Ecology, 93(3), 2012, pp. 608-618
© 2012 by the Ecological Society of America
C hanges in d iato m p atch-size d istrib u tio n and d eg rad atio n
in a spatially self-organized in te rtid a l m u d flat ecosystem
E. J. W
e e r m a n , 1’2’6
J. Y a n B e l z e n , 1 M . R i e t k e r k , 3 S. T e m m e r m a n ,4 S. K
é f i,5
P. M . J. H
erm an,1and
J. Y a n
de
K oppel1
1Centre fo r Estuariae and Marine Ecology, Netherlands Institute o f Ecology ( N IO O -K N A W ), P.O. B ox 40, 4400 A C Yerseke,
The Netherlands
2Aquatic Ecology and Ecotoxicology (IB E D ), University o f Amsterdam, P.O. B ox 94240, 1090 GE Amsterdam, The Netherlands
3Department o f Environmental Sciences, Utrecht University, P.O. B ox 80115, 3508 TC Utrecht, The Netherlands
4University o f Antwerpen, Department o f Biology, Universiteitsplein 1, 2610 Wilrijk, Belgium
3Institut des Sciences de l ’Evolution, C N R S U M R 5554, Bat 22, second floor, Université de Montpellier II, CC 065, 34095 Montpellier
Cedex 05, France
Abstract. Self-organized spatial p a tte rn s have been p ro p o sed as possible indicato rs for
regim e shifts in ecosystem s. U n til now , this hypothesis has only been tested in drylands. H ere,
we focus o n in tertid al m udflats w here reg u lar spatial p a tte rn s develop in early spring from the
interactio n betw een d iato m gro w th a n d sedim entation b u t d isap p ear w hen benthic herbivore
abundan ce increases in early sum m er, accom panied by a d ram atic shift to a b are m udflat. W e
follow ed the patch-size distrib u tio n s o f d iato m biofilm s durin g this d e g rad atio n process. As
tim e progressed, we fo u n d a tem p o ral change in the spatial co n fig u ratio n occurring
sim ultaneously w ith the loss o f the d iato m -sed im en t feedback. T his indicates a g rad u al
failure in tim e o f the self-organization process th a t underlies reg u lar p atte rn in g in this
ecosystem . T he p a th to d eg rad atio n co-occurred w ith the loss o f the larg er patches in the
ecosystem , w hich resulted in a decrease o f the tru n ca tio n in the patch-size distrib u tio n . H ence,
o u r study in m udflat ecosystem s confirm s th e general hypothesis th a t spatial p a tte rn s can
provide im p o rta n t clues a b o u t the level o f d eg rad atio n . N evertheless, o u r study highlights the
need fo r th o ro u g h study a b o u t the type o f spatial p a tte rn s a n d the n a tu re o f the underlying
feedbacks before a reliable assessm ent o f ecosystem statu s can be m ad e, as changes in patchsize d istrib u tio n differed m arkedly w ith those observed in o th er ecosystems.
Key words: diatom-sediment feedback; herbivory; intertidal mudflats; regime shifts; scale-dependent
feedbacks; spatial patterns.
patches, before the ecosystem collapses to a degraded state
(R ietkerk et al. 2004). In M ed iterranean ecosystems, a
local facilitation m echanism due to the am eliorating effect
o f the vegetation on its local abiotic environm ent is
p ro p o sed to generate self-organized spatial p atterns.
These feedbacks can result either in spatial patterns w ith
a d o m in an t p atch size, characterized by a tru n cated pow er
law (M aestre an d E scudero 2009, Kéfi et al. 2007, Lin et
al. 2010), or in irregular spatial p atterns, characterized by
a pow er law patch-size d istribution (Kéfi et al. 2007).
These studies investigated w hether predictable changes in
the statistical characteristics o f spatial vegetation patterns
could be used as indicators for ongoing d egradation to a
desert state. It w as suggested th a t w hen a M editerranean
d ry la n d becom es m o re deg rad ed , because, e.g., o f
overgrazing, the patch-size d istribution progressively loses
its larger patches an d becomes m o re tru n cated (Kéfi et al.
2007; b u t see discussion in M aestre a n d E scudero 2009,
Kéfi et al. 2010, M aestre a n d Escudero 2010). Since
desertification m ight involve tipping points at unknow n
thresholds an d is often difficult to reverse, the develop­
m ent o f indicators based o n spatial patterns could be
im p o rtan t for ecosystem m anagem ent to predict w hen
catastrophic change is looming.
I n t r o d u c t io n
Self-organized spatial p attern s have been described in a
range o f terrestrial a n d aquatic ecosystems (Pascual and
G uich ard 2005, R ietkerk an d V an de K oppei 2008). These
p atterns develop from strong feedback m echanism s th a t
can generate coherent spatial patterns at a large spatial
scale, ranging from regular to irregular pattern s depend­
ing on the underlying m echanism s (Pascual a n d G uichard
2005, R ietkerk an d V an de K oppei 2008). Recently, self­
organized spatial patterns have been p u t fo rw ard as
potential indicators fo r ecosystem degradation in response
to changing levels o f environm ental o r biotic stress in arid
ecosystems (R ietkerk et al. 2004). In sub-S aharan d ry ­
lands, a com bination o f low rainfall an d scale-dependent
feedback betw een vegetation an d its lim iting resource,
w ater, can induce regular, self-organized spatial vegeta­
tio n patterns (B arbier et al. 2008). Decreases in rainfall are
predicted to induce a sequence o f changes in these spatial
patterns, the breakdow n o f regular p attern s in sm aller
M anuscript received 5 April 2011; revised 20 September
2011; accepted 29 September 2011; final version received 4
Novem ber 2011. Corresponding Editor: J. J. Stachowicz.
6 E-mail: ellenweerm an(®gm ail.com
608
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CH A N G ES IN D IA TO M PA TCH -SIZE
D ue to the fact th a t the search for predictable changes
in characteristics o f self-organized spatial patterns has
focused on vegetation patchiness in drylands (R ietkerk et
al. 2004, Kéfi et al. 2007, 2011, G u ttal an d Jay ap rak ash
2009, M aestre an d E scudero 2009, Lin et al. 2010, von
H ardenberg et al. 2010, Pueyo 2011), application o f this
theory is restricted to sem iarid ecosystems. M oreover,
m ost studies tested changes in patch-size distributions by
com paring spatially distinct systems along a gradient of
decreasing rainfall o r increasing grazing intensity (Kéfi et
al. 2007, M aestre a n d E scudero 2009, Lin et al. 2010).
W hen com parin g spatially d istinct ecosystem s, the
environm ent m ay vary, introducing possible confounding
factors. W hether these pattern s also show consistent
changes preceding a tem poral shift to a degraded state
rem ains unstudied. H ence, the hypothesis th a t self­
organized pattern s show a coherent, predictable change
in spatial structure w hen developing to w ard a degraded
state w ould benefit from fu rth e r testing in o th er
ecosystems, including the explicit analysis o f tim e series
o f how spatial pattern s change in time.
In this paper, we describe tem p o ral changes in the
spatial configuration o f benthic d iato m p a tte rn s on the
K ap elle b an k in tertid a l m u d flat in the N eth erlan d s.
R egular spatial p a tte rn s consisting o f diatom -covered
hum m ocks altern atin g w ith w ater-filled hollow s develop
each spring (B lanchard et al. 2000, de B rouw er et al.
2000, L an u ru et al. 2007; see P late 1), due to interactions
betw een d iato m gro w th a n d geom orphological processes
(W eerm an et al. 2010). The developm ent o f spatial
p attern s em erging from th e stress-divergence m echanism
has been described in a wide range o f ecosystem s, e.g.,
b oreal forests, w etlands, a n d in tertid al m udflats in
spatial p attern s (H iem stra et al. 2002, L arsen et al.
2007, Saco et al. 2007, T em m erm an et al. 2007, van
W esenbeeck et al. 2008). O n o u r in tertid al m udflat, 80%
o f the area is covered w ith reg u lar spatial pattern s. In
the rem aining 20%) o f the study area, a n irregular patch y
structure o f benthic diatom s is visible, b u t bed level
differences are ab sen t, suggesting the lack o f strong
feedback m echanism s in these areas. O n the w hole study
area, as tim e progresses, a g rad u al a n d seasonal increase
in benthic herbivory causes a sudden change fro m a
spatially p atte rn e d in te rtid a l flat w ith high d ia to m
biom ass to a topograp h ically hom ogeneous sedim ent
a t a ro u n d early Ju n e each year (W eerm an et al. 2011).
T he tem p o ral scale o f spatial p a tte rn fo rm atio n in
m udflats is, thus, m uch sm aller th a n the tem p o ral scale
o f spatial p a tte rn s in drylands. In d rylands, shifts
betw een desert an d vegetated state occur a t very long,
geological tim e scales. O n in tertid al m udflats, spatial
p attern s degrade each y ear w hen m acro b en th o s biom ass
increases; in th e next sp rin g , w hen m a c ro b e n th o s
biom ass is low, spatial p a tte rn s can develop again.
H ence, this intertid al m udflat ecosystem provides unique
characteristics th a t m ake it a n extrem ely interesting case
study: (1) the presence o f spatial p attern s, b o th regular
an d irregular, an d (2) the bu ild u p a n d collapse o f the
609
system, w hich can be observed a t sh o rt tim e scales a n d is
rep eated every year.
H ere, we investigate the hypothesis th a t tem poral
changes in patch-size distributions precede degrad atio n in
spatially self-organized m udflat ecosystems. T o this end,
we to o k aerial photo g rap h s during the season, starting
w hen spatial pattern s were clearly visible (April) until the
period w hen spatial pattern s h a d degraded due to high
benthic herbivore num bers (June). W e subsequently
analyzed the patch-size distributions o f observed diatom
patches from the classified aerial p h otographs. Since, in
undistu rb ed conditions, diatom -covered m udflats form
regular patterns (W eerm an et al. 2010) characterized by a
do m inan t p atch size, we expect th a t w ith increasing
grazing pressure the patch-size distribution w ould change
from a tru n cated to a less tru n cated pow er law as
disturbance by grazing increases a n d fragm ents the
patches. L urtherm ore, we studied how changes in other
signatures th a t reflect the feedback processes underlying
spatial self-organization in o u r system (e.g., d ia to m sedim ent feedbacks) changed w ith increased grazing
pressure. Linally, we p u t these results in the b ro ad er
context o f the literature o n spatial indicators.
M a t e r ia l s a n d M e t h o d s
S tud y site and experim ental setup
A field study w as p erfo rm ed a t the K apellebank, a
tid al flat along the edges o f the W esterschelde estuary, in
the N eth erlan d s (51°27' N , 3°58' E). E ach year, from
early spring until the onset o f sum m er, a reg u lar spatial
self-organized p a tte rn o f diatom -covered hum m ocks
a n d w ater-filled hollow s are observed o n this in tertid al
flat (A ppendix A). These p a ttern s develop w hen the
in teractio n betw een the accu m u latio n o f sedim ent o n the
h um m ocks a n d drain ag e o f w ater to w a rd the hollow s
g enerates a scale-dependent feedback o f local-scale
fa c ilitatio n a n d lo n g er ra n g e in h ib itio n o f d ia to m
g row th, p roviding an ex p lan a tio n fo r regular spatial
p a tte rn fo rm atio n w hen herbivore densities are low
(W eerm an et al. 2010). Sim ilar reg u lar spatial d iato m
p a tte rn s have been described in o th er in tertid al m udflats
(C hristie et al. 2000, de B rouw er et al. 2000, Le H ir et al.
2000, P aterso n et al. 2000, L a n u ru et al. 2007). In o u r
system, the d iato m p attern s have a stro n g seasonality
a n d face tem p o ral variability in h y drodynam ic c o n d i­
tions th ro u g h o u t the season (de B rouw er et al. 2000,
W eerm an et al. 2011).
Six 12 X 12 m plots w ere m a rk e d o n the K apellebank,
in w hich sedim ent bed level a n d d iato m cover were
d eterm ined in A pril, M ay, an d June 2008. T hree plots
w ere chosen in an area w ith reg u lar h u m m o ck -h o llo w
stru ctu re (hereafter referred to as the “reg u lar p lo ts’’);
three co n tro l plots were chosen in a n area on flat
sedim ent lacking reg u lar sp atial p a tte rn s (h ereafter
referred to as the “irreg u lar p lo ts’’). W e analyzed the
six plots fo r spatial p attern s o f benthic algae an d
sedim ent bed level durin g these m onths.
610
E. J. W EE R M A N ET AL.
Spatial patterns o f benthic algae
A erial photograp h s for p attern analysis were tak en w ith
a digital cam era (Sony C ybershot DSC-V3; Sony Elec­
tronics, San D iego, C alifornia, U SA ) attach ed to a
helium -inflated blim p-shaped balloon (F lo ato g rap h T ech­
nologies, Silver Spring, M aryland, U SA ), w hich was
attached to a tether line. P hoto g rap h s were obtained from
approxim ately 50 m height covering a n area o f ap p ro x ­
im ately 50 X 40 m (3072 X 2304 pixels). The corners o f the
plots were m arked w ith a colored m ark er th a t was used to
locate the plots during the im age processing.
Landscape m orphology
T o collect m orph o lo g ical d a ta o f the landscape in the
six plots a Riegl L SM Z-210 3D laser scanner (Riegl
In stru m en ts, H o rn , A u stria) w as used an d con tro lled by
the softw are R iScan P ro (Riegl In strum ents). T his laser
scanner collects d a ta p oints o f „v, v, ■ co o rd in ates o f the
sedim ent surface, using a n in frared laser beam em itted in
precisely defined a n g u lar directions co n tro lled by a
spinning m irro r arran g em en t. P rio r to th e scans, five
reflectors were placed a ro u n d the plo t, the p o sitio n o f
these reflectors w as m easured using a D G P S (T hales
G ro u p , N euilly-sur-S eine, F ran c e) a n d these w ere
auto m atically located by the R iS can P ro softw are,
w hich used the D G P S d a ta fo r georeferencing the d ata
points m easured by the laser.
D ata analysis
Indicators fo r spatial self-organization.— F irst, we
analyzed the regularity o f the d iato m p a tte rn s using
spatial au to co rrela tio n (M o ra n I ) o f the d ia to m patches
(L egendre an d L egendre 1998). Sim ilar to W eerm an et
al. (2010), we analyzed the intensity o f the blue channel
w ithin the R G B im ages, since this co rresp o n ds to
diato m biom ass m ost closely, a n d therefore these pixel
values w ere used fo r subsequent analysis. W e applied a
tw o-dim ensional an iso tro p ic m a trix im p lem en tatio n ,
w hich calculates a correlogram fo r fo u r m a jo r directions
(0, 45, 90, an d 135 degrees) in M atlab 2007b (M ath W orks, N atick , M assachusetts, U SA ). The alg o rith m is
constrained to relatively sm all im ages because o f its
m em ory use. W e selected a square o f 75 X 75 pixels
(corresponding to 3 X 3 m ) in th e m iddle o f each p lo t for
au to co rrelatio n analysis. O f the fo u r d irectional correlogram s, we selected the one w ith the highest co rrelatio n
fo r in terp retatio n . This w as, in all cases, the correlogram
w ith a direction perp en d icu lar to the m ain d irection o f
the w ater current. H igh positive au to co rrela tio n co rre­
sponds to m ore sim ilar d ia to m biom ass a t a certain
distance, while dissim ilarity results in negative a u to c o r­
relatio n (L egendre a n d L egendre 1998). Second, we
investigated the underlying m echanism s o f these p a t­
terns by checking fo r the presence o f positive feedbacks.
T herefore, we generated a digital elevation m atrix for
each p lo t from the landscape m o rp h o lo g y d a ta m e a ­
sured w ith the laser scanner. A fter fixing th e corners o f
these plots by using their D G P S coordinates, the p oints
Ecology. Vol. 93. No. 3
from the Riegl laser scanner were in terp o lated in to 300 X
300 m atrix , w here each pixel co rresponds to 4 cm, using
a n earest-neighbor interp o latio n . Sim ilarly, the aerial
p h o to g rap h s were rescaled into the same resolution o f
the laser scanner d a ta o f 300 X 300 pixels using a sliding
n eig h b o rh o o d filter in M a tla b 2007b. Since d iato m
co n ten t is based o n the intensity o f the blue channel in
the R G B pictures, we calculated the relative d iato m
co n ten t as difference from the average intensity o f the
blue channel in each picture. W e th en analyzed the
co rrelatio n betw een relative d iato m co n cen tratio n an d
sedim ent bed level o f 3000 ran do m ly selected p oints o f
the aerial p h o to g ra p h s a n d landscape m o rp h o lo g y d a ta
im ages using P ea rso n ’s co rrelatio n coefficient. W hen
scale-dependent feedbacks are in tact, we expect high
d iato m co n ten t on to p o f the hum m ocks an d low d iato m
co n ten t in the hollows. T herefore, a positive co rrelatio n
betw een diato m s a n d sedim ent bed indicates a fu n ctio n ­
al scale-d ep en d en t feed b ack b etw een d ia to m s a n d
sedim ent (W eerm an et al. 2010).
P atch-size distribution.— F ro m the raw aerial p h o to ­
graphs, the 12 X 12 m plots were selected a n d a binary
im age w as c re ate d fro m each p lo t by m ax im u m
likelihood classification on the R G B pictures. This
m e th o d w as u sed to classify th e pixels fo r each
p h o to g ra p h in to tw o classes: diato m s o r bare sedim ent.
The classes were based o n m anually selected pixels (n —
15 pixels) in each class fro m w hich the brightness in the
red, green, a n d blue b a n d w as recorded an d ex trap o lated
to the o th er pixels in the image. F o r each picture, the
classification m eth o d w as checked by co m p arin g the
bin ary im ages w ith the raw p h o to g ra p h s (A ppendix B).
F ro m th is b in a ry im age, th e cover fra c tio n w as
calculated a n d patches w ere assigned using a M oore
n eig h b o rh o o d o f eight ad jacen t pixels. A m inim al p atch
size w as set at fo u r pixels to av o id artifacts a t p atch
edges affecting patch-size distrib u tio n s. F o r each unique
p a tch size, the n u m b er o f occurrences w as calculated.
F ro m this vector o f p atc h sizes a n d th eir occurrences,
the inverse cum ulative d istrib u tio n w as calculated an d
a n u p p er-tru n cated pow er law w as fitted to the inverse
cum ulative d istrib u tio n according to B urroughs an d
T ebbens (2001). N o te th a t it differs fro m the fitting
pro ced u re typically used in previous studies fo r noncum ulative patch-size distrib u tio n s, e.g., by Kéfi et al.
(2007) or M aestre a n d E scudero (2009). These a u th o rs
used a binning-based m eth o d b u t this takes aw ay the
in fo rm atio n ab o u t the p atch -area d istrib u tio n w ithin
each b in (W hite et al. 2008). T herefore we used a
cum ulative d istrib u tio n in w hich n o b inning is used. The
patch-size distrib u tio n s were fitted using the follow ing
e q u a tio n describ in g a n u p p e r-tru n c a te d cum u lativ e
num ber-size d istrib u tio n based o n a p ow er law (B u r­
ro ughs a n d T ebbens 2001):
M {r) = C (U Y- r f 1)
(1)
w here M (r) is the cum ulative fitting fu n ctio n o f patches
o f size r (in cm 2), C is a c o n stan t, y is the scaling
M arch 2012
CH A N G ES IN D IA TO M PA TCH -SIZE
611
A) R egular patterns, April
B) Regular patterns, May
C) Regular patterns, June
D) Irregular patterns, April
E) Irregular patterns, May
F) Irregular patterns, June
F ig . 1. Aerial photographs of plots in April, M ay, and June for the location with regular spatial patterns (A -C ) and the
location with irregular spatial patterns (D -F ). Brown areas correspond to diatom abundance while gray areas correspond to bare
sediment. Plot size is 12 X 12 m. See Appendix B for the binary images.
ex p o n en t, a n d rT is th e p a tc h size a t w hich the
tru n catio n occurs. F o r the fitting procedure, we used a
p se u d o -ra n d o m search a lg o rith m (pricefit m odule),
w hich is provided in the R package ecolM od (Soetaert
an d H erm an 2009). A ppendix A shows th a t, alth o u g h
this m eth o d is sensitive to the size o f th e plots, the
tru n catio n is determ ined by the size o f the observed
patches, ra th e r th a n a n a rtifa ct o f plo t size.
Kéfi et al. (2007, 2011) suggested th a t the patch-size
d istrib u tio n o f vegetation in M ed iterran ean ecosystem s
should sw itch from a pow er law to a tru n ca ted pow er
law w hen the ecosystem is ap p ro ach in g desertification.
A recent p ap er o f P ueyo (2011) show ed th a t, for
fun d am en tal reasons, we should m ove aw ay fro m the
pow er law vs. tru n c a te d pow er law d ichotom y to o th er
categorizations. M o re precisely, a tru n cated pow er law
can be fitted to all the d a ta sets (if tak e n a t a large
enough scale) a n d we expect th a t tru n ca tio n becom es
stro n g er w hen a d ry la n d a p p ro a c h e s d e g ra d a tio n
(follow ing sim ilar reasoning as Kéfi et al. [2007]). In
line w ith this, all o u r patch-size distrib u tio n s were fitted
using Eq. 1. T o evaluate the degree o f the tru n c a tio n of
the curves, we defined the observed tru n ca tio n to be the
ratio betw een the intercept M (r) o f the full tru n c ate d
pow er law m odel a n d o f the p ow er law m odel w ith o u t
tru n c a tio n , b u t w ith sim ilar scaling exponent (A ppendix
A). The observed tru n c a tio n is a m easure o f the degree
o f bending independent o f w here the bending occurs. Its
c alcu latio n involves c o m p arin g th e fitted tru n c a te d
p ow er law m odel w ith a p u re pow er law m odel th a t
uses the scaling exponent fro m the p rio r, tru n ca ted fit.
N o te th a t this “p u re ” pow er law does n o t characterize a
“h ealth y ” reference state, as w as assum ed in Kéfi et al.
2007, b u t is m erely derived to calculate the degree o f
bending w ithin the rep o rted d a ta range. D ifferences in
cover, average p atc h size, the scaling exponent (y), the
p atc h size a t w hich the tru n c atio n occurs (rT ), an d the
observed tru n c a tio n betw een different sam pling times
w ere analyzed using S tu d en ts’ p aired t test (tw o-tailed).
R esu lts
In b o th regular a n d irregular p a tte rn ed plots, the
cover fractio n o f diato m s decreased significantly b e­
tw een A pril a n d M ay (Figs. 1 a n d 2A; regular, t2 =
20.29, P < 0.01; irregular, t2 = 8.04, P < 0.05). This
d eg rad atio n co-occurred w ith a decrease in average
p atc h size in the regular p attern e d plots (Fig. 2B; t2 =
12.34, P < 0.01) while p a tc h sizes in the irreg u lar
p attern e d plots did n o t change (Fig. 2B; t2 = 4.00, P >
0.05). In June, no d iato m patches could be detected, a n d
612
E. J. W EE R M A N ET AL.
0 .6
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patterns
Irregular
patterns
- ,
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0 .2
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April
May
April
May
F ig . 2. (A) Cover fraction and (B) average patch size of the
irregular and regular plots in April and May. Light gray bars
represent the regular spacing patterns, and dark gray bars
represent the irregular patterns (n = 3; error bars indicate ±SE).
* P < 0 .0 5 ; ** P < 0.0 1 ; *** P < 0.001.
therefore we argue th a t the ecosystem can be considered
as com pletely degraded. In the rest o f this p ap er, we thus
focus on the analysis o f the p a tte rn s in A pril a n d M ay.
A erial p h o to g ra p h s o f the plots revealed clear visual
differences betw een the regular a n d irregular plots (Fig.
1), w hich w ere confirm ed by au to co rre la tio n analysis.
T he regular plots show ed positive au to c o rre la tio n u p to
20 cm lag distance, follow ed by significant negative
au to co rrelatio n from 20 to 80 cm (Fig. 3A). This
confirm s th at, in these plots, ban d s o f high d iato m
biom ass w ere regularly d istrib u te d in th e d irection
p erpendicular to the flow d irection w ith a w avelength
o f roughly 1 m . In M ay, this regularity w as lost, since
only positive M o ra n I values w ere fo u n d (Figs. IB an d
3B). The irregular plots show ed only positive M o ra n I
Ecology. Vol. 93. No. 3
values in b o th A pril a n d M ay, indicating a lack o f
regularity in these plots (Fig. 3C a n d D).
T o investigate possible feedbacks un d erly in g the
observed p attern s, we lo o k ed at the co rrelatio n betw een
d ia to m a b u n d a n c e (as estim ate d fro m th e aerial
p h o to g rap h s) an d sedim ent bed-level elevation in A pril
a n d M ay (Fig. 4). In the reg u lar plots, a strong positive
co rrelatio n w as fo u n d in A pril (Fig. 4A), while the
co rrelatio n w as ab sen t o r very w eak in M ay (Fig. 4B).
T his suggests th a t the change in spatial configuration
observed in th e reg u lar plots co-occurred w ith the
disappearance o f the scale-dependent feedback betw een
d iato m gro w th a n d sedim entation processes. In the
irreg u lar plots, n o o r very w eak co rrelatio n w as fo u n d in
b o th A pril a n d M ay (Fig. 4C a n d D ), w hich suggests
th a t no scale-dependent feedbacks w ere underlying the
observed irreg u la r spatial pattern s.
C o n sisten tly w ith th e reg u la rity o f th e p a tte rn s
revealed by au to c o rre la tio n analysis, th e patch-size
distrib u tio n s show ed consistent changes. T he regular
plots in A pril w ere ch aracterized by a n excess o f patches
o f in term ediate size th a n can be expected based o n a
p u re p o w er law. T his suggests th e presence o f a
d o m in an t spatial scale, w hich is a characteristic o f
reg u lar p a ttern s (Fig. 5A). T he o th e r d istrib u tio n s
(regular plots in M ay a n d irreg u lar plots in A pril an d
M ay) ap p ro ach ed a pow er law d istrib u tio n (Fig. 5B -D ).
F o r the regular plots, th e scaling exponent (y) w as fo u n d
to be h igher in M ay co m p ared to A pril (Fig. 6A; regular,
?2 = —9.13, P — 0.05). The sam e tren d w as observed in
the irreg u lar plots, b u t w as n o t significant (Fig. 6A; t2 =
—2.88, P > 0.05). A t the sam e tim e, we observed a clear
decrease o f the tru n ca tio n p a ram eter in the reg u lar plots
betw een A pril an d M ay (Fig. 6B, t(2) = 22.27, P < 0.01),
while this w as n o t significant (b u t also decreasing) in the
irreg u lar plots (Fig. 6B; t2 = 1.73, P > 0.05). L ooking
m o re in to the details o f the d istrib u tio n shapes, the
observ ed tru n c a tio n w as significantly d ifferen t fo r
reg u lar plots betw een A pril a n d M ay (Fig. 6C; t2 =
12.02, P < 0.01), w hich indicates th a t the degree o f
tru n c a tio n decreases, as d e g ra d a tio n increases. The
irreg u lar plots did n o t show an y significant change
betw een these m o n th s (Fig. 6C; t2 — 2.34, P > 0.05).
D is c u s s io n
R ecent studies have p ro p o sed th a t changes in the
spatial configuration o f self-organized vegetation p a t­
terns in d rylands can serve as possible indicato rs o f
ecosystem d e g rad atio n (R ietk erk et al. 2004, Kéfi et al.
2010). T o investigate if this applies to o th er ecosystem s
as well, we studied the changes in spatial p attern s o f
diato m s d u rin g the d eg rad atio n process on intertidal
m udflats (W eerm an et al. 2011). O u r results show ed
consistent changes in the patch-size d istrib u tio n o f the
self-o rg an ized re g u la r p a tte rn s as th e d istu rb a n c e ,
caused by herbivores, increased. This is generally in
agreem ent w ith the idea th a t the spatial o rg an izatio n o f
M arch 2012
CH A N G ES IN D IA TO M PA TCH -SIZE
1-0-|
A) R egular patterns, April
613
B) R egular patterns, May
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F ig . 3. A utocorrelation analysis o f the diatom patterns with the M oran I values for the regular patterns in (A) April and (B)
May and irregular plots in (C ) April and (D) May. The three different shades o f lines indicate the three different plots.
ecosystem s m igh t provide in fo rm atio n regarding the
level o f ecosystem degrad atio n .
M o st o f o u r study area w as covered by regular
p attern s o f d iato m biofilm s due to a scale-dependent
feedback betw een the diatom s a n d sedim entation (W eer­
m an et al. 2010). W ith ongoing d eg rad atio n , the scaledependent d iato m -sed im en t feedback w as lost, w hich
resulted in hom ogenous flat sedim ent. Sim ilar regularity
o f d iato m patches (W eerm an et al. 2010) a n d the
seasonal shift fro m p a tte rn e d to hom ogeneous m udflat
have been described fo r different sites in o th er years (de
B rouw er et al. 2000, W eerm an et al. 2011). T his change
in to p o g rap h y co-occurred w ith the loss o f regularity of
the spatial p attern s a n d associated changes in the shape
o f the d istrib u tio n to w a rd a pow er law. This was
reflected by an increase in the scaling exponent a n d a
decrease o f the tru n c a tio n p aram eter, clearly indicating
a loss o f the larger patches from the d istrib u tio n as the
ecosystem becom es m ore deg rad ed an d fragm ented.
C hanges in patch-size d istrib u tio n in response to
increased grazing intensity have been rep o rte d fo r b o th
M ed iterran ean a n d M o n g o lian d ry grasslands (K éfi et
al. 2007, L in et al. 2010). Y et, increased grazing intensity
effected patch-size d istrib u tio n differently in o u r study
com pared to grassland ecosystem s, as the above studies
re p o rted o n an increase o f tru n c a tio n o f the patch-size
d istrib u tio n w ith increasing grazing intensity (K éfi et al.
2007, b u t see M aestre a n d E scudero 2009), while we
re p o rt on a decrease. These seemingly opposing findings
can be explained by differences in th e type o f spatial
p a tte rn , an d the m echanism th a t underlies spatial self­
o rg a n iz a tio n in these system s. T h e reference state
p ro p o sed in the study by Kéfi et al. (2007) is a pow er
law, w hich becom es increasingly tru n c ate d as grazing
intensity increases as large patches are progressively lost
a n d fragm ented. O n in tertid al m udflats, local feedback
processes betw een d iato m grow th, w ater drain ag e a n d
sedim entation generates clear reg u lar p a tte rn s w hen
u n d istu rb ed , ch aracterized by strongly tru n c a te d patchsize d istrib u tio n s. W h en g razing intensity increases
th ro u g h the season, patches are fragm ented by the
direct an d indirect effects o f grazing (W eerm an et al.
2011). As a result, tru n ca tio n d isappears, an d patch-size
d istrib u tio n ap p ro ach es a pow er law w ith increased
g razin g inten sity . H ence, in th e in te rtid a l m u d flat
studied here, the tra n sitio n to d eg ra d a tio n w as associ­
a te d w ith a shift in the processes th a t govern p attern
fo rm atio n ; fro m self-organized reg u lar p attern s, c h a r­
acterized by a d o m in an t spatial scale, to irreg u lar a n d
fra g m e n te d p a tte rn s, ch arac te rize d by p a tc h sizes
614
E. J. W EE R M A N ET AL.
Ecology, Vol. 93, No. 3
201 A) R egular patterns, April
/
10
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/
OH
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+c
-10
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R 2 = 0.22
i
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R 2 = 0.21
i--------- 1----------i--------- 1----------1
i--------- i----------1--------- 1----------1
B) Irregular patterns, April
10
M
OH
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c=
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R 2 = 0.008
i
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1--------- 1----------1--------- 1
R 2 = 0.0003
R 2 = 0.0001
i----------1--------- 1----------1--------- 1
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C) Regular patterns, May
0
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R 2 = 0.0007
R 2 = 0.04
R 2 = 0.02
i-----------1----------- 1-----------1-----------1
i-----------1----------- 1-----------1----------- 1
i-----------1----------- 1-----------1----------- 1
D) Irregular patterns, May
10
oH
-
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_2o -I
R 2 = 0.09
R 2 = 0.18
i----------- 1-----------1----------- 1-----------1
i-----------1-----------1----------- 1-----------1
R2 = 0.18
i-----------1-----------1----------- 1-----------1
-4 0
40
-4 0
40
-4 0
40
Sediment bed level (mm)
F i g . 4. The response of relative diatom abundance as a function of bed level. The data are split into 15 classes of the variables,
with an equal num ber of observations in each class, and the plots show the m ean value of each class and the 95% confidence
intervals. Values are given for the adjusted R 2 of the model fit to the data.
lacking any characteristic scale. This co m p ariso n h igh­
lights the co ntext dependency o f the use o f spatial
p attern s as indicato rs o f d eg rad atio n in ecosystems.
A lthou gh several studies have argued th a t spatial
p a tte rn s co u ld be u sed to p red ict the o n set o f
deg rad atio n and cata stro p h ic collapse (R ietk erk et al.
2004, Kéfi et al. 2007), the use o f patch-size d istrib u tio n
as a m o n itoring to o l to gauge ecosystem d eg rad atio n
levels is still in its infancy, as show n by the recent
discussions in the literatu re (Kéfi et al. 2007, 2010,
M aestre an d E scudero 2009, 2010, Pueyo 2011). O ne o f
the m ain challenges is to develop p ro p e r statistics an d
ro b u s t w ays o f ev alu a tin g th e tru n c a tio n o f th e
distrib u tio n s (Pueyo 2011). O u r results co n trib u te to
this discussion an d suggest th a t the changes in spatial
patte rn s th a t can be expected w ith ongoing d eg rad atio n
M arch 2012
CH A N G ES IN D IA TO M PA TCH -SIZE
10000
100
10000
615
—,A) R egular patterns, April
-
—
,B) Irregular patterns, April
100-
LL
C) Regular patterns, May
1 0 0 0 0 —,
100
-
1 0 0 0 0 —I
D) Irregular patterns, May
100-
Patch size (cm2)
F ig . 5. Patch-size distribution of diatom patches from three replicas of each location and m onth. The v-axis represents the
patch size (n r), and the y-axis represents frequency of patch size. Circles are observed values, and the gray line is the fitted model.
are determ ined by the type o f p attern s th a t characterizes
the u n d istu rb ed ecosystem , an d hence by the ecological
m echanism s underlying the p attern s. U n d erstan d in g the
“p attern a ttra c to r,’’ i.e., the type o f p a tte rn th a t can be
expected u n d er u n d istu rb ed conditions (e.g., regular or
irregular, self-organized o r n ot), is essential before
predictions on how d e g rad atio n can affect the patchsize d istrib u tio n can be safely m ade. T herefore, we argue
th a t, at the very least, the presence o f self-organization
processes in an y spatially hetero g en eo u s ecosystem
needs to be em pirically verified, before spatial p attern s
can be used as in d icato r fo r ongoing o r im m inent
degrad ation.
T he loss o f cover fractio n o f vegetation, o r o f o th er
organism s, is the m o st direct w ay to assess the degree o f
d e te rio ra tio n o f ecosystem s (R eynolds et al. 2007,
M aestre an d E scudero 2009, 2010). H ow ever, ecosys­
tem s w ith strong feedback m echanism s can respond
n o n lin early , in volving tip p in g p o in ts, to g rad u ally
increased stress (R ietk erk et al. 2004, Scheffer et al.
2009). In those cases, the cover fractio n a t w hich a
tip p in g p o in t occurs is u n know n, a n d cover fractio n
alone is n o t sufficient to indicate the proxim ity o f a
tip p in g p o in t in the ecosystem (K éfi et al. 2010). O u r
study d em o n strates th a t the change o f the scaling
exponent reflected increasing frag m en tatio n by grazing
616
E. J. W EE R M A N ET AL.
Regular
patterns
Irregular
patterns
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500 o
NS
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400-
300-
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>
200-
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A p ril
M ay
A p ril
M ay
F ig . 6. Fitted param eters front our patch-size distribution
analysis describing the (A) scaling exponent y. (B) truncation
param eter rT, and (C ) observed truncation for regular and
irregular patterns in April and May. Light gray bars represent
the regular spacing patterns, and dark gray bars represent the
irregular patterns (n = 3; error bars indicate ±SE).
* P < 0.05; ** P < 0.01; *** P < 0.001; NS. not significant.
activity, as the scaling exponent y increases w ith level o f
d e g ra d a tio n . N ev erth eless, increase in th e scaling
exponent alone provides no in d icatio n o f the break d o w n
o f key feedback processes, n o r could it signal a possible
c atastro p h ic response. T his is u n derlined by a n equally
strong change in the scaling exponent fo u n d in plots on
Ecology. Vol. 93. No. 3
th e m u d fla t th a t only co n ta in e d irre g u la r d ia to m
patches. In those plots, the scale-dependent feedback
w as less im p o rta n t as a stru ctu rin g force o f the d iato m
com m unity. N onetheless, the scaling exponent increases
w ith increased d istu rb an ce levels, suggesting th a t the
scaling exponent m atch the level o f frag m en tatio n . So,
in this study, the level o f tru n c a tio n is a n indicatio n o f
feedback strength, w hereas the scaling exponent reflects
level o f fragm entation.
O th er indicato rs fo r possible n o n lin ear responses, like
increased spatial a u to c o rre la tio n an d variance in p ro x ­
im ity o f a tipping p o in t have recently been p ro p o sed
(G u tta l an d Ja y a p ra k ash 2009, D ak o s et al. 2010,
C arp en te r et al. 2011). The au to co rrela tio n in o u r study
d ro p s durin g deg rad atio n , w hen the regularity o f the
p a ttern s becom es w eaker. T his is in line w ith a recent
m odel study by D ak o s et al. (2011) w here they fo u n d
th a t d eg rad a tio n in reg u lar self-organized p attern s failed
to show increase in rising variance a n d au to co rrelatio n .
The com bined results o f the th eoretical study by D ak o s
et al. (2011) a n d the results in o u r em pirical study im ply
th a t the spatial a u to c o rre la tio n solely is n o t a reliable
in d icato r in predicting regim e shifts in reg u lar self­
o rganized p attern s. T his suggests th a t a set o f indicators
m ight be m ore pow erful in predicting regim e shifts th a n
a single in d icato r (K éfi et al. 2011). T herefore, we
suggest th a t, fo r reg u lar self-organized p a tte rn s, a
co m b in atio n o f the observed tru n c atio n a n d a u to co rre ­
latio n , b o th signatures o f regularity, are the m ost
reliable assessm ent o f ecosystem health.
C oncluding, o u r results show th a t changes in the
stru ctu re o f spatial p a tte rn s can provide im p o rtan t clues
a b o u t the level o f d eg rad atio n in self-organized ecosys­
tem s. H ow ever, the sequence in w hich p attern s change
w ith ongoing d eg rad atio n , as well as the type o f changes,
depends on th e u nderling stru ctu rin g m echanism s th a t
generate these p attern s, e.g., w hether they result from
feedback leading to self-organization, a n d w h at type o f
self-organization. W e suggest th a t spatial indicato rs take
th eir full value w hen they are com bined w ith m easures
o f ecological m echanism s. W e can test a n d com pare
different m easures o f the spatial stru ctu re (patch-size
distrib u tio n s a n d m an y others such as spatial a u to c o r­
relation, spatial variance, a n d m ean p a tc h size) a n d we
can evaluate those along tran sitio n s (in experim ental
systems a n d m odels). In parallel to th a t, we can m easure
the feedback m echanism s, such as we describe in this
p ap er. T h erefo re, we p ro p o se th a t, befo re sp atial
p a ttern s can be used to predict d e g rad atio n in ecosys­
tem s, it is im p o rtan t to (1) resolve the m echanism s th a t
underlie b o th the fo rm atio n a n d d e g rad atio n o f spatial
p a tte rn s, (2) develop a d escrip tio n o f th e p a tte rn
a ttra c to rs th a t describe the expected p a tte rn s in u n d is­
tu rb e d conditions a n d how it changes w hen d isturbed,
a n d (3) develop indicato rs o f b o th the stru ctu re o f the
spatial p attern s a n d o f the stren g th o f the underlying
feedback m echanism s, before a reliable assessm ent o f
ecosystem status can be m ade. O nly w hen fulfilling
M arch 2012
CH A N G ES IN D IA TO M PA TCH -SIZE
617
P l a t e 1.
Regularly patterned landscape o f diatom -covered hummocks alternating with water-filled hummocks at the
Kapellebank, The Netherlands. Photo credit: E. I. W eerman.
above three criteria, spatial stru ctu re can becom e a
prom ising in d icato r to address the p roxim ity o f a
no n lin ear response to w a rd com plete d egradation.
A cknow ledgm ents
The authors thank Nico de Regge for help with the 3-D laser
scanner equipment, and Ios van Soelen and L ennart van
Ilzerloo for their valuable help in the field. The w ork of I. van
Beizen was financed by the EU project THESEUS. D avid
Alonso, Fernando T. M aestre, and Simon T hrush provided
valuable comments on earlier drafts of the m anuscript. This is
N IO O publication num ber 5118.
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S u p p le m e n ta l M a t e r i a l
Appendix A
Detailed description of the study site and m ethods (Ecological Archives E093-054-A1).
Appendix B
Aerial photographs of our plots and their binary images after imaging processing (Ecological Archives E093-054-A2).