Self-Organized Patchiness and Catastrophic
Shifts in Ecosystems
Max Rietkerk,
1
*
Stefan C. Dekker,
1
Peter C. de Ruiter,
1
Johan van de Koppel
2
Unexpected sudden catastrophic shifts may occur in ecosystems, with concomitant
losses or gains of ecological and economic resources. Such shifts have been theoretically
attributed to positive feedback and bistability of ecosystem states. However,
verifications and predictive power with respect to catastrophic responses to a changing
environment are lacking for spatially extensive ecosystems. This situation impedes
management and recovery strategies for such ecosystems. Here, we review recent
studies on various ecosystems that link self-organized patchiness to catastrophic shifts
between ecosystem states.
E
cosystems are exposed to changes in
climate, nutrient loading, or biotic
exploitation. How ecosystems undergo
such environmental changes on different
scales of space and time is one of the main
frontiers in ecology. Although environmental
change can be slow and gradual, it may lead
to sudden catastrophic change in the struc-
ture and functioning of ecosystems (1). Such
catastrophes are commonly attributed to the
existence of two alternative stable states in
ecosystems (2), meaning that the dynamics
of these systems are determined by two
attracting states. Here, we define this as
bistability.
Positive feedback control between con-
sumers (e.g., plants) and limiting resources
(e.g., water, nutrients) is considered to be the
principle underlying catastrophic ecosystem
shifts (1–3). This picture emerged from
models that ignore spatial interactions.
Hence, these so-called mean field models
predict bistability in ecosystems as a conse-
quence of positive feedback. We interpret
this as local bistability. Such mean field
analysis is particularly helpful for under-
standing catastrophic shifts in homogeneous
or well-mixed ecosystems. The sudden loss
of transparency in shallow lakes provides an
illustrative example (4, 5). However, verifi-
cations and predictive power of catastrophic
shifts are lacking for spatially extensive,
heterogeneous ecosystems. As a result,
sustainable management and recovery strat-
egies for such ecosystems have been difficult
to devise; they require an understanding of
the relation between feedback and spatial
scale.
We review recent ecosystem studies that
include feedback control and spatial scale
(Table 1 and Fig. 1). These studies link feed-
back control to self-organized patchiness of
consumers and resources, and they show that a
resource concentration mechanism invoked by
consumers explains the diversity of spatial
structures in these ecosystems. Such consum-
ers have previously been called Becosystem
engineers[ (6). Spatial self-organization is
not imposed on any system but emerges from
fine-scale interactions owing to internal
causes (7). Moreover, model outcomes show
that ecosystems where this resource concen-
tration mechanism operates exhibit bistability
between a specific spatially structured and
homogeneous ecosystem state. We define the
bistability at large spatial scales predicted by
these spatially explicit models as global
bistability.
Similar to the mean field models, global
bistability in spatially explicit models is asso-
ciated with catastrophic shifts at large spatial
scales between coexisting stable states.
Hence, these results stress the importance of
self-organized patchiness for a better under-
standing of catastrophic shifts. Increased re-
source scarcity leads to spatial reorganization
of consumers and resources in these model
ecosystems, and an ecosystem state develops
with localized structures observed in reality.
Once resource scarcity reaches a threshold,
the system shifts toward a homogeneous state
REVIEW
1
Department of Environmental Sciences, Copernicus
Institute, Utrecht University, P.O. Box 80115, 3508
TC Utrecht, Netherlands.
2
Spatial Ecology Depart-
ment, Netherlands Institute of Ecology, P.O. Box 140,
4400 AC Yerseke, Netherlands.
*To whom correspondence should be addressed.
E-mail: m.rietkerk@geog.uu.nl
Table 1. Overview of references describing self-organized patchiness in some major ecosystems and the mechanisms involved.
Ecosystem References Pattern characteristics (scale) Mechanisms involved
Arid (8, 11) Spots, labyrinths, gaps (1 m) and stripes (10 m)
(Fig. 1C)
Redistribution of soil water due to positive feedback
among plant biomass, extent of root system, and
water uptake
(9, 14) Periodic spots and bands (10 to 100 m) Short-range facilitation and long-range competition
for limiting water
(12) Spots, labyrinths, gaps, and stripes (10 to 100 m)
(Fig. 1, A and B)
Redistribution of surface water due to positive
feedback between plant cover and water infiltration
(13) Disordered spots and clustered spots on hillslope
contours (10 to 100 m)
Competition for limiting water
Savanna (15) Isolated spots of trees and shrubs in grass matrix
(10 to 100 m) (Fig. 1, D and E)
Short-range facilitation and long-range competition
for limiting nutrients
Peatland (24) String patterns (10 m) Ponding of surface water upstream from hummocks
combined with positive feedback between hum-
mock occurrence and water table depth
(25) Maze and string patterns perpendicular to flow
direction (10 m) (Fig. 1, F and G)
Convective transport of limited nutrients in the
groundwater toward areas with higher plant
biomass, driven by differences in transpiration rate
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1926
without consumers functioning as ecosystem
engineers. Increasing resource availability
does not recover these localized structures,
because the resource concentration mecha-
nism fails. This phenomenon is called hyster-
esis, meaning that specific spatial structures
may develop in real ecosystems that only
arise when resource availability is de-
creased, but not when increased. There-
fore, we propose the hypothesis that
imminent catastrophic shifts in ecosys-
tems can be predicted by self-organized
patchiness.
Arid Ecosystems
Self-organized patchiness and the re-
source concentration mechanisms in-
volved have been reported from various
ecosystems (Table 1 and Fig. 1), among
whicharidecosystemsarethemost
prominent (8–14). The self-organized
patchiness in these ecosystems differs
in scale and shape. Patterns reported are
gaps, labyrinths, stripes (‘‘tiger bush’’)
(Fig. 1, A to C), and spots (‘‘leopard
bush’’).
The general mechanism underlying
this self-organized patchiness is a pos-
itive feedback between plant growth and
availability of water. Higher vegetation
density allows for higher water infiltra-
tion into the soil (because of root
penetration) and lower soil evaporation
(because of shading). As a result, vege-
tation persists once present, but bare soil
is too hostile for recolonization after the
vegetation disappears, implying that the
present state of the vegetation depends
on its history (3).
Recent studies link this positive feed-
back with subsequent redistribution of
water resources (10–12). Lateral flow of
subsurface soil water at a scale of 0.1 m,
driven by differences in evapotranspira-
tion, explains regular patterning of grasses
in the Negev desert (11) (Fig. 1C).
Redistribution of surface runoff water
at a scale of 10 m, driven by differences
in water infiltration, elucidates the for-
mation of self-organized patchiness in
arid bushlands (12) (Fig. 1, A and B).
These observations show that similar
patterns of self-organized patchiness
may emerge at different scales. Eco-
system transitions involve a sequence
of emerging patterns of various forms
induced by decreased rainfall. Vegeta-
tion states include homogeneous cover,
gaps, labyrinths or stripes, and spots, in
that order (11, 12, 14). More important,
in these models the vegetation shifts
catastrophically from the spotted state
to a bare homogeneous state if rainfall
is decreased beyond a threshold. This
can be attributed to global bistability
of the spotted and bare states. Hence, a
predictable form of self-organized patchi-
ness may indicate imminent catastrophic
shift to a bare homogeneous state. Increased
rainfall may not recover the spotted state,
because the resource concentration mecha-
nism (concentration of soil water under veg-
etated patches) fails (11).
Savanna Ecosystems
In nutrient-poor Savanna ecosystems, periodic
and aperiodic isolated spots of trees and shrubs
Fig. 1. Field observations. (A to C) Arid ecosystems: (A) Labyrinth of bushy vegetation in Niger [(12), *
2002 University of Chicago]; (B) Striped pattern of bushy vegetation in Niger; (C) Labyrinth of perennial
grass Paspalum vaginatum in Israel [(11), * 2001 American Physical Society]. (D and E) Savanna
ecosystems: Aerial and ground photographs of spots of tree patches in Ivory Coast and French Guiana,
respectively [(15), * 2002 American Physical Society]. (F and G) Peatlands: Regular maze patterns of
shrubs and trees in western Siberia [(25), * 2004 University of Chicago]. Scales of oblique aerial
photographs [all panels except (E)] are order-of-magnitude approximations of distance in the x direction
shown in the scale bars.
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at a scale of 10 to 100 m in grassland are
observed (15) (Fig. 1, D and E). Lejeune et al.
(15) proposed an interaction-redistribution
model of vegetation dynamics generating
these patterns even under homogeneous con-
ditions. Their model is grounded on the
balance between short-range facilitation and
long-range competition. The mechanistic base
is provided by observations that in nutrient-
poor environments, trees and shrubs can have
positive effects on each other and on them-
selves because of local nutrient accumulation
as well as the ability of long superficial roots
to track scarce nutrients from the surroundings
(16–18).
Other plausible mechanisms coupling
short-range facilitation with long-range com-
petition are nutrient retention by the binding
of soil by roots, raindrop interception, and
runoff retention, all of which prevent erosion
(3). This forms the mechanistic base of the
concept of ‘‘islands of fertility’’ (19),
explaining soil fertility under canopies of
trees and shrubs by local nutrient accumula-
tion and recycling. The observed patterns are
interpreted as localized structures arising
from global bistability between a ‘‘bare’’
state (no trees and shrubs) and a self-
organized patchy state. Hence, Lejeune
et al.(15) predicted the possibility of a sta-
ble homogeneous state and a self-organized
patchy state for the same resource avail-
ability, with catastrophic shifts be-
tween these states. As resource avail-
ability diminishes, the vegetation goes
through a predictable sequence of
emerging patterns comparable to that
described above for arid ecosystems
(11, 12, 14, 15).
Peatland Ecosystems
Bogs in North America and Eurasia
commonly show various spatial pat-
terning (20, 21), including regular
string patterns of densely vegetated
bands at a scale of 10 m (hummocks
forming ridges) oriented perpendicular
to the slope, alternating with more
sparsely vegetated wetter zones (hol-
lows forming pools) (22–24). Other
regular patterns recently reported are
maze patterns: bands densely vege-
tated by vascular plants at a scale of
10 m in a more sparsely vegetated
matrix of predominantly nonvascular
plants (25) (Fig. 1, F and G). A gen-
eral mechanism underlying patterning
in these ecosystems is a positive
feedback between plant productivity
and groundwater depth on elevated,
drier sites, mainly due to increased
production of vascular plants.
Rietkerk et al.(25)proposedthe
convective transport of nutrients in
the groundwater toward areas with
higher vascular plant biomass, driven by
differences in transpiration, as a mechanism
to explain regular string and maze patterns.
If plant productivity is limited by nutrient
flow, this local ‘‘nutrient accumulation’’
mechanism may lead to self-organized patch-
iness such as the observed string patterns on
slopes and maze patterns on flat ground.
Mean field models including this positive
feedback allow for the occurrence of lo-
cal bistability (thin peat with high water
table coexisting with thick peat with low
water table) for the same precipitation lev-
el, and catastrophic shifts between these
states (26, 27). Rietkerk et al.(25)pre-
dicted the possibility of global bistability
(nonhomogeneous equilibrium with vas-
cular plants and homogeneous equilibrium
without vascular plants) for the same pre-
cipitation and nutrient input level, and cat-
astrophic shifts between these states. Here,
the vegetation also goes through a sequence
of predictable patterns with decreasing nu-
trient input.
Self-Organized Patchiness and
Catastrophic Shifts
Mean field models that ignore the relation
between feedback and spatial scale predict
local bistability and catastrophic shifts in the
ecosystems discussed here (1, 3, 26–28).
Recent studies show that spatially explicit
models including the resource concentration
mechanism predict global bistability associ-
ated with catastrophic shifts at large spatial
scales and self-organized patchiness. Obser-
vations confirm the model results. A variety
of mechanisms in ecosystems lead to
resource concentration through consumer-
resource feedback. The consumers harvest
resources from their surroundings; in the
ecosystems discussed here, harvest is facili-
tated by mass flow of resources toward
consumers, triggered by the consumers them-
selves. Furthermore, consumers spread rela-
tively slowly as compared to flow of
resources. A general pattern emerging from
these observations is that consumers are
positively associated with resource abun-
dance at short spatial range, but negatively
at long spatial range (29). Thus, a common
principle applies to these locally reinforced
consumers, in that there is a positive feed-
back effect that is short-ranged and a
negative feedback effect that is long-ranged.
This is a necessary condition for self-
organized patchiness to form (14).
We generated new results from a simple
cellular automaton based on the model of
Thiery et al.(30) exemplifying how such
scale-dependent feedback can explain a diver-
sity of patterns in ecosystems (Fig. 2,
supporting online text, and movie S1). The
differences in structure and scale of patchiness
are the result only of varying strength and
scale of feedback influence (14), illustrat-
ing the general nature of the underlying
scale-dependent mechanisms explaining self-
organized patchiness in ecosystems.
The notion of scale-dependent feedback
controlled by the resource concentration
mechanism is crucial for a predictive theory
of catastrophic shifts in ecosystems. This sug-
gests that catastrophic shifts can be predicted
by self-organized patchiness (Fig. 3). There-
fore, the concepts of catastrophic shifts and
self-organized patchiness are tightly linked,
whereby a scale-dependent feedback is
triggered by resource concentration.
Ecosystems with scale-dependent feedback
resemble the activator-inhibitor system first
described by Turing (31). In the ecosystems
discussed here, the inhibition effect results
from the large-scale depletion of a resource
that is consumed during the localized produc-
tion of the activator (consumer). The activator
effect results from the local positive feedback
control between the consumer and its limited
resource (water or nutrient availability). These
ecosystems represent a class of activator-
inhibitor system that has been recognized
earlier as ‘‘activator-depleted substrate sys-
tems’’ (32). Indeed, theoretical analyses of an
activator-depleted substrate system also predict
global bistability and catastrophic shifts be-
tween spotted and uniform states (33). Exper-
imental evidence of global bistability and
Fig. 2. Model results from a modified version of the
Thiery et al.(30) cellular automaton, showing stable
isotropic vegetation patterns after time step t 0 15
(supporting online text and movie S1). Grid size is
500 500 cells. Black areas represent vegetation in
maximum state 5; white areas represent bare soil in
minimum state 0. Simulations were started by ran-
domly introducing vegetation state 2 on 5% of the
cells. Vegetation patterns are the result of fine-scale
positive feedback and coarse-scale negative feedback.
On the x axis, the strength of the positive feedback is
increased; on the y axis, the scale of influence is
decreased. Patterns change from spots to labyrinths
and gaps at different spatial scales.
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1928
hysteresis between states of spots and stripes
comes from such a system as well (34, 35).
Most theoretical approaches to self-
organized patchiness in ecosystems are
based on the same framework of models as
are used to explain pattern formation in
chemical systems and biological pattern for-
mation on sea shells (32) and animal coats
(36). Here, we concentrated on the overlap
between ecosystems exhibiting both self-
organized patchiness and catastrophic shifts
due to global bistability. The resource concen-
tration mechanism invoked
by ecosystem engineers
provides a general expla-
nation, because ecosystem
engineers at low densities
may be unable to harvest
resources from the sur-
roundings. We suggest that
all ecosystems with self-
organized patchiness re-
sulting from a resource
concentration mechanism
will also exhibit cata-
strophic shifts.
Challenges Ahead
Linking self-organized
patchiness with cata-
strophic shifts by the
resource concentration
mechanism may help to
bridge the present gaps
among theory, observation,
and management (2). The
link may be crucial to a
predictive theory of cata-
strophic shifts from which
early-warning systems can
be developed on the basis
of spatial explicit time-
series data. This is because
predictable forms of self-
organized patchiness may
indicate imminent cat-
astrophic shifts if resource input decreases
in time (Fig. 3). For instance, the spotted state
may develop only when resource input is de-
creased, not when it is increased. This means
that a snapshot in time of a spotted state would
already indicate imminent catastrophic shift.
Human management strategies could be
directed toward preserving and restoring
self-organized patchiness and its natural
resource concentration function (12, 37).
Vegetation structures in resource-poor agro-
ecosystems, such as the African Sahel, may
lose this function because of overgrazing by
cattle, leading to catastrophic shifts to a
desertified ecosystem state. Adequate graz-
ing management of rangelands and patchy
crop production to conserve resources in
marginally arable lands may help to optimize
productivity, thereby preventing such cata-
strophic shifts.
Although this is a promising perspective,
we are far from quantitative predictions. For
that, we need to move away from models that
ignore space and therefore generate only
qualitative predictions. A key question con-
cerns how local geological and soil differ-
ences, seasonality in rainfall, and random
processes affect self-organized patchiness
and ecosystem resistance against catastroph-
ic shifts. Furthermore, the fact that self-
organized patchiness and catastrophic shifts
may occur at different spatial and temporal
scales (11, 12) provides new perspectives for
fine-scale and relatively short-term experiments
to predict large-scale self-organized patchi-
ness and catastrophic shifts in ecosystems.
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Supporting Online Material
www.sciencemag.org/cgi/content/full/305/5692/1926/
DC1
SOM Text
Movie S1
Resource input
Equilibrium density of
ecosystem engineer
Catastrophic shift
from self-
organized
patchy to
homogeneous
state
Catastrophic shift
from
homogeneous to
self-organized
patchy state
Region of
global bistability
Fig. 3. Model showing how ecosystems may undergo a predictable sequence of
emerging self-organized patchiness as resource input decreases or increases (11, 12, 14,
25). Thick solid lines represent mean equilibrium densities of consumers functioning as
ecosystem engineers. Dotted arrows represent catastrophic shifts between self-
organized patchy and homogeneous states, and vice versa. Dark colors in the insets
represent high density. The range of resource input for which global bistability and
hysteresis exists is between these dotted arrows. Solid arrows represent development
of the system toward the coexisting self-organized patchy state or homogeneous state,
depending on initial ecosystem engineer densities.
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![Fig. 1. Field observations. (A to C) Arid ecosystems: (A) Labyrinth of bushy vegetation in Niger [(12), * 2002 University of Chicago]; (B) Striped pattern of bushy vegetation in Niger; (C) Labyrinth of perennial grass Paspalum vaginatum in Israel [(11), * 2001 American Physical Society]. (D and E) Savanna ecosystems: Aerial and ground photographs of spots of tree patches in Ivory Coast and French Guiana, respectively [(15), * 2002 American Physical Society]. (F and G) Peatlands: Regular maze patterns of shrubs and trees in western Siberia [(25), * 2004 University of Chicago]. Scales of oblique aerial photographs [all panels except (E)] are order-of-magnitude approximations of distance in the x direction shown in the scale bars.](/figures/fig-1-field-observations-a-to-c-arid-ecosystems-a-labyrinth-w6tdr50x.webp)
