Unraveling landscapes with phytogenic mounds (nebkhas): An exploration of spatial pattern

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Acta Oecologica 49 (2013) 53e63

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Acta Oecologica

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Original article

Unraveling landscapes with phytogenic mounds (nebkhas):An exploration of spatial pattern

Jan J. Quets a,*, Stijn Temmerman b, Magdy I. El-Bana c,d, Saud L. Al-Rowaily c,Abdulaziz M. Assaeed c, Ivan Nijs a

a Plant & Vegetation Ecology (PLECO), Dept. of Biology, Univ. of Antwerp, Universiteitsplein 1, BE-2610 Wilrijk, Belgiumb Ecosystem Management, Dept. of Biology, Univ. of Antwerp, Universiteitsplein 1, BE-2610 Wilrijk, BelgiumcCollege of Agriculture, Dept. of Plant Production, King Saud Univ., P.O. Box 2460, Riyadh, Saudi ArabiadDept. of Biology, Faculty of Education, Suez Canal Univ., Al-Arish, Egypt

a r t i c l e i n f o

Article history:Received 10 May 2012Accepted 6 March 2013Available online 30 March 2013

Keywords:NebkhaSpatial patternPair correlation functionMesquiteTamarixCalligonum

* Corresponding author. Tel.: þ32 (0)3 265 29 53;E-mail addresses: [email protected], jquets@hotm

1146-609X/$ e see front matter � 2013 Elsevier Mashttp://dx.doi.org/10.1016/j.actao.2013.03.002

a b s t r a c t

Phytogenic mounds (nebkhas) often are symptoms of desertification in arid regions. Interactions amongnebkhas and between nebkhas and their environment are however poorly examined. To this end, threemain hypotheses of nebkha pattern formation were evaluated in this study. These state that nebkhapatterns are either shaped by: (i) biologically induced recruitment inhibiting zones, (ii) biologicallyinduced recruitment encouraging zones, or (iii) by the spatial distribution of abiotic factors which are notbiologically driven. Contrasting nebkha landscapes were examined: a highly dense New Mexicanmesquite (Prosopis glandulosa) and snakeweed (Gutierrezia sarothrae and Gutierrezia microcephala)ecosystem, and a low-density mixed Tamarix aphylla and Calligonum comosum field in central Libya.Spatial second-order statistics of strategically chosen nebkha subpatterns were compared with those ofnull models in which observed patches were spatially randomized without overlap. Null model de-viations were assessed with goodness-of-fit tests, and interpreted in terms of hypothesized mechanismsof nebkha pattern formation. Our results suggest that biologically induced recruitment inhibiting zonessurround adult mesquite nebkhas. The configuration of Calligonum and Tamarix nebkhas may be drivenby spatial dynamics of abiotic microsites which are not caused by nebkha interactions. Hence weconclude that both biotic and abiotic drivers can shape nebkha spatial patterns.

� 2013 Elsevier Masson SAS. All rights reserved.

1. Introduction

Nebkhas are vegetated mounds originating from cumulativedeposition of wind- and waterborne sediment around burial-tolerant host plants (Batanouny, 2001). Since, nebkha landscapesrequire unconsolidated transportable sediment, they are often foundin deserts. A majority of authors argue that recently establishednebkhas are symptoms of land degradation and aridification (Duet al., 2010; Gile, 1975; Rango et al., 2000; Tengberg, 1995; Wanget al., 2008). Indeed, a decrease in environmental resources (e.g.aridification under climate change) or an increase indisturbance (e.g.grazing pressure), may induce vegetation loss, and thereby promotesedimenterosion, and subsequently favorburial-tolerant (i.e. nebkhainitiators) over burial-intolerant plant species (Havstad et al., 2000).Land degradation and aridification have several definitions (Raviet al., 2010) of which most have negative connotations, suggestingtheir symptoms (i.e. nebkhas) are undesirable too. However, nebkhas

fax: þ32 (0)3 265 22 71.ail.com (J.J. Quets).

son SAS. All rights reserved.

can have positive aspects: (i) They can act as biodiversity agents bynursing herbaceous species which, under the same climatic condi-tions, would not survive unsheltered (Brown and Porembski, 1997);(ii) They also trap airborne sediment (Bendali et al., 1990; Gibbenset al., 2005; Zhang et al., 2011), hereby impeding desert expansion;(iii) Nebkhas enrich soil with nutrients (Reyes-Reyes et al., 2002),although it is not yet clear whether these are locally reallocated, orare brought newly into the ecosystem (Du et al., 2010); (iv) Nebkhalandscapesmay also increase total soil water content with respect tobare landscapes. Indeed, higher infiltration rates are often observedwithin vegetated patches as compared to surrounding barren soil(Martinez-Meza and Whitford, 1996), where freshly fallen water ismore prone to evaporation, especially in deserts (Glover et al.,1962);(v) Nebkha fields are probably intermediate between grasslands andsandy barren states, and in this respect, they might be useful in landrestoration (El-Bana et al., 2003).

Spatial patterns of vegetation patches have already been exten-sively examined, especially in arid lands (e.g. Haase et al.,1996; Giladet al., 2007). However, few studies examined nebkhas in a spatialstatistical manner. Goslee et al. (2003) did analyze New Mexican

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mesquite nebkha patterns with Ripley’s K function, but they focusedon inter-nebkha scales larger than 25 m. This study as well wants toverify whether local interactions play a role in resulting patch con-figurations. Therefore smaller inter-nebkha scales were alsoincluded. We propose three alternative hypotheses which couldexplain spatial configurationsof observednebkhas. Afirsthypothesisstates that adult nebkhas either deplete resources from, or releaseallelopathic substances in their near surroundings, hereby inducinglocal zones around nebkhas which inhibit seedling and juvenilerecruitment. These zones should be reflected into the pattern whenpatch density is sufficiently high: younger vegetationpatches shouldappear repulsed from adult nebkhas. A second hypothesis presumesthat adult nebkhas enhance vegetation patch recruitment in theirspatial proximity, either by distance-restricted seed dispersal, or byimproving resources near their canopies (Schlesinger and Pilmanis,1998). These two processes could lead young vegetation patchesappear to be clustered around adult nebkhas. A last hypothesis pos-tulates that nebkha landscapes are driven by spatial heterogeneitiesof resources or stresseswhich are not caused by nebkha interactions.Such heterogeneities could govern local success rates of recruitment,hence as well introducing clusters of young patches. These clustersshould be located near adult patches when the aforementionedheterogeneities do not change position during the time frame inwhich the landscape was formed. However, when microsites dochangepositionover time (e.g. due to changing sanddepths), clustersof young patches could lay independent from adult patches.

We analyzed spatial nebkha patterns based on air and space-borne images from two different areas (New Mexico, USA andLibya). The main objective was to identify whether biotic or abioticdrivers underlie observed nebkha patterns. To this end, nebkhapatterns were examined on their spatial configurationwith second-order spatial statistics. Results were interpreted in terms of hy-potheses on nebkha pattern formation, as mentioned above.

2. Methods

Several nebkha fields mentioned in peer reviewed articles werescreened for use in this study (Appendix A). Of those, only the fielddescribed by Langford (2000), located in the Mesilla basin about13 km to the north of the US-Mexico border (31� 550 3300 North, 106�

540 700 West), was finally withheld. This landscape is dominated bythe nebkha host plant species Prosopis glandulosa (mesquite) (EdFredrickson, personal communication), while interspaces are pre-dominated by two small persistent bushes Gutierrezia sarothrae(broom snakeweed) and Gutierrezia microcephala (snakeweed)(Brandon Bestelmeyer, personal communication). Both Gutierreziaspecies will further be simply addressed as snakeweed. Literatureshows that the northern Chihuahuan desert evolved from grasslandto a nebkha ecosystem during the second half of the 19th century(Gibbens et al., 2005). This transition was induced by a change inland use (more livestock) and enhanced by a series of drought in-cidents. Since mesquite and snakeweed are unpalatable to livestock,they were less affected by increased grazing pressure, which ex-plains their current dominance (McDaniel and Ross, 2002). Seedpods and seeds of mesquite are however highly palatable for live-stock, rodents and other wildlife. The latter often act as vectors oflong-distance seed dispersal via fecal deposition of viable seeds(Brown and Archer, 1988; Kramp et al., 1998). According to Langford(2000), mesquite nebkha diameters can extent to 40 m, whileSterling et al. (2000) observed that snakeweed patch diameters canreach about 1 m in New Mexican snakeweed populations. Airborneimagery of this landscape, produced on June 13, 2010 was obtainedfrom Google Earth (GE) (Appendix B). The exact resolution of theimage source was not provided. However, after close inspection,isolated patches with areas of at least 0.09 m2 could clearly be

identified as perennial vegetation patches. All patches with areassmaller than this value were omitted to exclude possible annuals.Fortin and Dale (2005) stated that a study site’s spatial extent shouldbe large enough to fully capture all ecological processes under study,but not too large as to introduce unwanted large-scale heterogene-ity. With the latter taken into account, two separate study sites weredelineated from this nebkha field. In the first, both snakeweed andmesquite were examined in a 90m� 90m sized area (Fig.1a). In thesecond study site, only mesquite patches were studied by excludingsnakeweeds from analysis in a 250 m � 250 m plot (Fig. 1b).Snakeweeds were assumed excluded by eliminating patches withdiameters smaller than 1.6 m. Indeed, this threshold size goestogether with distinct patch textures and is higher than maximumobserved snakeweed sizes in literature (i.e. about 1 m, as mentionedabove). Moreover, ranked patch sizes of combined snakeweed andmesquite patches form a bilinear curve with a breakpoint at 1.6 mdiameter (see Appendix C), which additionally supports this choiceof threshold size. A number of small mesquite patches might beremoved when eliminating patches below 1.6 m in Fig. 1b. However,this does not strongly affect the conclusions drawn from this anal-ysis, as the size range of mesquite will only be slightly reduced.

A second withheld nebkha landscape (27� 140 4000 North, 14� 360

000 East) is located in central Libya (Fig. 1c). This study site can beeasily found on Google Maps. It is very close to Tamanhint city (nearSabha) and its small airfield. There is only 1 km between the studysite and the edges of Tamanhint city. A 2006 field visit revealedTamarix aphylla and Calligonum comosum as the most dominatinghost species present (all individuals of these species formed neb-khas in this region). This study site belongs to a protected area, andtherefore is without livestock grazing. The majority of Tamarixaphylla nebkhas were larger than Calligonum comosum nebkhas(only very few of them had sizes falling in the size range of Calli-gonum comosum). Both Tamarix aphylla and Calligonum comosum aretypical wind dispersers and their seeds may end up far from parentplants (Danin,1996; Di Tomaso,1998). An image of a 700m� 700mnebkha field of which the source image was produced on July 25,2006 with IKONOS (a spaceborne sensor with 0.8 m resolution) wasacquired from GE. Since no exact size ranges were recorded on thefield, and because both species could not be distinguished on theimage, size ranges were estimated from literature: Calligonumcomosum patches have been reported not having diameters largerthan 3.5 m (Koller, 1956) while typical Tamarix aphylla diametershave been assumed between 5 and 15 m (Hayes et al., 2009). Libyanstudy site patches, smaller and larger than 3.5 m, were thereforerespectively assumed to be Calligonum and Tamarix nebkhas. In thisway, a number of Tamarix juveniles smaller than 3.5 m might havebeenwrongfully labeled as Calligonum. However, based on the 2006field observations, we assume this number negligibly small.

Spatio-temporal information was implicitly assumed byconsidering larger patches older than smaller patches in a singlespecies pattern, as was already observed for mesquite nebkhas byGadzia and Ludwig (1983). Patch ages are considered ordinal, notabsolute. This sizeeage relationship was used to divide observedpatterns into two subpatterns which correspond to distinct classesof patch age. Hereto, for each single species pattern, a threshold size(TS) was chosen to divide the pattern’s total fractional cover intohalf. Such derived subpatterns were addressed as SPS and SPL,respectively comprising small and large vegetation patches. SPS andSPL thus each represent half of the total fractional cover of thesingle species pattern. Pattern divisions are in this way lessdependent on image resolution compared to divisions based onmore common central tendencies (e.g. the mean or median patchsize). The latter is especially true when patch size distributions arenegatively skewed, as commonly reported in literature for vege-tation patches (Kéfi et al., 2007; Scanlon et al., 2007).

Fig. 1. Map (a) depicts the New Mexican study site where both snakeweed andmesquite were analyzed. Map (b) shows the New Mexican study site in which onlymesquite was considered for analysis. Map (c) depicts the Libyan study site holdingTamarix aphylla and Calligonum comosum nebkhas. (source: Google Earth).

Fig. 2. Repulsing nebkhas (black discs) having diameters D1 and D2, and repulsion radiiRR1 and RR2. The pair distance (PD) contributing to the PCF (when both nebkhas arefrom the same pattern) or PCCF (when both nebkhas belong to distinct patterns),equals the sum of both nebkha and repulsion radii.

J.J. Quets et al. / Acta Oecologica 49 (2013) 53e63 55

The same pattern separation was additionally performed on thecombined pattern of snakeweed and mesquite, since snakeweedbushes are considered both younger and smaller than adultmesquite nebkhas. Indeed, mesquite seedlings are very rare inadult stands (Brandon Bestelmeyer, personal communication), and

mesquite adults are extremely persistent (Goslee et al., 2003),attaining ages of several centuries (Phillips and Comus,1999), whilesnakeweed longevity is only estimated between 4 and 7 years(Ralphs and McDaniel, 2011).

Suppose that X represents S (small) or L (large). The subpatternsof this study were then either presented as (i) SPX SWþMQ, (ii) SPXMQ,(iii) SPXCC or (iv) SPXTA, depending on whether their correspondingpatterns respectively include (i) both snakeweed and mesquite, (ii)mesquite, (iii) Calligonum comosum or (iv) Tamarix aphylla, asmentioned abbreviated in superscript.

The pair correlation function (PCF) and pair cross-correlationfunction (PCCF) have respectively been recommended as the mostinformative spatial summary characteristics to assess univariate andbivariate spatial point configurations (Illian et al., 2008). Within aPCF, the frequency distribution of distances between all pairs ofobserved points (here nebkhas) is compared between an observedpoint pattern and an equally dense completely spatial random (CSR)point pattern (Diggle, 1983). PCF values close to 1 at all consideredscales (pair distances) suggest CSR distributed points. PCF valueslower than 1 at low inter-point scales should reflect a patternwherepoints seem repelled from each other, since they indicate that lesspairs of near points are present compared to CSR. Conversely, PCFvalues higher than 1 at low inter-point scales illustrate the presenceof points concentrating in groups (clusters). In order not to berestricted to CSR as a null model of choice, and to be able to quantifysignificances of null model departures, PCF envelopes were gener-ated from Monte Carlo (MC) simulations of specifically chosen nullmodels explained below (Illian et al., 2008). When a PCF of anobserved pattern falls out of such an envelope, a deviation from anull model can be suspected. However, the significance level of suchan envelope departure can only be assured for single pair distances,and not for departures over a range of pair distances (Loosmore andFord, 2006). To accomplish the latter, goodness-of-fit (GoF) testswere applied which calculate a specific univariate test statistic u(Diggle, 1983) for (i) the observed pattern (uobs), and (ii) each of then simulated patterns of the null model (usim,i; i ε {1, 2, ., n}). Eachtest statistic incorporates a group of adjacent PCF values (this groupmay consist of only 1 PCF value)which are suspected to deviate froma null model. The ranking order of uobs in the set of values {uobs,usim,1, ., usim,n} then delivers an unbiased estimate of the signifi-cance level for a one-tailed significance test. According to Marriott(1979), the variance of the significance level estimator can be suf-ficiently reduced by settingm ¼ 5, withm ¼ p*(nþ1), where p is thetarget significance level, and n is the number of MC simulations ofthe null model. For this study, p was set to 0.01, forcing the numberof MC simulations to 499. The above mentioned test mechanismswere also applied with PCCFs, but here points of point pairs belongto distinct subpatterns. All PCFs and PCCFs of this study were built

Table 1Analyzed patterns are mentioned in the first column. Pattern signatures composedof (i) univariate SPS patch configurations and (ii) bivariate SPL-SPS patch configu-rations are respectively depicted in the second and third column. Hypotheses (H1,H2 or H3) of nebkha pattern formation which agree with specific pattern signaturesare shown in the fourth column. Configurations were analyzed with PCFs and PCCFs,and compared against respective null models CSR and AC (antecedent condition).Both null models were complemented with NOD. Configurations were signified byeither (i) 0, (ii) þ or (iii) e, respectively representing (i) absence of, (ii) positive and(iii) negative deviations from null models. H1 assumes that zones surrounding adultnebkhas inhibit recruitment whilst H2 presumes that zones close to adult nebkhasenhance recruitment. H3 supposes that nebkha configurations are shaped by anabiotic driven spatial distribution of microsites which favor seedling recruitment.

Analyzed patterns PCF(SPS) PCCF(SPS,SPL) Hypotheses not rejected

CSR AC

SW þ MQ þ � H1MQ 0 � H1CC þ þ H2, H3TA þ 0 H3

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from Epanechnikov kernels of which bandwidths were determinedby a rule of thumb proposed by Stoyan and Stoyan (1994), based onthe estimated intensity of the point process. Edge corrections ofPCFs and PCCFswere performedwith Ripley’s isotropic correction asmentioned in Stoyan and Stoyan (1994) as well.

Nebkhas and other vegetation patches (i.e. snakeweed) weredistinguished frombackgroundpixels on imagerywithuseof theOtsuTresholding algorithm in imageJ (Abramoff et al., 2004). This algo-rithm, described in Otsu (1979) is designed to choose an optimumthreshold value of pixel intensity to separate foreground (lower in-tensity) from background (higher intensity) pixels, based on bimo-dality in image histograms. Isolated foreground objects were thendefined as vegetation patches. As a consequence, any small youngestablished plants will not be recognized when located below can-opies of oldmature vegetationpatches.However, since anebkha is thewhole of (i) the sandmound, (ii) the nebkha initiator species, and (iii)possible individuals benefitting from intra-nebkha facilitation (El-Bana et al., 2007), the latter limitation does not hinder the correctdetection of the spatial nebkha pattern. Point patterns underlying thePCFs and PCCFs of this study are composed of centroids of vegetationpatches. Because observed patches cannot overlap by definition,centroids of neighboring patcheswill at least be separated by the sumof their patch radii (in contrastwithCSRdistributedpoints). Therefore,biased conclusions could follow after comparing PCFs of patchy pat-terns with those of CSR patterns: randomly distributed patchy pat-terns could be mistakenly assessed as non-randomly distributed(Simberloff, 1979; Wiegand et al., 2006). To address this problem, aproperty called NOD (Non-Overlapping Discs) was incorporated into

Fig. 3. Frequency distribution of (a) mesquite nebkha sizes and (b)

eachnullmodel of this study (seeAppendixD for the translation intoRcode). NODdoes not allowarea-preserving circular representations ofobserved patches to overlap during the randomization process.Wiegand et al. (2006) used a property similar to NOD in their nullmodels, and they even retained patch shapes. But in their softwareProgramita, patches are composed of pixels, with each pixel contrib-uting to inter-patch pairs comprising the PCF (or PCCF). Therefore,Programitamightheavilyemphasize the configurationof thepattern’slargestpatches,becausethesemayhavemuchmorepixels.Nuskeetal.(2009) showed this pixel-based approach spreads out possible PCF (orPCCF) peaks, making the effect of specific spatial patch configurationsless pronounced. For this reason, each patch pair is only counted oncein this study, and the distance measure is centroid-based.

In order to test the validity of the three proposed hypotheses onnebkha pattern formation, a dual approach was followed. For eachpattern under study, (i) the PCF of SPS was compared with asimulated PCF envelope derived from the null model which ran-domizes SPS patches on areas not occupied by SPL patches, and (ii)the PCCF between SPL and SPS was comparedwith a simulated PCCFenvelope derived from a null model called antecedent condition(AC) (Wiegand and Moloney, 2004), which assumes that an earlierestablished subpattern (here SPL) stays fixed while a later estab-lished subpattern (here SPS) is being randomized. Results of both (i)and (ii) were combined in pattern signatures which are neversimultaneously compatible with all three hypotheses, herebylimiting the number of potential applicable ones. Additionally, SPLconfigurations were analyzed. However, the latter are not includedinto the pattern signatures which are used to test our hypotheses.

SinceHypothesis 1 (H1) implies a progressive decrease of availablespace for patch establishment (disregarding the space already occu-pied by fractional cover), processes explained in H1 should formnebkha patterns where young SPS patches seem repulsed from olderSPL patches. When fractional cover is high (and available space islimited), inhibition zones can force recently established patches togroup in clusters. SPS clusters could also be formed by attractionamong SPS patches. However, when SPS clusters are simultaneouslyobserved with repulsion zones around adult nebkhas, clusters of SPSpatches are assumed to be caused by repulsion zones around SPLpatches, and not because SPS patches attract each other. Tests ofpattern independencebetweenSPSandSPL could in theorydistinguishbetween both causes of clustering (Goreaud and Pelissier, 2003). Un-fortunately, independencebetweenpatterns cannot be testedwithoutbias with non-overlapping patchy patterns (Wiegand et al., 2006).

A PCCF which negatively deviates from its null model (beneaththe envelope), at realistic scales where nebkhas still can influencetheir surroundings, might demonstrate that SPL nebkhas have

snakeweed bush sizes. Both are expressed in surface area (m2).

Table 2Minimum, median and maximum diameters of SPS and SPL patches of four different nebkha patterns: (i) the joint NewMexican snakeweed and mesquite pattern (SW þMQ),(ii) the New Mexican mesquite pattern (MQ), (iii) the Libyan Calligonum comosum pattern (CC) and (iv) the Libyan Tamarix aphylla pattern (TA). A threshold size (TS) dis-tinguishes SPL from SPS nebkhas, and simultaneously acts as the minimum and maximum size for SPL and SPS respectively. All diameters are expressed in meter. Precisionestimates are based on source image resolution. With unknown resolutions, pessimistic estimates were made, as in SW þMQwhere only patches larger than 0.09 m2 (0.34 mdiameter) were clearly identified as vegetation patches. With MQ, resolution was artificially lowered to 0.62 m due to a zooming operation in GE. The image of the Libyannebkha field originates from the IKONOS sensor (with 0.8 m resolution).

SPS SPL

min (m) med (m) TS (m) med (m) max (m) Estimated precision (m)

SW þ MQ 0.34 0.75 6.61 8.31 11.80 �0.17MQ 1.60 3.50 8.67 10.30 16.13 �0.31CC 0.88 1.97 2.71 3.05 3.41 �0.40TA 3.52 5.43 7.73 8.21 12.94 �0.40

J.J. Quets et al. / Acta Oecologica 49 (2013) 53e63 57

repulsion zones hereby inhibiting establishment of SPS patches.Repulsion zones are however overestimated by PCFs and PCCFs since(i) centroid-to-centroid pair distances include patch radii, and (ii)repulsion radii of nebkha pairs are added together (Fig. 2). Theformer is difficult to precisely correct since each subpattern consistsof patches having a range of radii. Therefore a single valued sizerepresentative (themedian radius)was chosen for correction.Hence,the following equation applies (under the assumption of H1):

RR1 þ RR2 ¼ PDMAX � ðD1 þ D2Þ=2 (1)

RR1 andRR2 areestimatesof repulsion radii surroundingpatchesofSP1 and SP2, while D1 and D2 are median patch diameters associatedwith these subpatterns. PDMAX signifies the pair distance associatedwith the maximum interaction scale, as indicated by the maximumPCCF pair distance where deviation from the null model due torepulsion still occurs. Note that, because patches do not overlap,comparisons of PCFs (or PCCFs) of observed patterns with their en-velopes (derived from simulated patterns) are only meaningful forscales larger than the sum of radii of neighboring patches having

Fig. 4. Spatial summary statisticsofNewMexicannebkhapatterns. Envelopes are enclosedbymwhere PCFOBS(r) and PCFSIM,i(r) signify pair correlation functions calculated either among SPS [randomized patterns under NOD (i ε {1, 2, .,499}). During the randomization of SPS patches,PCCFOBS(r) (lower border) andmax[PCCFSIM,i(r)]e PCCFOBS(r) (higher border),where PCCFOBS(r)patch centroids of the observed and 499 simulated randomized patterns under NOD (SPL patcpattern (SW þ MQ). The bottom three subfigures only concern mesquite patches (MQ). SPS(FC:50-50). Envelopeswhich fall completely aboveor beneath thenull line, for a range of pairdisaccording to GoF tests (p ¼ 0.01). Adjacent significant distances are represented by a horizonta

repulsion zones. When considering repulsion zones of SPS negligiblecompared to those of SPL, it follows that RRS ¼ 0, and that:

RRL ¼ PDMAX � ðDS þ DLÞ=2; (2)

with SPS ¼ SP1 and SPL ¼ SP2. Note that the presence of repulsionzones can be demonstrated with an a priori defined level of sig-nificance. Specific values of repulsion radii can only be roughlyassigned with unknown precision by applying Eq. (2). Repulsionradii estimates were nonetheless presented in this study becausethey give an impression of the scales of interaction. Repulsion radiiamong SPL nebkhas (when applicable) were estimated with:

RR ¼ ðPDMAX � DÞ=2; (3)

which is a simplified version of Eq. (1) where SP1 ¼ SP2, and sub-sequently RR ¼ RR1 ¼ RR2 and D ¼ D1 ¼ D2.

With Hypothesis 2 (H2), SPS patches are expected to clusteraround SPL nebkhas, since seedlings would have a higher chance toestablish near adult nebkhas. The latter configuration could be

in[PCFSIM,i(r)]ePCFOBS(r) (lowerborder) andmax[PCFSIM,i(r)]ePCFOBS(r) (higher border),(a) and (d)] or among SPL [(b) and (e)] patch centroids of the observed and 499 simulatedSPL patches were held fixed. (c) and (f) show envelopes enclosed by min[PCCFSIM,i(r)] eand PCCFSIM,i(r) represent pair cross-correlation functions calculated between SPL and SPShes held fixed). The upper three subfigures concern the combined snakeweed-mesquiteand SPL represent subpatterns each contributing half of the combined fractional covertances, indicate deviations at those scales. Arrowspinpoint significant declareddeviationsl segment at the arrow base (no segment for isolated significant distances).

Table 3Intervals where PCFs (of SPS and SPL) or PCCFs (between SPS and SPL) significantlydeviate from their null models in the four different patterns under study. Thesepatterns are: (i) the joint New Mexican snakeweed and mesquite pattern(SWþMQ), (ii) the NewMexican mesquite pattern (MQ), (iii) the Libyan Calligonumcomosum pattern (CC) and (iv) the Libyan Tamarix aphylla pattern (TA). PCF and PCCFprotrusions above null model envelopes have positive signs, negative protrusionshave negative signs. When the summary statistic completely follows the null model,NA (Not Applicable) was displayed. Intervals are expressed in m.

PCF(SPS) PCF(SPL) PCCF(SPS,SPL)

SW þ MQ ‒[0.5]þ[1 e 6]þ[7]þ[18]þ[19 e 20]

NA ‒[4 e 5.5]þ[11]

MQ NA ‒[10.5 e 14] ‒[8.5 e 10]CC þ[16 e 46]

þ[118 e 134]NA þ[17 e 30]

TA þ[2 e 29]þ[36 e 43]‒[82 e 95]

NA NA

J.J. Quets et al. / Acta Oecologica 49 (2013) 53e6358

indicated when the PCCF of the observed pattern protrudes aboveits PCCF envelope under AC, given the presence of SPS clusters.

WhenHypothesis 3 (H3) applies, SPS patches are also expected toform clusters. However, H3 could be divided in two subhypotheses.When recruitment encouraging microenvironments did not moveduring the time span in which the nebkha pattern was formed, SPSclusters are expected tobestill inproximity toSPLnebkhas, as inH2. Ifsuch microenvironments did change location over time, SPS clusterswould however not be confined to be closely located to SPL nebkhas.

For the sake of fully exploiting image data, reflective values (pixelintensity) of areas not occupied by nebkhas were conceived as po-tential values of an unknown environmental parameter influencingnebkha recruitment. A correlation between specific reflective valuesand SPS nebkha clusters could in this way support H3. Obviously, notall environmental parameters are visible on image, but some may.

Fig. 5. Spatial summary statistics of Libyan nebkha patterns. Envelopes are enclosed by min[where PCFOBS(r) and PCFSIM,i(r) signify pair correlation functions calculated either among SPS [randomized patterns under NOD (i ε{1, 2, .,499}). During the randomization of SPS patches,PCCFOBS(r) (lower border) andmax[PCCFSIM,i(r)]e PCCFOBS(r) (higher border), where PCCFOBS(SPS patch centroids of the observed and 499 simulated randomized patterns under NOD (SPLpattern (CC). The bottom three subfigures concern Tamarix aphylla patches (TA). SPS and SPL reEnvelopes which fall completely above or beneath the null line, for a range of pair distancescording to GoF tests (p ¼ 0.01). Adjacent significant distances are represented by a horizonta

The graphical results of this study show differences between thePCFs (or PCCFs) and their accompanying envelopes. The deviationstrength of a PCF (or PCCF) from its envelope at a specific scale, isrelated to the proportion between the absolute deviation and theenvelope’s localwidth. The latter is ameasure for the local variance ofthe null model. For each interval where a PCF (or PCCF) protrudes itsenvelope, a GoF test (p¼ 0.01)was performed. GoF tests were alwaysperformed on separate and independently created envelopes underthe same nullmodel. All spatial summary statistics of this studywerecalculated with the R-package spatstat (Baddeley and Turner, 2005).

3. Results

Table 1 summarizes all pattern signatures which are observedfrom the analyzed patterns, and that go together with thecompatible hypotheses on nebkha pattern formation.

3.1. New Mexico

Both snakeweed and mesquite sizes have strong negativelyskewed frequency distributions: i.e. smaller patches are morecommon (Fig. 3). In the combined mesquite-snakeweed pattern,smaller patches are more common as well because the consideredpatch density of snakeweed (1312/ha) is much higher than ofmesquite (128/ha). Patch diameter ranges and medians of thesesubpatterns are summarized in Table 2. Fig. 4 shows null modelenvelopes relative to the PCFs and PCCFs denoted by DPCF (left andmiddle column) and DPCCF (right column). The significance of eachscale interval where PCFs or PCCFs deviate from their envelope, wastested with a GoF test (p ¼ 0.01). Only scales smaller than 20 m areshown on Fig. 4, since all summary statistics lie within their en-velopes at larger scales (the largest measured scale equals half thelength of the study area). Classification of unvegetated area did notshow any structured spatial configuration (not shown). Significant

PCFSIM,i(r)] e PCFOBS(r) (lower border) and max[PCFSIM,i(r)] e PCFOBS(r) (higher border),(a) and (d)] or among SPL [(b) and (e)] patch centroids of the observed and 499 simulatedSPL patches were held fixed. (c) and (f) show envelopes enclosed by min[PCCFSIM,i(r)] er) and PCCFSIM,i(r) represent pair cross-correlation functions calculated between SPL andpatches held fixed). The upper three subfigures concern the Libyan Calligonum comosumpresent subpatterns each contributing half of the combined fractional cover (FC:50-50)., indicate deviations at those scales. Arrows pinpoint significant declared deviations ac-l segment at the arrow base (no segment for isolated significant distances).

Fig. 6. Image classifications of the Libyan study site. Nebkhas are portrayed in black.Gray and white areas respectively represent background pixels which are darker andbrighter than a threshold value. The threshold is higher (brighter) in (a) than in (b).

J.J. Quets et al. / Acta Oecologica 49 (2013) 53e63 59

declared deviating intervals were summarized in Table 3, andpinpointed with arrows in Fig. 4. Adjacent significant distances arerepresented by a horizontal segment at the arrow base (no segmentfor isolated significant distances). Data from Table 2 and Table 3sufficed to estimate repulsion radii according to Eq. (2) and Eq. (3).

Fig. 4aec show summary statistics of subpatterns derived fromthe combined snakeweed and mesquite pattern. The patternsignature constructed from Fig. 4aec strongly suggest that adultmesquite nebkhas are surrounded by inhibition zones (Table 1).Indeed, (i) SPSSWþMQ patches form clusters (Fig. 4a), and (ii) signif-icant fewer SPSSWþMQ patches surround SPLSWþMQ patches, ascompared to the null model (Fig. 4c). SPLSWþMQ patches appearrandomly established (Fig. 4b). Snakeweed patches repulse eachother at very small scales (about 0.5m centroid-to-centroid), whichcould be an extra indication that SPSSWþMQ clusters observed inFig. 4a did not arise from attraction among SPSSWþMQ patches. PCFdeviations of SPSSWþMQ nearby 20 m scales (Fig. 4a), most likelyindicate commonly observed inter-cluster distances. Repulsionradii around SPLSWþMQ nebkhas (median diameter ¼ 8.31 � 0.17 m)affecting SPSSWþMQ patches, are roughly estimated 1 m (Eq. (2)).

Summary statistics shown in Fig. 4def only concernmesquite. Thecorresponding pattern signature is different from the previous one(Table 1), butbothsignatures indicate thatH1underlies bothpatterns.Adult mesquite nebkhas thus inhibit establishment of youngmesquite as well as snakeweed bushes in their close proximity.Repulsion radii of adult SPLMQ mesquite nebkhas (mediandiameter ¼ 10.30 � 0.31 m), affecting SPSMQ patches are roughlyestimated3m(Eq. (2)). SPLMQnebkhasthemselvesare regularlyspaced(Fig. 4e), indicating competition among the most aged mesquitenebkhas which repel each other up to 2 m from their edges (Eq. (3)).

3.2. Lybia

SPSCC and SPSTA both form strong clusters with diameters of about45 m (Fig. 5a,d). Tamarix pattern signatures rejected all proposedhypotheses, except for H3 (Table 1). Calligonum signatures onlyrejectedH1asapossibleunderlyingmechanismofpattern formation.The nullmodel deviation between118 and134m, as shown in Fig. 5a,indicatescommon inter SPS clusterdistances. Thedeviationsbetween90 and 99 m (Fig. 5d) suggest that SPSTA clusters appear slightly butsignificantly repelled. These pattern signatures strongly indicate thatabiotic microsites are responsible for at least SPSTA clusters. Unvege-tated area was classified in two classes based on reflective valuesbeing above or below a threshold. No class was found to eithercorrelate with locations of SPSCC or SPSTA clusters, though several at-tempts were made by choosing from a range of threshold values.However, bothmost bright (white area in Fig. 6a) andmostdark (darkarea in Fig. 6b) regions appear side by side as oblong features of 10e20 m in length in the southwest direction behind many individualnebkhas. These featuresmost likely represent shady and sunny dunesides since the solar azimuth angle during the image production timewas directed east-southeast. The latter strongly suggest that Libyannebkhas interact with their environment by trapping sedimentbehind their canopies at leeward sides (Hesp, 1981).

4. Discussion

4.1. New Mexico

SPSSWþMQ, SPSMQ, SPLSWþMQ and SPLMQ are groups of vegetationpatches which have median sizes that are progressively larger.These subpatterns change from being strongly spatially clustered inFig. 4a, over spatially random in Fig. 4b,d, and eventually regular inFig. 4e. Under the assumption that larger vegetation patches haveestablished earlier and have grown over a longer period of time

(Gadzia and Ludwig,1983), this observation indicates together withthe results from Fig. 4c,f, that early established New Mexicanmesquite nebkhas were able to gradually develop zones aroundtheir perimeters which inhibited mesquite and snakeweedrecruitment. Competition among large (old aged) mesquite neb-khas is visible in the pattern as well. Together, these observationssuggest that repulsion zones can (at least partly) limit fractionalcover in nebkha landscapes in the northern Chihuahuan desert ofNew Mexico. Since these zones surround mesquite nebkhas, theyare most likely biologically driven, but specific underlying mecha-nisms still remain uncertain. Repulsion zones could be caused bylateral extending roots extracting water and nutrients beyondcanopy perimeters (Ho et al., 1996), or may be induced by release ofallelopathic substances. In the end, a more experimental approachis needed to reveal the specific mechanisms causing inhibitionzones around adult mesquite nebkhas as observed in this study.

4.2. Lybia

SPSCC clusters having diameters of 45 m are centered around SPLCC

nebkhas. Table1 indicates that thispattern couldbeexplainedbybothH2 andH3. Sand dune landscapes, such as in the Libyan study site, areknowntobeverydynamic (Bagnold,2005). Itmaybethat recruitmentbeneficial microenvironments may change location over time. Adult

J.J. Quets et al. / Acta Oecologica 49 (2013) 53e6360

Tamarix aphylla nebkhas, which are known to have deep tap roots(Walker et al., 2006), may survive such changes well, whilst Calligo-num comosum nebkhas, having only shallow root systems (Walkeret al., 2006), may survive these changes less. This may explain whyCalligonum juveniles (SPSCC) are confined toparentpoint surroundings,whilst Tamarix juveniles (SPSTA) are not. Sand tails pinpointed byFig. 6aeb indicate that the Libyan nebkhas influence their localenvironment far beyond their canopies, but the overall nebkha den-sity is too lowtoverifywhether thesesandtails could in turn influencerecruitment processes. In summary, these observations suggest thatthe sparse fractional cover of the Libyan study site, has no (direct)biological cause, and ismost likely completely driven abiotically. How(both the New Mexican and Libyan) nebkhas affect recruitmentwithin their own borders (i.e. intra-nebkha) remains unknown, asnewly established plants undermature vegetation canopieswere notdetectable from our imagery. If on-nebkha regeneration occurs inthese systems, nebkhas might outlive the host plants which initiatedthem, possibly reducing the rate of change in the nebkha patternrelative to on-nebkha regeneration being absent.

5. Conclusion

The studied nebkha landscapes in New Mexico and Libya havecontrasting patterns. The New Mexican nebkha configuration in-dicates that it is at least partly biologically driven, formed by inhi-bition zones which gradually develop around adult mesquitenebkhas. These zones of repulsion both limit mesquite and snake-weed establishment, and may force them to group in clusters. Suchinhibiting zones are not observed around Libyan nebkhas. However,the Libyan nebkha pattern is not configured randomly, most likelydue to abiotically driven microsites which favor establishment ofCalligonum comosum and Tamarix aphylla nebkha seedlings, andwhich move in time. The extent to which nebkha host plantsregenerate on nebkhas could not be explored in this work, but itmight be an interesting topic for future research. Understandingnebkha ecosystems is a requirement to ultimately assess theirresistance and resilience to climate change (e.g. decreasing precip-itation) and to create nebkha landscapes, for example by plantingcuttings. Such artificial creation is unlikely to yield good results if itgoes against the patterns that would emerge naturally.

Fig. A1. Diameters of snakeweed and mesquite patches, ranked from smallest tolargest (gray curve). The left and right linear parts were respectively assumed asso-ciated with subpatterns of snakeweed (SPSW) and mesquite (SPMQ). TZ represents aninterval of diameters where patches could belong to SPSW and SPMQ. 1.6 m is chosen asthe size which separates SPSW from SPMQ.

Acknowledgments

The authors extend their appreciation to the Deanship of Sci-entific Research at King Saud University for funding the workthrough the research group project No RP-VPP-031. Prof. Dr. IvanNijs was supported by the King Saud University visiting professorsprogram. Dr. Brandon Bestelmeyer and Dr. Ed Fredrickson of the

Jornada Experimental Range are acknowledged for communicatingecological information of the New Mexican study site. Dr. RolfTurner and Prof. Adrian Baddeley are thanked since they were verycooperative in the translation of the NOD null model into R code.Finally, we are grateful for the valuable feedback received from thepeer-reviewers. This research was supported by the Flemish FWO(No. G.0147.09 N).

Appendices

A Screened nebkha fields

Several nebkha fields mentioned in peer reviewed articles werescreened for use in this study. Grouped by country, these articlesare: Burkina Faso (Dhief et al., 2009), China (Tengberg and Chen,1998), Egypt (Wang et al., 2008), Israel (El-Bana et al., 2003), Ice-land (Ardon et al., 2009; Bornkammet al., 1999), Kuwait (Mountneyand Russell, 2006), Mali (Brown and Porembski, 1997; Khalaf et al.,1995), New Mexico (Nickling and Wolfe, 1994), South-Africa(Gibbens et al., 2005; Langford, 2000; Parsons et al., 2003),Tunisia (Dougill and Thomas, 2002; Hesp and McLachlan, 2000)and U.S. (Tengberg and Chen, 1998). This study withheld onlynebkha fields of which (i) exact locations were known, (ii) highresolution imagery was available, and (iii) species were identified.

B Google Earth as image provider

Google Earth (GE) is a GIS application of Google Inc. whichprojects a mix of satellite and aerial source images of differentspatial resolution on a virtual three dimensional WGS84 ellipsoid(Eldridge and Rosentreter, 2004). This ellipsoid in turn is projectedorthographically on a computer monitor. Due to the earth’s cur-vature, the map scale on screen is not uniform when viewing largeportions of our globe on GE. Nevertheless, deviation from uniformscale is negligible when viewing only small parts of the earth’ssurface: screen pixels at the edge of 10 km � 10 km fields havesurface areas which are only 0.00014% larger as compared to pixelsfrom the centers of these fields. All sites of this study have di-mensions smaller than 10 km � 10 km, and are considered uni-formly scaled. The ground area represented by a screen pixel [here:projected pixel area (PPA)] can be manipulated with GE’s zoomfunction. The PPA can be calculated by counting the number ofscreen pixels on GE’s scale bar. The spatial resolution of most sat-ellite images behind most GE-scenes can easily be found bycomparing online catalogues of main providers of satellite imagery(GeoEye and Digital Globe) with image information given by GE.Resolution information of aerial source imagery is mostly notprovided by GE, but was roughly estimated by the size of thesmallest recognizable object.

C Mesquite Snakeweed separation

It is known that adult mesquite shrubs attain bigger sizes thanadult snakeweed shrubs (Wan et al., 1993). Additionally, mesquiteseedlings are very rare in adult mesquite stands (Brandon Bes-telmeyer, personal communication). This suggests that size rangesof snakeweed shrubs and mesquite nebkhas are highly distinct.When showing patch diameters of Fig. A1, ranked from small tolarge (gray curve in Fig. A1), two linear parts can be discerned: Theleft and right linear parts are respectively assumed associated withsubpatterns of snakeweed (SPSW) and mesquite (SPMQ). Bothsnakeweed and mesquite could presumably have sizes within thetransition zone (TZ). The TZ center is 1.6 m and is exactly the samesize which divides the pattern into two types of patches withdistinct patch texture and color (color image not shown).

D NOD null model into R code

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