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Spatial Scaling in Ecology

J. A. Wiens

Functional Ecology, Vol. 3, No. 4. (1989), pp. 385-397.

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Functional E S S A Y REVIEWEcology 1989,3,385-397 Spatial scaling in ecology1

J . A . W I E N SDepa rtmen t of Biology and N atural ResourceEcology Laboratory, Colorado State University,Fort C ollins, Colorado 80523, U S A

'The only things that can be universal, in a sense,are scaling things'

(Mitchell Feigenbaum2)

IntroductionActs in wh at Hutc hinson (1965) has called the'ecological theatre' are played out on variousscales of space and time. To understan d the drama ,we must view it on the appropriate scale. Plantecologists long ago recognized the importance ofsampling scale in their descriptions of the disper-sion or distribution of species (e.g. Greig-Smith,1952). However, many ecologists have behaved asif patterns and the processes that produc e them areinsensitive to differences in scale and havedesigned their studies with little explicit attentionto scale, Kareiva & Andersen (1988) surveyednearly 100 field experiments in communityecology and found that half were conducted onplots no larger than l m in diameter, despiteconsiderable differences i n the sizes and types oforganisms studied.

Investigators addressing the same questionshave often conducted their studies on quitedifferent scales. Not surprisingly, their findingshave not always matched, and arguments haveensued. The disagreements among conservationbiologists over the optimal design of naturereserves (see Simberloff, 1988) are at least partlydue to a failure to appreciate scaling differencesamong organisms. Controversies about the role ofcompetition in structuring animal communities(Schoener, 1982; Wiens, 1983, 1989) or aboutthe degree of coevolution in communities (Con-ne11, 1980: Ro~~ghgardec,983) may reflect th e

' Adapted f rom the f i r s t Kathar ine P. Douglass Dist in-gui shed Lecut re a t t he Rocky Mounta in Bio log i ca lLabora tory , G oth i c , Colorado , 23 J u l y 1 9 8 7 .Quoted i n Gle ick , 1987 , p. 1 8 6 .

imposition of a single scale on all of the spec ies inthe community. Current ecological theories dolittle to resolve suc h debates, because most of thesetheories are mute on scale - they can be applied atany scale on which the relevant parameters can bemeasured.

Recently, however, ecologist studying a widerange of topics havt! expressed concern aboutscaling effects (see Dbyton & Tegner, 1984; Wienset al . , 1986a; Giller & Gee, 1987; Meetenmeyer &Box, 1987; Frost et al . , 1988; Rosswall, Woodman-see & Risser, 1988). Scale' is rapidly becoming anew ecological buzzword .

Scientists in other disciplines have recognizedscaling issues for some time. The very foundatio nof geography is scaling. In the atmospheric andearth scienc es, the physical processes thatdetermine local and global patterns are clearlylinked (e.g. Sch umm & Lichty, 1965; Clark, 1985;Dagan, 1986; Ahnert, 1987) and their imp ortanceis acknowledged in hierarchies of scale that guideresearch and define subdisciplines within thesesciences. Physical and biological oceanographersoften relate their findings to the spectrum ofphysical processes from circulation patterns inoceanic basins or large gyres to fine-scale eddies orrips (e.g. Ilaury, McGowan & Wiebe, 197 8; Steele,1978; Legrende & Demers, 1984; Hunt &Schneider, 1987; Platt & Sathyendranath, 1988).Physicists and mathematicians studying fractalgeometry, strange attractors, percolation theory,and chaos address scaling as a primary focus oftheir investigations (Nittman , Daccord & Stanley,1985; Orbach, 1986; Grebogi, Ott & Yorke, 1987;Gleick, 1987 ).

Why have ecologists been so slow to recognizescaling? Ecologists deal with phenomen a that areintuitively familiar, and we are therefore morelikely to perceive and study such phenomena onanthropocentric scales that accord with our ownexperiences. We have also been somewhat tradi-tion-bound, using quadrats or study plots of aparticular size simply because previous workersdid. Unlike the physical and earth sciences (andmany laboratory disciplines of biology),where ourperceptual range has been extended by tech-nology, few tools have been available to expand

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386 our view of ecological phenomena (but see Platt &j. A . IViens Sathyendranath, 1988; Gosz, Dahm & Risser,1988).

My thesis in this paper is that scaling issues arefundamental to all ecological investigations, asthey are in other sciences. My comments arefocused on spatial scaling, but similar argumentsmay be made about scaling in time.

The effects of scaleSome exampiesThe scale of an investigation may have profoundeffects on the patterns one finds. Consider someexamples:

In hardwood forests of the north-easternUnited States, Least Flycatchers (Empidonaxminimus Baird & Baird) negatively influence thedistribution of American Redstart (Se topha ga ruti-cilla L.) territories at the scale of 4-ha plots.Regionally, however, these species are positivelyassociated (Sherry & Holmes, 198 8). Apparentlythe broad-scale influences of habitat selectionoverride the local effects of interspecific compe-tition. Similar scale-depende ncy has been foundin the habitat relationships of shrubsteppe birds(Wiens, Rotenberry & Van Horne , 1 986b), inter-specific associations among plant species (e.g.Beals, 1973) or phytoplankton and zooplankton(Carpenter & Kitchell, 1987) , and the patterns ofcoexistence of mosses colonizing moose dung(Marino, 1988) or of ant s on mangrove i slands(Cole, 1983) .

In the Great Barrier Reef of Australia, thedistribution of fish species among coral heads atthe scale of patch reefs or a single atoll may bestrongly influenced by chance events duringrecruitment and the species composition of localcommunities of fish may be unpredictable (Sale,1988; Clarke, 1988).At t he broader scales of atollsor reef systems, community composition is morepredictable, perhaps because of habitat selection,niche diversification, or spatial replacement ofspecies within trophic guilds (Ogden & Ebersole,1981; Anderson et a l., 1981; Green, Bradbury &Reichelt, 1987; Galzin, 1987).

On the basis of experiments conducte d at thescale of individual leaf surfaces, plant physiolo-gists have concluded that stomata] mechanismsregulate transpiration, whereas meterologistsworking at the broader scale of vegetation haveconcluded that climate is the principal control(Jarvis& McNaughton, 1986; Woodward, 1987).In

a similar manner, most of the variation in litterdecomposition rates among different species at alocal scale is explained by properties of the litterand the decomposers, but at broader regionalscales climatic variables account for most of thevariation in decomposition rates (Meentemeyer,1984).

Domestic cattle grazing in shortgrass prairieuse elements of local plant communities quitenonrandomly on the basis of short-term foragingdecisions, but use of vegetation types is propor-tional to their coverage at the broader scale oflandscape mosaics (Senft et al., 1987).

The distribution of phytoplankton in marinesystems is dominated by horizontal turbulentdiffusion at scales up to roughly 1km (Platt, 1972;Denman & Platt, 1975). At somewhat broaderscales, phytoplankton growth, zooplankton graz-ing, and vertical mixing over ride these local effects(Denman & Platt, 1975; Lekan & Wilson, 1978;Therriault & Platt, 1981). At scales of >5km,phytoplankton patchiness is controlled largely byadvection, eddies, and local upwelling occurringover areas of 1-100km (Gower, Denman & Holyer,1980; Legrende & Demers, 1984). The same con-trols operate in lakes, although the transitionsoccur at finer scales (Powel l et al., 1975).

These examples could easily be extended. Thesalient point is that different patterns emerge atdifferent scales of investigation of virtually anyaspect of any ecological system.

Linkages between physical an d biological scalesIn the marine phytoplankton and other aquaticsystems, physical features may be primarydeterminants of adaptations of organisms, andphysical and biological phenomena may scale inmuch the sa me way. However, in many terrestrialenvironments, at mospheric a nd geological influ-ences may often be obscured by biological inter-actions (Clark, 1985). The relationships betweenclimate and vegetation that are evident at broadscales, for example, may disappear at finer scales,overridden by the effects of competition andother biological processes (Greig-Smith, 1979;Woodward, 1987) . Local biological interactionshave the effect of decoupling systems from directphysical determination of patterns by introducingtemporal or spatial lags in system dynamics orcreating webs of indirect effects. However, atbroader scales, physical processes may dominateor dissipate these biological effects (Levin, 1989).There are exceptions: plant distributions on fine

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388J. A.Wiens

Fig. 1. The effects of changing the grain and extent of a study in a patchy landscape. As the extent of the study isincreased (large squares), landscape elements that were not present in the original study area are encountered. As thegrain of samples is correspondingly increased (small squares), small patches that initially could be differentiated arenow included within samples and th e differences among them are averaged out.

sam ple loc ations ) , the log- log p lo t of var ianceversus grain (or N) h as a s lo p e o f -1 (Fig. 2a). In ah e te ro g en eo u s a r ea , th i s s lo p e w i l l g en era l ly b eb e t w e e n -1 a n d 0 (O 'Neil l et a l . , u n p u b l i s h e d ) ,a l th o u g h th e r e la t io n sh ip m ay b e cu rv i l in ear (Fig .2a; Levin , 1989) . As grain increa ses , a greaterpropor t ion of the spatial heterogeneity of thesy s tem i s co r i ta in ed w i th i n a sam p le o r g r ain an d i slos t to our r t?so lu tion ,wh i le b e tween -g ra in h e te ro -geneity (= var iance) decreases (Fig . 2b) . If th eo ccu r r en ce o f sp ec ies in q u ad ra ts i s r eco rd edb ased o n a m in imal co v erag e cr i te rio n , ra r e sp ec ieswil l be less l ikely to be recorded as grain s izeincrea ses; th is ef fect is more prono unc ed if thesp ec ies a r e w id e ly sca t te r ed in smal l p a tch es th a nif they are h ighly aggregated (Turner et a l . , u n -p u b l i s h e d ) , If th e me asu remen t c r i te rio n i s s imp lyth e p r esen ce o r ab sen ce o f sp ec ies in q u ad ra ts .h o we v er , mo re r a r e sp ec ies w i ll b e r eco rd ed asgrain increase s , an d d ivers i ty wil l increase ratherth an d ecrease w i th in c r easin g g r a in . Exac t ly h o wv a r ia n c e c h a ng e s w i i h g r a i i ~ ~ d l eh u s clepci~dso nth e m ag n i tu d e a n d fo rm o f th e h e te ro g ene i ty o f anarea (M i ln e , 1 9 8 8 ,u n p u b l i s h e d ; P a l m e r . 1 9 8 8 )a n do n th e ty p e of measu reme n t tak en .

Sp a t ia l v a r ian ce i s a lso d ep en d en t o n th e ex ten tof an invest igation . Hold ing grain consta nt , an

in crease in ex ten t w i l l in co rp o ra te g r ea te r sp a t ia lheterogeneity , as a greater var iety of pat ch types orl a n d s c a p e e l e m e n t s i s i n c l u d e d i n t h e a r e a b e i n gs tu d ied (F ig . 1 ) .Between -g ra in v ar ian ce in c r easeswith a broade ning of scale (ex ten t) (Fig . 2b) .

Th es e co n s id era t io n s a l so r ela te to th e p a t te rn sof tempora l var iat ion or equ il ibr ium of ecologicalsystems. Ecologis ts have of ten d isagreed aboutwh et h er o r n o t eco lo g ica l sy s tems a r e equilibria1(e .g .Wien s , 1 9 8 4 , in p r es s ; Ch esso n & Case , 1 9 8 6 ;DeAngelis & Waterh o u se , 1 9 8 7 ; Sa le , 1 9 8 8 ) .Wh eth er ap p aren t ' eq u i l ib r iu m ' o r ' n o n eq u i l i -b r iu m ' i s p e r ce iv ed in a sy s tem c lea r ly d ep en d s o nth e scale of observation . Unfor tuna tely , curren tth eo r ies p ro v id e l i tt l e g u id an ce as to wh a t w emig h t ex p ec t : mo d e ls in p o p u la t io n b io log y ( e .g .M ay & Oster , 1 9 7 6 ; Sch af f e r, 1 9 8 4 ; M ay , 1 9 8 9 )a n d p h y s i cs ( G l ei c k , 1 9 8 7 ) s h o w t h a t o r d e r a n dstab il i ty may be der ived at broad scales f romfiner-scale chaos or that f ine-scale determinismm a y p r o d u c e b r o a d- s ca l e c h a o s , d e p e n d i n g o nc i r cu ms tan ces . Pe rh ap s eco lo g ica l sy s tem s fo l lo wpr inci p les of universal i ty , their f inal s tates atb ro ad sca les d ep en d in g o n g en era l sy s temp ro p er t ies r a th er th an f in e - sca le d e ta i l s ( c f .F e i g e n b a um , 1 9 7 9 ) . B r o w n ( 1 9 8 4 ) h a s c h a m -p io n e d th i s v iew , b u t we s t il l k n o w f ar to o l i tt l e

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389Scale inecology

-n - heterogeneous0 C 2

change inextentGroin scale ( lo g)

Fig. 2. (a)As the grain of samples becomes larger, spatialvariance in the stu dy system as a whole decreases, albeitdifferently for homogeneous and heterogeneous areas.This is related to the with in- and between -grain (sample)compon ents of variation. (b)With increasing grain scale,less of the variance is du e to differences between sam plesand more of the overall variation is included withinsamples (and therefore averaged away). An increase inthe extent of the investigation may increase the beween-grain component of variance by adding new patch typesto the landscape surveyed (Fig. I ) , but within-grainvariance is not noticeably affected.

abo u t t he sca l i ng behav i our o f eco l og i ca l sys t emst o c o n s i d e r u n i v er s a li ty a s a n y t h i n g o t h e r t h a n a ni n t r igu i ng hypot he s i s .

Predictability and sp ace-tim e scalingBecause t he e f f ec ts of l oca l he t e rogene i t y a r eaveraged ou t a t b roader s ca l es , eco log i ca l pa t t e rn so f t en a p p e a r t o b e m o r e p r e d i c t a b le t h e r e . W h e t h e ro r n o t t h e p r e d i c t i o n s a r e m e c h a n i s t i c a l ly s o u n dd e p e n d s o n t h e i m p o r t a n c e of t h e f i n e- s ca lede t a i l s . T h e L ot ka -Vol t er r a compe t i t i on eq ua t i onsm a y p r e d i c t c o m p e t i t i v e e x c l u s io n o f s p e c i e s t h a ti n f ac t a r e ab l e t o coex i s t because o f f i ne - sca l espa t i a l he t e rogene i t y t ha t is ave raged awa y (e.g.M o l o n e y , 1 9 8 8 ) . T h e s e p r e d i c t io n s a r e n o t r e a ll ys c a l e - in d e p e n d e n t b u t a r e i n s t e a d i n s e n s i t i v e toi m p o r t a n t s c a l e - d e p e n d e n t c h a n g e s .

O u r a b i l i t y t o p r e d i c t e c o l o g i c a l p h e n o m e n ad e p e n d s o n t h e r e l a t io n s h ip s b e t w e e n s p a ti a l a n d

t empora l s ca l es o f va r i a t i on (F i g . 3 ) . W i t hi n c r e a s e d s p a t i a l sc a l e, t h e t i m e s c a l e o f i m p o r t a n tp r o c e ss e s a l s o i n c r e a s e s b e c a u s e p r o c e s s e s o p e r a t ea t s l o w e r r a t e s , t i m e l a g s i n c r e a s e , a n d i n d i r e c te f f ec t s become i nc reas i ng l y i mpor t an t (De l cour t ,De l cour t & W e b b , 1 9 8 3 ; C la r k , 1 9 8 5 ) . T h e d y n a -m i c s o f d i f f e r e n t e c o l o g i c a l p h e n o m e n a i nd i f fe r en t sys t ems , how ever , f o l l ow d i f f e r en t t ra j ec -t o ri e s i n s p a c e a n d t i m e . A n a r e a o f a f e w .s q u a r em e t r e s of g r a s s la n d m a y b e e x p o s e d t o u n g u l a t eg r a z in g f o r o n l y a f e w s e c o n d s o r m i n u t e s , w h e r e a st h e t e m p o r a l s c a l e o f m i c r o t in e s i n t h e s a m e a r e am a y b e m i n u t e s t o h o u r s a n d t h a t o f so i l a r t h r o -p o d s d a y s t o m o n t h s o r y ea r s . T h e r e a r e n os t a n d a r d f u n c t i o n s t h a t d e f i n e t h e a p p r o p r i a t eu n i t s f o r s u c h s p a c e - ti m e c o m p a r i s o n s in eco l ogy .M o r e o v e r, t h e c o n t i n u o u s l i n e a r s c a l e s w e u s e t om e a s u r e s p a c e a n d t i m e m a y n o t b e a p p r o p r i a t e f o ro r g a n is m s o r p r o c e s s e s w h o s e d y n a m i c s o r r a t e sva ry d i scon t i nuous l y ( e .g . ' phys i o l og i ca l t i me 'a s s o ci a te d w i t h d i a p a u s e i n i n s e c t s ; T a y l o r , 1 9 8 1 ) .

A n y p r e d i c t i o n s o f t h e d y n a m i c s o f s p a t i a l l yb r o a d -s c a le s y s t e m s t h a t d o n o t e x p a n d t h e t e m p o -r a l s c a l e a r e pseudopredictions. T h e p r e d i c t i o n sm a y s e e m t o b e q u i t e r o b u st b e c a u s e t h e y a r e m a d eo n a f i n e t im e s c a l e re l a ti v e t o t h e a c t u a l d y n a m i c so f t h e s y s t e m ( Fi g. 3 ) , b u t t h e m e c h a n i s t ic l i nk a g e sw i l l n o t b e s e e n b e c a u s e t h e t e m p o r a l e x t e n t of t h es t u d y i s to o s h o r t . I t is a s if w e w e r e t o t a k e t w o

space-t ime/scal inglow predictability

high apparentpredictability~ t i m ecaleo f interest

Spatial scaleFig. 3. As the spatia l scaling of a system incre ases, so alsodoes its temporal scaling, although these space-timescalings differ for different systems. S tudies co ndu ctedover a long time at fine spatial scales have low predictivecapacity. Investigations located near to the space-timescaling functions have high predictive power. Short-term stud ies cond ucted at broad spatial scales generallyhave high appar ent predictability (pseudopred~ctabil i ty)because the n atural dynam ics of the system are so muchlonger than the period of study. often, ecologists andresource managers have been m ost interested in makingand testing predictions on relatively short time scales,regardless of the spatial scale of the investigation.

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390 snapshots of a forest a few moments apart and use likely to emerge at broader scales. Because theI. A. W i e n s the first to predict the second. This problem may time-frame of ecological processes tends to be

be particularly severe in resource management longer at broader scales (Fig.3 ) , long-term investi-disciplines, where the application of policies to gations are more often necessary to reveal thelarge areas is often based on very short-term dynamics of the system. The scale of investigationstudies. thus determines the range of patterns and pro-

cesses that can be detected. If we study a system atan inappropriate scale, we may not detect itsDetecting patterns and inferring processes actual dynamics and patterns but may instead

The characteristics of ecological systems at rela- identify patterns that are artifacts of scale. Becausetively fine scales differ from those at relatively we are clever at devising explanations of what webroad scales (Table I ) , and these differences see, we may think we understand the system wheninfluence the ways ecologists can study the we have not even observed it correctly.systems. The possibilities for conducting rep-licated experiments vary inversely with the scaleof investigation. The potential for sampling errors Dealing with scaleof several kinds are greater at finer scales, although Scale arbitrarinessthe intensity of sampling is generally lower atbroader scales. Fine-scale studies may reveal The most common approach to dealing with scalegreater detail about the biological mechanisms is to compare patterns among several arbitrarilyunderlying patterns, but generalizations are more selected points on a scale spectrum. In his analysis

Table 1.General chara cteristics of various attribu tes of ecological systems and in vestigatio ns at fine and broad scales ofstudy. 'Fin e ' and 'broad' are defined relative to t he focus of a particular investigation, and w ill vary between studies.Scale

Attribu te Fine BroadNumber of variables im portant in correlations many fewRate of processes or system change fast slowCapacity of system to track sho rt-term environmental variations high lowPotential for system open ness high lowEffects of ind ividual mov ements o n patterns large smal lType of heterogeneity patch landscape

mosaicFactors influencing species' distribution resourceihabitat barriers,distribution, dispersalphysiologicaltolerancesResolution of detail high lo wSampling adequacy (intensity) good poorEffects of sam pling e rror large smallExperimental manipulations possible difficultReplication possible difficultEmpirical rigor high lo wPotential for deriving generalizations lo w highForm of models mechanistic correlativeTestability of hypotheses high lo wSurveys quantita tive qualita tiveAppro priate duration of study short long

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391Scale inecology

of reef-fish communities, for example, Galzin(1987) compared distributions wi thin a singletransect, among several transects on the sameisland, and among five islands. Roughgarden et al .(1987) compared the dynamics of rocky intertidalbarnacle communities and assemblages of Anol i slizards on islands at 'small', 'medium', and 'large'spatial scales. Senft et al . (1987) examined herbi-vore foraging in relation to vegetation patterns atthe scales of the local plant community, thelandscape, and the region. Multiscale studies ofbirds have considered patterns at three to fivescales, and Wiens et al . (1986a) recognized fourscales of general utility in ecological investi-gations.

In these examples, the definition of the differentscales makes intuitive sense and the analysesreveal the scale-dependency of patterns. Castingthe relationships in the context of hierarchy theory(Allen & Starr, 1982; O'Neill et al . , 1986) mayfurther sharpen our focus on scaling by emphasiz-ing logical and functional linkages among scales.The scales chosen for analysis are still arbitrary,however: they tend to reflect hierarchies of spatialscales that are based on our own perceptions ofnature. Just because these particular scales seem'right' to us is no assurance that they are appro-priate to reef fish, barnacles, anoles, cattle, orbirds. We need nonarbitrary, operational ways ofdefining and detecting scales.

Dependence on object ives and organismsWhat is an 'appropriate' scale depends in part onthe questions one asks. Behavioural ecologists,population ecologists, and ecosystem ecologists,for example, all probe the relationship betweenresources and consumers, but differences in theirobjectives lead them to focus their investigationsat different scales (Pulliam & Dunning, 1987).Conservation of key species or habitats may targetparticular patches or landscape fragments formanagement, whereas programmes emphasizingspecies richness or complexes of communitiesmay concentrate on preserving broader-scale land-scape mosaics (Noss, 1987; Scott e t a l . , 1987).

Differences among organisms also affect thescale of investigation. A staphylinid beetle doesnot relate to its environment on the same scales asa vulture, even though they are both scavengers.What is a resource patch to one is not to the other.The scale on which an oak tree 'perceives' itsenvironment differs from that of an understoreybluebell or a seedling oak (Harper, 1977). Local

populations of vagile organisms may be linkedtogether into larger metapopulations and theirdynamics may be less sensitive to the spatialconfiguration of local habitat patches than moresedentary species (Morrison & Barbosa, 1987;Fahrig & Paloheimo, 1988; Taylor, 1988). Chroni-cally rare species may follow different dispersaland scaling functions than persistently commonspecies. Consumers that use sparse or clumpedresources are likely to operate at larger spatialscales than those using abundant or uniformlydistributed resources, especially if the resourcesare critical rather than substitutable (Tilman,1982; O'Neill e t a ] . , 1988).

Such scaling differences among organisms maybe viewed in terms of 'ecological neighbourhoods'(Addicott et al . , 1987) or 'ambits' (Hutchinson,1953; Haury et al . , 1978);areas that are scaled to aparticular ecological process, a time period, and anorganism's mobility or activity. The ecologicalneighbourhood of an individual's daily foragingmay be quite different from that of its annualreproductive activities. The ecological neighbour-hood of the lifetime movements of a tit in a Britishwoodland may comprise an area of a few squarekilometres whereas a raptor may move over an areaof hundreds or thousands of square kilometres; anomadic teal of ephemeral desert ponds inAustralia may range over the entire continent.Incidence functions (Diamond, 1975) or fragmen-tation response curves (Opdam, Rijsdijk &Hustings, 1985) depict the ecological neighbour-hoods of species with respect to colonization andpersistence of populations in areas of differentsizes (scales).

To some extent, differences in ecological neigh-bourhoods among taxa parallel differences in bodymass. This raises the possibility of using allo-metric relationships (e.g. Calder, 1984) to predictscaling functions for organisms of different sizes.On this basis, for example, one might expect thescale of the home range of a 20-g lizard to beapproximately 0.3 ha, whereas that of a 20-g birdwould be in the order of 4ha; the parallel scale fora 200-g bird would be 92ha. Although such anapproach ignores variation in allometric relation-ships associated with diet, age, season, phylogeny,and a host of other factors, it may still provide anapproximation of organism-dependent scalingthat is less arbitrary than those we usually use.

Because species differ in the scales of theirecological neighbourhoods, studies of interactionsamong species may be particularly sensitive toscaling. The population dynamics of predatorsand of their prey, for example, may be influenced

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392 A1.A. Wiens Important elements ofpattern or controls components of patternsor mechan~smsorn~tted averaged out

---_.A _ -7 r - L

8 study scalef

broodScaleFig. 4. (A) The do main of scale of a particular ecological phenomenon (i.e. a combination of elements of a naturalsystem, the questions we ask of it, and the way we gather observations) defines a portion of the scale spectrum withinwhich process-pattern relationships are consistent regardless of scale. Adjacent domain s are separated by transitions inwhich system dynamics may ap pear chaotic. If the focus is on phenomena at a particular scale do main , studiesconducted at finer scales will fail to include important features of pattern or causal controls; studies restricted tobroader scales will fail to reveal the pattern or mechanistic relationships because such linkages are averaged out or arecharacteristic only of the particular domain. Comparative investigations based on sampling the scale spectrum atdifferent points in relation to the distribution of scale domains and transitions (solid and das hed vertical arro ws) willexhibit different pattern s. (B ) If a reductionist approach is adopted to examine patterns found at a particular scale ofstudy, the findings (and inferences about causal mechanisms) will differ depending on how far the reductionism isextended toward finer scales and how many doma ins are crossed (compare a, b , and c).

by factors operating on different scales (Hen- changes in patterns and processes. If this is so,geveld, 1987),and attempts to link these dynamics generalizations will be ha rd to find, for the range ofdirectly without recognizing the scale differences extrapolation of studies at a given scale will bemay lead to greater confusion than enligh tenment. severely limited. If the scale spectrum is notThe competitive interactions among species scal- contin uous, however, there may be domains ofing the environment in similar ways may be more scale (Fig.4a) , regions of the spec trum over which,direct or symmetrical than those between for a particular phenomenon in a particular ecolo-organisms that share resources but operate on gical system, patterns either do not change orquite different scales. If we arbitrarily impose a change monotonically with changes in scale.particular scale (e.g. quadrat size) on a community Domains are separated by relatively sharp transi-of organisms that operate on different scales, we tions from dominance by one set of factors totrunca te the interactions to different degrees for dominance by other sets, like phase transitions indifferent species. physical systems. Normally well-behaved

deterministic systems may exhibit unpredictablebehaviour at suc h transitions (Kitchell et al.,Domains of scale 1988), and nonlinear relations may become un-

Scale-dependency in ecological systems may be stable (O'Neill, personal comm unicat ion). Thecon tinuous , every change in scale bringing with it resulting chaos makes translation between

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393 domains difficult (Heaps & Adam, 1975; May,Scale in 1989). The argument over the relative merits ofecology linear versus nonlinear models in ecology (e.g.

Patten, 1983) may reflect a failure to recognize thedifferences in system dynamics within versusbetween domains.

How may we recognize domains of scale in away that avoids the arbitrary imposition of pre-conceived scales or hierarchical levels on naturalvariation? Several statistical approaches are basedon the observation that variance increases astransitions are approached in hierarchical systems(O'Neill et a l . , 1986). If quadrats in which plantspecies abundances have been recorded are aggre-gated into larger and larger groupings, the varianceof differences in abundance between pairs ofcontiguous groups fluctuates as a function of groupsize (scale). Peaks of unusually high varianceindicate scales at which the between-group differ-ences are especially large, suggesting that this mayrepresent the scale of natural aggregation orpatchiness of vegetation in the communities(Greig-Smith, 1952, 1979) , he boundary of a scaledomain. Similar techniques may be used toanalyse data gathered on continuous linear tran-sects (Ludwig & Cornelius, 1987). Coincidence inthe variance peaks of different features of thesystem (e.g. plants and soil nutrients , seabirds andtheir prey) may indicate common spatial scalingsand the possibility of direct linkages (Greig-Smith,1979; Schneider & Piatt, 1986).For a series of pointsamples, the average squared difference (semi-variance) or the spatial autocorrelation betweentwo points may be expressed as a function of thedistance between them to estimate the scale ofpatchiness in a system (Sokal & Oden, 1978;Burrough, 1983). Other investigators have usedspectral analysis (Legrende & Demers, 1984) ordimensional analysis (Lewis & Platt, 1982).Obvi-ously, the degree to which any of these methodscan reveal scales of spatial patterning is sensitiveto grain and extent.

Another approach involves the application offractal geometry (Mandelbrot, 1983; Peitgen &Saupe, 1988) to ecological patterns. In manyphysical systems, such as snow crystals, clouds, orflowing fluids , the configuration of patterns differsin detail at different scales but remains statistically'self-similar' if the changes in patternmeasurements are adjusted to the changes inmeasurement scale (Burrough, 1983; Hentschel &Procaccia, 1984; Nittman et a l . , 1985).The way inwhich detail differs with scale is characterized bya fractal dimension, D, which indexes the scale-dependency of the pattern. Statistical self-simila-

rity of patterns (constant D) occurs when pro-cesses at fine scales propagate the patterns tobroader scales, although self-similar patterns mayalso arise from the operation of different butcomplementary processes (Milne, 1988).A changein the fractal dimension of a pattern, on the otherhand, is an indication that different processes orconstraints are dominant. Regions of fractal self-similarity of pattern may therefore representdomains of scale, whereas rapid changes in fractaldimension with small changes in measurementscale (e.g. the landscape patterns analysed byKrummel et a] . , 1987 or Palmer, 1988) mayindicate transitions between domains. There is arelationship between the sizes and movementpatterns of organisms and the fractal dimensionsof their habitats (Morse et al., 1985; Weiss &Murphy, 1988, Wiens & Milne, in press), so it maybe possible to define ecological neighbourhoods ordomains using functions that combine allometryand fractals.

Domains of scale for particular pattern-processcombinations define the boundaries of generali-zations. Findings at a particular scale may beextrapolated to other scales within a domain, butextension across the transition between domainsis difficult because of the instability and chaoticdynamics of the transition zone. Measurementsmade in different scale domains may therefore notbe comparable, and correlations among variablesthat are evident within a domain may disappear orchange sign when the scale is extended beyond thedomain (as in the examples of species associationsgiven on p. ?). Explanations of a pattern in terms oflower-level mechanisms will differ depending onwhether we have reduced to a scale within thesame domain, between adjacent domains, oracross several domains (Fig. 4b). The peril ofreductionism in ecology is not so much the pros-pect that we will be overcome by excessive detailor distracted by local idiosyncrasies but that wewill fail to comprehend the extent of our reductionin relation to the arrangement of domains on ascale spectrum.

Of course, not all phenomena in all systems willexhibit the sort of discontinui ties in scale-dependence necessary to define domains. Somephenomena may change continuously acrossbroad ranges of scale. The boundaries of evenwell-defined domains may not be fixed but mayvary in time, perhaps in relation to variations inresource levels. The notion of domains, like otherconceptual constructs in ecology, may help us tounderstand nature a bit better, but it should notbecome axiomatic.

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394 Developing a 'sc ience of scale' in ecologyJ.A. W i e n s Recently, Meentemeyer & Box (1987) have called

for the development of a 'science of scale' inecology, in which scale is included as an explicitlystated variable in the analysis. I think that we mustgo further, to consider scaling issues as a pr imaryfocus of research efforts. Instead of asking how ourresults vary as a function of scale, we should beginto search for consistent patterns in these scalingeffects. How does heterogeneity affect the size ofscale domains? Are the ecological neighbour-hoods of organisms in high-contrast landscapesscaled differently from those in areas where thepatch boundaries are more gradual? Are thereregularities in the transitions between orderly andseemingly chaotic states of ecological systemswith changes in scale, in a manner akin to tur-bulence in fluid flows? Do selective forces influ-ence how organisms scale their environments, sothat particular life-history traits are related toresponses to particular scales of environmentalpatchiness? If one adjusts for the size differencesbetween organisms such as a beetle and an ante-lope that occur in the same prairie, can they thenbe seen to respond to the patch or fractal structureof the 'landscapes' they occupy in the same way?Are differences between them interpretable interms of differences in their physiology, reproduc-tive biology, or social organization? Does thespatial heterogeneity of soil patterns at differentscales have different effects on how forest eco-systems respond to climatic changes? Is the spreadof disturbances a function of the fractal structure oflandscapes? Does nutrient redistribution amongpatches at fine scales lead to instability or stabilityof nutrient dynamics at broader scales?

To address such questions, we must expand andsharpen the ways we think about scaling. Ourability to detect environmental heterogeneity, forexample, depends on the scale of ourmeasurements, whereas the ability of organisms torespond to such patchiness depends on how theyscale the environment. Proper analysis requiresthat the scale of our measurements and that of theorganisms' responses fall within the same domain.Because of this, however, the 'proper' scale ofinvestigation is usually not immediately apparent.Moreover, the ecological dynamics within adomain are not closed to the influences of factors atfiner or broader domains; they are just different.Ecologists therefore need to adopt a multiscaleperspective (Legrende & Demers, 1984; Clark,1985; Wiens et al . , 1986a; Blondel, 1987; Addicottet al . , 1987).Studies conducted at several scales or

in which grain and extent are systematicallyvaried independently of one another will providea better resolution of domains, of patterns andtheir determinants, and of the interrelationshipsamong scales.

We must also develop scaling theory thatgenerates testable hypotheses. One particularfocus of such theory must be on the linkagesbetween domains of scale. Our ability to arrangescales in hierarchies does not mean that weunderstand how to translate pattern-process rela-tionships across the nonlinear spaces betweendomains of scale, yet we recognize such linkageswhen we speak of the constraining effects ofhierarchical levels on one another or comment onthe openness of ecological systems. Perhaps thereis a small set of algorithms that can serve totranslate across scales. Discovering them requiresthat we first recognize that ecological patterns andprocesses are scale-dependent, that this scale-dependency differs for different ecologicalsystems and for different questions that we ask ofthem, that ecological dynamics and relationshipsmay be well-behaved and orderly within domainsof scale but differ from one domain to another andbecome seemingly chaotic at the boundaries ofthese domains, and that an arbitrary choice ofscales of investigation will do relatively little todefine these scaling relationships.

AcknowledgmentsA Katharine P. Douglass DistinguishedLectureship at Rocky Mountain Biological Labora-tory provided the atmosphere and the impetus tofocus my thinking about scaling, and I thank thestaff of the laboratory for their hospitality and MrsDouglass for endowing the lectureship. PaulDayton, Kim Hammond, Victor Jaramillo, NatashaKotliar, Bruce Milne, Bob O'Neill, Eric Peters,LeRoy Poff, Rick Redak, Bill Reiners, DavidSchimel, Dick Tracy, Monica Tu rner , James Ward,and Greg Zimmerman commented on the manu-script and agreed on almost nothing. Si Levin, BobMay, Bruce Milne, and Bob O'Neill shared un-published manuscripts. Ward Watt provideduseful editorial suggestions. My investigations ofecological scaling are supported by the UnitedStates National Science Foundation (BSR-8805829) and Department of Energy (DE-FGOB-88ER60715).

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