Can isotropy vs. anisotropy in the spatial association of plant species reveal physical vs. biotic facilitation?

- Isotropy vs. anisotropy in the spatial association of plant species - 127

Journal of Vegetation Science 12: 127-136, 2001© IAVS; Opulus Press Uppsala. Printed in Sweden

Abstract. In dryland ecosystems and other harsh environ-ments, a large part of the vegetation is often clustered, appear-ing as ‘islands’. If ‘independent’ species, usually colonizers,can be distinguished from species which are ‘dependent’ onthe presence of the colonizing species for successful establish-ment and/or persistence, the type of spatial pattern of theassociation – isotropic (spatially symmetric) or anisotropic(spatially asymmetric) – can give information on the underly-ing environmental factors driving the process of association.Modified spatial pattern analysis based on Ripley’s K-func-tion can be applied to bivariate clustered patterns by cardinaldirection in order to detect possible anisotropy in the pattern ofassociation. The method was applied to mapped distributionpatterns of two types of semi-arid shrubland in southeasternSpain. In shrubland of Retama sphaerocarpa, low shrubs ofArtemisia barrelieri were significantly clustered under thecanopy of the Retama shrubs in all four cardinal directions,suggesting an isotropic facilitation effect. In low shrublanddominated by Anthyllis cytisoides and Artemisia barrelieri,Anthyllis shrubs occurred more frequently than expected onthe eastern side (and downslope) of an Artemisia shrub. Thepossible environmental factors driving the two associationpatterns are discussed and recommendations for further appli-cations of the analytical method are given.

Keywords: Aggregated pattern; Bivariate pattern; Clusteredpattern; Competition; Facilitation; K-statistics; L-statistics;Nurse-plant effect; Ripley’s K-function; Second-order spatialanalysis.

Nomenclature: Sagredo (1987).

Introduction

Non-random bivariate spatial distribution patternscan either be clustered, suggesting positive associationbetween two species or life stages (e.g. Prentice &Werger 1985; Haase et al. 1996a, 1997), or show aregular trend, implying repulsion that may be an effectof interspecific competition (e.g. Fonteyn & Mahall1978; Sterner et al. 1986; Kenkel 1994; Martens et al.1997). Although the importance of competition in shap-ing plant communities has been stressed, many commu-nities reveal a certain degree of clustering of different

Can isotropy vs. anisotropy in the spatial association of plant speciesreveal physical vs. biotic facilitation?

Haase, Peter

Dyckerhoffstrasse 3, D-49525 Lengerich, Germany; Tel. +49 5482 97295; E-mail [email protected]

species at some spatial scale, implying facilitation ef-fects, or, at least tolerance (Bertness & Callaway 1994;Økland 1994; Callaway 1995; Callaway & Walker 1997).

In dryland ecosystems and other harsh environments,a large proportion of the vegetation is frequently clus-tered in form of ‘islands’ (e.g. Prentice & Werger 1985;Garner & Steinberger 1989; Pugnaire et al. 1996a, b),which can either contain species of similar size andphysiognomic habit (Kikvidze & Nakhutsrishvili 1998;Nuñez et al. 1999), or a ‘centre species’ of larger size,which is surrounded by an undergrowth of lower vege-tation (Garner & Steinberger 1989; Weltzin & Coughenour1990; Pugnaire et al. 1996b; Barnes & Archer 1999).Although competition may be an important driving forcealso in low-resource environments (Fowler 1986; Vilà& Sardans 1999), the negative effect of interspecificcompetition can be offset by facilitation effects if theusually harsh physical conditions are sufficiently im-proved by the central species in such ‘micro-ecosystems’(Garner & Steinberger 1989; Valiente-Banuet & Ezcurra1991; Bertness & Callaway 1994). The facilitation ef-fect of focal plants can, in theory, be either isotropic(possessing the same physical properties in all spatialdirections), e.g. accumulation of litter and related en-richment in soil organic matter and improvement of thenutrient status, or anisotropic, e.g. the spatial and tem-poral distribution of irradiation (except diffuse skylight)and related extremes of temperature and evapo-transpiration – which are more strongly expressed athigher latitudes (Franco & Nobel 1988; Weltzin &Coughenour 1990; Valiente-Banuet & Ezcurra 1991;Suzán et al. 1996), or the distinction between exposedand sheltered sides in regions with a predominant winddirection (Table 1).

In otherwise homogeneous environments, such aniso-tropic effects of facilitation can lead to a spatially non-symmetric distribution of the undergrowth, or of par-ticular species in it, under the canopy of the focal plant.It may be assumed that, if such anisotropic spatial distri-butions can be detected, the physical aspects of thefacilitation predominate, but when the distribution isisotropic, the biotic aspects might prevail. In practice,both physical and biotic effects are often combined

128 Haase, P.

(e.g. Pugnaire et al. 1996b; Moro et al. 1997a, b; Rousset& Lepart 1999, 2000), and a decomposition, if at allpossible, can only be attempted with spatial statisticalmethods.

Although several aspects have been considered instudies of facilitation (Franco & Nobel 1988; Weltzin &Coughenour 1990; Valiente-Banuet & Ezcurra 1991;Suzán et al. 1996; Rousset & Lepart 1999, 2000), thequantitative description of anisotropy in spatial pointpatterns has been largely restricted to the mathematicalliterature, e.g. the ‘point pair orientation distributionfunction’ of Stoyan & Stoyan (1994). On the other hand,spatial pattern analysis based on Ripley’s K-function(Ripley 1976, 1981) is continuing to be a favourite ana-lytical tool of many plant ecologists. In recent papers,Martens et al. (1997) used this method of pattern analysisto distinguish between above-ground and below-groundcompetition, and Podani & Czárán (1997) extended itsanalytical power to investigate multi-species assem-blages. Goreaud & Pélissier (1999) provided formulasfor consideration of areas of complex shapes. In thispaper, I describe a further extension of Ripley’s K-function, by which anisotropy in aggregated bivariatepatterns can be detected. The method is tested andapplied to field data of two types of semi-arid shrublandin southeastern Spain.

Methods

Definitions

In plant ecology, the terms ‘symmetry’ and ‘asym-metry’ are used to denote the hierarchy of competitiveinteractions (Begon 1984; Weiner 1990; Eccles et al.1999). Although definitions may vary for its subtypes(cf. Connell 1990; Økland 2000), competition betweentwo given individuals is asymmetric if one plant claimsmore than its proportional share (in relation to its size)of resources. To avoid confusion, we prefer to use theterms ‘isotropy/anisotropy’ when spatial relationshipsare addressed, instead of ‘spatial symmetry/asymme-try’, these former terms were also used by Rossi et al.(1992) in studies of ecological spatial dependence.

Statistical background

Spatial point pattern analysis uses all point-to-point(plant-to-plant) distances for a statistical description oftwo-dimensional distribution patterns. A circle of radiust is centred on each point and the number of neighbourswithin the circle is counted. The density λ = n/A givesthe mean number of points within a defined area, wheren is the number of events (plants) in the analysed plotand A is the area of the plot. In univariate (single

Table 1. Potential effects of focal plants on their undergrowth.

Category Factor Ecological effect Spatial pattern of effect

Physical factors Strong direct insolation Shading by canopy affects Anisotropic (Franco & Nobel 1988; evapotranspiration, soil Weltzin & Coughenour 1990; temperate and water status Valiente-Banuet & Ezcurra 1991;

Suzán et al. 1996; Rousset & Lepart 1999, 2000)

Predominant wind direction Evapotranspiration, abrasion Anisotropic of tissue, accumulation of debris and disseminules

Sheet water flow Soil water status, accumulation Anisotropic (Montaña et al. 1995) of debris and disseminules

Precipitation – throughfall Soil water status (Pressland 1973) IsotropicPrecipitation – stemflow Soil water status (Pressland 1973) Anisotropic

Biotic factors

Direct effects Litterfall Soil cover, enhanced germination, Isotropic nutrient recycling (Moro et al. 1997a,b)

Soil amelioration Organic matter, nutrients (Pugnaire Isotropic* et al. 1996b)

Root competition Water-, nutrient status isotropic

Attraction Birds (perching) – Nitrogen status, enhanced Preferred perching places droppings, passed seeds germination (Debussche &

Isenmann 1994)

Foliage-eating insects Nitrogen status Isotropic – droppings

Obstruction and Impeded access for browsing Enhanced survival and regeneration Probably isotropic protection ungulates and rodents, distracting (Jaksic & Fuentes 1980; McAuliffe 1984,

smell or taste 1986; Rousset & Lepart 1999, 2000)

* Usually secondary effect due to differential decomposition rates as a result of anisotropic physical factors.


species) analysis, the function λK(t) gives the expectednumber of further points within radius t of an arbitrarypoint. Ripley (1976, 1981) suggested as an approxi-mately unbiased estimator for K(t):

ˆ – –K t n A w I uij t iji j

( ) = ( )∑∑≠

2 1(1)

where It is a counter variable which is set to 1 if thedistance uij between events i and j is ≤ t, and wij is aweighting factor to correct for edge effects (Ripley1981; Diggle 1983; Haase 1995).

If the point pattern is Poisson random at scale t, thevalue of K(t) equals πt2, i.e. the area of a circle of radiust. The frequently used transformation L(t) = √[K(t)/π]yields a linear plot of the sample statistic against t(Besag 1977), and a further transformation to L(t) =√[K(t)/π] – t = 0 gives zero expectation for all values oft, which is the most convenient output format for com-parative purposes. The latter transformation of the K-function has also been called L(t) – t, but both termshave been used inconsistently in the literature. In thefollowing, we refer to this derived K-function as L(t).

In bivariate analysis, the spatial relationship of twospecies, which may have different densities, λ1 = n1/Aand λ2 = n2/A, is investigated. The function λ1 K12(t) isdefined as the expected number of individuals of species2 within a radius t of an arbitrary individual of species 1,while the function λ2 K21(t) gives the expectation for theopposite spatial relationship (Diggle 1983; Andersen1992; Kenkel 1994). The corresponding estimators

ˆ – –K t n n A w I uij t ij12 1 2

1 1( ) = ( ) ( )∑∑ (2)

and

ˆ – –K t n n A w I uji t ji21 2 1

1 1( ) = ( ) ( )∑∑ (3)

are combined to a weighted (by n1 and n2) mean singleestimator (Lotwick & Silverman 1982). Edge correc-tions were calculated using Ripley’s local weightingmethod (Ripley 1977, 1979; Haase 1995).

Analysis of bivariate patterns considering cardinaldirection

In this extension of bivariate pattern analysis, it isnecessary to distinguish between an ‘independent’ (i)and a ‘dependent’ species (j) (or life stage, or size class).In some cases, e.g. adults vs seedlings, two different sizeclasses, etc., the dependency might be easy to hypoth-esise, but for two species of similar size and physiog-nomy, or live and dead individuals of the same species,this distinction has to be made on the basis of ecological

experience or preliminary hypothesis. In a pair of live anddead shrubs, for example, the dead individual could havedied as a result of intraspecific competition (isotropiceffect) or – and now – provide shelter for the remainingliving individual (anisotropic effect). In any case, theresult of the analysis should yield the relative position ofthe dependent with respect to the independent species.

If we postulate that the location of species 2 dependson that of species 1, it is appropriate to consider thesingle estimator K12(t) given in Eq. (2) instead of theweighted average of K12(t) and K21(t). The correspond-ing L-statistic for bivariate analysis is then calculated as:

ˆ –L t K t t12 12( ) = ( ) π (4)

The extended method of bivariate pattern analysis dis-tinguishes four quadrants or semi-circles during calcu-lation. A separate counter variable is assigned to each ofthe four quadrants (e.g. SW, NW, NE, SE) of the circlecentred on any point i of the pattern (Fig. 1). In theexample, only the counter variable It(NE)(uij) is incre-mented by 1 (Fig. 1a). If an edge correction is necessary(cf. Haase 1995), the value can be > 1, and if adjacentquadrants also participate in the edge correction, theirrespective counter variables are also incremented by avalue based on the proportion of the circumference ofthe circle uij which lies within the plot boundary in therespective quadrant (Fig. 1b). Furthermore, while for afull circle, the expected number of non-conspecific pointswithin distance t of an arbitrary point equals πt2, theexpected number of non-conspecific points within dis-tance t in one particular quadrant is reduced to πt2/4 (orto πt2/2 in semi-circles). For bivariate pattern analysisconsidering cardinal direction, this results in an updatedformula for the L-statistic:

ˆ –L t K t tq q12 124( ) = ( ) π (5)

where q denominates the quadrant and can vary from1 to 4. For the consideration of semi-circles, the firstmultiplicator under the square root is 2.

Field examples

The modified method of spatial pattern analysis wasapplied to data from two types of semi-arid shrublandat the Rambla Honda field site, a dry valley ca. 40 kmnorth of Almería, Andalucía, Spain (37° 08' N, 2° 22'W, 600 - 1000 m a.s.l.). Three semi-natural vegetation typescan be distinguished along a hill-slope to valley-bottomcatena (Puigdefábregas et al. 1996). Stipa tenacissima

130 Haase, P.

tussock grassland covers the rocky slopes up to theridges at 800 - 1000 m, low shrubland, dominated by thesummer-deciduous Anthyllis cytisoides, occupies thealluvial fans at the foot of the mountain slopes, andevergreen shrubland of Retama sphaerocarpa coversthe sandy valley bottom.

Haase et al. (1996a) investigated the bivariate distri-bution pattern of the leafless, stem-photosynthetic shrubRetama sphaerocarpa (Fabaceae) and its woody under-growth, which consisted mainly of Artemisia barrelieri(Asteraceae). A strongly clustered pattern was detectedat scales of up to 2.5 m, which was interpreted as afacilitation effect of the Retama canopies on their under-growth, which also included a large number of non-woody perennial and annual species (Pugnaire et al.

1996a, b; Moro et al. 1997a, b; The strength of theclustering and the cluster radius increased with increas-ing canopy diameter of the Retama shrubs (Haase et al.1996a). In this semi-arid environment with high levelsof irradiation, even the sparse canopy of Retama pro-vides substantial reductions in irradiation and tempera-ture extremes (Moro et al. 1997a), but these effects arestrongly anisotropic and much more pronounced on thenorthern side of the shrub. It is therefore hypothesizedthat the local density and floristic composition of theundergrowth may reflect this spatial asymmetry. I re-analysed data from a 100 m × 20 m plot (designated plot1 in this paper), described by Haase et al. (1996a),varying t in steps of 0.1 m over the range 0 to 5 m.Because smaller Retama shrubs had little undergrowth(Haase et al. 1996a; Pugnaire et al. 1996b), only Retamashrubs of at least 1 m canopy diameter (n = 95) wereconsidered and the attention was restricted to Artemisiabarrelieri as the only species of the understorey (n = 186).

In shrubland dominated by the summer-deciduousshrub Anthyllis cytisoides (Fabaceae), this species waspositively associated with the subdominant Artemisiabarrelieri at scales of 0.4 - 0.7 m which was within therange of the crown diameters of the Anthyllis shrubs(Haase et al. 1997). This pattern of positive associationchanged to one of repulsion in another plot whichappeared to represent a later stage of succession andwhere only few individuals of Artemisia remained(Haase et al. 1997). The observed patterns were inter-preted as an initial nurse-plant effect by the browse-tolerant Artemisia bushes, which were eventuallyoutcompeted by Anthyllis because of its higher growthrate and larger adult size. I re-analysed the bivariatedata sets for two plots, designated plot 2a (Artemisia =61, Anthyllis = 64, aspect = 135° (SE), slope 8°) andplot 2b (Artemisia = 56, Anthyllis = 116, aspect 45 - 90°(NE-E), slope 13.5°), increasing t in steps of 0.1 mfrom 0 to 2.5 m.

Simulation, randomization, and significance of results

During 1000 simulations of each of the bivariatepatterns, new random coordinates were assigned to the‘dependent’ species only, thus maintaining the spatialpattern of the ‘independent’ species. This toroidal shift-ing is the standard procedure (Diggle 1983; Upton &Fingleton 1985; Andersen 1992; Kenkel 1994) sinceonly the distances between non-conspecific points areof interest.

The means ± 1.96 standard deviation (2.5 % tails) ofthe 1000 simulations were used to construct a confi-dence envelope for the L-statistic (data) for each valueof t. These confidence envelopes are given for diagnos-tic purposes only (e.g. Martens et al. 1997); they cannot

Fig. 1. Decomposition of spatial pattern analysis on cardinaldirection: (a) The relative position of point j with respect topoint i is the NE quadrant (the counter variable It(NE)(uij) is setto 1). (b) The relative position of point j with respect to pointi is the SW quadrant. The calculation requires the considera-tion of an edge correction (the counter variable It(SW)(uij) is setto 1, It(NE)(uij) and It(SE)(uij) are weighted by the proportion ofthe circumference of the circle of radius uij which is inside theplot boundary within their respective quadrants.


be used to infer significant deviation of the samplestatistic from complete spatial randomness (CSR) overthe full range of t investigated. For this overall test ofCSR, I used a Cramer-von Mises type of test that inte-grates the squares of the deviations of the sample statis-tic from the expected value (which equals t) (Diggle1983; Berg & Hamrick 1994; Martens et al. 1997).Since the definition of the derived sample statistic wasL(t) = L(t) – t, the corresponding equation is simplifiedto:

L L t dtq= ( )[ ]∞

∫ ˆ12

2

0(6)

The result of the integration of the L-statistic calculatedfrom the field data was ranked together with the resultsof the 1000 randomizations and this ranking was trans-lated into significance probability:

p s n= +( ) +( )1 1 (7)

where s is the number of simulations yielding values ofthe statistic that are higher than the value obtainedfrom the data and n is the total number of simulations.The null hypothesis (CSR) was rejected at the p < 0.05level. Preliminary tests of significance were performedby integration over the complete range t = 0 to t = tmaxof the analysis. Unless these tests yielded significantresults, tmax was reduced to the upper limit of the rangeover which ‘significant’ deviation of the sample statis-tic with respect to the confidence envelope had beenobserved.

Results

Retama - Artemisia

Retama sphaerocarpa and Artemisia barrelieri (plot1) showed strong clumping at scales of 0.5 m to ca. 2.5m (Fig. 2a). While the central 0.5 m ‘exclusive’ zonerepresents the area occupied by the multiple stems of theRetama shrubs, the upper limit corresponds to theirmean canopy diameter (2.78 ± 0.14 m; mean ± SE; n =95). Analysis by cardinal direction revealed that signifi-cant clumping occurred in all four quadrants repre-sented by the major cardinal directions, although to alesser degree in the western quadrant (Fig. 3). The lesserabundance of Artemisia in this latter quadrant, and alsoat scales of 0.5 - 1.0 m in the southern quadrant (Fig. 3)was related to the presence of other shrub species inthese quadrants (W) or their central part (S; results notshown). Although shrubs other than Artemisia onlyaccounted for less than 10% of all woody undergrowth

species (18 vs 204), the most frequent, Marrubiumvulgare (Lamiaceae) and Anthyllis cytisoides, were oflarger size and thus occupied more space which thusbecame unavailable to Artemisia. It is therefore ex-pected that in the absence of the other perennial species,Artemisia would occur in equal densities in all quad-rants. This suggests that the positive association be-tween Artemisia and Retama results from a facilitationeffect of an isotropic nature.

Fig. 2. Second-order spatial analysis of the bivariate distribu-tion of Retama sphaerocarpa and Artemisia barrelieri in plot1 (a), and Artemisia barrelieri and Anthyllis cytisoides in plot2a (b) and plot 2b (c). The sample statistic L12(t) is plottedagainst t (solid line). The dotted lines give a 95% confidenceenvelope for complete spatial randomness (CSR). A value of p< 0.05 implies rejection of CSR in the overall test of signifi-cance. Unless a range is given, the integral L was calculatedfor the complete interval of t shown on the x-axis.

132 Haase, P.

Fig. 3. Second-order spatial analysis of thebivariate distribution by cardinal directionof Retama sphaerocarpa and Artemisiabarrelieri in plot 1 (n1 = 95, n2 = 186). Thesample statistic Lq12(t) is plotted against t(solid line). Legend as in Fig. 2.

Fig. 4. Second-order spatial analysis of thebivariate distribution by cardinal directionof Artemisia barrelieri and Anthylliscytisoides in plot 2a (n1 = 61, n2 = 64). Thesample statistic Lq12(t) is plotted against t(solid line). Legend as in Fig. 2.

Artemisia - Anthyllis

In the second type of shrubland, clumping betweenArtemisia barrelieri and Anthyllis cytisoides was ob-served over the range 0.0 - 0.6 m in both analysed plots(Fig. 2b, c). Resolution by cardinal direction showedthat in plot 2a clumping was significant in the easternquadrant only and expressed to a lesser extent in thenorthern quadrant (Fig. 4). In plot 2b, no significantclumping was found for the main cardinal directions(results not shown), but clumping was significant at t =0.5 m in the northeastern quadrant (Fig. 5). The south-western and southeastern quadrants also showed peaksof the spatial association at the same distance (t = 0.5 m),however, so that a preferred direction of the spatialassociation was much less evident in this plot.

Discussion

The environmental causes of spatial associations

If an analysed distribution pattern suggests a signifi-cant non-random association of two plant species, allrelevant environmental factors must be evaluated aspossible causes for this association, be it positive ornegative. At finer spatial scales, one individual mayoccupy a given space exclusively. This zone of exclusionis often related to the canopy diameter and assumed to bethe result of above-ground competition (e.g. Martens etal. 1997). In dryland ecosystems, the zone of exclusioncan be much larger than actual canopy diameters, whichhas been interpreted as an effect of below-groundcompetition between root systems (Martens et al. 1997).


In the Retama component of the shrubland investigatedby Haase et al. (1996a), observed univariate distributionpatterns suggested intraspecific competition betweenshrubs in the larger size classes (Haase et al. 1996a), butbivariate patterns were predominantly aggregated. Thispositive association was enhanced by niche differentia-tion; canopy and understorey species differ significantlyin size and their root systems exploit different soilhorizons and sources of water (Haase et al. 1996a, b;Pugnaire et al. 1996b). The clustering of Artemisia andmany other species under the canopy of Retama shrubscould be related to interception and accumulation ofdisseminules by Retama canopies, better conditions forgermination and growth due to higher soil fertility andbetter soil water status, or amelioration of the extremeclimatic conditions under the shrubs’ canopies. In thelatter case of a mere physical shelter effect, an anisotropicdistribution of Artemisia under the canopy of Retamashrubs would be expected, with a preference for the moresheltered quadrants, i.e. northwest to northeast. Artemisia,however, is well adapted to the prevailing high light, hightemperature, and low humidity environment and alsogrows successfully in the open spaces between Retamashrubs and in other low vegetation types (Freitag 1971;Haase et al. 1997). The results of the spatial patternanalysis by cardinal direction rather suggest an isotropicdistribution of Artemisia; its spatial association withRetama shrubs probably being mainly due to the highernutrient status under the canopy (Pugnaire et al. 1996b;Moro 1997a, b). A secondary trend of anisotropy wasdetected in one of the ‘sheltered’ quadrants, however, inwhich taller, more mesic understorey species to someextent displaced Artemisia which is considered a poorcompetitor (Freitag 1971). Pugnaire et al. (1996b) alsoobserved a general trend in the spatial distribution of

understorey plants in that drought-resistant species, alsotypical of the open spaces between Retama shrubs, weredisplaced from the centre of the understorey by taller,more mesic species as the shrubs grew older and taller.

Aggregation of plants under the canopies of tallerwoody species is common in dry or seasonally dryenvironments (e.g. Garner & Steinberger 1989; Weltzin& Coughenour 1990; Vetaas 1992; Barnes & Archer1999). The taller, focal species are usually deep-rootedand, besides accessing water resources, can extract, andthus accumulate, nutrients from a large volume of soil.In most cases, the tree or shrub species in the centre ofclumps are also symbiotic N-fixers. Many of theunderstorey plants are attracted to these ‘fertile islands’mainly because of the higher nutrient status (Garner &Steinberger 1989), but several mesic species are unableto persist in the open space because shelter from envi-ronmental extremes is the decisive factor.

Spatial association over much shorter distances wasevident in the Anthyllis shrubland. Haase et al. (1997)suggested that the positive association between Anthyllisand Artemisia could be related to a nurse-plant effect byArtemisia, based on its strongly aromatic smell and tastewhich served as a browse-deterrent, and which alsoextended to other species growing in close proximity.Such an effect would be expected to be isotropic. In oneof the plots the association between Anthyllis shrubs andtheir assumed nurse plant, Artemisia, was anisotropicwith Anthyllis shrubs growing more often than expectedin the eastern quadrant relative to an Artemisia shrub. Inthe second plot, this same spatial association was sig-nificant at only one discrete distance. Both plots had aslight slope towards easterly directions. Particularly inthe afternoon, when plant water potentials and rates ofassimilation of Anthyllis (and other perennial species)

Fig. 5. Second-order spatial analysis of thebivariate distribution by cardinal directionof Artemisia barrelieri and Anthylliscytisoides in plot 2b (n1 = 56, n2 = 116). Thesample statistic Lq12(t) is plotted against t(solid line). Legend as in Fig. 2.

134 Haase, P.

drop to daily minima (Haase et al. 1999a, b, 2000), thisspatial relationship – Anthyllis seedlings or juvenilesgrowing in close proximity downslope, and in the par-tial shade of an Artemisia shrub – would increase thechances of establishment and survival of Anthyllis. Onthe other hand, the slight slope may provide some addi-tional environmental gradient, e.g. accumulation of lit-ter and nutrients on the downslope side of Artemisiashrubs, favouring the establishment and survival ofAnthyllis. Whereas Haase et al. (1997) assumed that thenurse-plant effect was based mainly on the browse-deterrent properties of Artemisia, expected to act iso-tropically, the observed anisotropic association of thetwo species (in one of the plots) suggests a physicalshelter effect as the main or as an additional underlyingcause.

In the case of the nurse-plant effect, lower-growingspecies, commonly shrubs or other perennials, provideshelter for certain tree species during their seedling andjuvenile stages, eventually being overtopped by theadult tree. Examples have been given from the Mediter-ranean-climate regions of North America and Europe,where a number of Quercus species are closely associ-ated with and protected by various species of shrubsduring their juvenile phase (Callaway 1992; Callaway& Davis 1998; Rousset & Lepart 1999, 2000). Sug-gested reasons for the spatial relationship include cach-ing of acorns under shrubs by birds, reduced competi-tion from grasses in shrub patches, and protection fromgrazing animals, but differences in the density of Quercusseedlings between the north- and south-facing margin ofshrub clumps have also been observed, implying addi-tional effects of abiotic stress (Callaway & Davis 1998;Rousset & Lepart 1999, 2000). In more arid environ-ments, successful regeneration of certain species ofcacti depends on the presence of shrubs or trees, andpreferential recruitment occurs on certain sides of thenurse plants (Steenbergh & Lowe 1969; Franco & Nobel1989; Valiente-Banuet et al. 1991).

My results suggest that decomposition of positivespatial association of two plant species on cardinaldirection can yield more detailed insights into plant-plant relationships and the biotic and physical environ-mental factors driving them. This type of analysis pri-marily distinguishes between isotropic and anisotropicclustering; if the latter pattern is found, possible envi-ronmental causes for the ‘preferred’ or ‘avoided’ as-pects can be hypothesised, but should preferentially besupported by collection of environmental data or resultsfrom field experiments.

Recommendations for further applications: plotorientation and sample size

If field data are to be used to analyse bivariate patternsby cardinal direction, plots should preferentially be ori-ented so that they extend in the N and E direction with theorigin in the SW-corner (x = 0, y = 0). Besides the pair ofcoordinates for each plant, it is useful to record othervariables like canopy height, stem and/or crown diam-eter, etc., because this allows consideration of age, size,or viability classes during analysis. With those additionaldata, bivariate analysis (including consideration of cardi-nal direction) can also be performed with data from‘monospecific’ stands. Coordinates of plants from fieldplots which have been established at a right (90°) or 45°angle to the recommended orientation, can be recalcu-lated on a SW-corner basis. In the latter case, the shift of45° means that the major cardinal directions, W, N, E, S,become, NW, NE, SE, SW, and vice versa.

Spatial pattern analysis considering cardinal direc-tion should normally be performed after a preliminaryanalysis of a bivariate spatial pattern has shown signifi-cant positive association (clustering) at some spatialscale. Analysis by cardinal direction can then be re-stricted to the range of t over which significant cluster-ing was observed. There are hypothetical bivariate pat-terns, however, where only the resolution by cardinaldirection will reveal the true nature of the spatial asso-ciation. If non-conspecific plants are clustered at onlyone aspect of a focal plant and this cluster effect isequalised by larger numbers which are not shelteringunder its canopy, the standard bivariate analysis mightsuggest a random pattern. Decomposition of the samepattern by cardinal direction, however, is likely to detectan anisotropic clustered pattern and thus yield vitalecological information.

With the distinction of up to four quadrants and,usually, a reduction in the range of t (see above) inbivariate spatial pattern analysis considering cardinaldirection, the effective sample size may decrease con-siderably, thus increasing variation and reducing thesignificance of the results. Therefore, a recommendedminimum sample size is approximately 100 points, withthe condition that the number of points for the depend-ent species is approximately equal to, or preferablygreater than, the number of the independent species.

A computer program for spatial point pattern analy-sis (SPPA, Version 1.1.1), which can also performbivariate pattern analysis by cardinal direction, hasbeen implemented in Visual C++ by the author. Theprogram has been developed for Windows95 (or higher)and can be downloaded, together with documentation,at http://home.t-online.de/home/haasep/index.htm


Acknowledgements. The field data analysed in this paperwere collected as part of the MEDALUS II (MediterraneanDesertification and Land Use) collaborative research project,funded by the EC under its Environment Programme, contractnumber EV5V CT92-0164. I thank Raphael Pélissier and oneanonymous referee for suggestions on an earlier version of themanuscript.

References

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Received 25 November 1999;Revision received 25 June 2000;

Final revision received 11 September 2000;Accepted 19 September 2000.

Coordinating Editor: R.H. Økland.

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