© 2008 The Authors DOI: 10.1111/j.1466-8238.2008.00413.xJournal compilation © 2008 Blackwell Publishing Ltd www.blackwellpublishing.com/geb

1

Global Ecology and Biogeography, (Global Ecol. Biogeogr.)

(2008)

RESEARCHPAPER

Blackwell Publishing Ltd

The global biogeography of semi-arid periodic vegetation patterns

Vincent Deblauwe

1

*, Nicolas Barbier

2

, Pierre Couteron

3

, Olivier Lejeune

4

and

Jan Bogaert

1

ABSTRACT

Aim

Vegetation exhibiting landscape-scale regular spatial patterns has beenreported for arid and semi-arid areas world-wide. Recent theories state that suchstructures are bound to low-productivity environments and result from a self-organization process. Our objective was to test this relationship between periodicpattern occurrence and environmental factors at a global scale and to parametrize apredictive distribution model.

Location

Arid and semi-arid areas world-wide.

Methods

We trained an empirical predictive model (Maxent) for the occurrenceof periodic vegetation patterns, based on environmental predictors and knownoccurrences verified on Landsat satellite images.

Results

This model allowed us to discover previously unreported pattern locations,and to report the first ever examples of spotted patterns in natural systems. Relation-ships to the main environmental drivers are discussed.

Main conclusions

These results confirm that periodic patterned vegetations areubiquitous at the interface between arid and semi-arid regions. Self-organizedpatterning appears therefore to be a biome-scale response to environmental conditions,including soil and topography. The set of correlations between vegetation patternsand their environmental conditions presented in this study will need to be reproducedin future modelling attempts.

Keywords

Aridity, banded vegetation, bioclimatic envelope, hierarchical partitioning, maximum

entropy, periodic vegetation pattern, self-organization, tiger bush.

*Correspondence: Vincent Deblauwe, Université Libre de Bruxelles, Laboratoire d’Écologie du Paysage, CP 169, Avenue F. Roosevelt 50, B-1050 Bruxelles, Belgium. E-mail: vdeblauw@ulb.ac.be

1

FRIA Fellow, Laboratoire d’Ecologie du

Paysage, Université Libre de Bruxelles, CP 169,

B-1050 Bruxelles, Belgium,

2

FNRS – Wiener

Anspach Post-Doctoral Research Fellow, Service

de Botanique Systématique et Phytosociologie,

Université Libre de Bruxelles, CP 169, B-1050

Bruxelles, Belgium/Oxford University Center for

the Environment (OUCE-ECI), Oxford OX1

3QY, UK,

3

French Institute of Pondicherry

(IFP), Pondicherry 605 001, India/Institut de

Recherche pour le Développement (IRD),

Joint Research Unit (UMR) botAny and

coMputAtional Plant architecture (AMAP),

Montpellier, F-34398 France,

4

Département

de Mathématiques Appliquées, Ecole Normale

Supérieure, 75230 Paris Cedex 05, France/

Faculté des Sciences, Université Libre de

Bruxelles, CP 231, B-1050 Bruxelles, Belgium

INTRODUCTION

Competition for resources is obvious in (semi-)arid regions and

is reflected by the low overall vegetation biomass. However, plant

cover is usually not homogenously sparse, and dense vegetated

patches are often dispersed within areas of lower (Dunkerley,

2002) or null productivity (e.g. Mabbutt & Fanning, 1987;

Cornet

et al

., 1988; Valentin & D’herbes, 1999), suggesting the

involvement of other kinds of inter-plant interactions and/or

redistribution mechanisms. In fact, limiting resources and

important biogeochemical processes have been found to be

concentrated within these dense patches, for which the term

‘islands of fertility’ has been coined (Schlesinger

et al

., 1990; Ludwig

et al

., 2005). In a number of cases, patchy arid vegetation can

display landscape-scale patterns that are strikingly regular in

space and easy to recognize on aerial views. These spatially

periodic vegetation patterns (PVP) have been reported as being

formed of gaps, labyrinths or stripes (Fig. 1) at scales ranging

from tens to hundreds of metres, therefore exceeding by more

than one order of magnitude the size of individual plants. The

observed heterogeneities of surface and soil properties, such as

soil crusting, structure, texture, organic matter content, salt

concentration or even a consistent microtopography, can be

explained directly by feedbacks induced by the vegetation itself

(Valentin

et al

., 1999; Saco

et al

., 2007).

Most field studies have focused on the case of stripes on gently

sloped terrains (but see Barbier

et al

., 2008), which are sometimes

referred to as ‘tiger bush’, and have been interpreted as natural,

runoff-based, water harvesting systems (Tongway

et al

., 2001).

Beyond stripes, progress towards a unified understanding of this

patterning phenomenon has been achieved recently within the

framework of self-organization theory (Nicolis & Prigogine,

V. Deblauwe

et al.

© 2008 The Authors

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Global Ecology and Biogeography

, Journal compilation © 2008 Blackwell Publishing Ltd

1977; Cross & Hohenberg, 1993). Mechanistic models have

shown that the observed variety of landscape-scale vegetation

patterns can result from plant–plant interactions mediated by

the collection, sheltering and consumption of key resources. Due

to the lack of sufficient field observations and experiments, the

effective pattern formation mechanisms still remain hypothetical.

Those models either invoke an active transport of resources,

mainly water, through roots (see Lefever & Lejeune, 1997,

Couteron & Lejeune, 2001, for theory and Barbier

et al

., 2008, for

field account) or a passive transport via diffusion underground

or flow over the soil surface (Klausmeier, 1999; Hillerislambers

et al

., 2001; Von Hardenberg

et al

., 2001; Rietkerk

et al

., 2002).

The latter case may also involve redistribution of sediments (Saco

et al

., 2007). However, all self-organization models converge on

the prediction that regular patterning occurs when the negative

effects of individual plants on resource availability (competition)

are balanced by positive effects (facilitation) and when the scale

of resource transport, either the root system size or the diffusion

range, exceeds the other spatial scales, namely the facilitation or

the plant dispersion ranges. As environmental constraints limit-

ing biological productivity increase, competition gets harsher

and correlatively the role of facilitation becomes more important

(Callaway, 1995). Self-organization models predict the following

sequence of PVP morphologies in isotropic environments as

constraints increase above a critical threshold (Lejeune & Tlidi,

1999; Couteron & Lejeune, 2001; Von Hardenberg

et al

., 2001;

Rietkerk

et al

., 2002): (1) gaps of bare soil appear in an initially

uniform vegetation cover; (2) bare gaps elongate and merge

to form stripes without dominant orientation, i.e. labyrinths;

(3) the corresponding stripes of vegetation break into spots that

eventually disappear. To our knowledge no field account of

the latter has yet been reported. Anisotropic factors such as

ground slope may induce a shift from gaps, labyrinths or

spots of vegetation to stripes with a dominant orientation, i.e.

tiger bush (Lefever & Lejeune, 1997; Von Hardenberg

et al

.,

2001).

So far, this fundamental prediction of self-organization

models has not been verified at the biogeographical scale. The

increasing accessibility and resolution of global-scale data sets of

both satellite imagery and environmental variables offers an

unprecedented opportunity to address its relevance. Indeed, the

validity of self-organization models necessitates that: (1) PVPs

should consistently be observed within a restricted range of

environmental conditions, determined by the existence of critical

thresholds; (2) it should be possible to identify key environmental

predictors among the available set of climatic and edaphic variables

documented at a global scale; (3) all periodic morphologies

predicted by self-organization models should be found in natural

systems. We addressed these hypotheses by means of an empirical

model in which the environmental envelope encompassing

Figure 1 Oblique (a, b, d, e) and vertical (c) satellite images of periodic vegetation patterns. These are formerly unrecordedlocations the occurrence of which was predicted by the potential distribution model that include spots (a, 11°37′ N, 27°57′ E), labyrinths (b, 11°08′ N, 27°50′ E) and stripes and gaps (c, 11°04′ N, 28°18′ E) in the Sudan, gaps in eastern Africa (d, 0°42′ N, 40°24′ E) and bands in Baja California Peninsula (e, 26°49′ N, 112°52′ W). QuickBird © DigitalGlobe, distributed by Eurimage (a, b, d, e). European OASIS project, © CNES 2001 – Spot Image distribution (c).

Global biogeography of periodic vegetation patterns

© 2008 The Authors

Global Ecology and Biogeography

, Journal compilation © 2008 Blackwell Publishing Ltd

3

known PVP occurrences was defined and served as a predictive

tool to outline potential areas of occurrence.

MATERIALS AND METHODS

Occurrences

Published occurrences of PVPs, as summarized in Table 1, were

used as reference points to map PVPs on Landsat Enhanced

Thematic Mapper + panchromatic satellite images acquired

from 1997 to 2003. The neighbourhood (up to 50 km) around

the published field records was visually explored on images and

all observed PVPs were digitized. Due to the image resolution (15

m), only periodic vegetation displaying a wavelength of at least

60 m was recorded. Of these, patterns obviously reflecting

pre-existing substratum heterogeneities (such as dunes) were

rejected in order to focus on potentially self-organized PVPs. A

presence–absence grid (0.5

°

×

0.5

°

cells) was constructed from

the polygons delineating the reference PVP areas. The grid

resolution was set to match the lowest spatial resolution available

for the environmental predictors (see below). Hereafter, grid cells

with PVP presence will be referred to as presence points. The

aforementioned approach allowed us to determine 249 PVP

location points.

Environmental predictors

We started by considering 29 potentially relevant environmental

predictors (GIS layers) dealing with climatic (various indices

related to the annual distribution of both temperature and

precipitation), topographic and soil attributes. (1) Climate-related

indices: annual mean temperature; mean diurnal range;

temperature annual range; isothermality (i.e. mean temperature

diurnal range divided by temperature annual range); temperature

seasonality (i.e. standard deviation of monthly temperatures);

maximum temperature of warmest month; minimum temperature

of coldest month; mean temperature of wettest, driest, warmest

and coldest quarters; mean annual precipitation; precipitation of

the wettest and driest months; precipitation seasonality (i.e.

coefficient of variation of monthly precipitation); precipitation

of wettest, driest, warmest and coldest quarters; all taken from

WorldClim global climate layers (1950–2000) (Hijmans

et al

.,

2005); mean annual potential evapotranspiration (1987–88)

calculated by the Penman–Monteith equation (Choudhury,

1997); a humidity index, defined as the ratio of mean annual

rainfall to mean annual potential evapotranspiration (UNEP,

1992). (2) Topography-related indices: altitude and slope derived

from Shuttle Radar Topography Mission (SRTM). (3) Soil

characteristics: bulk density; field capacity; available water

capacity; total nitrogen density and wilting point from the

Global Soil Data Task Group, 2000, Global Gridded Surfaces of

Selected Soil Characteristics (International Geosphere–

Biosphere Programme – Data and Information System; http://

www.daac.ornl.gov).

The spatial resolution of the analysis is determined by that of

the coarsest data set, i.e. the humidity index, with a 0.5

°

pixel size

(

c

. 50 km in the tropics). All other layers had to be upscaled (via

averaging) to match this resolution.

Table 1 Detail of the field data used for model training. Mean annual precipitation (MAP; mm), and humidity index (HI: MAP/annual evapotranspiration), were extracted from the corresponding gridded data set.

Region Perennial vegetation MAP (HI) Reference

Eastern Africa

Somalia (N of lat. 8°) Tussock grasses (Andropogon kelleri or Chrysopogon aucheri) and

few shrubs (e.g. Acacia bussei)

160–400 (0.05–0.24) Boaler & Hodge (1964)

Ethiopia (Ogaden) Not described 200–410 (0.14–0.21) Riché & Ségalen (1971)

Sudan (western Kurdufan) Shrubs (Acacia mellifera, Terminalia brownii) 350 (0.17) Wickens & Collier (1971)

Sahelian Africa

Niger (Tillabéri and Dosso) Shrubs (Combretum micranthum, Guiera senegalensis) 400–790 (0.11–0.40) Valentin & d’Herbès (1999),

Barbier et al. (2006)

Mali (Mopti) Shrubs (Combretum micranthum) 350–630 (0.10–0.23) Leprun (1999)

Mauritania (Hodh) Grass (Andropogon Gayanus) and few shrubs (e.g. Pterocarpus lucens) 270–340 (0.08–0.09) Audry & Rossetti (1962)

Senegal (Ferlo/Saint-Louis) Shrubs (Combretum micranthum, Pterocarpus lucens) 340–420 (0.12–0.19) De Wispelaere (1980)

Australia

Western Australia Mulga (Acacia aneura) shrubs 270–580 (0.10–0.20) Mabbut & Fanning (1987)

Northern Territory Mulga (Acacia aneura) shrubs in groves and perennial grass in

intergroves

300–350 (0.16–0.18) Dunkerley (2002)

Western New South Wales Tussock grass (Astrebla pectinata) and chenopod shrub

(Atriplex vesicaria)

190–230 (0.11–0.16) Dunkerley & Brown (1999)

South-Western Queensland Mulga (Acacia aneura) shrubs and grass 270–460 (0.13–0.27) Tongway & Ludwig (1990)

Mexico

Chihuahuan desert Shrubs (Flourensia cernua, Prosopis glandulosa) and grass

(Hilaria mutica)

210–450 (0.15–0.29) Cornet et al. (1988)

V. Deblauwe

et al.

© 2008 The Authors

4

Global Ecology and Biogeography

, Journal compilation © 2008 Blackwell Publishing Ltd

A jackknife procedure (Guisan & Zimmermann, 2000) was

applied to remove the environmental predictors displaying only

a weak influence on model goodness of fit.

Potential distribution

We used a maximum entropy (Maxent version 2.3) modelling

approach to delineate the environmental envelope encompassing

a random 75% subset (the rest being kept for validation, see

below) of recorded occurrences of PVPs. This enabled us to

generate a potential distribution model for PVP occurrence and

to derive a global predictive map.

Maxent is a machine learning algorithm available as PC-

implemented software (Phillips

et al

., 2006) that has been shown

to be particularly efficient for modelling species distributions

(Elith

et al

., 2006). It is a nonparametric method offering a good

trade-off between interpretability and ability to take into account

complex response curves. The algorithm iteratively computes the

probability distribution of the response that maximizes entropy

(i.e. is closest to a uniform distribution) while meeting the constraint

that the expected value of each environmental predictor (or its

transform) under this estimated distribution matches its empirical

average (Phillips

et al

., 2006). The output values for the predicted

distributions are cumulative, with the output value of a grid cell

being the sum of the probabilities of all grid cells of lower or equal

value to the probability of the considered grid cell. In other

words, the set of values higher than 5% incorporates the 95% of

the probability distribution around the ecological optimum.

Partition of explained variability

Hierarchical partitioning (HP) (Chevan & Sutherland, 1991;

Mac Nally, 2000) aims at partitioning the explained variability

(goodness-of-fit) in a multivariate setting between individual

predictors displaying substantial multicolinearity, and at

estimating the independent versus the conjoint effects of each

predictor. The main purpose of HP is not to select the most

parsimonious model but rather to give a basis for inferring probable

causality. HP was applied with our own Matlab® implemented

routines, on the log-likelihood (deviance) of the potential distribution

map computed with the training presence points, which was

used as a measure of goodness of fit (Phillips

et al

., 2006).

Performance evaluation

We tested the predictive success of the potential distribution

model by cross-validation (Guisan & Zimmermann, 2000) using

independent test points (i.e. the 25% of known location points

excluded from model building) for presence and a random set of

1000 pseudo-absence points (Phillips

et al

., 2006). The latter

were taken in arid and semi-arid regions (i.e. for a humidity

index ranging from 0.05 to 0.5; UNEP, 1992) in order to avoid an

overestimation of the rate of well-predicted absence. Per-

formance of the model was assessed by calculating the area under

the curve (AUC) of a receiver operating characteristic (ROC)

plot (Fielding & Bell, 1997; Guisan & Zimmermann, 2000). This

index has been extensively used in the literature on the

prediction of species distribution since it is a nonparametric,

class-prevalence-insensitive and threshold-independent index of

overall accuracy. An AUC of 0.5 indicates a random relationship

between predicted and observed classes, while an AUC of 1

corresponds to perfect prediction.

RESULTS

Jackknifing of the environmental variables allowed us to exclude

indirect (e.g. altitude), redundant or irrelevant predictors. Only

nine predictors were kept to build the final potential distribution

map (Figs 2 & 3): humidity index, mean temperature of wettest

quarter, temperature seasonality, wilting point, mean annual

precipitation, temperature mean diurnal range, precipitation of

warmest quarter, precipitation seasonality and slope. The values

on the map represent the statistical envelope surrounding the

modelled ecological optimum based on these predictors. Each

predictor kept in the model independently contributed to a

substantial part of the explained variability in the occurrence of

PVPs, according to the ‘hierarchical partitioning approach’

(Fig. 3). A notable multicolinearity was still present in the data

set, as was shown by the conjoint effects (i.e. effects shared by at

least two predictors). The humidity index, given by the ratio of

the mean annual rainfall to the mean annual potential evapotran-

spiration, was the predictor accounting for the largest independent

part of variance explained by our model.

Figure 4 shows the observed (bars) and predicted (line)

frequency distribution of PVPs as a function of the four most

important explanatory variables in terms of independent effect.

The relation between PVP occurrence and the humidity index

was clearly unimodal, and was situated between 0.04 and 0.33. It

shows that PVPs only occur when the evapotranspiration is at

least three times as high as the rainfall. For the second most

important variable, namely the mean temperature of the wettest

quarter, the distribution was slightly bimodal, showing an

anecdotic peak for PVPs occurring in wet winter areas (south-west

Australian ‘mediterranean’ areas), whilst the great majority of

PVPs belonged to tropical wet summer areas. The third factor,

temperature seasonality, showed a clearer bimodal distribution,

distinguishing the subtropical African PVPs, which were found

for nearly constant temperature regimes, from PVPs occurring in

Mexico and Australia (including the aforementioned ‘mediterranean’

areas as a special case) where temperature seasonality is higher.

The fourth explanatory variable, soil wilting point, showed that

soil properties, and in particular soil texture, are a determining

factor in addition to climatic features. For instance, low wilting

point values, associated with sandy soils, appeared to be unsuitable

for the occurrence of PVPs. Other important environmental

predictors (figures not shown) were, in order of decreasing

independent contribution: the annual precipitation, which must

be less than 400 mm except in the Sahelian band where it can

reach up to 700 mm; the temperature diurnal range which is

characteristically high in arid environments, with patterns

occurring within the 12–18

°

C range; the precipitation seasonality

which shows a bimodal distribution, with a less marked seasonal

Global biogeography of periodic vegetation patterns

© 2008 The Authors

Global Ecology and Biogeography

, Journal compilation © 2008 Blackwell Publishing Ltd

5

regime in Australia and Mexico than in Africa, which is the

opposite pattern to temperature seasonality; finally the slope,

which must be less than 2%.

The AUC (Fielding & Bell, 1997; Guisan & Zimmermann,

2000) reached a score of 0.96 (95% CI,

±

0.01). This index is com-

puted as the probability for randomly selected presence points to

obtain a higher predicted score than a random selection of

absence points (Elith

et al

., 2006; Phillips

et al

., 2006). This result

therefore indicated a strong predictive power of the potential

distribution model. Visual examination of images from the area

encompassing 75% of the probability distribution function around

the ecological optimum (i.e. all values on the map superior to

0.25) confirmed the pertinence of these predictions by revealing

extensive, yet previously unreported, areas featuring PVPs. These

areas include the Sonoran Desert down to the Baja California

Peninsula (Figs 1e, 2d), the Argentinean arid Chaco (Fig. 2a), the

fringes of the Kalahari Desert, some areas in East Africa (Figs 1d,

2b) and the Australian Gibson Desert (Fig. 2c) (see Appendix S1

in Supplementary Material for a complete global map). Small

isolated areas of PVPs were also noticed on images from mediter-

ranean North Africa (33

°

47

′

N, 2

°

35

′

W) and from the Thar

Desert of India (27

°

23

′

N, 70

°

44

′

E), thereby closing the bound-

ary between the extremely arid Saharo-Sindian Desert and the

surrounding semi-arid regions.

Some types of patterns, though predicted by self-organization

models, had not or had only rarely been observed in the field.

Labyrinthine patterns, previously described from the African

Sahel (Tongway

et al

., 2001), were also found to occur in

Figure 2 Predicted and real distribution map of periodic vegetation patterns with enlarged subsets. Orange levels correspond to envelopes of the cumulative probability distribution around the ecological optima. For instance, the 5% envelope delineates the area including 95% of the distribution. Blue areas represent periodic vegetation patterns localized using the available literature and used for constructing and testing the map. Areas with periodic vegetation discovered using map predictions are shown in green. See Appendix S1 for the complete global map.

V. Deblauwe

et al.

© 2008 The Authors

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Global Ecology and Biogeography

, Journal compilation © 2008 Blackwell Publishing Ltd

Australia, and we report here for the very first time observations

of ‘spots’, that is thickets regularly distributed in a bare matrix

(Fig. 1a). They were found in the Sudan, at the arid extreme of a

sequence of patterns of varying morphology including labyrinths

(Fig. 1b), bands and gaps (Fig. 1c).

DISCUSSION AND CONCLUSIONS

This study represents the first attempt to produce an empirical

predictive model for PVPs. Using known arid and semi-arid PVP

locations and global-scale environmental predictors, new

locations were discovered and the ubiquity of the phenomenon

in all tropical and subtropical arid areas was evidenced. There is

now verified PVP occurrence for 0.4% of arid to semi-arid lands,

sensu

UNEP (1992), which cover one-third of emerged land. This

figure still underestimates the reality, as patterns with wavelengths

below 60 m were not taken into account in our analysis, due to

imagery resolution constraints. These include, for instance,

known large areas of gapped bush in south-west Niger displaying

wavelengths of

c

. 50 m (Barbier

et al

., 2006) or the Sudanese

Butana grass patterns, with wavelengths of

c

. 30 m (Worrall,

1959). Moreover, other stressful non-arid environments are

favourable for the occurrence of PVPs (see for examples Rietkerk

& Van De Koppel, 2008), which our model, designed to deal with

arid PVPs, cannot predict.

Despite the coarseness imposed by the environmental pre-

dictors fed into the model, false positives, i.e. areas clearly devoid

of PVPs while predicted to be highly suitable, were relatively rare.

Such false positives are mostly related to long histories of human

occupation, which may have suppressed natural PVPs, as in the

Thar Desert of India for instance. The spatial resolution of

variables related to the substratum (wilting point derived from

the United Nations Food and Agriculture Organization soil map

and slope) was also too low to match with the local extension of

PVPs and to thoroughly explore their influence on patterning

occurrence (see discussion on wilting point, below).

Our aim was not to build the most parsimonious model in

terms of predictors but rather to optimize the prediction power

as well as to explore the potentially causal/explanatory relation-

ships between PVP occurrence and environmental predictors.

However, as always in correlative studies, evidence for strict

causality remains hard to come by, especially in the presence of a

set of highly intercorrelated predictors.

Figure 4 Relative observed and predicted frequency distributions of periodic vegetation patterns in relation to the four most important environmental predictors. Bars: distribution of patterns used for model training and evaluation (249 point locations). Lines: world average model prediction.

Figure 3 Proportion of explained variability accounted for by the nine most relevant environmental predictors used to build the distribution model. Hierarchical partitioning of the log-likelihood goodness of fit (deviance) was used to assess the independent (open bars) and conjoint (black bars) contribution of each predictor. HI, humidity index; TWQ, mean temperature of wettest quarter; TS, temperature seasonality; WP, wilting point; AP, mean annual precipitation; TDR, temperature mean diurnal range; PWQ, precipitation of warmest quarter; PS, precipitation seasonality and S, slope.

Global biogeography of periodic vegetation patterns

© 2008 The Authors Global Ecology and Biogeography, Journal compilation © 2008 Blackwell Publishing Ltd 7

Published empirical and theoretical knowledge (Tongway

et al., 2001, and references therein; Rietkerk et al., 2004) points

towards aridity, soil infiltration rate and slope as important

environmental drivers for PVP formation. Aridity, as summarized

by the humidity index does indeed come first in the hierarchy of

predictors. Mean annual precipitation alone lacks explanatory

power, as shown by the Sahelian case, where PVPs occur under

relatively high rainfall, but where evapotranspiration is also

higher. Precipitation seasonality also accounts for a substantial

part of independent predictive power. The temporal distribution

of resources is known indeed to be a critical parameter for plant

survival in arid areas (Noy-Meir, 1973). Models showed that

seasonal (dry season length) and interannual variations in

precipitation (not included in this study) can modulate patterning

even when the average (e.g. precipitation) values are kept

constant (see, for example, D’odorico et al., 2006; Ursino &

Contarini, 2006; Guttal & Jayaprakash, 2007). The importance

of temperature, and more particularly of its seasonality (mean

temperature of wettest quarter, temperature seasonality and

temperature mean diurnal range), is difficult to interpret directly

from the existing set of simplified mechanistic models, which do

not take into account the seasonal patterns of rainfall and

temperatures. As for rainfall seasonality, these variables possibly

add a stress component which is not integrated by the average

value of the humidity index. The seasonal variation and timing

of the evaporative demand might play a prominent role in

pattern triggering. Overall, PVPs seem to belong to either one of

two possible classes: PVPs with a seasonal pattern of rainfall and

a constant temperature versus those with a more homogeneous

distribution of rainfall but a seasonally varying temperature. As a

matter of fact, temperature has also been hypothesized as a

controlling factor (S. Kéfi, pers. comm.) via its physiological

effect on productivity.

The physical properties of soil (wilting point) also come early

in the partition of explained variance, although the importance

of soil parameters is still, to a large extent, undermined by the

low resolution and reliability of the available global information.

In western Africa for instance, PVPs that were used for model

training are known to only occur on shallow loamy soils on iron-

capped plateaus. However, as Aeolian sand deposits dominate

the landscape, the whole area is mapped with a low wilting point

(see reference in Table 1). Fortunately, very large and homogeneous

sandy areas (e.g. the Kalahari Sands and the Simpson Desert)

which are deprived of patterns can still be used as evidence for

the fact that sandy areas are not favourable to PVP formation and

to confirm the wilting point as a relevant predictor. Finer-scale

soil maps, and in particular estimates of soil depth or of its

inclination to form impermeable biological crusts, would be

particularly needed.

Soil texture is of course central in hydrological processes.

However, the fact that PVPs do not develop on sand does not

permit one to decide between the different mechanistic pattern

formation processes which have been proposed, namely root

competition (Lefever & Lejeune, 1997; Barbier et al., 2008) or

water redistribution through runoff (Hillerislambers et al., 2001;

Von Hardenberg et al., 2001). A high soil infiltration rate indeed

both precludes runoff and promotes deep pivoting root systems

at the expense of shallow tracing ones (Schenk & Jackson, 2005).

Slope did not grade high in terms of explanatory power. This

could be due to several reasons beginning with the resolution of

the slope data set, averaged from a 2.5 arcmin (c. 4.5 km in the

tropics) to a 0.5° resolution. This pixel size, of nearly 50 km in

the tropics, generally encompasses several geomorphological

features, while patterns are known to be limited to very flat

landscapes (e.g. plateaus).

Beyond the correlations evidenced, field studies are needed to

understand how the environmental variables influence growth

or spatial interactions at the plant scale. Similarly, new modelling

attempts will have to reflect and explain the observed frequency

distribution of PVPs along the main environmental variables (see

Fig. 4). The broad-scale occurrence of PVPs on all continents

shows that the phenomenon is not limited to the dominance of

any given botanical taxa, as is also apparent from numerous field

accounts (Table 1). However, global patterns of common functional

traits could possibly be found between dominant species. For

instance, in the rare case where the root systems of the dominant

species have been examined, shallow, laterally extended root

systems were reported: namely for Acacia aneura (mulga) in

Australia (Anderson & Hodgkinson, 1997), Combretum micranthum

in West Africa (Barbier et al., 2008), Acacia mellifera in Sudan

(Adams, 1967) and Acacia bussei in the Horn of Africa (Glover,

1951). In accordance with the concept of a self-organized

response to aridity, PVPs appear in a predictable way within a

specific range of environmental conditions. Although a number

of local studies had already given fragmented information on

these ranges (Tongway et al., 2001), this study is the first systematic

approach to characterize the parameter space in which PVPs

develop. The confirmed existence of threshold effects is crucial,

as there must be an upper and a lower limit to the existence of

PVPs in terms of average productivity and biomass. When the

aridity is not limiting, vegetation reaches the maximum biomass

corresponding to a uniform close-packed distribution of plants,

at least for the herbaceous strata as in tropical savannas. In the

opposite limit, the population becomes so sparse that plant–

plant interactions are negligible and self-organization becomes

impossible. Self-organized patterning can therefore be viewed as

a biome-scale feature of arid and semi-arid vegetation.

The objective of this study was not to systematically quantify

pattern succession (i.e. the variation in wavelength and morphology

along gradients), even though our observations generally agree

with theoretical predictions in this regard (Lejeune & Tlidi, 1999;

Von Hardenberg et al., 2001; Rietkerk et al., 2002). Formal

demonstration of the phenomenon requires a more detailed

(and thus local) approach, involving the quantitative character-

ization of pattern properties (e.g. via Fourier textural analysis;

Barbier et al., 2006), and will be addressed elsewhere.

PVPs have been shown to respond to variations in climate and

human activities (Barbier et al., 2006), in accordance with

self-organization models predicting that PVPs are modulated by

the balance between biomass production and suppression

(Lefever & Lejeune, 1997; Couteron & Lejeune, 2001; Von Harden-

berg et al., 2001; Rietkerk et al., 2002). A straightforward

V. Deblauwe et al.

© 2008 The Authors8 Global Ecology and Biogeography, Journal compilation © 2008 Blackwell Publishing Ltd

extension of the present work would be to incorporate environ-

mental layers as predicted by different climate change scenarios.

Moreover, in semi-arid regions such as in the West African Sahel,

regional climate is known to be subjected to strong positive

feedbacks induced by vegetation, through the enhancement of

evapotranspiration and the lowering of surface albedo (Zeng

et al., 1999). Dekker et al. (2007) recently suggested that local

plant–water feedback occurring in PVPs might increase this

large-scale positive effect exerted by vegetation on precipitation

by up to 35%. The PVP distribution map presented here should

therefore help climate modellers to take these local-scale

processes into account.

ACKNOWLEDGEMENTS

We thank R. Lefever, M. Rietkerk and one anonymous referee for

constructive suggestions and T. Brncic, M. Visser, K. Parr, J. Fisher

and J. Curtis for improving the manuscript. This research was

supported by FRIA, FNRS and Wiener Anspach grants. We are

grateful to the Global Land Cover Facility, http://www.landcover.org/,

for providing the Landsat imagery free of charge.

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SUPPORTING INFORMATION

Additional supporting information may be found in the online

version of this article:

Appendix S1 High-resolution predicted and real distribution

map of periodic vegetation patterns.

Please note: Blackwell Publishing is not responsible for the con-

tent or functionality of any Supporting Information supplied by

the authors. Any queries (other than missing material) should be

directed to the corresponding author for the article.

Editor: Brad Murray

BIOSKETCHES

Vincent Deblauwe is a spatial ecologist who specializes

in studying macroecological patterns in vegetation at

multiple scales.

Nicolas Barbier is a post-doctoral FNRS fellow. The

main focus of his research concerns the characterization,

causality and dynamics of spatial structure in tropical

vegetation.

Pierre Couteron is researcher at the Institut de

Recherche pour le Développement (IRD) and has

contributed to several studies about periodic vegetation

patterns. His present fields of interest also include spatial

patterns of tree diversity in the tropical forests.

Olivier Lejeune is a theoretical physicist. Population

dynamics is the general framework of his research. His

interest covers diverse topics such as pattern formation in

vegetation, immune response to cancer or control of

infectious diseases.

Jan Bogaert is a landscape ecologist. Quantitative

analysis of landscape and vegetation patterns and their

dynamics are the focus of his research unit.