hurricane Allen
(Knowlton et ai, 1990) could lead to a transition
between states.
due to predation. When staghorn became
rare, its predators maintained a preference
for staghorn but survived on other prey. A
similar pattern of interaction between corals
and their predators leading to further collapse of corals after an initial physical disturbance was seen on eastern Pacific reefs
following the 1982-83 El Nino (Glynn,
1990; Glynn and Colgan, 1992).
Isoclines of prey and predator leading to
multiple stable states are shown in Figure
3. As with two competitors, there are two
equilibria whose domains of attraction are
delineated by a separatrix. The shapes of
these isoclines imply several biological
assumptions (Harrison, 1986). First,
although not strictly necessary, a prey isocline that rises gradually and drops precipitously as carrying capacity is approached
increases the probability of multiple intersections. Such an asymmetry implies little
intraspecific competition until prey are relatively abundant. This clearly describes
competition among corals for light, as photons cannot be diverted by competitors, and
678
NANCY KNOWLTON
#
•
Stable equilibrium
Unstable equlllbrtum
Fertuibatian
PREY
FIG. 4. Dynamics of algae and herbivores shown in
a simplified two dimensional version of a three dimensional interaction between palatable algae, unpalatable
algae, and herbivores. The two dimensional version
assumes that less palatable forms replace highly palatable forms as total algal abundance increases. The
dotted line shows how a sudden increase in algal abundance (such as that resulting from a rapid increase in
the amount of substratum available for colonization
by opportunistic algae) could lead to a transition from
highly palatable microalgae to less palatable macroalgae.
harvest of photons in one area does not affect
their rate of arrival elsewhere apart from
the area directly shadowed. Second and more
critical, the predator isocline, instead of
being linear, levels off at high prey densities,
producing the second stable equilibrium. A
flattened predator isocline implies that
predators are not limited by food at high
prey densities. This appears to be the case
for predators on staghorn, as staghorn abundance declined dramatically while predator
numbers were relatively unaffected for years
following the hurricane (Knowlton et al,
1990).
For predator-prey interactions, one must
also consider the stability of intersections
as well as their number (Harrison, 1986).
The high equilibrium point is intrinsically
stable, although self-replacement at high
abundance is implicitly assumed (as it is for
competitive and single species models). This
generally implies that sexual or asexual
recruits to the population are the product
of resident adults. Staghorn populations satisfy this assumption because reproduction
occurs almost exclusively via growth and
fragmentation rather than widely dispersing
larvae. The lower equilibrium, in contrast,
can be unstable or show cyclic or point stability. Factors which contribute to stability
at low prey abundance include (1) the predator's use of alternative prey and resistance
to starvation, (2) refuges for the prey, and
(3) comparable reproductive potential in
prey and predator. All seem to apply to staghorn coral and its predators (Knowlton et
al., 1990; unpublished data).
Competition and predation
One of the first explicit references to multiple stable states on reefs was Hatcher's
(1984) analysis of the apparently persistent
shift from palatable to unpalatable algae on
a reef damaged by a boat grounding. He
argued that the sudden increase in substratum available for colonization by algae
exceeded the ability of resident herbivores
to keep it well grazed. Consequently, unpalatable algae reached a size which made them
recognizable to herbivores and avoided.
Once established, high densities were maintained by locally settling larvae.
Multiple stable states for three or more
dimensions {e.g., palatable algae, unpalatable algae, and herbivores) are more difficult
to analyze and visualize, but a two dimensional version in which one assumes that
algae are highly palatable when scarce and
less palatable when abundant captures the
essence of the problem (Fig. 4). In this case
the predator (or more specifically herbivore)
isocline actually dips as algae become more
abundant, primarily because algal unpalatability is increasing at the same time. As
a consequence, herbivore numbers at high
algal abundance may be comparable to or
even lower than herbivore numbers at low
algal abundance.
Although the particular circumstance
Hatcher (1984) described was rather
unusual, replacement of coral and microalgal communities by macroalgae has occurred
in a variety of settings over the past several
decades {e.g., Done, 1992a, b) and is of particular concern on many Caribbean reefs
MULTIPLE STABLE STATES IN REEF DYNAMICS
following the demise of D. antillarum. In
the latter case, response to the loss of this
important grazer has been highly variable
(Lessios, 1988). Heavily fished reefs such as
those in Jamaica are now overwhelmingly
dominated by unpalatable macroalgae, but
in Panama, where fishing is less intense,
many reefs have not been overgrown by
algae. Nevertheless, reefs in Panama with
large amounts of recently dead staghorn
resemble the Jamaican situation, and on
these reefs herbivorous fishes focus their
attention on small islands of palatable algae
found in damselfish gardens (personal
observation). It would appear that growth
of algae can escape control by the grazing
of even abundant herbivorous fish if large
amounts of substratum rapidly become
available, thus permitting eventual domination by unpalatable algae via the mechanisms outlined by Hatcher. Isocline analyses illustrate why virtual elimination of D.
antillarum invariably leads to high algal
biomass on overfished reefs (Fig. 5A), may
or may not lead to algal domination on
lightly fished reefs (Fig. 5B), and makes relatively little difference on reefs subjected to
high nutrient loads (Fig. 5C).
679
#
Stable equffibrtum
Algal Isocline
#
Unstable etjuUfbrlum
Herbivore Isocline
CHARACTERISTICS OF REEFS FAVORING
MULTIPLE STABLE STATES
A disproportionate number of the examples of multiple stable states come from
marine systems (Knowlton, in preparation).
Table 1 categorizes possible reasons for this
pattern in terms of the nature of disturbances leading to transitions, the role of
Allee effects, the potential for multiple equilibria in predator-prey systems, and the stability of equilibria (see also Steele, 1985).
Among marine ecosystems, reefs (and other
subtidal tropical ecosystems) may be particularly likely to show multiple stable states
ALGAE
because they are not subject to routine, seasonal resetting from strong, annual changes atable algae are avoided to a greater extent by fishes
FIG. 5. Hypothetical dynamics of algae and herbivores (see Fig. 4) on Caribbean reefs, showing different
combinations of nutrients, urchin abundance, and fish
abundance. The differences in shape between herbivore
isoclines before and after D. antillarum mortality represent the finding that common, shallow-water unpal-
than by urchins (Morrison, 1988). (A) Dynamics before
and after D. antillarum mortality for low nutrients and
overfishing. (B) Dynamics before and after D. antillarum mortality for low nutrients and high fish abundance. Absence of overfishing results in more steeply
rising predator isoclines compared to (A). ( Q Dynamics before and after D. antillarum mortality for high
nutrients and either low or high fish abundance. Higher
nutrient levels are indicated by the higher algal isocline
compared to (A) and (B).
680
NANCY KNOWLTON
erally and herbivorous insects are the far
greater tendency for feeding specialization
in insects and the much larger discrepancy
Transitions
1. Potential for regional disturbances with inter- in generation time between many insects
and their food plants (Hay et ai, 1987; Hay
regional transport of recruits.
2. Occasional rather than routine catastrophic dis- and Fenical, 1988; Hughes and Gliddon,
turbance.
1991) (Table 1, items 7 and 9).
TABLE 1. Features of reefs which favor multiple stable
states.
Allee effects
3. External fertilization, particularly with sessile
habit.
Predator-prey interactions
4. Absence of long-distance competition.
5. Selectivity of predation dependent on prey
abundance.
Stability of low prey abundance
6. Clonal habit providing a refuge in partial mortality.
7. Predators are generalists.
8. Predators with flexible metabolic strategies reducing probability of starvation.
9. Predators and prey with comparable reproductive potential.
Stability of high prey or competitor abundance
10. Self-replacement via asexual propagation or
short-distance dispersal of offspring.
in the physical environment (Table 1, item
2).
Diadema antillarum serves as a convenient example of several of the attributes of
Table 1. This urchin (1) is subject to occasional catastrophic and widespread mortality from pathogens carried by currents, (2)
depends on external cross-fertilization and
is thereby vulnerable to Allee effects, (3) is
a generalist feeder, (4) has primary predators capable of switching to other prey when
it is rare, (5) has aflexiblemetabolic response
to starvation, and (6) has a generation time
roughly comparable to many of the items
upon which it feeds (in comparison, for
example, to aphids on oak trees) (Robertson, 1987; Lessios, 1988; Levitan, 1988,
1989, 1991). Other marine organisms share
many of these traits.
Particularly striking is the difference
between marine and terrestrial plant-herbivore interactions. Westoby (1989) argued
that marine systems more often reside at a
lower plant-abundance state than do terrestrial systems because terrestrial vertebrate
grazers are less resistant to starvation than
are their ecological analogs, urchins and fish,
in the sea (Table 1, item 8). The biggest
differences between marine herbivores gen-
IMPLICATIONS FOR RESEARCH
As mentioned earlier, much of the debate
on multiple stable states has concerned the
validity of proposed examples. Although I
have taken these examples at face value for
purposes of discussion, this does not mean
that further empirical work is not required.
There are two general aspects which need
to be pursued in understanding multiple stable states in the natural world: transitions
between and stability of states. What then
are the best approaches?
Those attempting an experimental study
of transitions between states must remember that the standard protocol of replicate
cages will generally not be appropriate or
adequate. Experimental manipulations are
usually small in scale and continuously
applied (press perturbations sensu Bender
et ai, 1984), while natural transitions are
usually prompted by large-scale pulse perturbations. It is no accident that proposed
examples involve Caribbean-wide epidemics, El Nifios, hurricanes, or ship groundings, events which would be both impractical and unethical to experimentally mimic
once, much less five times. Thus studying
transitions generally requires the use of natural experiments or the fossil record (Jackson, 1992). Natural experiments are by their
nature unreplicated and poorly controlled,
and the mechanisms responsible for past
transitions may be difficult to identify with
certainty.
Studying state stability is equally difficult,
for as Connell and Sousa (1983) rightly point
out, generation times of the participants
often preclude meaningful observations
within human lifetimes, particularly on
reefs. Moreover, the failure of a state to persist does not necessarily imply that it is
intrinsically unstable, for extrinsic disturbances may move the system from one state
to another. For example, recovery of D.
antillarum may currently be occurring
through an inexorable albeit slow increase
MULTIPLE STABLE STATES IN REEF DYNAMICS
in numbers, or recovery may be thwarted
until one or more extrinsically driven pulses
of recruitment occur (Karlson and Levitan,
1990). Distinguishing between these possibilities is not easy, yet only in the latter case
would the apparent failure to recover be an
example of an alternative stable state. One
approach to this problem is to examine the
dynamics of major participants at alternative states using observations and experiments, to determine if the state has characteristics compatible with persistence (see
Dublin et ai, 1990 for a terrestrial example). Again we have the problem of a tightly
controlled experiment, however, as results
will be confounded by either space or time.
Analysis of the dynamics can be based on
data from small scale replicates of/alternative densities maintained simultaneously at
one site {e.g., Levitan, 1991), but confirmation of their validity for natural examples of multiple stable states is highly desirable. One can also examine the duration of
alternative states in the fossil record,
although establishing the similarity of environments across major shifts in community
composition is a problem. Nevertheless, the
fossil record is an invaluable source of information, because the relative sizes of domains
of attraction for alternative states should be
related to their average durations (Jackson,
1992).
Multiple stable states may be difficult to
study using traditional experimental methods, but their theoretical and applied
importance is undeniable (Sinclair, 1989).
Acceptance of their role dramatically alters
our interpretation of variability in time and
space. Moreover, the response of reefs to
natural and man-made disturbances may be
difficult to understand and predict without
considering them. Like astronomers (who
have more substantial problems of spatial
and temporal scale), we must creatively
combine theory, natural experiments, analysis of patterns, and manipulative tests of
predictions (Lawton, 1991) to make progress in studying this difficult but crucial issue.
ACKNOWLEDGMENTS
Many of the ideas for this paper were
developed while the author was on sabbatical at the Department of Zoology and Wolfson College, University of Oxford and in
681
response to audience comments at seminars
throughout the U.K. J. B. C. Jackson, H.
Lessios and D. Levitan critiqued the manuscript, and others made many useful suggestions during the symposium. F. Bouche
prepared the figures.
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