Spatial Scaling In Ecology - WordPress
FunctionalEcology 1989,3, 385-397ESSAY REVIEWSpatial scaling in ecology1J. A. WIENSimposition of a single scale on all of the species inDepartment of Biology and Natural Resourcethe community. Current ecological theories doEcology Laboratory, Colorado State University,little to resolve such debates, because most of theseFort Collins, Colorado 80523, USAtheories are mute on scale - they can be applied atany scale on which the relevant parameters can bemeasured.'The only things that can be universal, in a sense,are scaling things'Recently, however, ecologist studying a widerange of topics have expressed concern about(Mitchell Feigenbaum2)scaling effects (see Dayton & Tegner, 1984; Wienset al., 1986a; Giller & Gee, 1987; Meetenmeyer &IntroductionBox, 1987; Frost et al., 1988; Rosswall, Woodman-Acts in what Hutchinson (1965) has called thenew ecological buzzword.see & Risser, 1988). 'Scale' is rapidly becoming a'ecological theatre' are played out on variousScientists in other disciplines have recognizedscales of space and time. To understand the drama,scaling issues for some time. The very foundationwe must view it on the appropriate scale. Plantof geography is scaling. In the atmospheric andecologists long ago recognized the importance ofearth sciences, the physical processes thatsampling scale in their descriptions of the disper-determine local and global patterns are clearlysion or distribution of species (e.g. Greig-Smith,linked (e.g. Schumm & Lichty, 1965; Clark, 1985;1952). However, many ecologists have behaved asDagan, 1986; Ahnert, 1987) and their importanceif patterns and the processes that produce them areis acknowledged in hierarchies of scale that guideinsensitive to differences in scale and haveresearch and define subdisciplines within thesedesigned their studies with little explicit attentionsciences. Physical and biological oceanographersto scale. Kareiva & Andersen (1988) surveyedoften relate their findings to the spectrum ofnearly 100 field experiments in communityecology and found that half were conducted onplots no larger than 1 m in diameter, despiteconsiderable differences in 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 (Connell, 1980; Roughgarden, 1983) may reflect thephysical processes from circulation patterns inoceanic basins or large gyres to fine-scale eddies orrips (e.g. Haury, McGowan & Wiebe, 1978; 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 phenomena 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 tradition-bound, using quadrats or study plots of aparticular size simply because previous workers1 Adapted from the first Katharine P. Douglass Distinguished Lecutre at the Rocky Mountain Biological385did. Unlike the physical and earth sciences (andmany laboratory disciplines of biology), where ourLaboratory, Gothic, Colorado, 23 July 1987.perceptual range has been extended by tech-2 Quoted in Gleick, 1987, p. 186.nology, few tools have been available to expandThis content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
386 our view of ecological phenomena (but see Platt &J. A. Wiens Sathyendranath, 1988; Gosz, Dahm & Risser,a similar manner, most of the variation in litterdecomposition rates among different species at alocal scale is explained by properties of the litter1988).My thesis in this paper is that scaling issues areand the decomposers, but at broader regionalfundamental to all ecological investigations, asscales climatic variables account for most of thethey are in other sciences. My comments arevariation in decomposition rates (Meentemeyer,focused on spatial scaling, but similar arguments1984).may be made about scaling in time.* Domestic cattle grazing in shortgrass prairieuse elements of local plant communities quiteThe effects of scalenonrandomly on the basis of short-term foragingSome examplestional to their coverage at the broader scale ofThe scale of an investigation may have profoundlandscape mosaics (Senft et al., 1987).effects on the patterns one finds. Consider someexamples:* In hardwood forests of the north-easternUnited States, Least Flycatchers (Empidonaxdecisions, but use of vegetation types is propor-* The distribution of phytoplankton in marinesystems is dominated by horizontal turbulentdiffusion at scales up to roughly 1 km (Platt, 1972;Denman & Platt, 1975). At somewhat broaderminimus Baird & Baird) negatively influence thescales, phytoplankton growth, zooplankton graz-distribution of American Redstart (Setophaga ruti-ing, and vertical mixing override these local effectscilla L.) territories at the scale of 4-ha plots.(Denman & Platt, 1975; Lekan & Wilson, 1978;Regionally, however, these species are positivelyTherriault & Platt, 1981). At scales of 5km,associated (Sherry & Holmes, 1988). Apparentlythe broad-scale influences of habitat selectionoverride the local effects of interspecific competition. Similar scale-dependency has been foundin the habitat relationships of shrubsteppe birds(Wiens, Rotenberry & Van Horne, 1986b), interspecific associations among plant species (e.g.Beals, 1973) or phytoplankton and zooplankton(Carpenter & Kitchell, 1987), and the patterns ofcoexistence of mosses colonizing moose dungphytoplankton patchiness is controlled largely byadvection, eddies, and local upwelling occurringover areas of 1-100 km (Gower, Denman & Holyer,1980; Legrende & Demers, 1984). The same con-trols operate in lakes, although the transitionsoccur at finer scales (Powell 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.(Marino, 1988) or of ants on mangrove islands(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 the 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 al., 1981; Green, Bradbury &Reichelt, 1987; Galzin, 1987).Linkages between physical and 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 same way. However, in many terrestrialenvironments, atmospheric and geological influ-ences may often be obscured by biological interactions (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 interactions* On the basis of experiments conducted at thehave the effect of decoupling systems from directscale of individual leaf surfaces, plant physiolo-physical determination of patterns by introducinggists have concluded that stomatal mechanismstemporal or spatial lags in system dynamics orregulate transpiration, whereas meterologistscreating webs of indirect effects. However, atworking at the broader scale of vegetation havebroader scales, physical processes may dominateconcluded that climate is the principal controlor dissipate these biological effects (Levin, 1989).(Jarvis & McNaughton, 1986; Woodward, 1987). InThere are exceptions: plant distributions on fineThis content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
387 scales may be controlled by edaphic or microtopo-studies of the temporal dynamics of food webs asScale in graphic factors, and vegetation may influencewell (Carpenter, 1988). However, the ways inecology climate at regional scales.which fine-scale patterns propagate to larger scalesmay impose constraints on the broad-scale pat-System openness and the scale of constraintsEcological systems become closed when transferterns as well (Huston, DeAngelis & Post, 1988;Milne, 1988). Ecologists dealing with the temporaldevelopment of systems (e.g. forest insect epidem-rates among adjacent systems approach zero orics: Barbosa & Schultz, 1987; Rykiel et al., 1988)when the differences in process rates betweenrecognize this sensitivity to small differences inadjacent elements are so large that the dynamics offine-scale initial conditions as the effects of his-the elements are effectively decoupled from onetorical events on the subsequent state of theanother. In open systems, transfer rates amongsystem.elements are relatively high, and the dynamics ofpatterns at a given scale are influenced by factors atbroader scales. However, 'openness' is a matter ofscale and of the phenomena considered. At thescale of individual habitat patches in a landscapemosaic, for example, population dynamics may beinfluenced by between-patch dispersal, but at thebroader scale of an island containing that land-scape, emigration may be nil and the populationsclosed. The same island, however, may be openwith regard to atmospheric flows or broad-scaleclimatic influences.The likelihood that measurements made on asystem at a particular scale will reveal somethingabout ecological mechanisms is a function of theopenness of the system. The species diversity of alocal community, for example, is influenced byspeciation and extinction, and by range dynamicsat regional or biogeographic scales (Ricklefs,1987). Changes in population size at a locationmay reflect regional habitat alterations, eventselsewhere in a species' range, or regional abundance and distribution rather than local conditions (May, 1981; Vdisdnen, Jarvinen & Rauhala,1986; Roughgarden, Gaines & Pacala, 1987; Wiens,1989). Habitat selection by individuals may beExtent and grainOur ability to detect patterns is a function of boththe extent and the grain' of an investigation(O'Neill et al., 1986). Extent is the overall areaencompassed by a study, what we often think of(imprecisely) as its scale2 or the population wewish. to describe by sampling. Grain is the size ofthe individual units of observation, the quadrats ofa field ecologist or the sample units of a statistician(Fig. 1). Extent and grain define the upper andlower limits of resolution of a study; they areanalogous to the overall size of a sieve and its meshsize, respectively. Any inferences about scale-dependency in a system are constrained by theextent and grain of investigation - we cannotgeneralize beyond the extent without acceptingthe assumption of scale-independent uniformitarianism of patterns and processes (which we knowto be false), and we cannot detect any elements ofpatterns below the grain. For logistical reasons,expanding the extent of a study usually also entailsenlarging the grain. The enhanced ability to detectbroad-scale patterns carries the cost of a loss ofresolution of fine-scale details.determined not only by characteristics of a givensite but by the densities of populations in otherhabitats over a larger area (O'Connor & Fuller,1985). den Boer (1981) suggested that small localpopulations may frequently suffer extinction, onlyto be reconstituted by emigrants from other areas.The fine-scale demographic instability translatesinto long-term persistence and stability at the scaleof the larger metapopulation (Morrison & Barbosa,1987; DeAngelis & Waterhouse, 1987; Taylor,Variance, equilibrium and predictabilityWhen the scale of measurement of a variable ischanged, the variance of that variable changes.How this happens depends on whether grain orextent is altered. Holding extent constant, anincrease in the grain of measurement generallydecreases spatial variance. In a perfectly homogeneous area (i.e. no spatial autocorrelation among1988).Ecologists generally consider system opennessin the context of how broad-scale processes con-strain finer-scale phenomena. This is one of theprimary messages of hierarchy theory (Allen &1 This use of 'grain differs from that of MacArthur &Levins (1964), who considered grain to be a function ofhow animals exploit resource patchiness inenvironments.2 Note that what is a fine scale to an ecologist is a largeStarr, 1982) and of 'supply-side' ecologyscale to a geographer or cartographer, who express scale(Roughgarden et al., 1987) and it is supported byas a ratio (e.g. 1:250 000 is a smaller scale than 1:50 000).This content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
388J.A.s--Wiens-------/----X0 0-;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 the differences among them are averaged out.sample locations), the log-log plot of varianceincrease in extent will incorporate greater spatialversus grain (or N) has a slope of -1 (Fig. 2a). In aheterogeneity, as a greater variety of patch types orheterogeneous area, this slope will generally belandscape elements is included in the area beingbetween -1 and 0 (O'Neill et al., unpublished),studied (Fig. 1). Between-grain variance increasesalthough the relationship may be curvilinear (Fig.with a broadening of scale (extent) (Fig. 2b).2a; Levin, 1989). As grain increases, a greaterThese considerations also relate to the patternsproportion of the spatial heterogeneity of theof temporal variation or equilibrium of ecologicalsystem is contained within a sample or grain and issystems. Ecologists have often disagreed aboutlost to our resolution, while between-grain hetero-whether or not ecological systems are equilibrialgeneity ( variance) decreases (Fig. 2b). If the(e.g. Wiens, 1984, in press; Chesson & Case, 1986;occurrence of species in quadrats is recordedDeAngelis & Waterhouse, 1987; Sale, 1988).based on a minimal coverage criterion, rare speciesWhether apparent 'equilibrium' or 'nonequili-will be less likely to be recorded as grain sizebrium' is perceived in a system clearly depends onincreases; this effect is more pronounced if thethe scale of observation. Unfortunately, currentspecies are widely scattered in small patches thantheories provide little guidance as to what weif they are highly aggregated (Turner et a]., un-might expect: models in population biology (e.g.published). If the measurement criterion is simplyMay & Oster, 1976; Schaffer, 1984; May, 1989)the presence or absence of species in quadrats,and physics (Gleick, 1987) show that order andhowever, more rare species will be recorded asstability may be derived at broad scales fromgrain increases, and diversity will increase ratherfiner-scale chaos or that fine-scale determinismthan decrease with increasing grain. Exactly howmay produce broad-scale chaos, depending onvariance changes with graiii scale thus deputids oncircumstances. Perhaps ecological systems followthe magnitude and form of the heterogeneity of anprinciples of universality, their final states atarea (Milne, 1988, unpublished; Palmer, 1988) andbroad scales depending on general systemon the type of measurement taken.properties rather than fine-scale details (cf.Spatial variance is also dependent on the extentFeigenbaum, 1979). Brown (1984) has cham-of an investigation. Holding grain constant, anpioned this view, but we still know far too littleThis content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
389atemporal scales of variation (Fig. 3). WithScale inincreased spatial scale, the time scale of importantecologyprocesses also increases because processes operatehomogeneousat slower rates, time lags increase, and indirecteffects become increasingly important (Delcourt,Delcourt & Webb, 1983; Clark, 1985). The dynamics of different ecological phenomena in0heterogeneousdifferent systems, however, follow different trajtories in space and time. An area of a few squaremetres of grassland may be exposed to ungulategrazing for only a few seconds or minutes, whereasthe temporal scale of microtines in the same areamay be minutes to hours and that of soil arthro-pods days to months or years. There are nostandard functions that define the appropriateQ ri scl (lg)anunits for such space-time comparisons in ecology.Moreover, the continuous linear scales we use tomeasure space and time may not be appropriate fororganisms or processes whose dynamics or ratesvary discontinuously (e.g. 'physiological time'Fig. 2. (a) As the grain of samples becomes larger, spatialvariance in the study system as a whole decreases, albeitdifferently for homogeneous and heterogeneous areas.This is related to the within- and between-grain (sample)components of variation. (b) With increasing grain scale,less of the variance is due to differences between samplesand more of the overall variation is included withinsamples (and therefore averaged away). An increase inthe extent of the investigation may increase the beweengrain component of variance by adding new patch typesto the landscape surveyed (Fig. 1), but within-grainvariance is not noticeably affected.associated with diapause in insects; Taylor, 1981).Any predictions of the dynamics of spatiallybroad-scale systems that do not expand the temporal scale are pseudopredictions. The predictionsmay seem to be quite robust because they are madeon a fine time scale relative to the actual dynamicsof the system (Fig. 3), but the mechanistic linkageswill not be seen because the temporal extent of thestudy is too short. It is as if we were to take twospace-timescalingof systemlowabout the scaling behaviour of ecological systemspredictability A"to consider universality as anything other than anintriguing hypothesis.0Predictability and space-time scalingBecause the effects of local heterogeneity are/ high apparentpredictability-- -- ----- - - -----of interestaveraged out at broader scales, ecological patternsoften appear to be more predictable there. Whetheror not the predictions are mechanistically soundSpatial scaleFig. 3. As the spatial scaling of a system increases, so alsodepends on the importance of the fine-scaledoes its temporal scaling, although these space-timedetails. The Lotka-Volterra competition equationsscalings differ for different systems. Studies conductedmay predict competitive exclusion of species thatin fact are able to coexist because of fine-scalespatial heterogeneity that is averaged away (e.g.Moloney, 1988). These predictions are not reallyscale-independent but are instead insensitive toimportant scale-dependent changes.Our ability to predict ecological phenomenadepends on the relationships between spatial andover a long time at fine spatial scales have low predictivecapacity. Investigations located near to the space-timescaling functions have high predictive power. Short-term studies conducted at broad spatial scales generallyhave high apparent predictability (pseudopredictability)because the natural dynamics of the system are so muchlonger than the period of study. Often, ecologists andresource managers have been most interested in makingand testing predictions on relatively short time scales,regardless of the spatial scale of the investigation.This content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
390 snapshots of a forest a few moments apart and uselikely to emerge at broader scales. Because theJ. A. Wiens the first to predict the second. This problem maytime-frame of ecological processes tends to bebe particularly severe in resource managementlonger at broader scales (Fig. 3), long-term investi-disciplines, where the application of policies togations are more often necessary to reveal thelarge areas is often based on very short-termdynamics 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 processesactual dynamics and patterns but may insteadThe characteristics of ecological systems at rela-identify patterns that are artifacts of scale. Becausetively fine scales differ from those at relativelywe are clever at devising explanations of what webroad scales (Table 1), and these differencessee, we may think we understand the system wheninfluence the ways ecologists can study thewe have not even observed it correctly.systems. The possibilities for conducting replicated experiments vary inversely with the scaleDealing with scaleof investigation. The potential for sampling errorsof several kinds are greater at finer scales, althoughScale arbitrarinessthe intensity of sampling is generally lower atThe most common approach to dealing with scalebroader scales. Fine-scale studies may revealgreater detail about the biological mechanismsis to compare patterns among several arbitrarilyunderlying patterns, but generalizations are moreselected points on a scale spectrum. In his analysisTable 1. General characteristics of various attributes of ecological systems and investigations at fine and broad scales ofstudy. 'Fine' and 'broad' are defined relative to the focus of a particular investigation, and will vary between studies.ScaleAttributeFineBroadNumber of variables important in correlations many fewRate of processes or system change fast slowCapacity of system to track short-term environmental variations high lowPotentialforsystemopennesshighlowEffects of individual movements on patterns large s influencing species' distribution resource/habitat barriers,distribution, rorlowgoodlargepoorsmallExperimental manipulations possible thighlowPotential for deriving generalizations low propriate duration of study short longThis content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
391 of reef-fish communities, for example, Galzinpopulations of vagile organisms may be linkedScale in (1987) compared distributions within a singletogether into larger metapopulations and theirecology transect, among several transects on the samedynamics may be less sensitive to the spatialisland, and among five islands. Roughgarden et al.configuration of local habitat patches than more(1987) compared the dynamics of rocky intertidalsedentary species (Morrison & Barbosa, 1987;barnacle communities and assemblages of AnolisFahrig & Paloheimo, 1988; Taylor, 1988). Chroni-lizards on islands at 'small', 'medium', and 'large'cally rare species may follow different dispersalspatial scales. Senft et al. (1987) examined herbi-and scaling functions than persistently commonvore foraging in relation to vegetation patterns atspecies. Consumers that use sparse or clumpedthe scales of the local plant community, theresources are likely to operate at larger spatiallandscape, and the region. Multiscale studies ofscales than those using abundant or uniformlybirds have considered patterns at three to fivedistributed resources, especially if the resourcesscales, and Wiens et al. (1986a) recognized fourare critical rather than substitutable (Tilman,scales of general utility in ecological investi-1982; O'Neill et al., 1988).Such scaling differences among organisms maygations.In these examples, the definition of the differentbe viewed in terms of 'ecological neighbourhoods'scales makes intuitive sense and the analyses(Addicott et al., 1987) or 'ambits' (Hutchinson,reveal the scale-dependency of patterns. Casting1953; Haury et al., 1978); areas that are scaled to athe relationships in the context of hierarchy theoryparticular ecological process, a time period, and an(Allen & Starr, 1982; O'Neill et al., 1986) mayorganism's mobility or activity. The ecologicalfurther sharpen our focus on scaling by emphasiz-neighbourhood of an individual's daily foraginging logical and functional linkages among scales.may be quite different from that of its annualThe scales chosen for analysis are still arbitrary,reproductive activities. The ecological neighbour-however: they tend to reflect hierarchies of spatialhood of the lifetime movements of a tit in a Britishscales that are based on our own perceptions ofwoodland may comprise an area of a few squarenature. Just because these particular scales seemkilometres whereas a raptor may move over an area'right' to us is no assurance that they are appro-of hundreds or thousands of square kilometres; apriate to reef fish, barnacles, anoles, cattle, ornomadic teal of ephemeral desert ponds inbirds. We need nonarbitrary, operational ways ofAustralia may range over the entire continent.defining and detecting scales.Incidence functions (Diamond, 1975) or fragmen-tation response curves (Opdam, Rijsdijk &Hustings, 1985) depict the ecological neighbourDependence on objectives and organismsWhat is an 'appropriate' scale depends in part onhoods of species with respect to colonization andpersistence of populations in areas of differentsizes (scales).the questions one asks. Behavioural ecologists,To some extent, differences in ecological neigh-population ecologists, and ecosystem ecologists,bourhoods among taxa parallel differences in bodyfor example, all probe the relationship betweenmass. This raises the possibility of using allo-resources and consumers, but differences in theirmetric relationships (e.g. Calder, 1984) to predictobjectives lead them to focus their investigationsscaling functions for organisms of different sizes.at different scales (Pulliam & Dunning, 1987).On this basis, for example, one might expect theConservation of key species or habitats may targetscale of the home range of a 20-g lizard to beparticular patches or landscape fragments forapproximately 0 3 ha, whereas that of a 20-g birdmanagement, whereas programmes emphasizingwould be in the order of 4 ha; the parallel scale forspecies richness or complexes of communitiesa 200-g bird would be 92ha. Although such anmay concentrate on preserving broader-scale land-approach ignores variation in allometric relation-scape mosaics (Noss, 1987; Scott et al., 1987).Differences among organisms also affect theships associated with diet, age, season, phylogeny,and a host of other factors, it may still provide anscale of investigation. A staphylinid beetle doesapproximation of organism-dependent scalingnot relate to its environment on the same scales asthat is less arbitrary than those we usually use.a vulture, even though they are both scavengers.Because species differ in the scales of theirWhat is a resource patch to one is not to the other.ecological neighbourhoods, studies of interactionsThe scale on which an oak tree 'perceives' itsamong species may be particularly sensitive toenvironment differs from that of an understoreyscaling. The population dynamics of predatorsbluebell or a seedling oak (Harper, 1977). Localand of their prey, for example, may be influencedThis content downloaded from 128.111.121.42 on Mon, 22 Aug 2016 03:59:40 UTCAll use subject to http://about.jstor.org/terms
392J.A.AWiensimportant elements of components of patternspattern or controls or mechanismsomittedaveragedouttransition domain transition IABcAA4A.studyAAAscalebug , i/P, afineSScalebroadFig. 4. (A) The domain 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 domains are separated by transitions inwhich system dynamics may appear chaotic. If the focus is on phenomena at a particular scale domain, 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 dashed vertical arrows) willexhibit different patterns. (B) If a reductionist app
ecologists long ago recognized the importance of sampling scale in their descriptions of the disper-sion or distribution of species (e.g. Greig-Smith, 1952). However, many ecologists have behaved as if patterns and the processes that produce them are insensitive to differences in scale and have designed their studies with little explicit attention
Measurement and Scaling Techniques Measurement In Research In our daily life we are said to measure when we use some yardstick to determine weight, height, or some other feature of a physical object. We also measure when we judge how well we like a song, a File Size: 216KBPage Count: 23Explore further(PDF) Measurement and Scaling Techniques in Research .www.researchgate.netMeasurement & Scaling Techniques PDF Level Of .www.scribd.comMeasurement and Scaling Techniqueswww.slideshare.netMeasurement and scaling techniques - SlideSharewww.slideshare.netMeasurement & scaling ,Research methodologywww.slideshare.netRecommended to you b
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