Journal ofApplied Ecology0887\ 24\576Ð588

Þ 0887 BritishEcological Society

576

Simulated long!term vegetation response to grazing

heterogeneity in semi!arid rangelands

GERHARD E[ WEBER�\ FLORIAN JELTSCH�\ NOEL VAN ROOYEN$and SUZANNE J[ MILTON%�Department of Ecological Modelling\ UFZ Centre for Environmental Research\ PO Box 1\ D!93290 Leipzig\Germany^ $Botany Department\ University of Pretoria\ Pretoria 9991 South Africa^ %Fitzpatrick Institute\University of Cape Town\ Rondebosch 6699\ South Africa

Summary

0[ The long!term e}ects of small!scale spatial heterogeneity of livestock grazing onvegetation dynamics were studied with a grid!based model of major life forms ofsavanna vegetation[ Based on southern Kalahari ecology\ the model includes stoch!astic life!history variables\ resource competition for soil water\ and biomass pro!duction for annuals\ perennial grasses and shrubs[1[ Grazed at individual severities\ the model|s 14m1 grid cells de_ned the spatial scaleof heterogeneity[ Di}erent scenarios of grazing heterogeneity were generated bymodifying distributional and behavioural features of the grazing model[ Simulationswere run over 49 years under moderate to high constant stocking rates[2[ Results con_rmed a previously reported threshold response of shrub cover increase]under moderate grazing pressure\ little change in shrub cover occurred^ when grazingpressure exceeded a threshold\ shrub cover increased drastically[3[ Under moderate or high stocking rates\ grazing heterogeneity did not modifygrazing e}ects[ However\ within an intermediate range of stocking rates\ small!scaleheterogeneity determined the long!term impact of grazing[ In particular\ utilizationintensity at the threshold of shrub cover increase was 59) less under high comparedto low local grazing heterogeneity[4[ Sensitivity of vegetation dynamics to local grazing heterogeneity was also exem!pli_ed under a landscape!scale grazing gradient as observed at watering points] at agiven utilization intensity\ a wide zone of increased shrub cover occurred under largelocal grazing heterogeneity\ while under the least heterogeneous grazing only a narrowzone of slightly increased shrub cover occurred[5[ Because of the slow progress of shrub cover increase\ a mismatch of managementand ecological time scales was diagnosed and its implications for management arediscussed[6[ We conclude that knowledge of local grazing heterogeneity is crucial for correctassessment of livestock impact on vegetation dynamics[ Consequently\ managementaiming at sustainable land use should account for spatial grazing aspects[ Thesepoorly understood aspects form a gap to be _lled by both empirical and theoreticalstudies[

Key!words] grid!based model\ Kalahari\ livestock grazing\ shrub cover dynamics\vegetation change[

Journal of Applied Ecology "0887# 24\ 576Ð588

Introduction

In many semi!arid rangelands\ livestock production isthreatened by an increase in woody vegetation cover[

Correspondence] G[ E[ Weber\ "fax] 230 1242499^ e!mail]weberÝoesa[ufz[de#[

This increase has been reported from Australia"Hodgkinson 0868^ Hacker 0873#\ North America"Bu.ngton + Herbel 0854^ Archer 0878# and sou!thern Africa "Van Vegten 0872^ Skarpe 0889a#[ Gen!erally\ livestock grazing is considered a prime causalfactor of increased shrub establishment "Bu.ngton

577

Spatial grazingaspects affectrangelanddynamics

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

+ Herbel 0854^ Van Vegten 0872^ Skarpe 0889a# byreducing cover or competitive ability of perennialgrasses and herbs\ particularly when high grazingintensity coincides with periods unfavourable for her!baceous plants[

Recently\ the process of increasing shrub cover hasbeen studied with spatially explicit simulation modelsincorporating life!history traits and resource com!petition of ~oristic components\ rainfall\ _re and graz!ing as major determinants in rangeland dynamics"Jeltsch et al[ 0885^ Jeltsch et al[ 0886b#[ Obviously\most interactions among plants are con_ned to smallspatial scales due to their immobility during most oftheir life cycle\ and their morphological and repro!ductive traits[ Conversely\ grazing impacts mayappear to act at a larger spatial scale\ and may seem toshow a relatively uniform distribution[ Consequently\the emphasis of spatially explicit rangeland modelshas so far been mostly on plantÐplant interactions"Jeltsch et al[ 0885#\ while spatial aspects of plantÐanimal interactions have rarely been considered"Coughenour 0880#[ The few studies including suchspatial components have focused on large!scaleheterogeneities such as grazing gradients aroundwatering points "Pickup 0883^ Jeltsch et al[ 0886a#[

This de_cit may at least partly be due to the as yetenigmatic nature of the spatial component of her!bivory "Coughenour 0880#[ Although grazing a}ectsrangelands over large scales\ the direct plantÐanimalinteraction is essentially a local event[ With theseevents taking place on a small local scale\ the groundis set for small!scale heterogeneity in grazing impacts[Indeed\ there are empirical studies documenting graz!ing heterogeneity at di}erent scales[ Patch grazing bydomestic livestock is reported for North Americansemi!arid grassÐshrub ranges "Ruyle\ Ogden + Rice0877# as well as pure grasslands "Ring\ Nicholson+ Launchbaugh 0874#\ tropical Australian savannas"Andrew 0875^ Mott 0876# and southern Africangrasslands "Gammon + Roberts 0867^ Fuls 0881^Kellner + Bosch 0881^ O|Connor 0881^ Lu�tge\ Hardy+ Hatch 0885#[ Only two of these studies containa quanti_cation of patch sizes[ Ring\ Nicholson +Launchbaugh "0874# reported cross!section lengths of0=4 m for patches addressed as {overgrazed|\ andLu�tge\ Hardy + Hatch "0885# indicated that animalsconcentrated their grazing within a radius of 9=3 m ofurine deposition[ In addition\ a map provided by Fuls"0881# suggests patch cross!section lengths of severalmetres[

A large number of factors in~uence grazing "Owens\Launchbaugh + Holloway 0880#\ acting and inter!acting over a range of scales from the individual plantto the patch\ the landscape and the regional scale[ Ata small scale\ heterogeneity in soil properties "Schles!inger et al[ 0889^ Tongway + Ludwig 0883#\ par!ticularly in_ltration capacities "MacDonald 0867# butalso relief!dependent redistribution of rainfall inputs"Noy!Meir 0870#\ generates heterogeneity in local

water availability a}ecting forage quantity and qual!ity\ due to phenological or ~oristic di}erentiation"Gammon + Roberts 0867^ MacDonald 0867^ Tong!way + Ludwig 0889#[ Thus\ livestock encountersheterogeneity in forage quantity and quality\ twomajor determinants of site selection for grazing "Senft\Rittenhouse + Woodmansee 0874#[ However\ even ona range with completely homogeneous soil\ water andnutrient resources\ restricted rates of livestockmobility\ the large paddock sizes usually used in semi!arid rangelands and behavioural determinants of live!stock grazing "Hobbs 0885# would lead to spatial het!erogeneity in the temporal distribution of the grazingimpact[ Given _rst that forage quality of ungrazedplants is not constant over time "Skarpe + Bergstro�m0875#\ and secondly that the response of plantsdepends on timing of the grazing impact "Cough!enour\ McNaughton + Wallace 0873#\ the spatial pat!tern of forage quality is likely to be a}ected by theinevitable spatiotemporal heterogeneity of the grazingimpact[ However\ whether grazing per se increases ordecreases spatial heterogeneity is determined by thefeedback of grazing and regrazing\ which largelydepends on regrowth potential "Hobbs 0885#[ Whereregrowth is su.cient\ grazers will tend to return topreviously grazed patches o}ering forage of lowercrude _bre and higher protein content\ and will avoidungrazed sites increasingly dominated by residualstems of low protein and high _bre content "Stobbs0862#[

A well!documented large!scale heterogeneity ingrazing utilization is the decreasing grazing intensitywith increasing distance from surface water "Valentine0836^ Lange 0858^ Martens 0860^ Hart et al[ 0882^Pickup + Chewings 0883#[ This grazing gradient isdue to the need for drinking water at short intervals Ðdaily or every other day Ð for sheep and cattle\ andtheir limited daily walking distance[ Consequently\when the spacing of water points exceeds daily walk!ing distances\ a zonation of livestock activity is detect!able\ for example in biomass of herbage or degree ofherbage defoliation[

To summarize\ next to physical\ chemical and ~or!istic heterogeneity\ physiological requirements and thebehaviour of domestic ruminants a}ect the grazingpattern[ Moreover\ complex feedback mechanisms inplantÐanimal interactions contribute to the spatialstructuring of grazing impacts on the range[ Theresulting heterogeneous pattern of utilization mightwell be regarded as an intrinsic property of grazing[However\ the existence of non!homogeneous spatialpatterns of grazing utilization at various scales hasbeen documented "Gammon + Roberts 0867^ Ring\Nicholson + Launchbaugh 0874^ Andrew 0875^ Mott0876^ Ruyle\ Ogden + Rice 0877^ Fuls 0881^ Kellner+ Bosch 0881^ O|Connor 0881^ Lu�tge\ Hardy + Hatch0885#\ and so has the process of a slow increase inwoody vegetation cover "Bu.ngton + Herbel 0854^Hodgkinson 0868^ Van Vegten 0872^ Hacker 0873^

578

G[E[ Weber et al[

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Archer 0878^ Skarpe 0889a#[ Despite these _ndings\the links between the spatial patterns of grazing andthe process of increasing woody cover have attractedvery little scienti_c attention so far[ However\ if graz!ing utilization is heterogeneous at a given patch scale\then none of the patches might experience the meangrazing pressure[ Hence\ model predictions scaling upvegetation response to the landscape level based onmean values of grazing pressure might deviate greatlyfrom predictions by models incorporating hetero!geneity[ Noy!Meir "0870# showed the problems arisingfrom neglecting spatial heterogeneity wheneverresponses to heterogeneous inputs are non!linear[ Heconcluded that incorporating spatial heterogeneity iscrucial for models of arid ecosystems[

Our study aimed to identify the e}ects of small!scale patch!level spatial heterogeneity of grazing util!ization\ on long!term shrub cover dynamics in a semi!arid savanna rangeland[ To this end\ a spatiallyexplicit simulation model was used[ It incorporatesstochastic life!history variables\ competition for soilwater\ and biomass production of three major lifeform groups] annuals\ perennial grasses and herbs\and shrubs[ Scenarios of di}erent small!scale het!erogeneities of grazing utilization were created bymodifying distributional and behavioural features ofthe grazing submodel[ Over a range of moderate tohigh constant stocking rates\ we compared the long!term e}ects of these scenarios on shrub cover dynam!ics[

Methods

STUDY SITE

The model represents a summer rainfall region with299Ð399 mm mean annual precipitation\ characteristicof the dry and sandy Molopo area of the Kalahariregion\ used for cattle ranching in Botswana "Field0866# and South Africa "Fourie\ Niekerk + Fouche�0874#[ In these areas\ prominent representatives of thewoody vegetation are Grewia ~ava DC and Acaciamellifera "Vahl# Bentham ssp[ detinens "Burch[#Brenan "Skarpe 0889a#[ The latter is the major speciesaccounting for higher density and cover of woodyplants in overgrazed areas "Skarpe 0889b#[ The her!baceous layer is dominated by perennial grasses suchas Schmidtia pappophoroides Steudel and Stipagrostisuniplumis "Licht[# De Winter[ Additionally\ in favour!able years\ annual grasses such as Aristida congestaRoemer + Schultes contribute signi_cant fractions tovegetation cover[

RANGELAND MODEL

We modi_ed a spatially explicit grid!based simulationmodel used by Jeltsch et al[ "0886a\ 0886b# for studiesof shrub cover dynamics in semi!arid savanna range!lands in the southern Kalahari[ Full documentation

of this model has been published elsewhere "Jeltschet al[ 0886a\ 0886b#[ Hence\ we give only a summaryof the basic model and then focus on the modi_cationsintroduced mainly in the grazing model[

Basic model

With annual time steps\ the model depicts dynamicsof the three major life forms] perennial grasses andherbs\ shrubs\ and annuals[ Vegetation dynamics aremodi_ed by soil water availability\ grazing and _re[

The modelled area is a rectangular grid of squarecells each of 4!m edge length[ The total simulated areaconsists of 09 999 cells covering 14 ha\ except whenstated otherwise[ Possible grid cell states are] empty\occupied by any life form\ or a mixture of any lifeform combination[ Probabilities of colonization byany life form and mortality of the perennials dependon the amounts of available soil moisture in the top!and the subsoil layer\ which are subject to resourcecompetition[ Annually available soil water in eachlayer is computed from daily rainfall data generatedwith a South African rainfall simulator "Zucchini\Adamson + McNeill 0881# for a site with a long!termmean annual rainfall of 283 mm located at 14>19? Sand 12>21? E in the Molopo area of the southernKalahari[

Water consumption by plants occupying a grid cellreduces the locally available soil moisture in top! andsubsoil layers[ The amount of moisture reduction bywater uptake depends on root distribution and evapo!transpiration "Jeltsch et al[ 0886b#[ Because lateralroot extension of shrubs is not limited to 14!m1 pat!ches "Belsky 0883# this life form reduces moisture inneighbouring grid cells as well[ In the current versionof the model\ the lateral moisture consumption wasreduced by 39) compared to the earlier version"Jeltsch et al[ 0886b# to account for the di}erence inwoody species[

For perennial life forms\ we distinguish threedi}erent classes of potential production levels] low\moderate and high[ The current production potentialof perennial grasses depends on previous year pro!duction\ actual rainfall\ biomass reduction by grazing\and grass _res[ For perennial grasses\ a productionof 799\ 0399 and 2999 kg ha−0 is estimated for therespective levels[ Hence\ compared to the originalmodel\ production in the moderate level is increasedby 199 kg ha−0\ in order to incorporate data reportedby Richter "0880#[ If su.cient soil moisture is avail!able for a perennial life form\ its potential productionis maintained or increases[ Given insu.cient moist!ure\ potential production decreases\ and perennialswith low production potential run a chance of localextinction "Jeltsch et al[ 0886b#[ For example\ in theabsence of available subsoil moisture\ a shrub in alow production potential runs a 4Ð29) chance ofextinction depending on the amount of available top!soil moisture "see table 1 in Jeltsch et al[ 0886b#[

589

Spatial grazingaspects affectrangelanddynamics

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Equally\ colonization of empty grid cells depends onsoil moisture[ For example\ shrub colonization doesnot occur in the absence of subsoil moisture[ Givensome\ but not more than 49 mm of subsoil moisture\an empty grid cell with a single shrub!occupied neigh!bour cell runs a chance of 9Ð4) for shrub colon!ization\ depending on topsoil moisture "see table 1 inJeltsch et al[ 0886b#[

Like colonization and extinction\ _re is modelledprobabilistically[ The _re model by Jeltsch et al["0886b# is employed unchanged[ No _re occurs whenthe fuel load Ð which is the residual grass biomassafter grazing Ð is less than the minimum thresholdof 0999 kg ha−0[ Above the minimum threshold\ _reprobability increases non!linearly up to 099) at themaximum fuel load of 2999 kg ha−0 given by the highlevel of production potential for perennial grasses andherbs[ A grass _re resets grass cells to the low pro!duction level[ Shrubs in or adjacent to burning grasscells stand a 4) chance of extinction[

Grazing model

The grazing model developed by Jeltsch et al[ "0886a#links cattle grazing and vegetation at the smallest spa!tial unit modelled[ The distributional and behaviouralfeatures of this model generate a speci_c pattern ofgrazing heterogeneity at the grid cell level[ Here\ we_rst present this original model\ and then describemodi_cations for generating di}erent patterns of graz!ing heterogeneity[

At an arbitrary small scale\ a grazing event is com!prised of the selection of a site\ and its subsequentdefoliation[ We follow the terminology given in Heit!schmidt\ Briske + Price "0889#] {defoliation intensity|"de# is the relative consumption of biomass in a singlegrazing event^ {defoliation frequency| "fa# is the totalnumber of grazing events on a particular site duringa period of interest "a whole year in this study#^ and{defoliation severity| "da# is the annual consumptionrelative to the available forage biomass resulting fromall the grazing events on a particular site in a givenyear[

Accordingly\ in the original grazing model "Jeltschet al[ 0886b#\ a grazing event consists of the selectionof a suitable grid cell and its defoliation[ The sequenceof grazing events in a given year continues\ until eitherthe forage requirements are met\ or no more forage isavailable[ Thus\ keeping stocking rates constant overtime implies that management provides for additionalfeed in years of insu.cient primary production[ Meandefoliation severity M is given as]

M � F:B eqn 0

with F "kg ha−0# giving total forage required annually\calculated from a constant stocking rate "ha lsu−0#and a constant daily intake of 09 kg lsu−0\ and B"kg ha−0# denoting total forage biomass produced[

Defoliation intensity of a grazing event de is calculatedas]

de � min "0\ M = r# eqn 1

with factor r denominating a random modi_er[ Theamount of biomass consumed in a grazing event ce"kg# is then given by]

ce � de = b eqn 2

with b "kg# denoting forage biomass in the selectedgrid cell[ In the original grazing model\ the randommodi_er r is drawn from an even distribution in ð9\ 1Ł\grid cells with any small amount of forage can beselected for a grazing event\ and there is no inter!annual memory of local defoliation severity[ Wemodi_ed the three features {distribution|\ {selectivity|and {memory| of the grazing submodel as summarizedin Table 0[

The _rst modi_cation is not based on a priori con!siderations of livestock behaviour but is a technicalway of generating utilization patterns di}ering in spa!tial heterogeneity[ In contrast with the originally usedeven distribution of the random factor r\ we draw rfrom a normal distribution "Table 0#[ In a third alter!native\ we exclude repeated site selection until mostof the available forage sites have been selected once\thus enforcing a minimum grazing frequency of oneevent per year on most of the forage sites[

The second modi_cation is motivated by behaviourof livestock that graze preferentially on sites of highforage density "Senft\ Rittenhouse + Woodmansee0874#[ In selectivity scenario N "non!selective#\ all gridcells with whatever small amount of forage can beselected for grazing[ In contrast\ in scenario S "selec!tive# only cells with a minimum amount of foragebiomass bmin "kg#\ given by]

bmin � 69 for M − 9=64

bpoor = "0−3 = M:2# for M ³ 9=64eqn 3

are selectable\ in which bpoor � 1 kg gives the pro!duction level in the lowest class of potential biomassproduction[ Thus\ for high grazing pressures withmean defoliation severity M − 9=64\ we assume thatall grid cells with any small amount of forage becomeselectable for grazing[ At lower grazing pressures withM ³ 9=64\ bmin decreases linearly with increasing graz!ing pressure[ This selectivity scenario is motivated byreasoning that livestock will accept sites with low for!age density only if there is a general shortage of forage[

The third modi_cation concerns spatiotemporalautocorrelation of the pattern of grazing utilization[Andrew "0875# and Mott "0876# reported that live!stock selectively grazed sites that had experienced highdefoliation severity in the previous year\ which wasattributed to locally increased forage quality[ Thus\the behavioural trait involved in spatiotemporal auto!correlation of grazing utilization is selectivity for for!age quality[ Lacking a quality component of forage

580

G[E[ Weber et al[

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Table 0[ Features of the grazing model employed to generate grazing scenarios of di}erent small!scale utilization heterogeneity[M � mean defoliation severity^ r � random factor modifying defoliation intensity in a local grazing event^ da � annual localdefoliation severity

Feature Level Description

Distribution 0 Even distribution of r in ð9\ 1Ł1 Normal distribution of r with mean 0\ and s � 9=02 Normal distribution of r with mean 0\ and s � 9=0\ repeated site selection excluded unless 88) of

available forage sites have been grazedSelectivity N Sites with any small amount of forage selectable for grazing

S Sites selectable only when amount of forage exceeds a threshold dependent on MMemory None No inter!annual memory of da

Y49 Inter!annual memory of da for sites with da × 9=4Y64 Inter!annual memory of da for sites with da × 9=64

and the respective grazing feedbacks\ our model can!not reproduce this self!organized pattern[ However\we introduced inter!annual site memory into the graz!ing process to simulate the resultant spatiotemporalautocorrelation[ In the scenarios with inter!annualmemory\ sites with defoliation severities above a mini!mum threshold are remembered by livestock[ Tech!nically\ the grazing routine is split into two phases[ Inthe _rst phase\ a randomized list of remembered sitesis grazed\ each site with its defoliation severity of theprevious year[ If the forage need is not met during this_rst phase\ grazing proceeds to the non!memory phasedescribed above[ At the end of the grazing process\livestock memory is updated\ scanning the grid againfor cells grazed at severities above the minimum mem!ory threshold[

SPATIAL SCALES OF HETEROGENEITY

The grazing scenarios introduced so far generatedi}erent grazing heterogeneities at the grid cell level[With a grid cell edge length of 4 m\ these hetero!geneities occur at a small spatial scale[ In order toexplore the e}ect of small!scale heterogeneity under asecond\ larger scale level of heterogeneity\ we studied agrazing gradient scenario typical for semi!arid rangeswith large distances between water!points[ We intro!duced distance from water as a factor controlling localdefoliation intensity of grazing events\ as described inJeltsch et al[ "0886a#[ Defoliation intensity de in thisbore hole scenario is then given as]

de � min "0\ M = r = 1 = exp "−9=9914 = l## eqn 4

with l denoting distance from water "number of gridcells#[ We assumed a linear water source at one of theshort edges of a rectangular grid of 39 = 539 grid cells"Jeltsch et al[ 0886a#[ To account for increased tram!pling mortality due to higher livestock density aroundthe water source\ the additional trampling mortalityfactor mt � exp "−9=94 = l# was introduced "Jeltschet al[ 0886a#[

SIMULATIONS

With respect to the features determining the grazingscenario "Table 0#\ we examined a set that we con!sidered instructive] "i# non!selective grazing scenarioswithout inter!annual memory under all three dis!tributions^ "ii# selective grazing scenarios withoutinter!annual memory under distributions 0 and 1\ "iii#non!selective grazing with inter!annual memory underdistributions 0 and 1[ For each of the grazing scen!arios\ stocking rates were varied from 3 to 19 ha lsu−0\thus covering a range of extremely high to moderateutilization intensity\ compared with recommendationsby Field "0866#[ In order to identify the e}ect of therandom sequence of rainfall events\ we used four setsof daily 49!year rainfall data generated with the simu!lator of Zucchini\ Adamson + McNeill "0881#[ Meansof annual rainfall of the four sets were between278 mm and 395 mm\ with coe.cients of variationbetween 10=2) and 15=4)[

Simulations were initialized with a map rep!resenting rangeland in good condition with relativegrid cell covers of c[ 1)\ 74) and 02) for annuals\perennial grasses and herbs\ and shrubs\ respectively[We generated this initial map by grazing a randomlyinitialized grid with 09)\ 69) and 04) relative coverover 19 years at a moderate stocking rate of 19 halsu−0[ Due to the colonization pattern of shrubs\assuming higher colonization probabilities for sitesneighbouring shrub!occupied grid cells\ the initialcover showed a clumped distribution of shrubs[ Notethat simulated cover refers to the fraction of grid cellsoccupied by a life form[

The model contains stochastic processes in the lifehistory of plants\ site selection for and defoliationintensity of grazing events\ as well as _re occurrenceand _re mortality[ Hence\ simulations were replicated"n � 14# and the results summarized statistically[However\ for the bore hole grazing scenario\ shrubcover maps are presented for single runs under a singleset of weather data\ since documentation of the gen!erated spatial structure of the shrub cover was

581

Spatial grazingaspects affectrangelanddynamics

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

intended[ For the bore hole grazing scenario\ simu!lations were run with a stocking rate of 01 ha lsu−0

over 49 years[

Results

Each grazing scenario is characterized by a speci_cpattern of small!scale heterogeneity[ Therefore\ we_rst present quantitative descriptions of thesepatterns[ Secondly\ shrub cover dynamics is analysedwith respect to the impact of grazing\ the time scaleand variability of change\ and grazing e}ects arounda bore hole[

QUANTIFYING HETEROGENEITY OF GRAZING

To quantify spatial heterogeneity of the grazing scen!arios\ we recorded grid cell!based annual defoliationfrequency fa and annual defoliation severity da for 2years with di}erent levels of mean defoliation severityM "Fig[ 0#[ In the scenarios under distributions 0 and1 "Fig[ 0\ rows 0\ 1\ 3 and 4#\ grid cell selection forgrazing is independent of prior grazing history in agiven year[ Hence\ the frequency distribution of fa isPoisson!random "Fig[ 0\ insets#[ In these scenarios\ c[14) of all grass cells remain ungrazed at a meandefoliation severity M � 49) "Fig[ 0\ middle column\except h#[ However\ for non!selective grazing\ underdistribution 0\ 04) of the grass cells are grouped inthe highest defoliation severity class "Fig[ 0b#\ whereasunder distribution 1 no more than 1) of the gridcells show such an extremely high defoliation level"Fig[ 0e#[ Under selective grazing "Fig[ 0\ rows 3 and4#\ the highest defoliation class is less frequent com!pared to the equivalent non!selective scenarios "Fig[ 0\rows 0 and 1#[ Overall\ the implementation of thegrazing process under scenarios 0 or 1 results in amore or less bimodal distribution of grazing pressure[Whereas some grid cells remain largely una}ected bygrazing\ others are subject to very high defoliationseverities[ For all four scenarios under distribution 0or 1\ it is noteworthy that only very small fractions ofthe landscape experience defoliation severities close tothe overall mean defoliation severity M[

Under scenario 2 "Fig[ 0 row 2#\ repeated grid cellselection for grazing in a given year is excluded aslong as less than 88) of the grass cells have beenselected for grazing[ In combination with a normallydistributed random modi_er of defoliation intensity\this results in a unimodal distribution of grid cell!based annual defoliation severity "Fig[ 0\ row 2#\ withmost of the cells selected only once for grazing "Fig[ 0\row 2\ insets#[ Even under an extremely high meandefoliation severity M � 64)\ less than 4) of theforage grid cells are grouped into the highest defoli!ation class "Fig[ 0i#[

With the frequencies of grid cells of extreme defoli!ation severities as a measure for spatial heterogeneityof grazing utilization\ the _ve grazing scenarios

depicted in Fig[ 0 can be ranked for increasing spatialheterogeneity as] N2 ³ S1 ³ N1 ³ S0 ³ N0[ Underthe lowest heterogeneity\ grazing pressure is normallydistributed over all grass cells\ whereas under higherheterogeneity\ grazing pressure is bi! or trimodal withhigh frequencies of extreme defoliation severities[

ANALYSING SHRUB COVER DYNAMICS

Effects of `razin` hetero`eneity

Shrub cover was not a}ected by grazing heterogeneityunder moderate and extremely high grazing pressure"Figs 1 and 2^ note that grazing pressure is higherfor stocking rates of lower numerical values#[ Undermoderate grazing pressure\ shrub cover remainedclose to the initial level\ however when stocking ratesreached critical levels shrub cover increased dras!tically[ This result con_rms the previously reportedthreshold behaviour of shrub encroachment "Jeltschet al[ 0886b#[ Stocking rate threshold levels and ratesof shrub encroachment were highly sensitive to small!scale spatial heterogeneity of grazing "Fig[ 1#[ Forgrazing scenarios with lower local grazing het!erogeneity "for example N2#\ threshold levels of shrubencroachment shifted towards higher utilizationintensity\ and at given critical stocking rates shrubencroachment was slower than for grazing regimeswith larger local heterogeneity "for example N0#[ After49 years of grazing\ a stocking rate of 09 ha lsu−0

resulted in a mean shrub cover of about 59) underthe high heterogeneity of grazing scenario N0\whereas under low heterogeneity of scenario N2 meanshrub cover remained close to the initial level "Fig[ 1c#[

To assess stocking rate!dependent risks associatedwith the grazing scenarios\ we calculated relative fre!quencies of simulation runs with at least double theinitial shrub cover after a given time span[ Adoptinga conservative attitude\ we assumed that not morethan a 09) chance of shrub cover at least doublingwas acceptable[ We then identi_ed the stocking rategiving the highest possible utilization intensity with aprobability of shrub cover doubling of not more than09)[ This value will be referred to as the thresholdstocking rate of shrub cover doubling "Table 1#[ Eco!logically\ we interpret this threshold as the maximumacceptable level of utilization intensity for a givengrazing scenario[ Within the non!selective grazingscenarios\ which cover a wide range of explored spatialheterogeneity\ 49!year doubling thresholds variedfrom 7 to 02 ha lsu−0 "Table 1#[ Thus\ at the thresholdlevel of utilization intensity\ about 59) more area perlivestock unit was required under the most het!erogeneous compared with the most homogeneous ofthe three non!selective scenarios[

According to their spatial heterogeneity\ thresholdsresulting from the two selective scenarios showed anintermediate level "Table 1#[ Nevertheless\ the behav!ioural feature {selectivity| did a}ect threshold levels[

582

G[E[ Weber et al[

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Fig[ 0[ Frequency distributions of annual cell!based defoliation severity grouped in 4) classes[ Insets depict frequencydistributions of cells grouped by defoliation frequency fa "�total number of annual grazing events in a cell#[ Grazing scenarioN0 "a\ b\ c#\ N1 "d\ e\ f#\ N2 "g\ h\ i#\ S0 "k\ l\ m#\ S1 "n\ o\ p#^ for details see Table 0[ Mean defoliation severity M] 14) "a\ d\g\ k\ n#\ 49) "b\ e\ h\ l\ o#\ 64) "c\ f\ i\ m\ p#[

For example\ under distribution 0\ the 49!year stock!ing rate threshold was about 19) higher under non!selective compared with selective grazing[

Equally\ inter!annual memory of grazing a}ectedshrub cover dynamics "Fig[ 2# and stocking ratethresholds "Table 1#[ Under scenarios with inter!annual memory\ shrub cover increase occurred atlower utilization intensity compared with non!mem!ory scenarios "Fig[ 2 and Table 1#[ Due to memoryfor preferred patches\ the frequency of grid cells withextremely high annual defoliation severities increased"undocumented#[ Thus\ consistent with the threshold|sdependence on grazing heterogeneity documented inFig[ 1\ increased heterogeneity due to memory e}ectsresulted in higher threshold stocking rates[ For exam!ple\ under scenario N1\ 25) more area per livestockunit was required at the stocking rate threshold dueto the memory e}ect "Table 1#[

Time scales and variability of change

In all grazing scenarios\ shrub cover increased slowlyand\ except for the most intense stocking\ after 4 yearsof grazing the resulting magnitudes in shrub coverchange would hardly be discernible in real rangelands"Fig[ 1a#[ After 19 years of grazing at a critical stock!ing rate of 09 ha lsu−0 under scenario N0\ mean shrubcover was up to about 19) compared with the initial02) "Fig[ 1b#] still a change that might well escape arangeland manager|s perception[ However\ after49 years of grazing at this stocking intensity shrubcover reached 59)[

Next to the long time scale\ a further characteristicof vegetation change in semi!arid rangelands is itsconsiderable variability[ With coe.cients of variationof about 19)\ variability of shrub cover after 49 yearsof grazing remained fairly constant when utilization

583

Spatial grazingaspects affectrangelanddynamics

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Fig[ 1[ Mean shrub cover after 4 "a#\ 19 "b# and 49 years "c#of continuous grazing by stocking rate and grazing scenario^for details see Table 0[ Simulations were run on a 099 × 099torus grid with 14 replicates for each of four weather datasets[ Graphs depict mean values[ Note that intensity of graz!ing utilization is higher at stocking rates of lower numericalvalues[

Fig[ 2[ Mean shrub cover after 49 years of continuous grazingby stocking rate\ grazing scenario and memory level^ grazingscenario N0 "a#\ N1 "b#^ for details see Table 0[ Simulationswere run on a 099 × 099 torus grid with 14 replicates foreach of four weather data sets[ Graphs depict mean values[Note that intensity of grazing utilization is higher at stockingrates of lower numerical values[

intensity was below the threshold level "Fig[ 3#[ Whenthreshold levels were exceeded\ variability increaseddrastically\ and at supercritical stocking rates varia!bility of shrub cover after 49 years of grazingdecreased again "Fig[ 3#[ In order to separate thecauses of shrub cover variability we performed ananalysis of variance of shrub cover after 49 years ofgrazing by weather scenario for each stocking rate ofthe grazing scenario N0\ and calculated the estimatedvariances[ As Fig[ 4 shows\ weather e}ects dominatedincreasing variability at critical utilization intensitiescompared with stochastic e}ects[ At utilization inten!sities that exceeded critical or threshold levels\ residualvariability decreased to near zero\ and weather e}ectswere the single cause of shrub cover variability[

The weather scenarios employed for the simulationruns were generated for a single location\ and weretherefore characterized by very small di}erences inmeans and variances "Zucchini\ Adamson + McNeill0881#[ Thus\ the e}ects were due to stochastic di}er!ences between the four sequences of daily rainfallevents[ These di}erences a}ected stocking rate thresh!olds as well "Table 1#[ At the threshold level of util!ization\ up to 14) more area per livestock unit wasrequired under the least favourable weather sequence\compared to the most favourable sequence of rainfallevents "Table 1#[

Grazing effects around bore holes

So far\ we have studied e}ects of small!scale het!erogeneity of grazing in a landscape characterized bythe absence of grazing heterogeneity at larger scales[Depicting a situation frequently found in semi!aridrangelands\ we introduced a large!scale gradient ofdecreasing grazing intensity with increasing distancefrom a water source[ Thus\ in this bore hole grazingscenario\ heterogeneity of grazing utilization was pre!sent at two distinct spatial scales] at a small local scalea patchy grazing pattern was characterized by patchcross!sections in the range of several metres\ while atthe landscape scale a grazing gradient extended overseveral kilometres[ E}ects of small!scale grazing het!erogeneity are exempli_ed by Fig[ 5\ showing initialand _nal shrub cover maps[ Under large local het!erogeneity "Fig[ 5b#\ shrub cover expanded dra!matically and a distinct zone of greatly increasedshrub cover was formed\ stretching up to 1 km fromthe water source[ If small!scale heterogeneity wasreduced to a lower level\ the zone of increased shrubcover remained limited to areas closer to the watersource "Fig[ 5c#\ and doubling of overall shrub coverdid not occur anymore[ If small!scale heterogeneitywas reduced further to a very low level\ only a narrowzone of expanded shrub cover was discernible\ withonly slightly increased shrub cover "Fig[ 5d#[ More!over\ in this least heterogeneous scenario\ overallshrub cover did not rise over the initial level[

Thus\ we observed strong interactions among

584

G[E[ Weber et al[

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Table 1[ Threshold stocking rates in ha lsu−0 "�maximum utilization pressure with shrub cover doubling probability ¾09)within a speci_ed time span# by time span and grazing scenario[ Weather scenarios 0Ð3 generated with rainfall simulator byZucchini\ Adamson + McNeill "0881# for a single location[ Inter!annual memory of grid cells with defoliation severity inprevious year greater than minimum value] Y49 minimum � 49)^ Y64 minimum � 64)[ For nomenclature of grazingscenarios see Table 0

Time span:years Weather scenarios considered Inter!annual memory Grazing scenario

N0 N1 N2 S0 S1

19 0\ 1\ 2\ 3 None 09 8 6 8 749 0\ 1\ 2\ 3 None 02 00 7 00 09

49 0\ 1\ 2\ 3 Y49 03 04 − − −49 0\ 1\ 2\ 3 Y64 04 04 − − −

49 0 None 02 00 7 00 0949 1 None 01 00 7 00 849 2 None 01 09 7 09 849 3 None 02 01 09 01 00

Fig[ 3[ Coe.cient of variation of shrub cover after 4 "a#\ 19"b# and 49 years "c# of continuous grazing by stocking rateand grazing scenario^ for details of grazing scenarios seeTable 0[

di}erent scales of spatial heterogeneity of grazing[Whether the large!scale heterogeneity came to bearon vegetation at the landscape scale depended on thelevel of small!scale grazing heterogeneity[ Conse!quently\ at a given stocking rate\ whether and to whatextent grazing brings about a zone of increased shrubcover depends on the small!scale heterogeneity ofherbage utilization[

Fig[ 4[ Variances estimated from ANOVA of shrub cover after49 years of continuous grazing by weather scenario[ Grazingscenario N0^ for details see Table 0[

Discussion

Grazing by ungulates is a complex process\ the con!trols of which are not directly linked to the resultingspatiotemporal pattern of utilization[ Rather\ the con!trols\ _ltered by the animals| perception\ act on arepertoire of behavioural rules[ Thus\ under a givenset of controls\ a particular behavioural pattern isexpressed and gives rise to a particular utilizationpattern[ We studied a set of grazing scenarios\ di}er!ing in utilization patterns\ with a spatial model ofsavanna vegetation dynamics[ It remains to show howthe model grazing patterns\ and the e}ects on veg!etation dynamics\ match with ecological knowledge\before considering implications for management[

GRAZING PATTERNS

In the model\ 14!m1 grid cells are grazed at individualseverities\ thus de_ning the spatial scale of hetero!geneity[ Interpreting a grid cell as a grazing patch\ the

585

Spatial grazingaspects affectrangelanddynamics

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

Fig[ 5[ Maps of shrub distribution in the bore hole grazing scenario in a grid of 39 × 539 cells[ "a# initial map^ "bÐd# after 49years of continuous grazing at 01 ha lsu−0[ Local heterogeneity of grazing utilization] "b# large "scenario N0#^ "c# moderate"scenario N1#^ "d# small "scenario N2#[ For details on grazing scenarios see Table 0[

order of magnitude of patch size matches empiricalresults by Ring\ Nicholson + Launchbaugh "0874#and Fuls "0881#[ However\ since we did not _ndempirical frequency distributions of annual defoli!ation severities at this spatial scale\ a quantitativeveri_cation of heterogeneity patterns is not possible[Nevertheless\ our results allow for biologically mean!ingful interpretations\ and sketch consequences ofgrazing behaviour for grazing heterogeneity[

With livestock selectively grazing both quantity andquality of forage "Senft\ Rittenhouse + Woodmansee0874#\ herbage utilization also re~ects spatial dis!tribution of forage quality[ At low grazing pressure\livestock would mainly select high quality sites\ leav!ing low quality sites ungrazed[ At moderate grazingpressure\ still a large fraction of low quality sitesremains ungrazed\ while the qualitatively best sites arealready overexploited[ With increasing grazing pres!sure\ the fraction of ungrazed sites decreases\ sincelivestock would increasingly accept sites of lower for!age quality when the overall supply gets scarcer[Equally\ the fraction of heavily grazed sites wouldincrease with grazing pressure\ creating {patch over!grazing| "Fuls + Bosch 0880^ Fuls 0881^ Kellner +Bosch 0881#[ Thus\ the frequency distributions ofdefoliation severity created by grazing scenario N0can be explained by the selectivity of grazers for foragequality on a spatially heterogeneous range[ By thesame reasoning\ scenario N1 represents a range withlower heterogeneity in forage quality\ and scenarioN2 describes a rather homogeneous range[

In the selective grazing scenarios\ we introduced aminimum threshold of forage biomass for grid cellsacceptable for grazing[ Because all cells grazed downto forage residuals below the threshold are excludedfrom further grazing\ this reduces the fraction of heav!ily defoliated sites[ Thus\ forage biomass selectivity isa behavioural trait of livestock\ which reduces small!scale heterogeneity of herbage utilization[ In contrast\inter!annual memory of preferred sites\ in our model\resulted in an increased fraction of heavily defoliated

sites\ thus increasing grazing heterogeneity[ This issupported by Andrew "0875# who reported that afterburning had removed the previous season|s patchygrazing pattern\ cattle grazed independently of priorpatch locations\ and grazing was more uniform[

GRAZING EFFECTS

Skarpe "0889a# reported canopy cover of shrubs of49) and 69) for two sites in Botswana that shecharacterized as overgrazed for longer periods\ with!out specifying stocking rates[ However\ these esti!mates for sites with about 299 mm and 399 mm ofannual rainfall\ respectively\ are close to the maximumsimulated shrub cover of 54) for our study site char!acterized by 283 mm rainfall[ Also\ Van Vegten "0872#reports 49Ð64) and on a few sites even 099) shrubcover from areas with 399Ð599 mm rainfall in Bots!wana[ Although there is not necessarily a linearrelationship between simulated cover Ð which is rela!tive grid cell occupancy Ð and canopy cover\ thenumerical agreement between maximum simulatedshrub cover and empirical data from Kalahari ran!gelands is remarkable[

Whereas stocking rate was the major determinantof grazing e}ects on vegetation\ grazing heterogeneitymodi_ed grazing e}ects[ As previously reported"Jeltsch et al[ 0886b#\ shrub cover increased only whengrazing pressure exceeded some threshold level[ Underlow or extremely high stocking rates\ grazing het!erogeneity did not modify grazing e}ects[ However\within an intermediate range of stocking rates\ small!scale heterogeneity was the crucial trait for the long!term impact of grazing at the landscape scale[ In par!ticular\ grazing heterogeneity a}ected the level of thestocking rate thresholds[ Thus\ our results support theview that spatial grazing aspects strongly a}ect rangedynamics "Coughenour 0880#\ and are also in accord!ance with the hypothesis that any process increasingheterogeneity of soil resources would ultimately pro!

586

G[E[ Weber et al[

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

mote increasing shrub cover in semi!arid rangelands"Schlesinger et al[ 0889#[

The bore hole scenario exempli_ed scale inter!actions in grazing heterogeneity of particular import!ance for semi!arid rangelands[ At a given stockingrate\ the level of small!scale grazing heterogeneitydetermined to what extent the large!scale utilizationgradient a}ected community composition at the land!scape scale[ These interactions among grazing pat!terns at di}erent spatial scales could explain partlycontradictory results on {piosphere| ðcoined by Lange"0858# from the Greek {pios| meaning {drink|Ł for!mation in semi!arid rangelands "compare Hannanet al[ 0880^ Hellden 0880^ Jeltsch et al[ 0886a#[ Givensu.cient di}erences among small!scale grazingpatterns\ grazing might generate extended piospherezones in one region\ while changes in community com!position will remain limited in another region[

We assumed that grazing acts as a disturbance ren!dering grass sites available for shrub colonization\when grass density is reduced below a minimumresidual[ Thus\ with respect to shrub cover dynamics\the frequency of heavily defoliated sites is critical[However\ the speci_c frequency distribution of defoli!ation severity in any given year depends on the overallgrazing pressure characterized by mean defoliationseverity[ Given a constant stocking rate and thereforea constant forage need\ rainfall becomes the dom!inating control of grazing pressure\ since it determinesbiomass production[ Thus\ years of unfavourablerainfall are forage bottlenecks with increased meanbiomass reduction[ In our study\ however\ sensitivityof range vegetation to grazing depends on the wayforage bottlenecks a}ect the frequency distribution ofsmall!scale defoliation severity\ rather than on theforage bottlenecks per se[ Hence\ con_rming empiricalresults by O|Connor "0880#\ the interaction betweenrainfall and grazing behaviour determines the grazingimpact on vegetation[ If the frequency of heavilydefoliated sites is highly sensitive to biomassproduction\ as in scenario N0 "high heterogeneity#\forage bottlenecks will have a large e}ect on veg!etation dynamics[ In contrast\ if the frequency of heav!ily defoliated sites is rather insensitive\ as in scenarioN2 "low heterogeneity#\ forage bottlenecks will havea much smaller e}ect[ Thus\ heterogeneous grazingwill favour shrub colonization\ due to the larger fre!quency of heavily grazed sites open for shrub colon!ization[ Consequently\ in ranges prone to shrub coverincrease\ low grazing heterogeneity is desirable"Owens\ Launchbaugh + Holloway 0880#[

In the model\ selectivity of grazing refers to theamount of forage biomass[ While this is one aspect ofselective grazing\ its second aspect Ð forage quality"Senft\ Rittenhouse + Woodmansee 0874# Ð was notincluded as an explicit factor[ However\ as discussedabove\ the grazing patterns in scenarios N0 to N2 canbe interpreted as results of quality selectivity on rangeswith di}ering levels of heterogeneity in forage quality[

Hence\ we conclude that selectivity for forage qualityis a behavioural trait of grazing\ which increases het!erogeneity of the grazing pattern and thus its impacton vegetation dynamics[ In contrast\ we identi_ed sel!ectivity for forage biomass as a behavioural traitreducing the frequency of heavily defoliated sites[Considering that this frequency is crucial for the graz!ing impact\ two conclusions arise] _rst\ selectivity forforage biomass is a stabilizing behavioural trait ofgrazing\ reducing the negative impact on the range^secondly\ ignoring this behavioural trait in simu!lations results in an overestimation of the grazingimpact[

With inter!annual memory of preferred grazingsites\ we forced spatiotemporal autocorrelation ontothe grazing process[ The speci_c implementation ofinter!annual memory increased grazing heterogeneity[We could not _nd any empirical work giving quan!titative results on spatiotemporal autocorrelation ofgrazing patterns[ However\ the qualitative report byAndrew "0875# suggesting decreased heterogeneity inthe absence of inter!annual memory supports ourassumptions[ Furthermore\ several authors supportthe view that patches grazed heavily in consecutiveyears are focal spots of range degradation "Mott 0876^Fuls 0881^ Kellner + Bosch 0881#[ With this reason!ing\ temporal autocorrelation of the patchy grazingpattern becomes a key factor for the negative impactof grazing on vegetation[ Moreover\ it is consistentwith the less detrimental e}ect of temporally uncor!related grazing in our model[

IMPLICATIONS FOR MANAGEMENT

Like any optimization process\ rangeland man!agement requires\ along with clearly de_ned objectivesand a set of possible actions\ a model predicting theconsequences of any actions on the system "Walker0877#[ Advocating the {state and transition| model ofrangeland dynamics "Westoby\ Walker + Noy!Meir0878#\ Jeltsch et al[ "0886b# suggested that stockingrate thresholds of shrub cover increase could be usedas markers of the boundary between a desirable {state|and an undesirable {transition|[ With poorly under!stood spatial grazing aspects\ our results seeminglyweaken this concept\ inherently di.cult due to thehigh stochasticity of shrub cover increase[ On theother hand\ our results point towards a way ofexplaining some of the variability of vegetation changeby discerning a factor open to quantitative analysis[Hence\ having identi_ed the factor\ its e}ect\ hithertohidden in overall stochasticity\ can be quanti_ed[Thus\ our understanding can be improved and theuncertainty of predictions reduced[ As yet\ given thescarce empirical knowledge on small!scale grazingpatterns\ we are far from improved predictability[However\ the mere identi_cation of this knowledgegap has a bearing on rangeland management[ Thehigh sensitivity of long!term grazing e}ects towards

587

Spatial grazingaspects affectrangelanddynamics

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

grazing heterogeneity renders respective quantitativeknowledge an essential prerequisite for assessing sus!tainability of management strategies[ Consequently\the failure to consider spatial components of her!bivory in so!called carrying capacity calculations cangreatly contribute to range degradation due to over!grazing "Coughenour 0880#[

A second management implication arises from theslow progress of degradation[ Due to this slow pro!gress long time spans of observation are required forthe identi_cation of a directional change in shrubcover[ Moreover\ these time spans usually exceed thetime horizons of managers[ The importance of eco!logically appropriate time horizons for managementbecomes obvious from a comparison of stocking ratethresholds calculated for di}erent time spans[ Forexample\ under scenario N0\ a manager looking 19years ahead might decide that stocking at 09 ha lsu−0

is ecologically sound\ since the risk of shrub coverdoubling is ¾09) "Table 1#[ When retiring after 19years\ he would have achieved his goal of preventingshrub cover doubling with a probability of 89)[ How!ever\ his successor continuing this {successful| stockingstrategy for another 29 years would face a 87) chanceof shrub cover at least doubling[ Worse still\ meanexpectation for shrub cover will be close to 59)"Fig[ 1#[ Hence\ due to the slow speed of change\ amismatch of ecological and management time scalesarises[ We showed this mismatch\ also diagnosed byJeltsch et al[ "0886b#\ to be particularly dangerous andprone to encourage inappropriate managementdecisions[

Conclusions

Our results support the view that in rangelands proneto increasing cover by woody vegetation\ a spatiallyuniform grazing distribution is desirable "Owens\Launchbaugh + Holloway 0880#[ However\ the e}ec!tiveness of management systems designed to improvegrazing distribution and reduce grazing e}ects det!rimental to the range has yet to be established "O|Re!again + Turner 0881#[ Hence\ patchy grazing util!ization might well be the predominant pattern insavanna rangelands[ Consequently\ we concur withKellner + Bosch "0881# that management aiming atsustainable land use has to account for grazing het!erogeneity at whatever scale it is present[ Stockingrates calculated merely from the amount of availablebiomass\ and the forage required per livestock unit"Fourie\ Niekerk + Fouche� 0874#\ underestimate theimpact of livestock on community dynamics\ since thedegrading e}ects of patch!overgrazing are notaccounted for[ Therefore\ research institutions andextension agencies working towards recom!mendations on stocking rates should explicitly con!sider the e}ect of spatial heterogeneity[

With long!term grazing e}ects on vegetationdynamics dependent on small!scale patterns of graz!

ing utilization\ our results con_rm that sustainabilityand persistence of grazing systems are strongly a}ec!ted by spatial grazing aspects "Coughenour 0880#[With these aspects poorly understood\ particularly atsmaller spatial scales\ a hitherto neglected limitationfor the predictability of range dynamics is revealed[Given the importance of a quantitative understandingof the prevailing spatial patterns of grazing utilizationon the one hand\ and the lack of such understandingon the other hand\ a gap to be _lled by both empiricaland theoretical studies becomes obvious[ However\ aquantitative description of the spatial grazing patternunder a particular situation alone can be but a startingpoint[ Because the pattern is extremely rapid in itsresponse to environmental variation\ such as overallgrazing pressure resulting from rainfall!driven ~uc!tuations in forage biomass\ what we need is a generalunderstanding of the behavioural rather than physio!logical links between grazing ungulates and theirenvironment "Hobbs 0885#[ Here\ modelling studiesaddressing spatial aspects of both vegetation dynam!ics and grazing utilization can promote under!standing\ provided that the spatial grazing pattern ofthe particular grazing model employed is quanti_edexplicitly[

Acknowledgements

We thank Christina Skarpe\ Ian Watson and a secondanonymous referee for comments that signi_cantlyimproved the manuscript[

References

Andrew\ M[H[ "0875# The use of _re for spelling monsoontallgrass pasture grazed by cattle[ Tropical Grasslands\ 19\58Ð66[

Archer\ S[ "0878# Have southern Texas savannas been con!verted to woodlands in recent history< American Natu!ralist\ 023\ 434Ð450[

Belsky\ A[J[ "0883# In~uences of trees on savanna pro!ductivity] tests of shade\ nutrients and tree!grass compe!tition[ Ecology\ 64\ 811Ð821[

Bu.ngton\ L[C[ + Herbel\ C[H[ "0854# Vegetational changeson a semidesert grassland range from 0747 to 0852[ Eco!logical Monographs\ 24\ 028Ð053[

Coughenour\ M[B[ "0880# Spatial components of plantÐher!bivore interactions in pastoral\ ranching and native ungu!late ecosystems[ Journal of Range Management\ 33\ 429Ð431[

Coughenour\ M[B[\ McNaughton\ S[J[ + Wallace\ L[L["0873# Simulation study of Serengeti perennial graminoidresponses to defoliation[ Ecological Modelling\ 15\ 066Ð190[

Field\ D[I[ "0866# Range Monitoring in Botswana "0862Ð0866#[ Ministry of Agriculture\ Gaborone\ Botswana[

Fourie\ J[H[\ Niekerk\ J[W[ + Fouche�\ H[J[ "0874# Wei!dingskapasiteitsnorme in die vrystaatstreek[ Glen Agric!ulture\ 03\ 3Ð6[

Fuls\ E[R[ "0881# Ecosystem modi_cation created by patchovergrazing in a semi!arid grassland[ Journal of AridEnvironments\ 12\ 48Ð58[

Fuls\ E[R[ + Bosch\ O[J[H[ "0880# The in~uence of below!

588

G[E[ Weber et al[

Þ 0887 BritishEcological Society\Journal of AppliedEcology\ 24\576Ð588

average rainfall on the vegetational traits of a patch!grazedsemi!arid grassland[ Journal of Arid Environments\ 10\ 02Ð19[

Gammon\ D[M[ + Roberts\ B[R[ "0867# Patterns of defoli!ation during continuous and rotational grazing of theMatopos Sandveld of Rhodesia[ III[ Frequency of defoli!ation[ Rhodesian Journal of Agricultural Research\ 05\ 036Ð053[

Hacker\ R[B[ "0873# Vegetation dynamics in a grazed mulgashrubland community[ I[ The mid!storey shrubs[ Aus!tralian Journal of Botany\ 21\ 128Ð138[

Hannan\ N[P[\ Prevost\ Y[\ Diouf\ A[ + Diallo\ O[ "0880#Assessment of deserti_cation around deep wells in theSahel using satellite imagery[ Journal of Applied Ecology\17\ 062Ð075[

Hart\ R[H[\ Bissio\ J[\ Samuel\ M[J[ + Waggoner\ J[W[ Jr"0882# Grazing systems\ pasture size\ and cattle grazingbehavior\ distribution and gains[ Journal of Range Man!agement\ 35\ 70Ð76[

Heitschmidt\ R[K[\ Briske\ D[D[ + Price\ D[L[ "0889# Patternof interspeci_c tiller defoliation in a mixed!grass prairiegrazed by cattle[ Grass and Forage Science\ 34\ 104Ð111[

Hellden\ U[ "0880# Deserti_cation Ð time for an assessment<Ambio\ 19\ 261Ð272[

Hobbs\ N[T[ "0885# Modi_cation of ecosystems by ungu!lates[ Journal of Wildlife Management\ 59\ 584Ð602[

Hodgkinson\ K[C[ "0868# The shrubs of poplar box "Euca!lyptus populnea# lands and their biology[ Australian Ran!geland Journal\ 0\ 179Ð182[

Jeltsch\ F[\ Milton\ S[J[\ Dean\ W[R[J[ + van Rooyen\ N["0885# Tree spacing and coexistence in semi!arid savannas[Journal of Ecology\ 73\ 472Ð484[

Jeltsch\ F[\ Milton\ S[J[\ Dean\ W[R[J[ + van Rooyen\ N["0886a# Simulated pattern formation around arti_cialwaterholes in the semi!arid Kalahari[ Journal of VegetationScience\ 7\ 066Ð077[

Jeltsch\ F[\ Milton\ S[J[\ Dean\ W[R[J[ + van Rooyen\ N["0886b# Analysing shrub encroachment in the southernKalahari] a grid!based modelling approach[ Journal ofApplied Ecology\ 23\ 0386Ð0498[

Kellner\ K[ + Bosch\ O[J[H[ "0881# In~uence of patch for!mation in determining the stocking rate for southernAfrican grasslands[ Journal of Arid Environments\ 11\ 88Ð094[

Lange\ R[T[ "0858# The piosphere] sheep track and dungpatterns[ Journal of Range Management\ 6\ 285Ð399[

Lu�tge\ B[U[\ Hardy\ M[B[ + Hatch\ G[P[ "0885# Plant andsward response to patch grazing in the Highland Sourveld[African Journal of Range and Forage Science\ 02\ 83Ð88[

MacDonald\ I[A[W[ "0867# Pattern and process in a semi!arid grassveld in Rhodesia[ Proceedings Grassland Societyof Southern Africa\ 02\ 092Ð098[

Martens\ H[E[ "0860# The e}ect of tribal grazing patterns onthe habitat in the Kalahari[ Botswana Notes and Records\0\ 123Ð130[

Mott\ J[J[ "0876# Patch grazing and degradation in naturepastures of tropical savanna in northern Australia[ Graz!ing Lands Research at the PlantÐAnimal Interface "edsF[W[ Horne\ J[ Hodgson\ J[J[ Mott + R[ Brougham#\ pp[042Ð050[ Winrock International\ Morrilton\ Australia[

Noy!Meir\ I[ "0870# Spatial e}ects in modelling arid eco!systems[ Arid Lands Ecosystems] Structure\ Functioningand Management "eds D[W[ Goodall + R[A[ Perry#\ pp[300Ð321[ Cambridge University Press\ Cambridge\ UK[

O|Connor\ T[G[ "0880# Local extinction in perennial grass!lands] a life!history approach[ American Naturalist\ 026\642Ð662[

O|Connor\ T[G[ "0881# Patterns in plant selection by grazingcattle in two savanna grasslands] a plant|s eye view[ Jour!nal of the Grassland Society of Southern Africa\ 8\ 86Ð093[

O|Reagain\ P[J[ + Turner\ J[R[ "0881# An evaluation of theempirical basis for grazing management recommendationsfor rangeland in Southern Africa[ Journal of the GrasslandSociety of Southern Africa\ 8\ 27Ð38[

Owens\ M[K[\ Launchbaugh\ K[L[ + Holloway\ J[W[ "0880#Pasture characteristics a}ecting spatial distribution of util!isation by cattle in mixed brush communities[ Journal ofRange Management\ 33\ 007Ð012[

Pickup\ G[ "0883# Modelling patterns of defoliation by graz!ing animals in rangelands[ Journal of Applied Ecology\ 20\120Ð135[

Pickup\ G[ + Chewings\ V[H[ "0883# A grazing gradientapproach to land degradation assessment in arid areasfrom remotely!sensed data[ International Journal ofRemote Sensing\ 04\ 486Ð506[

Richter\ C[G[F[ "0880# Gras!bosinteraksie in die bos!veldgebiede von Noord!Kaap "grassÐshrub interactions inthe savanna regions of the Northern Cape#[ PhD thesis\University of Bloemfontein\ South Africa[

Ring\ C[B[\ Nicholson\ R[A[ + Launchbaugh\ J[L[ "0874#Vegetational traits of patch!grazed rangeland in west!cen!tral Kansas[ Journal of Range Management\ 27\ 40Ð44[

Ruyle\ G[B[\ Ogden\ P[R[ + Rice\ R[W[ "0877# Defoliationpatterns of cattle grazing Lehmann Lovegrass[ AppliedAgricultural Research\ 2\ 066Ð070[

Schlesinger\ W[H[\ Reynolds\ J[F[\ Cunningham\ G[L[\Huenneke\ L[F[\ Jarrell\ W[F[\ Virginia\ R[A[ + Whitford\W[G[ "0889# Biological feedbacks in global deserti_cation[Science\ 136\ 0932Ð0937[

Senft\ R[L[\ Rittenhouse\ L[R[ + Woodmansee\ R[G[ "0874#Factors in~uencing patterns of cattle grazing behaviouron shortgrass steppe[ Journal of Range Management\ 27\71Ð76[

Skarpe\ C[ "0889a# Shrub layer dynamics under di}erentherbivore densities in an arid savanna\ Botswana[ Journalof Applied Ecology\ 16\ 762Ð774[

Skarpe\ C[ "0889b# Structure of the woody vegetation indisturbed and undisturbed arid savanna\ Botswana[ Veg!etatio\ 76\ 00Ð07[

Skarpe\ C[ + Bergstro�m\ R[ "0875# Nutrient content anddigestibility of forage plants in relation to plant phenologyand rainfall in the Kalahari\ Botswana[ Journal of AridEnvironments\ 00\ 036Ð053[

Stobbs\ T[H[ "0862# E}ect of plant structure on intake oftropical pastures[ II[ Di}erences in sward structure\ nutri!tive value and bite size of animals grazing Setaria ancepsand Chloris gayana at various stages of growth[ AustralianJournal of Agricultural Research\ 13\ 710Ð718[

Tongway\ D[J[ + Ludwig\ J[A[ "0889# Vegetation and soilpatterning in semi!arid mulga lands of Eastern Australia[Australian Journal of Ecology\ 04\ 12Ð23[

Tongway\ D[J[ + Ludwig\ J[A[ "0883# Small!scale resourceheterogeneity in semi!arid landscapes[ Paci_c Con!servation Biology\ 0\ 190Ð197[

Valentine\ K[A[ "0836# Distance from water as a factor ingrazing capacity of rangeland[ Journal of Forestry\ 34\638Ð643[

Van Vegten\ J[ "0872# Thornbush invasion in a savannaecosystem in eastern Botswana[ Vegetatio\ 45\ 2Ð6[

Walker\ B[H[ "0877# Autecology\ synecology\ climate andlivestock as agents of rangeland dynamics[ AustralianRangeland Journal\ 09\ 58Ð64[

Westoby\ M[\ Walker\ B[ + Noy!Meir\ I[ "0878# Range man!agement on the basis of a model which does not seek toestablish equilibrium[ Journal of Arid Environments\ 06\124Ð128[

Zucchini\ W[\ Adamson\ P[ + McNeill\ L[ "0881# A modelof southern African rainfall[ South African Journal ofScience\ 77\ 092Ð098[

Received 09 January 0887^ revision received 19 July 0887