AM=.
1
zoo^., 3 2 5 7 4 4 8 2 (1992)
Thresholds and Multiple Stable States in
Coral Reef Community Dynamics
NANCYKNOWLTON~
Smithsonian Tropical Research Institute, Apartado 2072,
Balboa, Ancon, Republic of Panama
tive stable states for
graphical analyses (Rc
Arthur, 1963; Vanden
the problem of whethc
alternative states is prl
approach focuses on
lates of theoretical
increase the likelihoo
states, drawing on pre
for examples of issues
I
SYNOPSIS.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 ofparticipants at that statesasgeneration 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.
INTRODUCTION
“The straw that broke the camel’s back”
describes the discontinuous response to
continuous change which is a defining 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-
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
when a single environment can stably support two or 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,
1969; Sutherland, 1974, 1990; Noy-Meir,
1975; May, 1977; Connell and Sousa, 1983;
Drake, 1990), and much recent debate has
focused on whether proposed examples Of
I From the Symposium on Long- Term Dynamics of
Coral Reefs presented at the Annual Meeting of the the phenomenon are legitimate. Here I wish
American Society of Zoologists, 27-30 December 199 1, to consider instead a more general question
at Atlanta, Georgia.
Alternate mailing address: Smithsonian Tropical (Drake, 1990): what features make multiple
Research Institute, Unit 0948, Apo AA 34002-0948, stable states more or less likely? I discuss
U.S.A.
previously proposed examples of alterna674
PROFQSED
EXAMPI
STABLEI
Single species interact.
Diadema antillarun
abundant and importa
on many Caribbean re1
fered catastrophic m
most of its range, wit1
areas exceeding two (
Since then in most pk
occurred, although lim
sists (Lessios, 1988, an
*AnAllee effect (All
plest way to model thc
text of multiple stable
Allee effects occur whe
inverse density depen
per capita reproduc
abundance) below a
result is two stable sta
zero density, or as IT
high density and ver
tained by recruitment
two states are separate
sity; populations just
will increase to carryin1
just below will decrea
or extinction.
Experimental work
varying densities in D
1991)supports the sua
Levitan, 1991) that
success at current lou
duce an Allee effect
thereby prevent recoj
ever, many empirical
this comparatively sin
at low density are larg
gametes, so that per cal
at high and low dens
similar than would b
MULTIPLE
STABLE
STATES
IN REEFDYNAMICS
: type
of com-
. Simple the-
ccies dynaminteractions
prey interactition. Poten5 include the
recover fol3algal turf by
If substratum
ns in general,
the existence
:s often need
:riments,” as
large spatial
ialyses of the
the potential
stence as an
ates strongly
ime and our
.vironmental
1
It does not result in
rophytes (Scheffer,
I a particular nutrient
ated by phytoplankMore generally, the
stable states exists
nent can stably supiunities. Sudden and
ige is typical of tran.live stable states.
tiple stable states has
derable interest and
decades (Lewontin,
4, 1990; Noy-Meir,
iell and Sousa, 1983;
:h recent debate has
oposed examples of
$timate. Here I wish
ore general question
tures make multiple
ess likely? I discuss
ramples of alterna-
675
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.
PROPOSED
EXAMPLES
OF MULTIPLE
STABLE
STATES
Single species interactions
Diadema antillarum was once the most
abundant and important generalized grazer
on many Caribbean reefs. In 1983-84 it suffered catastrophic mortality throughout
most of its range, with reductions in some
areas exceeding two orders of magnitude.
Since then in most places recovery has not
occurred, although limited recruitment persists (Lessios, 1988, and references therein).
An Allee effect (Allee, 1931) is the simplest way to model these events in the context of multiple stable states (Yodzis, 1989).
Allee effects occur when reproduction shows
inverse density dependence @e., declining
per capita reproduction with declining
abundance) below a critical density. The
result is two stable states, high density and
zero density, or as modelled in Figure 1,
high density and very low density maintained by recruitment from elsewhere. The
two states are separated by a threshold density; populations just above the threshold
will increase to carrying capacity, while those
just below will decrease to low abundance
or extinction.
Experimental work on fertilization at
varying densities in D. antillarum (Levitan,
1991)supports the suggestion(Lessios, 1988;
Levitan, 1991) that reduced fertilization
success at current low densities could produce an Allee effect in this species and
thereby prevent recovery. There are, however, many empirical uncertainties, even in
this comparativelysimple situation. Urchins
at low density are larger and produce more
gametes, so that per capita reproductiverates
at high and low densities are much more
similar than would be predicted based on
POPUIA’ITON SEE
FIG.1. Dynamics for a single population showing an
Allee effect, combined with some recruitment from
external sources (Yodzis, 1989). Two stable equilibria
are indicated: carrying capacity and a low abundance
maintained by recruitment from elsewhere. In the
absence of external recruitment, the low abundance
equilibrium would be at the origin. The dotted line
shows how catastrophicmortality, such as that suffered
by D. antillarum, could result in a transition from a
high to low abundance state.
fertilization studies alone (Levitan, 1991).
Thus individuals could be approximately
replacing themselves at both high and low
densities. Compensation between fertilization success and gamete production as
described for D. antillarum implies a near
zero growth rate for most population sizes
below the threshold population size (unstable equilibrium of Fig. 1). Alternatively,
decimated populations may be recruitmentlimited (Karlson and Levitan, 1990), with
most new recruits coming from a few source
populations (sensu Pulliam, 1988). Barbados is one possible source population, as
urchins were more abundant there both
before and after the epidemic, and the population appears able to “reseed” itself via
larvae trapped in local eddies (Lessios,
1988). Such a model implies that D. antillarum would go extinct throughout most of
its range in the absence of larval leakage
from source to sink populations (Pulliam,
1988).
In general, Allee effects seem to require
several conditions in order to produce multiple stable states. First, nearly complete
regional elimination is needed, where region
is defined by the limits of routine larval dispersal. This is because Allee effects do not
NANCYKNOWLTON
676
I”
COMPE3TrOR 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 a[.,
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 populationsare 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 Nifio 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 subsequentlygo 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
et al., 1987).
Competitive multiple stable states require
that the alternative dominant species have
broadly similar ecological requirements, for
if they do not, the is1
that intersection at
Given that isoclines
do better than specic
abundant, and specie
species 1 when speci
erwise, stable coexis
tiple stable states oc(
There are two gel
happen. One is whel
tition is more dama
than intraspecific cor
for example, if both
icals to which the con
sitive than the prod
mechanisms might al:
escalated aggressive
closely related specic
specifics, leading to I
cific than intraspecifi
ond way for this to c
ability is positively del
effects (Hutchinson,
non-linear isoclines
example, competitivc
groups than in isolat
generally, species whe
ify the environment
render it inhospitab
(Peterson, 1984). Thi
form of inhibitory SUI
Slatyer, 1977), may c
manence of phase h
dominated and algal
nities (Done, 1992 a,
the growth of corals (
are uncommon may cl
characteristics once a
of abundance to favoi
the detrimental effecdebris on water clarit:
Predation
The failure of stag1
followingdamage caus
in Jamaica has been in
ple of multiple stabk
Predation (Knowlton t
cies was a competitivt
of its rapid growth rai
to return to its presto]
decade (Graus et al., 1
timed to decline, with
MULTIPLE
STABLE
STATES
IN REEFDYNAMICS
populations are reduced
:nsities. Second, reprot decrease or mortality
y low densities for reanpetition or predation
:d below). Finally, if
occur, there must be
lpulations which both
and export recruits to
-marheorganisms this
tern of local and longrsal.
on versus survival are
:s in their own right.
by Allee effects may
i species distributions.
'82-83 El Niiio event
mmediate extinctions
reefs (Glynn and de
n and Colgan, 1992),
I only widely scattered
uently go extinct if they
on external cross-fer:tion, and have propadispersed. Similarly,
:ies are occasionally
Pacific reefs (Colgan,
heir failure to become
Le to low reproductive
her than persistent or
of the exotic habitat.
Y proposed examples
:s in reef composition
:rms of competition.
itive interactions on
msiderable attention
;ky, 1990, for corals),
le general features of
ited.
Ling multiple stable
is simply the case of
:Fig. 2), with stable
or the other species
iaratrix divides the
fthe two stable states,
:s depend on details
quations (Dorschner
:stable states require
minant species have
cal requirements, for
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 Humcane Allen
in Jamaica has been interpreted as an example of multiple stable states mediated by
predation (Knowlton et al., 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 al., 1984). Instead, it continued to decline, with substantial mortality
677
PREY
FIG.3. Dynamics of prey and predator showing alternative stable states of low prey and predatorabundance
versus high prey and moderate predator abundance.
One possible separatnx divides the two domains of
attraction.The dotted line shows how substantialmortality of prey coupled with more modest mortality of
the predator, as was seen in staghorn and staghorn
predator populations following hurricane Allen
(Knowlton et al., 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 Niiio (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 separatnx. 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
NANCYKNOWLTON
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).
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 increasein
the amount of substratum available for colonization
by opportunistic algae) could lead to a transition from
highly palatable microalgae to less palatable macroalgae.
*
i
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
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 communitiesby 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
following the demise
the latter case, respo
important grazer has
(Lessios, 1988). Heah
those in Jamaica are
dominated by unpal;
in Panama, where f
many reefs have nc
algae. Nevertheless,
large amounts of rc
resemble the Jamail
these reefs herbivor
attention on small is1
found in damselfit
observation). It WOL
of algae can escape
of even abundant hc
amounts of substr:
available, thus pern
nation by unpalatat
anisms outlined by
yses illustrate why v
antillarum invariab
biomass on overfish
or may not lead tc
lightly fished reefs (1
atively little differen
high nutrient loads
CHARACTERISTIC
I
MULTIPLE
A disproportiona
ples of multiple st
marine systems (Kn
Table 1 categorizes
pattern in terms o
bances leading to
Allee effects, the pol
libria in predator-p
bility of equilibria
Among marine eco:
subtidal tropical e(
ticularly likely to sh
because they are nc
sonal resetting fron
FIG. 5. Hypothetical
vores (see Fig. 4) on Cai
combinationsof nutriei
abundance. The differei
isoclines before and aft
resent the finding that I
MULTIPLE
STABLE
STATES
IN REEFDYNAMICS
.lation are the product
ighorn populations satbecause reproduction
sively via growth and
than widely dispersing
pilibrium, in contrast,
LOWcyclic or point stacontribute to stability
'e include (1) the predave prey and resistance
uges for the prey, and
'oductive potential in
1seem to apply to stagredators (Knowlton et
:d data).
dation
licit references to mul1 reefs was Hatcher's
:apparently persistent
o unpalatable algae on
1 boat grounding. He
:n increase in substraolonization by algae
sf resident herbivores
Consequently, unpalsize which made them
hivores and avoided.
I densities were maining larvae.
tes for three or more
itable algae, unpalatxes) are more difficult
ize, but a two dimenLch one assumes that
able when scarce and
bundant captures the
n (Fig. 4). In this case
;pecifically herbivore)
i s algae become more
because algal unpalat the same time. As
'ore numbers at high
be comparable to or
vore numbers at low
icular circumstance
mibed was rather
of coral and microalcroalgae has occurred
over the past several
192a, b) and is of parany Caribbean reefs
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
A
8
I
8
l2
2
@
CHARACTERISTICS
OF REEFSFAVORING
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 2
Allee effects, the potential for multiple equi- @
libria 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
because they are not subject to routine, seasonal resetting from strong, annual changes atable algae are avoided to a greater extent by fishes
8
+
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 differencesin shape between herbivore
isoclines before and after D. antillarum mortality represent the finding that common, shallow-waterunpal-
than by urchins (Morrison, 1988). (A) Dynamics before
and after D. antillarum mortality for low nutrients and
overfishing. (B) Dynamics before and after D. antilIarum mortality for low nutrients and high fish abundance. Absence of overfishing results in more steeply
rising predator isoclines compared to (A). (C) 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
TABLE1. Features of reefi which favor multiple stable
states.
Transitions
1. Potential for regional disturbances with interregional transport of recruits.
2. Occasional rather than routine catastrophic disturbance.
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 a flexible metabolic 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 ecologicalanalogs, urchins and fish,
in the sea (Table 1, item 8). The biggest
differences between marine herbivores gen-
erally and herbivorous insects are the far
greater tendency for feeding specialization
in insects and the much larger discrepancy
in generation time between many insects
and their food plants (Hay et al., 1987; Hay
and Fenical, 1988; Hughes and Gliddon,
1991) (Table 1, items 7 and 9).
IMPLICATIONSFOR 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 al., 1984), while natural transitions are
usually prompted by large-scale pulse perturbations. It is no accident that proposed
examples involve Caribbean-wide epidemics, El Niiios, 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.
Studyingstate 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
in numbers, or reco
until one or more ext
of recruitment occur
1990). Distinguishin
bilities is not easy, ye
would the apparent
example of an altern
approach to this pro
dynamics of major
tive states using ob
ments, to determinr
acteristics compatib
Dublin et al., 1990
ple). Again we have
controlled experimc
will be confounded
Analysis of the dyr
data from small SCL
tive densities maint
one site (e.g., Lev
mation of their va'
ples of multiple sta'
able. One can also
alternative states
although establishi
ronments across m
composition is a pr
fossil record is an ii
mation, because thc
of attraction for ab
related to their avc
1992).
Multiple stable
study using traditi
ods, but their t
importance is unc
Acceptance of the
our interpretation
space. Moreover,
natural and man-1
difficult to under:
considering them
have more subst:
and temporal sc
combine theory,
ysis of patterns,
predictions (Law
ress in studyingtk
Acm
Many of the
developed while
ical at the Deparl
son College, Ur
MULTIPLE
STABLE
STATES
IN REEFDYNAMICS
insects are the far
feeding specialization
uch larger discrepancy
ietween many insects
(Hay et al., 1987; Hay
Hughes and Gliddon,
s 7 and 9).
IUS
RESEARCH
er, much of the debate
ites has concerned the
examples. Although I
nples at face value for
n, this does not mean
I work is not required.
i1 aspects which need
rstanding multiple stairal world: transitions
of states. What then
les?
in experimental study
n states must rememprotocol of replicate
lot be appropriate or
tal manipulations are
Je and continuously
bations sensu Bender
atural transitions are
large-scale pulse perxident that proposed
ibbean-wide epidemines, or ship groundiuld be both imprac:xperimentally mimic
times. Thus studying
:quires the use of natie fossil record (Jackperiments are by their
nd poorly controlled,
responsible for past
ficult to identify with
FOR
ity is equally difficult,
sa (1983) rightly point
; of the participants
ingful observations
nes, particularly on
ilure of a state to perrily imply that it is
for extrinsic disturiystem from one state
iple, recovery of D.
:ently be occurring
albeit slow increase
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 al., 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 difficultbut crucial issue.
ACKNOWLEDGMENTS
Many of the ideas for this paper were
developed while the author was on sabbatical at the Department ofZoology and Wolfson College, University of Oxford and in
68 1
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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zoo^., 32:683-695 (
SYNOPSIS.
c
40 years of ec
variety of cal
known and di
tors include o
by sewage nu
causes, humc
bleaching. Th
different sites
is apparently
statistical ana:
in space and .
METI
Diving as a long-ter
tool was started in Ja
late Thomas F. Gore:
leagues and students
reefs the longest dii
marine ecosystem. D
1960s reefs all around
tographed, mapped,
filed, and their species
(Goreau, 1956, 1959;
1973; Goreau, unpub
notes provide unique 1
uating changes during
Before dying in 1970,
the Port Royal Marir
South Coast and the 1
Laboratory on the Nc
subsequent publicatio
well known, but these
tions are not reviewed
on single sites or specie
periods.
Reefs were studied
leagues by a variety c
snorkeling, SCUBA I
photographic quadrat:
From the Symposium o
Coral Reefs presented at tl
American Society of Zoologi
at Atlanta, Georgia.