ecol 86 815.1965 1966 - Ecology & Evolutionary Biology at ... · ﬁeld internationally. Today, the concepts of landscape ecology (e.g., patch dynamics, metapop-ulation theory, hierarchical

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SPECIAL FEATURE

Landscape Ecology Comes of Age1

Landscape ecology is a growing subdiscipline of ecology. Its main concern is with the studyof large-scale spatial heterogeneity, due to both natural and anthropogenic influences, and theeffects of this heterogeneity on ecological processes and species persistence. Originating fromEuropean traditions approximately 25 years ago, landscape ecology is now a well establishedfield internationally. Today, the concepts of landscape ecology (e.g., patch dynamics, metapop-ulation theory, hierarchical theory) and its tools (e.g., remote sensing, GIS, spatial statistics,spatially explicit modeling) are used widely in most ecological and related disciplines (e.g.,wildlife biology, forestry, conservation, resource management, geography, planning, etc.). As aresult, researchers who would not normally refer to themselves as landscape ecologists, generallyuse the same framework and approaches in their research. The interdisciplinary popularity oflandscape ecology is directly related to the awareness that landscape composition and spatialconfiguration has an undeniable, and all too often irreversible, impact on ecological processesand species survival. Indeed, as humans and other species compete for the same limited resources,landscape spatial patterns are altered, and habitat is lost or fragmented, these changes will alterecological functions and processes.

The thread linking the broadly different scopes of studies in landscape ecology is an explicitconsideration of the effects of spatial components (e.g., patch, boundary, corridor, matrix), spatialresolution (e.g., extent, grain, scaling), and spatial patterns (e.g., patchy, sparse) on ecologicalprocesses. The key research questions in landscape ecology are focused on understanding theinteraction between pattern and process: How does spatial heterogeneity affect ecological pro-cesses and species movements? How can we identify the scale(s) at which to study ecologicalprocesses? How do ecological processes transfer between and across scales? How can we accountfor uncertainty through space and time? Before these questions can be fully answered, however,several conceptual, statistical, and modeling challenges still need to be addressed. Within thescope of this Special Feature, the breadth of research in landscape ecology in the North Americantradition is reviewed by Turner. Much of this research deals with understanding pattern–processrelationships. The subsequent papers address the conceptual and methodological challenges anddevelopments needed to grasp the interaction between patterns and processes.

The first challenge is conceptual and is at the heart of landscape ecology: How should wedefine and quantify spatial heterogeneity given that it is scale dependent (Wagner and Fortin)?The question is therefore at which scale, or range of scales, should pattern and process be examinedfor a given question, species, or system under study. Hence, although the concepts of landscapeecology are generally adapted to different types of systems, their relevance depends on the matchbetween the scale of spatial pattern and the process under investigation. Furthermore, natural andanthropogenic disturbances operate at more than one spatial and temporal scale, generating frag-mented landscapes that can have a detrimental impact on biodiversity and species conservation.It is therefore important to understand and quantify how landscape spatial heterogeneity affectsanimal movement. As each species perceives landscape spatial patterns differently (i.e., landscapesare fragmented for some but not for other species due to different dispersal abilities, habitat, andfood requirements), knowledge about species behavioral responses to landscape spatial hetero-geneity is needed. Hence, in order to effectively implement conservation goals, such as speciespersistence in fragmented landscapes, structural and functional connectivity needs to be assessed.Belisle provides a perspective on this new emerging area integrating behavior into traditionallandscape ecology.

1 Reprints of this 53-page Special Feature are available for $8.00 each, either as PDF files or as hard copy.Prepayment is required. Order reprints from the Ecological Society of America, Attention: Reprint Department,1707 H Street, N.W., Suite 400, Washington, D.C. 20006.

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When trying to evaluate the long-term impacts of the synergy between disturbance regimesand policy changes at the landscape level, new challenges arise. In effect, researchers developingspatially explicit models are faced with trade-offs between using quantitative data over smallareas or qualitative data over larger areas. The challenge is therefore to determine which processesshould, and can, be translated from one scale to another. Urban shows how meta-models andgraph theory can be used to address these conceptual and methodological issues.

As landscapes are dynamic systems, the population persistence of many species is uncertain,and yet decisions on resource management must be made in spite of this uncertainty. Uncertaintyis mainly related to the quality of spatial data that are increasingly used as input layers in species–habitat distribution models. Furthermore, errors can accumulate through the process of overlayingand integrating these input maps. In addition to data sampling issues, uncertainty can result froman inappropriate formulation of the system or scale by the models themselves. To facilitateinformed conservation decisions, therefore, the various types and amounts of uncertainty needto be identified, understood, and modeled. Burgman et al. provide an overview of uncertaintyand show how to account for uncertainty in developing and applying predictive models forconservation purposes.

We expect that insights and new research directions emerging from this series of papers willbenefit not only the field of landscape ecology, but all connected and overlapping ecologicaldisciplines that recognize the importance of spatial considerations in their research.

—MARIE-JOSEE FORTIN

Guest EditorUniversity of Toronto

—ANURAG A. AGRAWAL

Special Features Editor

Key words: animal movement; graph theory; landscape connectivity; meta-models; pattern–process;predictive models; scale; spatial statistics; uncertainty.

q 2005 by the Ecological Society of America

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Ecology, 86(8), 2005, pp. 1967–1974q 2005 by the Ecological Society of America

LANDSCAPE ECOLOGY IN NORTH AMERICA:PAST, PRESENT, AND FUTURE

MONICA G. TURNER1

Department of Zoology, Birge Hall, University of Wisconsin, Madison, Wisconsin 53706 USA

Abstract. Landscape ecology offers a spatially explicit perspective on the relationshipsbetween ecological patterns and processes that can be applied across a range of scales.Concepts derived from landscape ecology now permeate ecological research across mostlevels of ecological organization and many scales. Landscape ecology developed rapidlyafter ideas that originated in Europe were introduced to scientists in North America. Keyresearch questions put forth in the early 1980s that catalyzed landscape-level researchfocused on the formative processes that produce spatial pattern; effects of spatial hetero-geneity on the spread of disturbance and fluxes of organisms, material, and energy; andpotential applications of landscape ecology in natural resource management. This articledescribes the development of landscape ecology in North America, discusses current ques-tions and new insights that have emerged, and comments on future directions that are likelyto produce new ecological insights. Ecology faces a broad array of challenging questionsthat require a plurality of approaches and creative insights. Landscape ecology shouldcontinue to push the limits of understanding of the reciprocal interactions between spatialpatterns and ecological processes and seek opportunities to test the generality of its conceptsacross systems and scales.

Key words: landscape context; landscape ecology; scale; spatial heterogeneity; spatial pattern.

INTRODUCTION

Concepts derived from landscape ecology now per-meate ecological research across most levels of orga-nization and many scales; indeed, perhaps the wide-spread infusion of a landscape perspective in ecologyindicates maturation of this field in North America.Landscape ecological research has contributed to sub-stantial advances in understanding the causes and eco-logical consequences of spatial heterogeneity and howrelationships between pattern and process vary withscale, and it has offered new perspectives on the func-tion and management of both natural and human-dom-inated landscapes. Methods derived from landscapeecology receive widespread use, and the potential im-portance of spatial heterogeneity is now regularly ac-knowledged in ecology. Landscape ecology has be-come mainstream, in sharp contrast to the mid 1980s,when the ideas were new and broad-scale studies werenot widely accepted. In this article, I consider the past,present, and future of landscape ecology in NorthAmerica, focusing on major research themes, new in-sights that have emerged, and both current and futurequestions. I focus on the interface between ecologicalpatterns and processes, and there is another body ofresearch, not covered in this essay, that directly ad-

Manuscript received 1 June 2004; revised 23 September 2004;accepted 27 December 2004; final version received 1 December2004. Corresponding Editor: M. Fortin. For reprints of this Spe-cial Feature, see footnote 1, p. 1965.

1 E-mail: [email protected]

dresses landscape and urban planning (e.g., Nassauer1997).

Landscape ecology has been defined variously (Ris-ser et al. 1984, Urban et al. 1987, Turner 1989, Pickettand Cadenasso 1995, Turner et al. 2001), but sharedamong definitions is the explicit focus on the impor-tance of spatial heterogeneity for ecological processes.Often, but not always, landscape ecology is also char-acterized by a focus on spatial extents larger than thosetraditionally studied in ecology. The scale-independentfocus of landscape ecology on the causes and conse-quences of spatial heterogeneity is distinct from howlandscape ecology is sometimes defined (e.g., Zonne-veld 1990, Bastian 2001, Opdam et al. 2001). Althoughthese two foci are not mutually exclusive, the differentperspectives have created some confusion about whatconstitutes landscape ecology. Some researchers alsoconsider the terrestrial terminology limiting (e.g., Re-iners and Driese 2001), but landscape ecology is ap-plied in aquatic and marine systems (e.g., Steele 1989,Bell et al. 1999, Teixido et al. 2002, Ward et al. 2002).The generality of the landscape perspective and its ap-plication across a wide range of systems and scales hascertainly given it wider applicability within ecology,and studies focused on larger areas have contributedto new understanding of ecological dynamics.

THE PAST: DEVELOPMENT OF LANDSCAPE ECOLOGY

IN NORTH AMERICA

‘‘Landscape ecology’’ was coined by the Germanbiogeographer, Carl Troll (1939), and the field subse-

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1968 MONICA G. TURNER Ecology, Vol. 86, No. 8

FIG. 1. Annual number of publications (1982–2003) fromthe ISI Web of Science database that included either ‘‘land-scape ecology’’ (diamonds) or ‘‘landscape AND ecology’’(circles) in their title, abstract, or key words. The search wasconducted on 7 April 2004 using the science database onlyand including all document types. Trendlines were fit in Mi-crosoft Excel.

quently developed in central Europe in close associa-tion with land planning (Schreiber 1990). However, theterm was largely absent from North American literatureuntil the 1980s when several ecologists from NorthAmerica attended European meetings focused on land-scape ecology, some influential publications appeared,and a workshop concentrated thinking on the emergingdiscipline. A lexicon and framework for consideringspatial patterns were introduced by Forman and Godron(1981) and developed further in their subsequent book(Forman and Godron 1986). A conceptual frameworkfor considering the potential influences of patch con-figuration and boundary permeability on lateral fluxeswas proposed by Wiens et al. (1985). Naveh and Lie-berman (1984) promoted the concept of the landscapeas a holistic, cybernetic system with a strong emphasison integrating humans into understanding of landscapefunction. In his study of the natural fire regime in Yel-lowstone National Park, Romme (1982) extended con-cepts of species diversity to successional stages in thelandscape, demonstrating nonequilibrium in a fire-dominated system. A 1982 workshop funded by theNational Science Foundation brought North Americanecologists together to explore the purview and potentialof landscape ecology and to set out an initial researchagenda (Risser et al. 1984). The first annual U.S. land-scape ecology symposium was held in 1986 and fo-cused on interactions between landscape heterogeneityand disturbance (Turner 1987); the U.S. chapter of theInternational Association for Landscape Ecology (US-IALE) was also formed at this meeting. The scope oflandscape ecology as perceived by North Americanecologists was further elaborated by Urban et al. (1987)and Turner (1989).

The new ideas about spatial heterogeneity found areceptive audience in North America, and landscapeecology began a period of rapid development. Publi-cations indexed by the Institute for Scientific Infor-mation illustrate this trend; landscape ecology publi-cations were scant throughout the 1980s (fewer than10 per year through 1991) but have increased dramat-ically since the early 1990s (Fig. 1). Several factorscontributed to this acceleration (Turner et al. 2001).First, important environmental challenges and land-management questions (e.g., global climate change,habitat fragmentation, nonpoint source pollution, cu-mulative effects, land-use change) were increasinglyposed at broad scales, yet ecological understanding wasbased largely on mechanistic studies in small homo-geneous areas over relatively short time periods. Otherconceptual developments were also spurring new think-ing in ecology. For example, the importance of naturaldisturbances (e.g., Romme 1982, Turner 1987) andpatch dynamics (Pickett and White 1985) for ecosystemstructure and function was increasingly acknowledged.Equilibrium theory was being critically questioned andconsidered more broadly (Wu and Loucks 1995, Perry2002), and the temporal scale of ecological studies was

being extended through new research programs, suchas the National Science Foundation’s Long-term Eco-logical Research (LTER) Program (Hobbie et al. 2003).Ecologists were anxious to develop and explore newapproaches that might inform broad-scale issues.

Second, the importance of scale and the developmentof conceptual frameworks for understanding scale de-pendence (e.g., Levin 1992) prompted ecologists to ex-amine critically the effect of scale and whether under-standing could be translated from one scale to another.The necessity of studies being scaled appropriately forthe organism or process of interest was recognized (Ad-icott et al. 1987, Wiens 1989), and Levin (1992) iden-tified the problem of relating phenomena across scalesas the central problem in biology and all of science.Understanding scale has remained closely associatedwith North American landscape ecology (Miller et al.2004).

Third, technological advances in computer science,remote sensing, and geographic information systems(GIS) made it possible and affordable to obtain, ma-nipulate and analyze spatial data during the 1980s. Al-though I do not suggest that the tools drove the science,the increased technical capacity for handling spatialdata and models certainly facilitated developments inlandscape ecology. Ecologists were able to look at theworld through a new lens and to address questions thatpreviously could not have been answered. Collectively,the new questions, technologies and attention to scalefostered the early development of landscape ecology.

The early North American landscape studies sharedseveral common themes, including the focus on scalementioned above. The role of humans in generatinglandscape patterns was an early theme, and understand-ing and predicting human land-use patterns receivedconsiderable attention (e.g., Burgess and Sharpe 1981).There also was an understandable initial emphasis onthe development and testing landscape metrics because

August 2005 1969LANDSCAPE ECOLOGY COMES OF AGE

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studying the causes and ecological implications of spa-tial heterogeneity required quantification of spatial pat-tern. The period of quantitative methods developmentcoincided with the advent of geographic informationsystems (GIS), but GIS was neither standardized norwidely available to ecologists; most landscape ecolo-gists programmed their spatial analyses directly. Land-scape ecologists were also developing methods basedon spatial statistics to understand how the magnitudeand scale of spatial autocorrelation in a variable ofinterest differed among landscapes (e.g., Legendre andFortin 1989). Thus, pattern analysis was a commontheme of early landscape studies in North America.

North American landscape ecological studies em-ployed (and still use) an array of approaches becausetraditional experimental approaches are often impos-sible to conduct at broad scales. Researchers studiedthe effects of spatial heterogeneity produced by naturalevents (e.g., disturbances) and management actions(e.g., forest harvesting; Sirois and Payette 1991, Mlad-enoff et al. 1993). Retrospective studies using dendro-chronology or paleoecological methods revealed howlandscapes change in both space and time (e.g., Romme1982, Delcourt and Delcourt 1988, Arsenault and Pay-ette 1997). Existing variability in landscapes was usedto examine the effects of habitat configuration on eco-logical responses, often in concert with simulationmodels (e.g., Wegener and Merriam 1979, Hendersonet al. 1985). Experimental model systems (EMS) inwhich small landscapes could be replicated and theresponses of small-bodied organisms to alternative spa-tial structures were evaluated were also implemented(Wiens et al. 1997). Spatially explicit simulation mod-els, in which a much wider range of conditions couldbe explored, were developed (Baker 1989, Sklar andCostanza 1991, Dunning et al. 1992). These variedmodes of inquiry also mirror the four approaches thatadvance ecological understanding identified by Car-penter (1998): theory and modeling, comparative stud-ies, experimental studies and long-term monitoring.

Despite its rapid growth, landscape ecology encoun-tered resistance from some ecologists in North Amer-ica. Skepticism focused on the questionable rigor ofbroad-scale studies, the challenges (and even rele-vance) of spatially explicit hypothesis testing, issuesof pseudo-replication, and a perception that patternanalysis was substituting for science. Indeed, some ofthese criticisms reflect true challenges that have beenmet with varying success. The emphasis on quantitativemethods development was sometimes esoteric and notalways linked to ecological questions. True replicationwas and still remains problematic for broad-scale stud-ies. The role of spatial heterogeneity may sometimeshave been overstated; clearly, it doesn’t matter for ev-ery ecological study and should be ignored when ap-propriate. However, progress has been made despitethese limits.

THE PRESENT: THE FOCUS OF LANDSCAPE ECOLOGY

IN NORTH AMERICA

What are the current foci of landscape ecology inNorth America? Landscape ecology studies are nowubiquitous, characterized by a diverse set of basic andapplied questions and studies conducted across a widerange of grains and extents. Many quantitative toolsare now readily available for characterizing both dis-crete and continuous representations of spatial hetero-geneity (McGarigal and Marks 1995, Gustafson 1998);current research that includes spatial pattern analysisemphasizes appropriate application of methods (e.g.,Dorner et al. 2002, Fortin et al. 2003) and how eco-logical responses or processes are related to pattern(e.g., Jones et al. 2001, Tischendorf 2001). In this sec-tion, I identify four general lines of research in con-temporary landscape ecology, purposefully grouped tocut across traditional levels of ecological organizationand to emphasize the broader conceptual questions. In-terested readers might also consult Wu and Hobbs(2002).

Conditions under which spatial pattern must beconsidered: when does space matter?

Although it is seldom stated so simply, this basicquestion lies at the heart of many studies that test forthe effect of spatial composition or configuration onsome ecological response, be it species presence orabundance, the spread of a disturbance or pest, or thedelivery of nutrients from a source location to a sinklocation. Including spatial heterogeneity as either a de-pendent or independent variable clearly adds a level ofcomplexity to ecological studies. Therefore, knowingwhen space is going to be influential and when it canbe safely ignored remains fundamentally important,both practically and conceptually.

A wide range of theoretical and empirical studies hascontributed to current understanding of when spacematters. Theoretical studies using neutral landscapemodels have demonstrated that the influence of spatialconfiguration varies with habitat abundance (With andKing 1997) but may be most important when habitatis of intermediate abundance. Recent studies of theeffects of habitat fragmentation suggest that the effectsof spatial configuration may be secondary to the effectsof habitat loss (Fahrig and Nuttle, in press). For pop-ulations, Fahrig and Nuttle (in press) suggested thatconfiguration will be important if it influences move-ments of organisms among patches and among-patchmovements have a large effect on population survival.Understanding when landscape configuration influenc-es populations remains important for responding tohabitat fragmentation (McGarigal and Cushman 2002).

A variety of studies have explored interactions be-tween spatial pattern and disturbance, focusing onwhether heterogeneity enhances or retards the spreadof disturbance (Turner et al. 1989), and whether some

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landscape positions are more or less susceptible to dis-turbance than others. Landscape position or spatial het-erogeneity appears to be important when disturbancehas a distinct directionality or locational specificitysuch that some locations are more exposed than others(e.g., Jules et al. 2002). If disturbance has no direc-tionality, landscape position may not have an effect(e.g., Frelich and Lorimer 1991). Current research isextending this research line to consider the interactionsof multiple disturbances (e.g., Paine et al. 1998, Bebiet al. 2003).

The effect of spatial pattern on lateral fluxes of mat-ter has also received considerable attention, particu-larly with regard to the movement of nitrogen and phos-phorus from terrestrial land covers to surface waters(e.g., Peterjohn and Correll 1984, Soranno et al. 1996).However, whether just the composition of the uplands(i.e., the amount of different land uses) matters, or ifthe spatial configuration is also important, remains un-resolved because studies have produced conflicting re-sults. Fluxes that move from aquatic to terrestrial sys-tems (e.g., Willson et al. 1998) or between land-covertypes (e.g., Seagle 2003) may also be very important.

The influence of landscape context and the scale atwhich characteristics of the surrounding landscape in-fluence a local response is another way in which theimportance of spatial pattern is considered. Effects oflandscape context have been demonstrated for a varietyof taxa (Mazerolle and Villard 1999) and also for someecosystem processes (e.g., Gergel et al. 1999). Overall,contemporary landscape research continues to probethe conditions under which spatial pattern must be con-sidered for a wide array of ecological responses.

Understanding spatial dynamics:the linkage of space and time

Understanding and predicting trajectories of land-scape change is another important focus of contem-porary research in landscape ecology. Paleoecologicalstudies have revealed the dynamic nature of landscapesover long periods. The distributions and abundances ofspecies changed dramatically with climate throughoutthe Holocene, and some contemporary species assem-blages have no past analogs. Major disturbance events(e.g., fires) also catalyzed past shifts in dominant spe-cies (Sirois and Payette 1991), and disturbances con-tinue to produce dramatic changes in contemporarylandscapes (e.g., Foster et al. 1998). North Americanlandscapes also changed profoundly in response toEuro-American settlement. Landscape ecologists seekto understand and predict changes in landscape struc-ture and function through time in response to a varietyof drivers including climate, natural disturbances andland use.

Studies of how landscapes change through time inresponse to natural disturbances have included man-agement implications of historical range of variability(Landres et al. 1999) and extension of equilibrium con-

cepts. Considerable attention has focused on the po-tential of natural disturbance regimes serving as a mod-el for the spatial pattern and timing of human distur-bances (e.g., Hunter 1993). The scale-dependent natureof equilibrium (Perry 2002) was elucidated—equilib-rium conditions may be observed at some scales ofspace and time, but nonequilibrium conditions are alsocommon and may even be prevalent.

Explaining and predicting patterns of land-usechange is an important topic that links space and timeand also underscores the role interdisciplinary studies.For example, in forested landscapes of the interior Co-lumbia Basin, the social system constrained the influ-ence of the biophysical factors on landscape changes(Black et al. 2003). Land ownership systems, economicmarket structure, and cultural value systems dominatedchanges in this landscape (Black et al. 2003). Under-standing the spatiotemporal dynamics of many land-scapes requires understanding the drivers of humanland use.

The potential importance of historical legacies forcontemporary species assemblages and landscape func-tion is another way in which spatial and temporal dy-namics are linked; the past continues to influence thepresent. Natural disturbances can produce enduringlegacies of physical and biological structure that influ-ence ecosystem processes for decades or centuries (e.g.,Foster et al. 1998). Similarly, patterns of historical landuse can influence contemporary forest composition andecosystem processes for a very long time (Dupouey etal. 2002). Understanding how landscapes changethrough time, including the long-term legacies of pastdisturbance or land use, is an important line of inquiryin contemporary landscape ecology.

Nonlinearities and thresholds:expecting the unexpected

Understanding nonlinear dynamics or thresholds andhow they influence landscape function is important be-cause outcomes may be unexpected (Groffman et al.,in press). An ecological threshold is the point at whichthere is an abrupt change in an ecosystem quality, prop-erty or phenomenon, or where small changes in anenvironmental driver produce large responses in theecosystem (Groffman et al., in press). Landscape anal-yses based on percolation theory and neutral landscapemodels (With and King 1997) have suggested the im-portance of critical thresholds in habitat abundanceabove or below which ecological processes are quali-tatively different. The numerical value of criticalthresholds depends on the particular process and land-scape, but the occurrence of the threshold does not(With and King 1997). Below the thresholds, patchesare small and isolated; above the threshold, patches arelarge and well connected. Changes in habitat abun-dance that occur near the critical threshold may producelarge, surprising changes in the system because thehabitat can suddenly become connected or discon-


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nected. Empirical studies support the existence of crit-ical thresholds in habitat abundance for bird and mam-mal populations (Andren 1994). The spatial spread ofdisturbances such as fire may also exhibit thresholdresponses related to habitat abundance (Turner et al.1989).

Thresholds can occur in a range of variables relatedto landscape pattern. For example, some organisms re-quire patches of a minimum size for persistence, al-though the generality of this has been debated (Bowersand Matter 1997). Patch size and shape influence theability of animals to persist in a landscape and mayshow threshold effects (Lindenmeyer et al. 1999), andpatch size influences nutrient dynamics in nonlinearways (Ludwig et al. 2000). Thresholds for land-useindicators (impervious surface, agricultural land use,lake shore development) and ecosystem services (fishcommunities, coarse woody debris, stream nitrate con-centrations) have also been suggested. For example,Paul and Meyer (2001) suggested a threshold of 10–20% impervious surface for maintaining stream eco-system integrity in developed watersheds, and activetests of this metric are underway. Not exceeding athreshold of 50% agricultural land in a watershed hasbeen suggested as critical for the maintenance of fishcommunities in Wisconsin streams (Wang et al. 1997).When considered in the context of landscapes changingthrough time, the identification of nonlinear relation-ships and threshold dynamics takes on particular im-portance. Identifying nonlinearites related to spatialpatterns and ecological responses remains a consistenttheme in landscape studies.

Planning, managing, and restoring landscapes

Demand for the scientific underpinnings of managinglandscapes and incorporating the consequences of spa-tial heterogeneity into land management is substantial(Perera et al. 2000, Liu and Taylor 2002). As the eco-logical science that focuses on spatial dynamics, land-scape ecology has been part of the discussions of howalternative spatial arrangements of land cover or landuse may influence ecological functions. Identifying anoptimal landscape configuration may be impossible, asthe optimal arrangement will depend on specific man-agement objectives that may conflict with one another.Nonetheless, land management decisions are made, andlandscape ecology should be at the table. Landscapestudies have quantified relationships between land-scape features and changes in land use and land cover(e.g., Black et al. 2003), and recent studies have ex-plored the ecological implications of low-density res-idential development that may be ‘‘under the canopy’’(e.g., Miller et al. 2003). Residential development hasreplaced agricultural and extractive uses in many ruralareas (Hansen et al. 2002), yet the ecological impli-cations of such development are poorly understood.

Landscape studies have also addressed questions ofecological restoration (e.g., Palik et al. 2000). Appli-

cation of a landscape perspective augments restorationapproaches based on community composition by con-sidering dynamic reference states and the spatial con-figuration of communities. Without this perspective,restoration may lack the spatial and historical contextneeded for success. Landscape ecology can and shouldcontribute to land planning, management, and resto-ration.

THE FUTURE: WHAT LIES AHEAD?

Landscape ecology has already influenced NorthAmerican ecology; explicitly accounting for spatialpattern and recognizing the influences of scale are like-ly here to stay. An informed decision about whether ornot to consider spatial heterogeneity is now pro forma.Contemporary landscape ecology studies are conductedover a wide range of spatial scales, not only in largeareas. Terrestrial studies predominate, but landscapeecology studies are not limited to the land. The inter-play between models, theory and empirical data is ahallmark of landscape ecology in North America.Wherein lie the key future research questions and di-rections? Here, I suggest several areas that are not yetwell developed in landscape ecology and where theremay be opportunities for substantial progress.

Broader representations of spatial heterogeneity

How spatial heterogeneity is conceptualized and thenput into practice needs to be broadened. Categoricalmaps and point data are the most common represen-tations of spatial heterogeneity (Gustafson 1998). Dis-crete space has often been used as a simplifying as-sumption, and indeed, much has been learned from this.However, many variables of ecological interest are con-tinuous (e.g., ecosystem process rates), and gradientsabound in many of the variables used as predictors(e.g., leaf area index). Habitat suitability for a partic-ular organism is another attribute that can vary con-tinuously. The conceptual framework for understand-ing spatial heterogeneity must be extended beyond apatch-based view to include both discrete and contin-uous representations of space, and furthermore, to ac-count for their changes through time.

Spatial heterogeneity in ecosystem function

Understanding the patterns, causes, and consequenc-es of spatial heterogeneity for ecosystem function is aresearch frontier in both landscape ecology and eco-system ecology (Lovett et al. 2005). Progress at theinterface of ecosystem and landscape ecology has beenrelatively slow compared to other areas, yet spatialfluxes of matter, energy and information influence thefunctioning of individual ecosystems and heteroge-neous landscapes. Spatial heterogeneity can affect boththe drivers of ecosystem processes, which are oftenmultivariate, as well as in the pools or flux rates thatare often response variables. Integrating the under-standing gained from ecosystem and landscape ecology

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would enhance progress in both disciplines while gen-erating new insights into how landscapes function.

Spatial cascades

The influence of spatial heterogeneity on interactionsamong species (rather than on individual populations)also represents an important future research direction.Much of the research on how spatial pattern affectsorganisms focuses on how variables like patch size,edge-to-area ratio, and interpatch distances influencepopulation presence or abundance, largely through ef-fects on key demographic parameters. However, somechanges in landscape patterns may have cascading in-fluences among species (Tallmon et al. 2003), and morework is needed on how spatial heterogeneity affectsspecies interactions.

Integrating new technologies and fields

New technologies and analytical capabilities offerconsiderable promise for expanding the empirical foun-dation of landscape ecology. For example, molecularpopulation genetics has been integrated with landscapeecology to explain observed spatial genetic patterns(e.g., clines, isolation by distance, genetic boundariesto gene flow, metapopulations) with landscape vari-ables (Manel et al. 2003). For mobile animals, the useof radiocollars with on-board global positioning sys-tems (GPS) is providing new data on movement andhabitat use at finer spatial and temporal resolution (e.g.,Johnson et al. 2002). The growing array of earth ob-serving sensors offers the ability to sense more func-tional response variables for both the land surface andvegetation (e.g., canopy foliar nitrogen concentrations;Smith et al. 2002). These methods have great promisefor extending landscape studies to three dimensions,e.g., by incorporating vertical structure in terrestrialand aquatic systems. New sampling designs derivedfrom spatial statistics are being used to sample acrossmultiple scales, providing new insights about spatialvariation (e.g., Burrows et al. 2002, Fraterrigo et al.2005). Spatial extrapolations based on simulation orstatistical models can be used as powerful tests of themechanisms underlying relationships between patternand process (Miller et al. 2004). While all these ad-vancements hold great promise, it is nonetheless im-portant to remember that spatially extensive measure-ment of many ecological processes remains a formi-dable challenge.

Conclusion

Landscape ecology has influenced how ecologistsview the world; its central theme of understanding thecauses and ecological consequences of spatial hetero-geneity has been widely embraced. Should landscapeecology of the future retain its distinctive identity?Does landscape ecology have sufficient theory and nov-el ideas to maintain separateness? Or, is landscape ecol-ogy an interdisciplinary or transdisciplinary science?

I suggest that a landscape ecological perspective hasbrought a unique set of questions and approaches toecology, and as such, it has developed an identity thatis useful to maintain. However, landscape ecologicalconcepts and methods are now used regularly in manyecological subdisciplines, and perhaps this widespreadincorporation of landscape ecology concepts and meth-ods should be viewed as a mark of success irrespectiveof whether the ‘‘landscape ecology’’ moniker is in-voked. Landscape ecology should continue to push thelimits of understanding of the reciprocal interactionsbetween spatial patterns and ecological processes andseek opportunities to test the generality of its conceptsacross systems and scales.

ACKNOWLEDGMENTS

I thank the guest editors of this Special Feature for theopportunity to prepare the manuscript. Constructive reviewsby Dean Anderson, Dan Kashian, Kris Metzger, David Mlad-enoff, Erica Smithwick, and two anonymous reviewers im-proved the paper. Ideas developed in this paper were basedon research funded by the National Science Foundation(LTER, Ecology, Ecosystems, and Biocomplexity programs),the Environmental Protection Agency (STAR program), andthe Andrew W. Mellon Foundation.

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SPATIAL ANALYSIS OF LANDSCAPES: CONCEPTS AND STATISTICS

HELENE H. WAGNER1,3 AND MARIE-JOSEE FORTIN2

1WSL Swiss Federal Research Institute, 8903 Birmensdorf Switzerland2Department of Zoology, University of Toronto, Ontario M5S 3G5 Canada

Abstract. Species patchiness implies that nearby observations of species abundancetend to be similar or that individual conspecific organisms are more closely spaced thanby random chance. This can be caused either by the positive spatial autocorrelation amongthe locations of individual organisms due to ecological spatial processes (e.g., speciesdispersal, competition for space and resources) or by spatial dependence due to (positiveor negative) species responses to underlying environmental conditions. Both forms of spatialstructure pose problems for statistical analysis, as spatial autocorrelation in the residualsviolates the assumption of independent observations, while environmental heterogeneityrestricts the comparability of replicates. In this paper, we discuss how spatial structure dueto ecological spatial processes and spatial dependence affects spatial statistics, landscapemetrics, and statistical modeling of the species–environment correlation. For instance, whilespatial statistics can quantify spatial pattern due to an endogeneous spatial process, thesemethods are severely affected by landscape environmental heterogeneity. Therefore, sta-tistical models of species response to the environment not only need to accommodate spatialstructure, but need to distinguish between components due to exogeneous and endogeneousprocesses rather than discarding all spatial variance. To discriminate between differentcomponents of spatial structure, we suggest using (multivariate) spatial analysis of residualsor delineating the spatial realms of a stationary spatial process using boundary detectionalgorithms. We end by identifying conceptual and statistical challenges that need to beaddressed for adequate spatial analysis of landscapes.

Key words: autocorrelation; landscape metrics; multivariate analysis; multiscale ordination;spatial analysis; spatial regression; stationarity.

INTRODUCTION

Ecology has seen a paradigm shift from the as-sumption of homogeneity to the recognition of hetero-geneity as a key for understanding the complexity ofnature (Wiens 1989). The explicit consideration of spa-tial structure and spatiotemporal interaction of pro-cesses in ecological research is the main contributionof landscape ecology to this paradigm shift. Acknowl-edging the importance of spatial pattern and scale haschanged the way ecological studies are designed andanalyzed, and has provided new insights about ecolog-ical processes (Allen and Hoekstra 1992). Most eco-logical processes are inherently spatial as they operatebetween neighboring units (Levin 1992). Processes arealso constrained by environmental conditions varyingin space and time and by the local interaction with otherprocesses, resulting in interwoven patterns at multiplespatial and temporal scales.

As the primary concern of ecology is the identifi-cation and understanding of ecological processes, com-plicating factors such as spatial heterogeneity were atfirst excluded from the conceptual framework of anal-

Manuscript received 3 June 2004; revised 26 August 2004;accepted 4 October 2004. Corresponding Editor: A. A. Agrawal.For reprints of this Special Feature, see footnote 1, p. 1965.


ysis (McIntosh 1991). By doing so, ecological studiescould assume homogeneity, permitting the incorpora-tion of environmental variation as a treatment or tocontrol for known relationships using covariates. Forinstance, the effects of different levels of an environ-mental factor can be tested in an experimental settingusing ANOVA-type analyses or analyzed along exist-ing gradients using regression-type analyses. Hence byassuming that the study area is locally homogeneouswith respect to that factor in space and time, each ex-perimental plot, or sampling unit, is attributed to asingle factor level and the neighborhood context of theplot or sampling unit does not matter (Fig. 1A). Incontrast, landscape ecology assumes that the neigh-borhood context affects the ecological processes withina plot and the interaction between plots (Fig. 1B). Afurther complication is that environmental heteroge-neity may occur at any spatial scale, and site conditionsmay vary in time.

The patchiness of species, and other ecological re-sponse variables, forms another type of spatial hetero-geneity that ecologists need to consider (Fig. 2). Patch-iness, created by ecological spatial processes such ascompetitive interactions or dispersal, violates the as-sumption of parametric tests that the residual errors areindependent (Legendre 1993: Fig. 1A). Indeed, patch-iness induces autocorrelation in the error structure of

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1976 HELENE H. WAGNER AND MARIE-JOSEE FORTIN Ecology, Vol. 86, No. 8

FIG. 1. Schematic representations of theconceptual framework of (A) ecological and (B)landscape ecological analysis. In the ecologicalframework, the ecological process (uppergraph) observed in a set of plots (white squares)depends on the level of the environmental factor(polygons in lower graph) measured at the plotlocation. Patches/plots are internally homoge-neous, plot context does not matter, and obser-vations are spatially independent. In the land-scape ecological framework, patches/plots maybe internally heterogeneous, plot context mayaffect local processes, and observations may notbe independent due to spatial interaction be-tween local processes.

an ANOVA or regression-type model (Fig. 1B), whichreduces the degrees of freedom of the associated sta-tistical tests (Dale and Fortin 2002).

The growing acceptance of the heterogeneous natureof ecological systems requires adapting ecological the-ory and methods to accommodate for ‘‘heterogeneity.’’There is, however, little consensus on the exact mean-ing of the term (Kolasa and Rollo 1991, Li and Reyn-olds 1995). Here, we define spatial heterogeneity as thespatially structured variability of a property of interest,which may be a categorical or quantitative, explanatoryor dependent variable.

When dealing with heterogeneity, one needs to con-sider some fundamental questions about the causes,types, and ecological consequences of heterogeneity.Approaches to answer these questions evolved in dif-ferent contexts, ranging from population genetics tospecies diversity and ecosystem processes. Methodswere borrowed from various fields, including geogra-phy, geology, spatial econometrics, physics, plant com-munity ecology, and complex systems theory. Whilethe different approaches can be contrasted by spatialdata representation (Gustafson 1998, Dale et al. 2002,Perry et al. 2002), objective (Liebhold and Gurevitch2002, Ver Hoef 2002), or disciplinary background(Liebhold and Gurevitch 2002), they often face similarchallenges in attempting to quantify heterogeneity.

This paper brings together some common analyticalthreads related to the spatial analysis of ecological dataat the landscape level, while pointing to unresolvedconceptual and statistical challenges. We start withsummarizing the causes, types, and ecological conse-quences of spatial heterogeneity, focusing on relevantaspects for the design and analysis of an ecologicalstudy. We then discuss how and to what degree threedifferent approaches (namely spatial statistics, land-scape metrics and statistical modeling), deal with theseaspects of spatial heterogeneity. Specifically, we high-light how these three spatial approaches can providenew insights about landscape spatial pattern and towhat degree these methods can disentangle the patternsdue to species response to a spatially structured en-vironment and those due to ecological spatial process-es. Finally, we point to promising new approaches at

meeting the challenges of spatial analysis in a hetero-geneous environment, including the statistical assess-ment of changes in space and time, the quantificationof local landscape structure, and the merging of discreteand continuous landscape models.

Causes of heterogeneity

Any spatial process operating between neighboringunits can cause spatial heterogeneity. Fig. 2A shows asimulated random distribution of a species in a ho-mogeneous environment, while Fig. 2B illustrates thepatchy distribution produced by a simple spatial pro-cess starting from the pattern in Fig. 2A. Spatial anal-ysis aims to assess the process generating these non-random patterns. As this process is stochastic, Fig. 2Brepresents only one of many possible outcomes of thesame process given the initial conditions in Fig. 2A(Fortin et al. 2003). In practice, however, we often haveonly one observed pattern representing a single reali-zation of the process of interest, which makes inferenceabout this process difficult.

Inference from a pattern on the underlying processis further hindered by variation in the process in spaceor time as well as by the presence of additional, con-founding processes. Fig. 2C shows the random distri-bution of the simulated species in Fig. 2A but con-strained by a linear environmental gradient, and Fig.2D reflects the confounded pattern of patchiness andan environmental gradient. In fact, most of the ob-served patterns result from more than one processesthat possibly interact with each other, such as biotic(e.g., ecological spatial processes) and abiotic (e.g.,environmental factors) drivers (Fig. 3).

Types of heterogeneity

The heterogeneity of a categorical variable is bestdescribed by a mosaic of patches. This includes thespecial case of binary data, where only one factor levelis of interest (e.g., patches of suitable habitat) and anyother levels are collapsed into one (e.g., matrix of non-habitat). The basic properties of a mosaic are compo-sition and configuration: composition describes thenumber and relative frequency of the factor levels (e.g.,habitat types), whereas configuration refers to the spa-


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FIG. 2. Simulated species distribution in a grid of 40 3 40 cells under different combinations of a homogeneous envi-ronment (A, B) or a linear environmental gradient (C, D) with random (A, C) or patchy (B, D) distribution of the species.

tial arrangement of the patches defined by the factorlevels (Gustafson 1998).

For a quantitative variable, the distinction betweencomposition and configuration is not as straightfor-ward. Composition refers to the density distributionfunction of the variable, whereas configuration is usu-ally described in terms of the spatial covariance struc-ture of the variable. The latter summarizes the strength,range, and directionality (anisotropy) of the spatial au-tocorrelation. The intensity of spatial autocorrelationis related to the degree of self-similarity of the valuesof a variable at nearby locations that can be expressedin terms of fractal dimension (Palmer 1992, McGarigaland Cushman 2005).

The type of heterogeneity depends on the nature ofthe variable rather than how it is sampled, analyzed,or displayed. For example, in geographic informationsystems (GIS), categorical data typically are repre-sented by vector data (polygon maps), whereas quan-titative data are treated as raster data (grid surfaces).However, drawing a line between two values of a quan-titative variable such as biomass is artificial. Similarly,displaying a qualitative variable as a mosaic-like gridsurface, by resampling a categorical map of patches atregular intervals, does not make the abrupt transitionbetween two patches any smoother. This example il-lustrates that ecological data may not always fit easily

in either GIS vector or raster data type, and the choicemay have implications for our ability to detect patternsand insights about the underlying processes that gen-erated them (Cova and Goodchild 2002, Cushman andMcGarigal 2004).

Ecological consequences of spatial heterogeneity

The pattern created by one process may affect an-other process and its resulting pattern (Levin 1992). Ina homogeneous environment, for instance, spatial pop-ulation dynamics can create heterogeneity in the abun-dance of a species. Nearby locations that are linked bydispersal tend to have interdependent population dy-namics, leading to autocorrelation in species abundance(Fig. 3). The land-use mosaic imposes additional con-straints on the local population dynamics, introducingspatial structure in species abundances due to the spa-tial distribution of site conditions and disturbance. Ina spatially structured environment, where nearby lo-cations tend to have similar site conditions, the patterninduced by species response to spatially structured en-vironmental factors may be mistaken for spatial au-tocorrelation due to a spatial ecological process. Hence,the environmental heterogeneity creates exogeneousspatial dependence in the species abundance, while thespatial interaction in the population dynamics is anendogeneous spatial ecological process. Not only may

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FIG. 3. Spatial effects in ecological data. Species are spatially structured for several reasons: (1) ecological processesare inherently spatial as they operate between neighboring individuals, thus creating autocorrelation; (2) species respond tovariation in environmental factors, which are themselves spatially structured, thus inducing spatial dependence in speciesdistributions; and (3) species respond to the environment at a specific scale, they may respond to the same factor differentlyat different scales, and the response may be nonlinear. Thus, the exogenous spatial structure may be more complex than thespatial structure of the environment.

the observed spatial pattern of abundance include bothtypes of underlying processes (Fig. 3), but these pro-cesses may interact in a linear or non-linear way. Forinstance, the land-use mosaic may constrain the dis-persal of organisms if some land-use types are moredifficult to traverse than others. Thus, the probabilitythat two habitat patches separated by a given distanceare connected by dispersal depends on the land-use in-between (D’Eon et al. 2002). It is clear from this ex-ample that species patchiness and the spatial structureinduced by environmental heterogeneity depend on theperspective of a specific organism, as habitat require-ments, life history attributes, and dispersal abilities willvary between species. Hence, species may respond toenvironmental heterogeneity in a non-linear manner(e.g., minimum threshold, or patch size requirements),it may require a specific combination of factor levelswithin its home range (Fahrig 2002), or it may respondto the temporal variability of environmental factors.Overlaps and interactions of different processes posea formidable challenge to ecological research that ex-plicitly investigates the spatial response of a species tolandscape heterogeneity, as is the case in metapopu-lation studies.

SPATIAL APPROACHES TO LANDSCAPE ANALYSIS

There are important practical considerations for thespatial analysis of landscapes (as summarized in Table1) that should be incorporated into students’ ecologicalcurricula. Here, we discuss the advantages and limi-tations of three analytic approaches to the analysis ofspatial heterogeneity: spatial statistics, landscape met-rics and spatial regression modeling. These approachesdiffer in their assumption on the number of underlyingprocesses and in their general objective (Table 2). To

better appreciate these considerations, we will first re-visit the main philosophical principles assumed byFisherian (parametric) statistical methods used in ecol-ogy.

Nonspatial (Fisherian) statistics

In controlled experiments, nonspatial statistics havebeen extremely powerful to quantify and test ecologicalrelationships. Unfortunately, when applied to hetero-geneous systems, most parametric statistics and mul-tivariate statistics (e.g., ordination) are usually appliedin inappropriate ways (e.g., Legendre 1993, Dale andFortin 2002). Correlation analysis, for example, quan-tifies the association between two response variables,such as the abundance of two species. The methodassumes independence of the residual errors which isusually achieved by using a random sample from ahomogeneous environment as depicted in Fig. 2A. Inthe presence of patchy data, a random sampling design(Fortin et al. 1989) and completely randomized exper-imental design (Legendre et al. 2004) do not guaranteethat the residual errors are independent. In order toaccount for patchiness (Fig. 2B), Dutilleul (1993) pre-sented a corrected t test for pairwise correlation co-efficients, which adjusts the degrees of freedom pro-portionally to the degree of spatial autocorrelation pre-sent in each variable. Alternatively, spatially con-strained (restricted) randomization tests have beenproposed for testing interspecific interactions while ac-counting for species-specific patchiness (cf. Roxburghand Matsuki 1999). Note that methods accounting forspecies patchiness may still be invalid due to environ-mental heterogeneity (Fig. 2C and 2D) if the correlationchanges with site conditions (Legendre et al. 2002,2004).


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TABLE 1. Six ‘‘points of wisdom’’ to keep in mind for the spatial analysis of landscapes.

Problem Practical implication

A random sample does not guarantee indepen-dent observations, but is designed to avoidbias (Fortin et al. 1989).

If the scale of patchiness is known, it can be used to enforce an ap-propriate minimum distance between observations for a systematicor a random sample (Dungan et al. 2002).

Spatial autocorrelation in the residuals may ren-der statistical tests too liberal (Cliff and Ord1981). Individual observations may not bringa full degree of freedom such that the signifi-cance of parametric statistics (e.g., correla-tion, regression, ANOVA) is not assessedwith the appropriate degree of freedom.

Tests adjusting the degree of freedom according to the degree of spa-tial autocorrelation in the data should be used (Dale and Fortin2002). When analyzing directional relationships (regression, ANO-VA), this is only necessary if there is autocorrelation in the residu-als, whereas autocorrelation in the raw data may not be a problem.

Based on data alone, it is not possible to distin-guish between exogenous deterministic struc-ture (spatial dependence) and endogenousspatial autocorrelation (ecological spatial pro-cess).

Hypothesis testing and experimental design are needed to disentanglethese two possibilities (Legendre et al. 2004).

The species–environment correlation is likely tochange with scale (Levin 1992).

A multiscale study design is needed unless the scale of response isknown (Fortin et al. 1989, Cushman and McGarigal 2004).

Stationarity assumptions concern the model ofthe underlying process and allow inferencefrom the observed pattern to the entire studyarea. Note that an observed pattern is a sin-gle realization of that process (Fortin et al.2003).

The presence of stationarity could be either assumed when the behav-ior of the underlying process is known or checked by estimating lo-cal mean and variance using a moving window approach.

Stationarity rarely prevails in real landscapes;the data may show a trend (change in mean)or local variability (change in variance) (For-tin et al. 2003).

When the data show a spatial trend it should be removed only if ithas an ecological interpretation, as the observed pattern may exhib-it trend-like structure by chance. In the case of local variability, en-vironmental heterogeneity needs to be measured and accounted forwhen quantifying spatial pattern (Wagner 2003).

ANOVA or regression models may be used for re-lating population density to one or several environ-mental factors, thus assuming independent observa-tions from a heterogeneous environment. Althoughsuch models explicitly include variability in at leastone environmental factor, they are susceptible to spatialeffects (Fig. 2C). Spatial autocorrelation in the resid-uals may render statistical tests too liberal, makingthem more likely to reject the null hypothesis when itis true. Autocorrelated residuals indicate that some pro-cesses are not accounted either in the sampling or ex-perimental design, as well as in the analyses. Further-more, parameter estimates may be wrong if there is anunmeasured spatially structured factor or if an envi-ronmental factor was measured at a scale different froman organism’s scale of response (Keitt et al. 2002).Spatial analysis of the residuals could reveal the pres-ence of unaccounted spatial structures and the scale ofan organism’s response (Henebry 1995).

Multivariate statistics are sometimes used for hy-pothesis testing in community analysis (Legendre andLegendre 1998). For example, constrained ordinationwith redundancy analysis (RDA) or with canonical cor-respondence analysis (CCA) is frequently used to testthe effect of a set of explanatory variables on multi-variate ecological response, such as species composi-tion (Borcard et al. 1992). As constrained ordinationis in effect a multivariate regression analysis (Legendreand Legendre 1998), these methods are subject to thesame problems as linear regression.

Spatial statistics

Even though spatial statistics were developed in dif-ferent fields (geography, ecology, economics, mining),many methods were developed as an adaptation of timeseries analysis to spatial problems. However, whiletime is a single dimension and temporal effects areunidirectional, geographic space has at least two di-mensions, and spatial processes may operate in anydirection and may not necessarily have the same in-tensity in all directions (i.e., anisotropic processes).The spatial statistical approaches most commonly usedby ecologists differ in their practical objectives. Geo-statistical methods focus on the estimation of the spatialcovariance structure of a spatially structured variable(e.g., variogram modeling) in order to use the spatialparameters to interpolate values at unobserved loca-tions (e.g., kriging). Spatial statistics, on the otherhand, aim at testing for the presence of a spatial processin order to model this process or to account for spatialautocorrelation when assessing the relationship be-tween spatially structured variables (Cliff and Ord1981, Fortin et al. 2001, Liebhold and Gurevitch 2002).

Spatial statistics that test for spatial autocorrelation(e.g., Moran’s I, Geary’s c) assume stationarity, mean-ing that the underlying process should have at leastroughly the same parameter values (mean and variance)for the entire study area (Fig. 2B). These global spatialstatistics (Boots 2002) further assume that the spatialcovariance structure of the variable (i.e., the values of

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TABLE 2. Main spatial approaches to analyze landscapes.

No. processes Spatial pattern analyses Spatial modeling analyses

One Global spatial statistics (continuous variable) Spatial regression analysisLandscape metrics (categorical variable) Spatial regression analysis

Several Local spatial statistics Partial canonical analysisLocal landscape metrics Residual analysis

Note: Approaches are grouped by the number of generating processes and on whether the analysis focuses on the descriptionor the modeling of spatial pattern.

spatial autocorrelation at different spatial distances orlags) is similar over the entire study area. Nonstation-ary processes imply that the mean, variance, or spatialcovariance structure of a variable vary across a studyarea which may pose severe problems to spatial sta-tistics. In spatially heterogeneous landscapes (Fig. 2D),nonstationarity is likely to occur, so that the test maybecome too liberal in rejecting the null hypothesis ofno autocorrelation.

Detrending is often used for addressing problems ofnon-stationarity (Haining 1997). For instance, a large-scale trend is removed prior to spatial analysis by fittinga linear or polynomial trend surface as a function ofthe geographic coordinates of the sampling units. De-trending removes the mean but does not affect the var-iance, which is often related to the mean and may stilldepend on the location. Non-parametric methods maybe more robust in moderate cases of non-stationarity(Bjørnstad and Falck 2001), and join-count statisticshave been extended to accommodate nonstationarity ofthe mean (Kabos and Csillag 2002). For instance, pop-ulation density is likely to be related to environmentalfactors. When these factors are spatially structured, theassumption of stationarity may be met by performingspatial statistics on the residuals of an environmentalresponse model (ANOVA, regression). However, theremay still be problems due to nonconstant variance, orthe spatial process itself may depend on the environ-mental factors.

Landscape metrics and related measures

The recent development of GIS provided ecologistswith a technical framework for landscape-scale anal-ysis (Greenberg et al. 2002). GIS include tools thatcharacterize and quantify the properties of data (area,perimeter, proportion). To these basic tools, some spa-tial statistics have been added to analyze spatial pat-terns. Spatial analyses of landscapes have also beenfacilitated by the availability of remotely sensed im-ages, from which land cover is derived into classes. Inecology, the landscape structure of such categoricaldata is usually quantified in terms of landscape com-position (i.e., proportions of habitat patches) or land-scape configuration (i.e., spatial arrangement of patch-es) using landscape metrics (O’Neill et al. 1988, Gus-tafson 1998; FRAGSTATS, available online).4

4 ^http://www.umass.edu/landeco/research/fragstats/fragstats.html&

Landscape metrics are often used as predictors ofecological processes, such as dispersal, which resultsin the observable distribution of organisms across alandscape, but this approach suffers from several prob-lems (Belisle et al. 2001). (1) While no single indexcan capture landscape structure, many landscape met-rics are strongly correlated (Gustafson 1998). Severalauthors have attempted, either empirically (McGarigaland McComb 1995, Riitters et al. 1995) or theoretically(Li and Reynolds 1995), to identify the intrinsic di-mensions (uncorrelated components) of landscapestructure, but this search has not yet resulted in a gen-erally applicable minimum set of landscape metrics(Gustafson 1998, Fortin et al. 2003). (2) Landscapemetrics are highly sensitive to scale, i.e., the assessmentof the structure of a landscape may change with thegrain (resolution) and extent (area covered) of the mapon which they are calculated (Cain et al. 1997, Turneret al. 2001, Wu et al. 2002). (3) An organism mayrespond to a landscape characteristic in a nonlinearway, such as requiring a specific minimum patch sizeor displaying threshold behavior in dispersal. In suchcases, landscape metrics need to be rescaled in termsof organism characteristics. Alternatively, the nonlin-ear behavior could be modeled with a nonlinear re-gression model (e.g., by choosing an appropriate linkfunction using generalized linear models; Guisan andZimmerman 2000). (4) Landscape metrics assume themapped property to be nominal or binary. In general,they do not consider ranks or other measures of gradualdifferences between factor levels, such as different lev-els of habitat suitability (Verbeylen et al. 2003). (5)Landscape metrics quantify the pattern of a categoricalmap and may be strongly affected by classification er-rors (e.g., if the map was derived from remote-sensingdata) or other forms of uncertainty introduced duringthe mapping process. Reliable results can only beachieved by assessing the mapping uncertainty and itspropagation in subsequent analysis (Hess 1994, Mow-rer 1999).

The statistical properties of landscape metrics cannotbe defined as they depend on the landscape composi-tion, which can vary in the presence of spatial hetero-geneity. Hence there are no standard tests for differ-ences between two observed patterns, or rather theirgenerating processes (Fortin et al. 2003). While eachobserved pattern corresponds to a single outcome of astochastic process, inference about the process requires


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knowledge of the distribution of patterns it may pro-duce. Stochastic models can be used to derive suchdistributions by simulation (e.g., neutral landscapemodels), but these models typically assume stationar-ity. The interpretation of landscape pattern indicesneeds to be based on stochastic models that handlelandscape heterogeneity and where spatial parametersare estimated from observed data (Fortin et al. 2003).

Quantifying landscape structure is rarely the ultimategoal for ecologists, but it is an important requisite forunderstanding how landscape structure affects ecolog-ical processes. However, it is not that easy to determinecausality between process and pattern, as the correla-tion between landscape metrics and ecological pro-cesses is often inconsistent (Tischendorf 2001). In fact,there is no a priori causal ordering in space as there isin time, and there are no statistical techniques that willunambiguously uncover species-landscape relation-ships in the absence of informed ecological understand-ing that poses the hypothetical relationships which thestatistics then test (Henebry and Merchant 2001). In ahypothesis-testing framework, graph theory in con-juncture with a resource selection model, offers a prom-ising approach to study species-environment relation-ships at the landscape level. This approach combinesthe topological spatial arrangement of landscape ele-ments (patches) and species responses to patch typesin terms of habitat preference (Urban and Keitt 2001,Manseau et al. 2002).

Statistical modeling

Modeling aims at quantifying the species–environ-ment relationships by specifying the underlying pro-cesses (dynamic modeling) or by predicting the ob-served patterns of the organisms from the spatial dis-tribution of environmental factors (statistical model-ing). A new realm of spatially explicit models exist tomodel ecological processes (Dieckmann et al. 2000) aswell as disturbances and their stochasticity (Mladenoffand Baker 1999). Here, however, we focus on statisticalmodeling in a regression context, highlighting threerather different approaches: (1) spatial regression mod-els where a spatial term is added to a regression; (2)partialling-out methods (e.g., ordination techniques)where the spatial component is factored out while es-timating species–environment relationships; and (3) re-sidual analysis following a multiscale ordination thatidentifies and characterizes spatial components due tounsampled environmental factors or ecological spatialprocesses.

Spatial regression modeling.—This approach is mostactively being developed in geography and spatialeconometrics, although it is increasingly used in ecol-ogy (e.g., autologistic model; Lichstein et al. 2002,Fortin et al. 2003, Burgman et al. 2005). Here, wediscuss three issues raised by Anselin (2002) in econo-metrics that are equally relevant for ecological appli-cations. First, spatial modeling may be based on either

of two data models, and the decision between the latticeand the random field models has far reaching impli-cations. A metapopulation is a good example of a sit-uation where the lattice model is appropriate. Thismodel implies that each data point represents a discretelocal population and that within the extent of the study,all local populations are included. The primary goal isextrapolation, or inference from the observed meta-population (n 5 1) to other metapopulations beyondthe study area. Spatial analysis is based on the network,or topology, of local populations and requires that theneighbors for each population are defined and assignedappropriate weights. The specification of neighborhoodand weights is essentially arbitrary, yet it may have agreat influence on the results.

A typical example of a random field is the plantspecies richness of nonadjacent sampling quadrats,where the observations represent a systematic or ran-dom sample of the surface of the study area. The pri-mary goal is the prediction (interpolation) of values atunobserved locations within the study area. The spatialcovariance structure (e.g., obtained by estimating a var-iogram model), is fitted directly as a function of thegeographic distance between quadrats without speci-fying neighbors or weights. However, quadrat size andshape, which are arbitrarily defined as part of the sam-pling design, may have a great effect on the estimatedcovariance structure (i.e., modifiable areal unit problem[MAUP]; Openshaw 1984, Dungan et al. 2002).

Second, it is important to distinguish between the-ory-driven and data-driven specification of the spatialregression model: is there a theoretical foundation fora spatial process, or does the residual spatial structurereflect shortcomings of the data? Spatial processes mayinclude situations where the behavior of an organismis affected by the neighbors’ decisions, either directlyor indirectly through the shared use of a limited re-source, or it may result from a spatial diffusion process.Alternatively, spatial structure in the data may be dueto a missing explanatory factor that is spatially struc-tured, a mismatch of the scales of the process and thedata, or spatially interpolated explanatory variables(Bradshaw and Fortin 2000, Dungan et al. 2002). Thedifferent processes may create similar patterns difficultto discriminate without experimental design and hy-pothesis testing. Nevertheless, a model should reflectthe assumptions about the process. For example, a hy-pothesized spatial interaction can be modeled by a spa-tial lag model, which includes an autoregressive term(Cressie 1993), where the response yi at location i is afunction of the neighboring values yj. A neighborhoodresponse of organisms to the environment can be mod-eled by a spatial cross-regressive term where yi is afunction of the environmental factor xj at neighboringlocations j. In data-driven model specification, the resid-ual spatial structure is interpreted as noise and modeledby a spatially correlated error term where the error «i atlocation i is a function of the neighboring errors «j.

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FIG. 4. (A) Variance components of regres-sion analysis or constrained ordination, (B) par-tial regression or ordination including space asa predictor, and (C) direct multiscale ordination.The components are (a) purely environmentaleffects, explained, not spatially structured var-iance; (b) overlap of spatial and environmentaleffects, spatially structured explained variance;(c) purely spatial effects, explained, spatiallystructured variance; and (d ) unexplained vari-ance that is not spatially structured. Compo-nents a and b appear in reversed order in (C)because a represents the nugget variance of thevariogram of explained variance

Third, a spatial error term can be fitted simulta-neously for all data points (AR model) or conditionallyfor each data point given the known values of its neigh-bors (CAR model; Cliff and Ord 1981, Griffith 1988,Keitt et al. 2002). Autoregressive models are often usedfor modeling a binary response variable describing theobserved presence or absence of a species. It is im-portant to understand that logistic regression modelsthe latent probability of occurrence, which cannot beobserved directly but only through its realized outcomeas presence or absence. Only the conditional model(CAR) can deal with a spatial latent variable. However,the conditional model cannot explain the spatial pat-tern, and prediction is essentially limited to missingobservations with known presence/absence informa-tion for all of its neighbors.

Partialling out the spatial component.—Spatial au-tocorrelation in the residuals may make statistical teststoo liberal and affect parameter estimates, so that theimportance of an environmental factor may be over- orunderestimated (Keitt et al. 2002, Lichstein et al. 2002).Dutilleul’s (1993) modified t test adjusts the degree offreedom according to the degree of spatial autocorre-lation in the data. Broad-scale spatial structure in thepredictor combined with local spatial autocorrelationin the response may, however, reduce the power ofDutilleuil’s modified t test (Legendre et al. 2002). Theeffect of any ecological factor (relevant or not) maybe overestimated if it shows a similar spatial patternas the observed response because both depend on thesame, unmeasured environmental factor (Legendre andLegendre 1998, Lichstein et al. 2002).

In order to avoid such problems of false correlation,partialling-out methods can remove trends or large-scale spatial structure in the data before estimating re-gression parameters or performing constrained ordi-nation. This can be achieved by fitting a polynomialtrend surface (Borcard et al. 1992) or more complexand flexible models of spatial structure derived fromthe relative spatial locations of the sampling units (Bor-card and Legendre 2002). However, spatial dependencemay not indicate spurious correlation (Lichstein et al.2002), nonspatial correlation does not guarantee cau-

sation, and the directionality and asymmetry of causalrelationships must be explicitly assessed. Imagine asimple gradient with a linear increase of moisture alonga transect. The plant species composition can be ex-plained equally well by moisture as by transect posi-tion. After partialling out the spatial component, mois-ture has no explanatory power, although it is the mois-ture that the plants respond to. It is clear from thisexample that the spatial-dependence component is partof the species–environment correlation and should notbe removed for parameter estimation without carefulconsideration. If the residuals are spatially correlated,however, this implies the presence of an unknown pro-cess, which may be accounted for by adding an auto-regressive term or a spatial error term in the regressionanalysis (Haining 1997, Keitt et al. 2002, Lichstein etal. 2002).

Residual analysis with multiscale ordination.—Re-sidual analysis may help to discriminate between spa-tial autocorrelation due to an ecological spatial processand spatial dependence induced by environmental re-sponse, and it may indicate specification errors such asthe omission of an important factor or a mismatch ofscales of observation and response. Ordinary regres-sion analysis and constrained ordination methods par-tition the total variance in the uni-or multivariate re-sponse into two components, the explained and theresidual variance (Fig. 4A). Regression residuals arecommonly checked for (1) evidence of heteroscedas-ticity, where the variance depends on the mean (2)systematic deviation from the normal distribution, (3)influential observations that may have a large impacton parameter estimates, and, increasingly, (4) spatialautocorrelation. However, there is no equivalent formultivariate analysis, where the large number of re-sponse variables may make the above methods im-practical. Partial constrained ordination can be used tofurther partition both the explained and the residualvariance into a spatially structured and a nonspatial part(Fig. 4B), so that the relative importance of purelyenvironmental (a) and purely spatial effects (c) can becompared and their degree of overlap (b) be assessed(Borcard et al. 1992).


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FIG. 5. Direct multiscale ordination with RDA (redun-dancy analysis) of the simulated species distribution in Fig.2D. Globally, the total variance of the binary variable is 0.25,the explained variance 0.10, and the residual variance 0.15.Each symbol shows a variance component estimated frompairs of cells separated by a specific distance, thus providinga spatial partitioning of the global estimates. Circles denotetotal variance (variogram of total variance), triangles denotethe variance explained by the position along the environ-mental gradient (variogram of explained variance), andsquares denote the residual variance (variogram of residualvariance). Only distances up to 25 cells are shown.

Spatial structure in the residuals may be due, how-ever, to a spatial process or an unaccounted spatiallystructured environmental factor, and we have littlepower to tell these apart. Urban et al. (2002) suggestedthe development of partial Mantel correlograms to fur-ther investigate the spatial structure of the variancecomponents. Direct multiscale ordination (MSO) withRDA or CCA (Wagner 2004) provides this informationby estimating the total variance, the explained and theresidual variance as well as the eigenvalues of ordi-nation axes for a series of distance classes (Fig. 4C).The distance-dependent variance components, whichare estimated from all pairs of observations that fallinto a given distance class, are plotted against distance,resulting in a set of empirical variograms that effec-tively partition ordination results by distance. Fig. 5provides an example of direct MSO for the simulatedspecies distribution in Fig. 2D, which mimics thepatchy distribution of a species along a simple envi-ronmental gradient. The global RDA results showed atotal variance of 0.25, an explained variance of 0.1 anda residual variance of 0.15. Spatial partitioning by MSOrevealed the spatial structure of the different variancecomponents. The variogram of the total variance (cir-cles) exhibited a continuous increase of variance withdistance. After accounting for the environmental gra-dient, the variogram of the residual variance (squares)showed an initial increase before reaching a constantlevel. The spatial structure at larger distances was con-

tained in the variance explained by the environmentalgradient (triangles). The results of MSO can be usedfor checking modeling assumptions:

1) The variogram of the residual variance (Fig. 4C,thin line) provides an estimate of the scale of patchinessand may indicate problems with non-stationarity. Fora stationary process, patchiness causes reduced vari-ance at short distances, whereas at larger distances be-yond the range, the variance reaches a constant level(sill). The range indicates the distance beyond whichobservations are spatially independent and may be usedas a minimum distance in subsequent sampling (Fortinet al. 1989, Dungan et al. 2002, Legendre et al. 2004).In the presence of a sill, a Mantel test can be used totest each distance class for significant spatial autocor-relation (Wagner 2003, 2004). A continuous increaseof the variance with distance, however, is often asso-ciated with spatial trend (Fig. 2C and D) and may in-dicate the presence of an unaccounted environmentalfactor that is spatially structured. If this is the case, thetrend-like structure, which often exhibits directional(anisotropic) behavior, is likely contained in the firstnon-canonical axis. This can be checked by investi-gating the variogram of the respective eigenvalue. Plot-ting the axis scores in geographic space may help toidentify the missing factor.

2) A systematic difference between the variogram ofthe total variance (Fig. 4C, bold line) and the sum ofthe variograms of the explained and residual variances(Fig. 4C, dashed line) may indicate problems withscale-dependence in the species–environment correla-tion. The global significance of an observed deviationcan be tested using a point-wise confidence envelopefor the variogram of total variance (Wagner 2004).

CONCEPTUAL AND STATISTICAL CHALLENGES

Assessing changes in space and time

A major step forward in landscape ecology will leadfrom the ‘‘snap-shot mode’’ quantification of landscapestructure to the ‘‘movie mode’’ assessment of changesin landscape structure in space and time. Testing thehypothesis that the generating process differs betweenlandscapes or between time steps will have to rely onmodeling of stochastic processes. Remmel and Csillag(2003) proposed a general framework for comparingtwo categorical maps, which might also be adapted toquantitative data: first, the composition and configu-ration of each map needs to be estimated accountingfor their interdependence (Fortin et al. 2003). Replicatelandscapes are simulated based only on these param-eters (cf. Hargrove et al. 2002, Fortin et al. 2003) andthe landscape metrics are computed for each realizationto generate a confidence interval at some specified level(conditional simulation). The two patterns are consid-ered significantly different if their confidence intervalsdon’t overlap. While this procedure is relativelystraightforward assuming a stationary process, the ex-

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tension to nonstationary processes poses a formidablechallenge both conceptually and computationally(Remmel and Csillag 2003).

Quantifying local landscape structure

It is likely that different species respond to theirenvironment at different scales and that these scalesare related to the movement ranges of organisms (e.g.,D’Eon et al. 2002, Holland et al. 2004). This impliesthat instead of analyzing global landscape patterns, oneshould quantify the local landscape structure acrossspace as it may be experienced by the organism ofinterest (Potvin et al. 2001, McGarigal and Cushman2005). Local versions exist for many spatial statistics(Boots 2002, 2003), but have not yet been widelyadopted by ecologists (Pearson 2002).

Holland et al. (2004) provided an algorithm for iden-tifying the scale of maximum correlation between spe-cies abundance and landscape characteristics throughresampling of spatially independent observations withincreasing size of the window within which the land-scape metrics are calculated. Thompson and McGarigal(2002) systematically varied both the grain and extentof the environmental predictors to assess the activity-dependent scale or multiple scales of environmentalresponse by maximizing a correlation measure.

Landscape metrics can be calculated within a spec-ified neighborhood around each cell using a movingwindow (Potvin et al. 2001; FRAGSTATS, see footnote4). Such moving window analysis provides a distri-bution of values for each landscape metric obtainedfrom all possible window positions. This implies thatmoving window analysis may be an alternative to con-ditional simulation for the statistical comparison of ob-served landscapes (Potvin et al. 2001), but this requiresthe assumption that the local landscapes are true rep-licates with an independent history but comparableconditions, so that the ecological processes are iden-tical.

Currently, most GIS and other software performingmoving window analysis are using geometric windows(e.g., circles or squares) of arbitrary size that do notreflect the spatial structure of the species or the envi-ronment (Bradshaw and Fortin 2000). Research in geo-graphical information sciences should address this is-sue in order to provide tools for detecting the patchinessor zone of influence of the data (e.g., by using localspatial statistics), and implementing flexible geograph-ical (e.g., watershed) or behavioral (e.g., home range)windows that can be adapted to a specific situation.

Merging of discrete and continuouslandscape models

Landscape ecologists have been preoccupied withthe patch–matrix model of discrete landscapes, whichis highly compatible with the theory of island bioge-ography and with metapopulations (Turner et al. 2001).The gradient-based concept of landscape structure

(McGarigal and Cushman 2005) is ideally suited forintegrating landscape analysis with niche theory andthe study of changes in ecological communities alongenvironmental gradients, a core topic of communityecology. Multiscale ordination as discussed above isbased on a formal integration of geostatistics with mul-tivariate ordination methods, and its great potential forthe empirical integration of spatial analysis and gra-dient analysis needs yet to be explored.

Gradient analysis in plant community ecology couldprofit from an explicit consideration of local hetero-geneity and the organism-specific scale of response:organisms including plants are likely to respond notonly to a local average of an environmental factor, butalso to its variability in space and time at a scale relatedto the organisms size, mobility, and life span. Thiscould be quantified by calculating the standard devi-ation or a local spatial statistic within a moving windowof an appropriate size. However, compared to landscapemetrics, these statistics for continuous variables pro-vide rather crude measures of the spatial configurationof the environmental factor. As an equivalent to land-scape metrics for continuous environmental data,McGarigal and Cushman (2005) proposed applyingsurface metrology metrics (Pike 2001), which are usedfor quantifying surface roughness in microscopy andmolecular physics.

The patch–matrix and the gradient concepts of land-scape structure represent two extremes of landscapestructure, with most real landscapes falling somewherein between. While the best choice will always dependon the research question, it will be increasingly im-portant to incorporate internal heterogeneity and grad-ual differences between habitat types into landscapemetrics as well as discontinuities into spatial statistics.Dorner et al. (2002) proposed modifications to land-scape metrics so as to reflect topographic variability.When applying spatial statistics to landscapes with adiscontinuous, mosaic-like structure, homogeneous ar-eas dominated by the same stationary process can bedelimited empirically using boundary detection algo-rithms (Fagan et al. 2003). Furthermore, ecologicalboundaries and ecotones determined from species datacan be spatially related to environmental boundaries(Fortin et al. 2000), so that their spatial coincidencecan be tested (Fortin et al. 1996) and their effects mon-itored.

Fuzzy set theory has been successfully applied to theproblem of gradual transitions between ideal vegetationtypes (Roberts 1989): rather than drawing an arbitraryline for classification, a degree of membership to eachtype is attributed to each observation. Habitat mapscould be represented in a similar way as multivariatesurfaces of membership. Such an approach would notonly accommodate internal heterogeneity within for-merly discrete, assumedly homogeneous patches, butalso retain information on mapping uncertainty, so that


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its propagation through subsequent analyses could beassessed (Brown 1998, Bolliger and Mladenoff 2005).

Wavelet analysis provides a promising alternative forcharacterizing and partitioning landscapes in the pres-ence of multiple, overlapping processes (i.e., not sta-tionary), and this method can easily handle large datasets (i.e., continuous data) such as remote sensing data(Bradshaw and Spies 1992, Csillag and Kabos 2002;McGarigal and Cushman 2005). The integration of dis-crete and continuous landscape concepts may also prof-it from attempts in geography and GIS to combine dis-crete and continuous data models through the definitionof fields of spatial objects (Cova and Goodchild 2002).Similar efforts are made towards representation ofspace–time data, another important shortcoming of GISthat is impeding the integration of spatial and temporalprocesses in ecology (Henebry and Merchant 2001,Peuquet 2001). Finally, spatiotemporal analysis oflandscape dynamics could help to assess the impor-tance of ecological memory or answer the question ofhow much randomness there is in real landscapes (Pe-terson 2002).

Conclusion

The basic problem of spatial analysis of landscapesis that several processes creating heterogeneity oftenoperate at the same time. These processes may interact,so that the parameters of one process change with theheterogeneity resulting from other processes. Thismeans that the observed pattern can rarely be attributedto a single, stationary process, as many methods ofspatial analysis assume. Furthermore, most spatial pro-cesses in ecology are stochastic, so that many replicatesare needed for an accurate quantification of the un-derlying process. However, replications are hard to ob-tain because the parameters of the process are likelyto change through space or time due to environmentalheterogeneity.

Local spatial statistics offer a way to accommodatespatial variation in pattern and even to obtain replicatelandscapes at a finer scale. However, the size of suchlocal landscapes needs to be determined in an ecolog-ically meaningful and methodologically sound way.Statistical methods for testing hypotheses about non-stationary processes urgently need to be developed. Asthe hypothesis concerns the spatial process (which isnot directly observable) rather than the empirical pat-tern, confidence intervals are best derived by condi-tional simulation. Local statistics and statistical teststhat can accommodate nonstationarity are needed forthe analysis of discrete patterns with landscape metricsas well as for the quantification of continuous surfaceswith spatial statistics. However, both gradients and dis-continuities are a reality in ecological systems, and weneed to find ways of integrating discrete and continuousaspects of heterogeneity.

Facing these challenges may enable ecologists to gobeyond quantifying patterns in order to finally address

the interaction between environmental heterogeneityand the ecological processes causing species patchi-ness. This can only be achieved by distinguishing, bothconceptually and empirically, between endogeneousautocorrelation due an ecological spatial process andexogeneous spatial dependence induced by environ-mental response.

ACKNOWLEDGMENTS

This work was partly funded by the Swiss National ScienceFoundation within the NCCR Plant Survival (H. Wagner) andNSERC (M.-J. Fortin). We thank Jacqueline Bolli, Jesse Kal-wij, Stephanie Melles, Bronwyn Rayfield, Christoph Schei-degger, Anurag Agrawal, Geoffrey Henebry, and Dean Urbanfor their valuable comments.

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MEASURING LANDSCAPE CONNECTIVITY: THE CHALLENGE OFBEHAVIORAL LANDSCAPE ECOLOGY

MARC BELISLE1

Departement de biologie, Universite de Sherbrooke, Sherbrooke, Quebec J1K 2R1 Canada, andCentre de recherche en biologie forestiere, Universite Laval, Quebec, Quebec G1K 7P4 Canada

Abstract. The recognition of behavior as a link between process and pattern in land-scape ecology is exemplified by the concept of functional connectivity: the degree to whichthe landscape facilitates or impedes movement among resource patches. In this paper, Ifirst argue that the actual operational definitions of this concept as applied to animal move-ment are not fully consistent with its formal definition. For instance, I question that a highlikelihood of movement among the different points of primary habitat implies a high con-nectivity and contend that such a view can lead to misinterpretations. I also address twomore hurdles to the measurement of functional connectivity: the fact that functional con-nectivity may not be equal along all axes and directions of movement and individualvariation in functional connectivity within a given landscape. These points bring me tosuggest that the concept of functional connectivity be bridged to the one of travel costsused in behavioral ecology. This would help define unequivocal operational definitions offunctional connectivity as its measurement would then be dictated by its ecological rolewithin specific models (e.g., travel costs within group membership models of foragingtheory). I argue further that this ecological role shall in turn determine the motivationunderlying the movement of individuals, implying that the latter should preferably bestandardized when measuring functional connectivity in the field. I finally present somemethods to do so. These include translocation and playback experiments, food-titration andgiving-up densities experiments, and manipulating feeding and breeding site locations andsuccess.

Key words: behavioral ecology; cost function; dispersal; field experiments; functional connec-tivity; gap-crossing behavior; landscape anisotropy; movement; travel costs.

BEHAVIOR: THE LINK BETWEEN PROCESS

AND PATTERN

One of the main focuses of landscape ecology is toexplain how ecological processes and patterns originatefrom or modify the composition and configuration ofhabitat patches within a given area. Although the actorsinvolved in such spatial processes and patterns may beabiotic, most are living organisms that react to oneanother, as well as to landscape structure, through be-havior. Recent studies on wintering parids illustratewell how landscape structure can influence the behaviorof organisms, and thereby generate patterns at the patchand landscape scales. For instance, these small, residentforest birds venture further out into open habitat toobtain food as forest cover decreases within a 500-mradius (Turcotte and Desrochers 2003). Yet, when sup-plemented with food for some weeks, they barely enterthe open to forage, and this, independently of forestcover within a 500-m radius (Turcotte and Desrochers2003). This suggests that parids in landscapes with low

Manuscript received 3 June 2004; revised 16 December 2004;accepted 21 December 2004; final version received 11 January2005. Corresponding Editor: M. Fortin. For reprints of this Spe-cial Feature, see footnote 1, p. 1965.


forest cover are energetically stressed and experiencea greater predation risk to gain access to food. Alongthe same line, parids living in small forest patches showdaily fattening patterns that indicate a trade-off be-tween accumulating reserves to counter an unpredict-able access to food and limiting their body weight toreduce predation risk (Tellerıa et al. 2001). The energystress experienced by parids within highly fragmentedlandscapes may not only result from a lower resourcedensity, but also from a greater exposure to adverseweather conditions that constrain individuals to feedand cache food towards the center of patches (Dolbyand Grubb 1999, Brotons et al. 2001). On another front,parids have a high propensity to follow forest edges(Desrochers and Fortin 2000) and are reluctant to moveamong forest patches surrounded by open areas (St.Clair et al. 1998, Grubb and Doherty 1999). In addition,parids experience lower survival when moving withinhighly fragmented landscapes (Doherty and Grubb2002). Taken together, these responses to conditionsemanating from the landscape structure may explainwhy the incidence, density, and social structure of par-ids are influenced by the area and isolation of forestpatches (Pravosudova et al. 1999, Doherty and Grubb2000).


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The recognition of behavior as a link between pro-cess and pattern by landscape ecologists is exemplifiedby the concept of landscape connectivity: ‘‘the degreeto which the landscape facilitates or impedes movementamong resource patches’’ (Taylor et al. 1993:571). Be-cause this formalization is associated to the ease withwhich processes such as dispersal can operate, it isoften referred to as the functional connectivity of land-scapes. This is to distinguish the latter from the struc-tural connectivity or connectedness of landscapes,which refers to the degree to which some landscapeelements of interest are contiguous or physically linkedto one another (With et al. 1997, Tischendorf and Fah-rig 2000a).

With respect to animal movement, the functionalconnectivity of a landscape is thought to depend onhow an organism perceives and responds to landscapestructure within a hierarchy of spatial scales. In fact,organisms are expected to alter their movements, aswell as experience differential fitness benefits or costs,according to the nature, form, and spatial arrangementof habitat patches and ecotones (Tischendorf and Fah-rig 2000a, Wiens 2001). Several behavioral constraintsunderpin this framework. For instance, the perceptionand response of individuals to landscape structure willbe influenced by their state and their motivation, whichwill dictate their needs, how much risk they are willingto take in order to fulfill those needs, and possibly theirspecific destinations. Thus, factors such as the percep-tual range of the organisms (sensu Lima and Zollner1996), their susceptibility to competition and preda-tion, as well as their level of conspecific attraction, willplay an important role at determining the movementsof individuals (Danielson 1992, Belisle 1998, Fraser etal. 2001, Greene and Stamps 2001). It follows that thefunctional connectivity of a landscape is likely to beboth species and context-dependent (Pither and Taylor1998, Jonsen and Taylor 2000, D’Eon et al. 2002).

Despite being considered as a key concept of land-scape ecology, the actual study of functional connec-tivity requires dealing with complex phenomena dif-ficult to sample, experiment on, and describe synthet-ically. This stems mainly from the multivariate natureof the processes involved as well as from the spatialand temporal scales at which they manifest themselves.In the remaining sections of the paper, I will discusshow functional connectivity can be operationally de-fined and measured in the field. After, I bring up twomore aspects that should be considered in measuringlandscape connectivity: the fact that functional con-nectivity may not be equal along all axes and directionsof movement and that it may vary strongly among in-dividuals within a given landscape. I then propose thatwe have much to gain from using a theoretical frame-work that stems from behavioral ecology to improveour measurement of functional connectivity. Specifi-cally, I suggest that the concept of functional connec-tivity be linked to the one of travel costs found in

behavioral ecology models that predict how animalsshould use resources heterogeneously distributed inspace. Within this framework, I finally present someapproaches to measure functional connectivity in thefield.

MEASURING FUNCTIONAL CONNECTIVITY

The lack of an operational definition

Landscape ecology recognizes the importance ofmovement with respect to habitat selection and geneflow, as well as population viability and stability. Yet,the limited empirical knowledge on how landscapestructure influences the movement of animals has sofar hindered the development of a strong theoreticalframework around the concept of functional connec-tivity. This is partly reflected by the lack of consensuson how to measure landscape connectivity (Tischen-dorf and Fahrig 2000a, b, Moilanen and Hanski 2001,Goodwin 2003). For instance, Taylor et al. (1993:572)suggested that functional connectivity ‘‘can be mea-sured for a given organism using the probability ofmovement between all points or resource patches in alandscape.’’ This operational definition is generally in-terpreted such that a high likelihood of movementamong the different points of primary habitat impliesa high functional connectivity. This interpretation,however, is hazardous if we stick to the conceptualdefinition of functional connectivity: ‘‘the degree towhich the landscape facilitates or impedes movementamong resource patches’’ (Taylor et al. 1993). Indeed,both dispersion and patch models in behavioral ecologysustain the possibility that two landscapes can haveidentical connectivity while the propensity of individ-uals to move can differ between the two landscapes.This claim, like the rest of the paper, assumes thatanimals tend to behave optimally (Krebs and Kacelnik1991) and that the travel costs they incur reflect thelevel of functional connectivity. Here are two ‘‘thoughtexperiments’’ that illustrate the rationale.

As a set up for both experiments, let’s assume twolandscapes, A and B, in which individuals experiencethe same ease of movement among resource patches(Fig. 1a). As a result, individuals incur the same travelcosts (e.g., energy, predation risk) as they search forand sample resource patches in both landscapes. More-over, the landscapes have the same number of resourcepatches. Furthermore, the frequency distributions ofpatch quality in the two landscapes have the samemean, variance, and kurtosis (Fig. 1b). On the otherhand, although the frequency distributions of patch qual-ity have the same skewness level, the distribution inlandscape A is skewed to the left, whereas it is skewedto the right in landscape B. As a consequence, the quan-tiles of the two distributions will differ and the medianpatch quality will be higher in landscape A.

The first ‘‘thought experiment’’ considers a simpledispersion model whereby individuals attempting to

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1990 MARC BELISLE Ecology, Vol. 86, No. 8

FIG. 1. Main aspects of the two thought experiments showing that two landscapes with identical functional connectivitycan lead to different movement rates or propensities in animals that attempt to maximize their gain rate. (a) Two landscapes(A and B) with ‘‘identical’’ structures (i.e., composition [forest vs. nonforest] and configuration) with respect to movementcosts. (b) Although the two landscapes are composed of habitat patches of the same mean quality, the frequency distributionof patch qualities is skewed to the left in landscape A (solid line) and to the right in landscape B (dotted line). (c) Theestimate of the average quality of the environment, as learned through sampling by foraging individuals, will decrease morerapidly in landscape B (dotted line) than in landscape A (solid line). Hence, individuals in landscape A will, on average,sample more habitat patches before they settle down into a patch to exploit its resources. (d) Once in a patch, individualsin landscape A (solid line) will, on average, gain benefits more rapidly than in landscape B (dotted line). Because traveltime is identical in both landscapes, individuals should, on average, leave patches sooner in landscape A (T ) than in*Alandscape B (T ).*B

maximize their rate of gain must distribute themselvesamong resource patches of unknown quality (Bernsteinet al. 1991, Beauchamp et al. 1997). These individualswill settle in or exploit resource patches showing abetter quality than their current estimate of the averagequality of the environment, which they must learn. Toavoid settling in a patch of poor quality, individualsmust initially be optimistic. Yet, as they sample, theydevaluate past experiences and their current estimateof the average quality of the environment turns out tobe mostly influenced by the qualities of recently en-countered patches (Giraldeau 1997). Frequently en-countered patch qualities will therefore have a sub-stantial effect on their current estimate. All other thingsbeing equal, then one is likely to observe more (sam-pling) movement in landscape A than in landscape B,as individuals would, on average, maintain a higherestimate of the average quality of the environment inlandscape A (Bernstein et al. 1991, Beauchamp et al.1997: Fig. 1c). Based on the widely accepted opera-tional definition which equates a high likelihood ofmovement among the different points of primary hab-

itat with a high functional connectivity, one would con-clude that landscape A has greater functional connec-tivity. This conclusion is, however, wrong if we stickto Taylor’s et al. (1993) conceptual definition; it is aseasy for individuals to move in both landscapes.

The second ‘‘thought experiment’’ considers patchmodels whereby individuals attempting to maximizetheir rate of gain must decide when to stop exploitinga resource patch and search for a new one (Stephensand Krebs 1986, Giraldeau and Caraco 2000). Not hav-ing perfect information about the location and qualityof resource patches, individuals are expected to exploitpatches in accord to the marginal-value theorem. En-countering resource patches of higher quality more fre-quently, individuals in landscape A will thus be morelikely to leave a resource patch early and resumesearching (i.e., move) compared to individuals in land-scape B, all other things being equal (Stephens andKrebs 1986, Giraldeau and Caraco 2000: Fig. 1d).Movement probabilities or rates will thus depend onthe rate at which individuals gain benefits through timewithin resource patches, not on functional connectivity.


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Note that the arguments presented in the two‘‘thought experiments’’ would have been much stron-ger if there had been greater discrepancies in the like-lihood of encountering patches of high quality betweenthe two landscapes. It is also important to realize thatthe above arguments are not restricted to a foragingcontext or to ‘‘local’’ processes, but can also be appliedto dispersal (Danielson 1992). Resources can be verydiverse and include food, mates, and territories, andthese can be exploited from a central place to whichindividuals periodically return (e.g., nest or roost) ornot. Moreover, similar critiques could be addressed toother operational definitions that were attributed tofunctional connectivity. Those include, among others,the proportion of individuals that immigrate into a newhabitat patch within a given amount of time and thetime required to settle in a new habitat patch (reviewedby Tischendorf and Fahrig 2000a, b, Goodwin 2003).Hence, it must be concluded that neither high proba-bilities of moving among points of primary habitat orhigh movement rates imply high functional connectiv-ity.

The lack of an operational definition based on es-tablished theories in behavioral ecology has probablyled to the notion that a lot of ‘‘moving around’’ byindividuals (e.g., high patch immigration rate) is prof-itable with respect to habitat selection and populationviability. It is indeed intuitive to equate an ease ofmovement among resource patches with a propensityto move. From this standpoint, and without preciselyknowing how much movement is necessary to maintainprocesses, a high level of functional connectivity isoften considered as a desirable property of landscapes.This notion, which was often implied or referred to instudies on wildlife corridors (Beier and Noss 1998) andpopulation viability (e.g., Thomas 2000), should nev-ertheless be applied carefully. For instance, favoring alandscape structure where high levels of dispersal occurmay result in recommending a landscape structure inwhich individuals experience poor breeding successand thus exhibit low philopatry, all other things beingequal (Switzer 1997, Doligez et al. 2002). This exampleillustrates the potential for misinterpretation, and may-be more importantly, the possibility of committing er-rors when applying the concept of functional connec-tivity in its actual form to conservation issues.

Two more hurdles: landscape anisotropyand individual variation

Whereas landscape ecologists are interested in theconnectivity of entire landscapes, metapopulation ecol-ogists are interested in the connectivity of single habitatpatches (Moilanen and Hanski 2001, Tischendorf andFahrig 2000a). In metapopulation ecology, connectiv-ity is restricted to the modeling of migration ratesamong habitat patches, which directly points towardsclear operational definitions amenable to field mea-surements and statistical modeling: e.g., the probability

that an empty patch will be colonized during a dispersalevent (Moilanen and Nieminen 2002). Implicit to thispatch-based approach is the fact that not all patchesare assumed to be of equal connectivity. The flow ofdispersing individuals may accordingly be polarizedalong certain axes and in certain directions within agiven landscape (Gustafson and Gardner 1996, Ferreras2001, Ovaskainen 2004). Polarized or anisotropic flowsof individuals may not only result from different abun-dances of dispersers that depend on the structure of thelandscape, but also from variations in the ease of move-ment along the different axes and directions of move-ment. Belisle and St. Clair (2001) have illustrated thispossibility with an experiment where they translocatedterritorial, mated male forest birds within a valley char-acterized by several parallel, linear strings of open hab-itat. Overall, the birds translocated across the valleyfloor, such that they would repeatedly encounter move-ment barriers, took longer to return to their territoriesthan birds translocated along the valley floor. They alsofound variation in response among species, suggestingthat life-history characteristics may modulate how in-dividuals perceive and respond to movement barriers.Such landscape anisotropy with respect to movementcertainly deserves to be taken into account given itspotential impacts on the structure and dynamics of pop-ulations and communities (Wiegand et al. 1999, Sher-ratt et al. 2003).

The fact that the ease of movement can vary amongdifferent axes within a landscape, as well as in oppositedirection along a given axis, certainly complicates thederivation of synthetic measures of functional connec-tivity (Gustafson and Gardner 1996, Belisle and St.Clair 2001). For that matter, it certainly proscribes sum-marizing functional connectivity by a single numberthat would originate from a simple integration or av-erage over all patches of ‘‘patch-based connectivities’’as suggested by some authors (e.g., Tischendorf andFahrig 2000a, b). In its simplest expression, functionalconnectivity should be characterized by a magnitudeand a direction (i.e., a vector), which would integratemeasurements taken along different axes and in dif-ferent directions. And depending on the theoreticalframework in which functional connectivity is beingused, it might even prove better to use a matrix ofdirectionally explicit, patch-to-patch measures. Notethat metapopulation ecologists have been able to syn-thesize the information of such a matrix into a singlemeasure relevant to population viability, namely meta-population capacity (Hanski and Ovaskainen 2000).

On another front, because individuals are likely toshow different levels of motivation when it comes tomove, we should expect individual variation in thefunctional connectivity of a given landscape. Thisamount of individual variation in functional connec-tivity may depend on landscape structure. If this werethe case, then we should not only pay attention to meanvalues of functional connectivity, but also to their var-

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iance, especially when the matrix is highly heteroge-neous (Fraser et al. 2001, Ricketts 2001). If we assumethat dispersal processes depend upon functional con-nectivity, then variation in functional connectivity cer-tainly merits attention given that variance in demo-graphic rates can influence population dynamics (Ken-dall and Fox 2002).

Incorporating behavior into functional connectivity

In spite of the above problems, I strongly believethat ecologists should not abandon the functional con-nectivity concept as defined by Taylor et al. (1993).Functional connectivity conceptualized as the ease ofmovement among points or resource patches is alreadyused in several behavioral ecology models that addressthe spatiotemporal distribution of individuals. Address-ing functional connectivity under the framework of-fered by these models would certainly help link processand pattern. For example, behavioral ecologists havedeveloped several models predicting the duration thatan individual should spend exploiting a resource patchas a function of travel time among patches (e.g., themarginal value theorem) for individuals that exploitresources solitarily (Stephens and Krebs 1986) or ingroups (Giraldeau and Caraco 2000). Travel time islikely to be strongly correlated with the ease of move-ment among resource patches as it integrates the rateof movement and the detours that landscape structuremay impose on individuals (Jonsen and Taylor 2000,Belisle and Desrochers 2002). Hence, measuring theresidence time within resource patches of known qual-ity and abundance could provide an indication of thetravel time experienced by moving individuals. Patchresidence time would be especially useful to assessfunctional connectivity for species whose movementsare difficult to track. Moreover, once properly adapted,patch models could be used to relate residence time tofunctional connectivity in terms of ‘‘integrative’’ fit-ness currencies (e.g., an integration of travel time andpredation risk as perceived by individuals).

Group size models (Belisle 1998, Giraldeau and Car-aco 2000) could also prove to be useful to assess func-tional connectivity. These models essentially predicthow individuals should distribute themselves amongresources patches (or territories) that vary in quality.Because it is assumed that individuals behave in a waythat maximizes their fitness and that the fitness expe-rienced by individuals depends on patch attendance, astable distribution is reached when individuals do notbenefit from unilaterally changing position. In the ab-sence of travel costs, this stable distribution is mostlydictated by patch quality. Yet, in the presence of travelcosts, individuals often cannot afford reaching the re-source patches that would convey the best returns uponexploitation. As a result, poor quality patches tend tobe overused (Bernstein et al. 1991, Beauchamp et al.1997). The level of discrepancies between observedand predicted distributions under the assumption of no

travel costs could therefore be used to assess functionalconnectivity. The implementation of such an approachshould be greatly facilitated by recent developments insocial foraging theory. For instance, the stringent as-sumptions whereby ideal free distribution (IFD) modelscould only be applied to very small and simply struc-tured landscapes are starting to be relaxed. Models cannow address the distribution of individuals among re-source patches at large spatial scales (Tyler and Har-grove 1997), among resource patches embedded withina hierarchy of spatial scales (Beauchamp et al. 1997,Belisle 1998), and along smoothly changing resourcegradients (Stephens and Stevens 2001).

By equating functional connectivity with travelcosts, landscape ecologists would benefit from a stron-ger theoretical framework to study the influence oflandscape structure on ecological processes and theiremerging patterns. As behavioral ecology models al-ready consider the influence of several factors otherthan travel costs on movement, merging the notion offunctional connectivity with the latter shall limit equiv-ocal interpretations of quantitative measures of func-tional connectivity. Such a transition should be rela-tively straightforward as many behavioral ecologymodels, especially the ones in foraging theory, are spa-tially implicit [see Stephens and Stevens (2001) for aspatially explicit, IFD model]. It goes without sayingthat this joint venture would also improve how behav-ioral ecologists treat landscape heterogeneity in theirmodels and scale-up their predictions. Nevertheless,measuring functional connectivity within the contextof complex models will bring its share of problems,especially regarding their structure and parameteriza-tion (e.g., South et al. 2002). It may necessitate field-intensive studies in order to assess, among other things,the quality and distribution of resource patches and howdifferent fitness currencies vary with patch attendance.In addition, both the physiological state of individualsand the fitness currencies that they may be maximizingwill have to be considered (Turcotte and Desrochers2003). At last, the measure of functional connectivitythat will be obtained will likely be model specific. Yet,the ways in which functional connectivity should bemeasured must be dictated by its ecological role withinspecific models or theories. This ecological role shallin turn dictate the kind of motivation underlying themovement of individuals.

Standardizing the motivation to move

Movement implies many decisions (Grubb and Bron-son 2001, Stamps 2001). An individual must first leavean area, then adjust its course and rate of travel, andultimately, settle somewhere. Those actions result frommotivations that are influenced by the state of the in-dividual. The motivation underlying the movement ofindividuals must therefore be taken into account whenmeasuring functional connectivity. For instance, it islegitimate to ask whether a forest bird moving along a


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forest edge indicates that open areas are barriers tomovement or that the forest edge is a prime foraginghabitat (Desrochers and Fortin 2000). Analogously, thelikelihood that Red-eyed Vireos (Vireo olivaceus) crossgaps in forest habitat depends on whether individualswere lured by a mobbing scene or an intruding con-specific (Desrochers et al. 2002). At last, the fact thatmovement may serve more than one need and that thosemay vary across individuals can complicate field mea-surements.

Since the cause of movement (or lack thereof) willbe difficult to identify under field conditions, especiallyat large spatial scales and during long time frames,experimental manipulations coupled with precise track-ing methods may offer the best option for obtainingmeaningful measures of functional connectivity (re-viewed by Desrochers et al. 1999). For instance, trans-locating animals allows standardizing motivationacross individuals, and if the latter happen to be sitetenacious, it also provides the individuals’ most likelydestination. Being aware of the potential destinationsthat individuals are trying to reach may be advanta-geous for determining the level of anisotropy of a land-scape with respect to its functional connectivity (Be-lisle and St. Clair 2001). The relevance of translocationexperiments for studying movement with respect tolandscape structure is starting to be recognized andapplied to various taxa such as insects (Pither and Tay-lor 1998), amphibians (M. J. Mazerolle and A. Des-rochers, unpublished manuscript), birds (Belisle et al.2001, Cooper and Walters 2002, Gobeil and Villard2002), and mammals (Bowman and Fahrig 2002,McDonald and St. Clair 2004). Playbacks to lure in-dividuals to a specific destination have also been usedsuccessfully as another means to standardize the mo-tivation of birds and address the permeability of variouslandscape elements to movement in different seasons(Harris and Reed 2001, Belisle and Desrochers 2002,Desrochers et al. 2002).

On another front, food-titration experiments couldhelp push the envelope further by allowing us to assessthe cost of reaching certain destinations (Todd andCowie 1990, Abrahams and Dill 1998). To my knowl-edge, this method has been used in landscape ecologyonly once (Turcotte and Desrochers 2003). Analo-gously, measuring giving-up densities (GUDs) in re-source patches embedded in landscapes of varyingstructures is yet another means by which travel costscould be assessed (Kohlmann and Risenhoover 1998,Price and Correll 2001). Manipulating the location ofnesting places or burrows with respect to landscapestructure and known food sources (of similar or dif-ferent quality) would also prove particularly useful toassess the travel costs implied when provisioning orhoarding food within heterogeneous landscapes (Huhtaet al. 1999, Hinsley 2000). Although manipulationssuch as food-titration experiments can be difficult toapply at spatial scales relevant to dispersal movements,

we could still induce individuals to leave or remainwithin their home range or territory by altering theirbreeding success (e.g., Doligez et al. 2002).

Studying movement is strongly hampered by the dif-ficulty of tracking animals over large expanses and dur-ing long time intervals. This is exacerbated by the tem-poral and financial constraints too often faced by ecol-ogists. Beside the sound option of pooling resourcesand working within experimental landscapes (e.g.,Haddad et al. 2003), part of the challenge of measuringfunctional connectivity will thus depend upon our abil-ity to design experiments addressing travel costs withinstandardized motivational contexts. As good ideas willeventually proliferate, it will become of interest to cor-relate the results obtained by different methods, in dif-ferent contexts, and across species with different life-histories (Desrochers et al. 1999).

CONCLUSION:ECOLOGISTS SHOULD GET ON THE MOVE

By questioning the actual operational definitions giv-en to landscape connectivity, I do not condemn the useof this concept, but call for research within a strongertheoretical framework. Behavioral ecology providessuch a framework. Many of its models already use aconcept analogous to the one of functional connectiv-ity, namely travel costs, to describe the degree to whichthe environment facilitates or impedes movementamong resource patches. Because these models predicthow animals should use resources in space and timewithin spatially-implicit landscapes, they offer a greatopportunity to link process and pattern. Landscapeecologists should be proactive and approach behavioralecologists to improve the models of the latter to thespatially-explicit nature of their own object of study:the influence of landscape structure on the abundanceand distribution of organisms. By quantifying func-tional connectivity within a stronger theoretical frame-work, landscape ecologists will certainly reduce thelikelihood of obtaining equivocal results that may havenegative implications not only for their science, butalso for biological conservation. I hope that this paperwill help favor a behavioral ecology of ecological land-scapes as advocated by Lima and Zollner (1996).

ACKNOWLEDGMENTS

Thanks to Marie-Josee Fortin for inviting me to participateto this Special Feature. Thanks also to Anurag Agrawal, Ma-rie-Josee Fortin, Marc Mazerolle, and two anonymous re-viewers for insightful comments on the previous versions ofthe manuscript. A Discovery Grant from the Natural Sciencesand Engineering Research Council of Canada financially sup-ported my work.

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MODELING ECOLOGICAL PROCESSES ACROSS SCALES

DEAN L. URBAN1

Nicholas School of the Environment and Earth Sciences, Duke University, Durham, North Carolina 27708 USA

Abstract. The issue of scaling impinges on every aspect of landscape ecology andmuch of ecology in general. Consequently, the topic has invited a vast commentary. Oneresult of scaling research is so-called scaling laws that describe how observations scale(e.g., as power laws). Importantly, such scaling rules seldom derive from a process-basedunderstanding of why they emerge. Alternatively, the task of scaling is often addressed viasimulation models. This is a scaling operation about which we are somewhat less confident,although recent advances in computing power and computational statistics provide for somepromising new solutions. Here, I focus on methods for scaling simulations developed atfine grain and small extent, to their implications over much larger extent. The intent inscaling is to simplify the model while retaining those details essential for larger-scaleapplications. This approach should lead to scaling rules that are well founded in fine-scaleecological process and yet useful for making predictions at the larger scales of managementand environmental policy.

Key words: aggregation; graph theory; hierarchy; landscape pattern; metapopulation; Markovmodel; scale; spatial heterogeneity; succession.

INTRODUCTION

A central challenge in ecology is a scaling dilemma:issues in management and policy are large scale butour best empirical understanding of ecological pro-cesses and patterns is at fine scales (Levin 1992, Urbanet al. 1999, Rastetter et al. 2003, Miller et al. 2004).Consequently, ‘‘scaling’’ is central to ecology in gen-eral and landscape ecology in particular. By ‘‘scaling,’’I mean the explicit extrapolation of details at fine grainand small extent, to their implications over larger ex-tent and generally at coarser resolution.

One result of scaling research is so-called ‘‘scalinglaws,’’ or rules that describe how processes scale, oftenexpressed as power laws:

bQ 5 km (1)

for quantity Q from measurement m, with constants kand b. Such laws seem to emerge readily in a widerange of physical and ecological systems (reviewed bySchneider 1994, 1998, 2001). While power laws seemcommon in nature, it must also be noted that these areoverwhelmingly phenomenological: we might be ableto fit the laws statistically, but we generally do notunderstand why they assume the fitted values (Schnei-der 2001). Exceptions to this are cases where the lawscan be derived from (often biophysical or thermody-namic) first principles; examples include laws based onsurface area/volume ratios (Peters 1983) or energy dis-sipation (e.g., Milne et al. 2002).

Manuscript received 3 June 2004; revised 3 September 2004;accepted 10 September 2004; final version received 26 January2005. Corresponding Editor: M. Fortin. For reprints of this Spe-cial Feature, see footnote 1, p. 1965.


More generally, ecological ‘‘first principles’’ mightbe expected to derive from basic natural history traitsand the behavior of individuals. From this perspective,the aim of scaling laws would be to integrate individualbehaviors such as habitat selection, breeding behavior,demographic processes, and dispersal to their land-scape-scale implications.

A review of the vast literature on scaling is wellbeyond the scope of this paper, and it is not my intentto provide such a review here (see, among many others,Levin 1992, Wessman 1992, Schneider 1994, Tilmanand Kareiva 1997, van Gardingen et al. 1997, Petersonand Parker 1998, Gardner et al. 2001). Rather, I intendto point to areas where research might lead to rapidand useful developments in scaling theory. I focus onmethods for extrapolating models from the typicallyfine grain and local extent of their implementation, tothe larger scales at which we would like to see thesemodels applied. In this, I emphasize how ecologicalprocesses, rather than patterns, can be scaled. Whilewe have made much progress in understanding howpatterns scale (e.g., Turner et al. 1989, Saura and Mar-tinez-Milan 2001, Shen et al. 2004, Wu 2004), ourunderstanding of process scaling lags somewhat behind(Tischendorf 2001, Wu and Hobbs 2002, Fortin et al.2003).

Scale and scaling

In this discussion, I will adhere to the conventionalusage of scale by ecologists, defined in terms of grain(or resolution)—the finest distinctions made in a dataset (or model), and extent—the scope of the study inarea or time. In lazy shorthand, small (or fine) scalewill refer to fine grain and small extent, while large


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(or coarse) scale will connote coarse grain and largeextent. Ecologists recognize that while nature itself hasfine grain and large extent, our measurements of naturetend to have correlated grain and extent: studies oversmall extent can record more detail, while studies overlarger extent tend to sacrifice grain for purely logisticalreasons.

There is a large and rapidly growing literature onscaling laws, much of this in the context of complexsystems and self-organizing criticality (Milne 1988,Schneider 2001, Strogatz 2001). From this, it can benoted that some very simple and general mechanismscan lead to power-law relationships. These include, forexample, gain and loss functions that are lagged orpartly coupled in space or time. Thus, the partiallydecoupled processes of local extinction and recoloni-zation in habitat patches can lead naturally to the fa-miliar species–area relationship, S 5 cAz. The typicalform of a scaling law, the power law (Eq. 1), describesthe allometric scaling of many ecological processes.Another form of the same relationship is

bQ(m)/Q(m ) 5 (m/m )0 0 (2)

where m0 is a measurement at a fine scale, m is somelarger scale, and the Q’s are quantities associated withmeasurements at those scales. This latter form makesit easier to define the scope of the observation system,expressed in terms of the grain (minimum resolution,m0) and extent (maximum extent, m) of measurements(Schneider 1998, 2001). Scope defines the scale domainover which the power law holds. (Without defining thescope, the implication is that the law holds over allscales.)

Models are the principle vehicle for scaling and ex-trapolation in ecology (Rastetter et al. 2003, Peters etal. 2004). Respecting the scope of a model is especiallyimportant in landscape- or larger-scale extrapolations,as an explicit goal in such applications often is to pushthe model beyond the scope of the data used to build it.

A hierarchical perspective (Allen and Starr 1982,O’Neill et al. 1986, Urban et al. 1987) provides a usefulheuristic framework for scaling: we scale correctly bybeginning at one grain and extent, then increasing ex-tent—probably encountering new constraints and newinteractions in the process—and then collapsing thegrain to define a new, higher level for analysis. In scal-ing models, this implies extending detailed, fine-scalesimulators to the landscape scale, then finding ways tosimplify these extended models so that they can beexercised usefully at larger scales.

There have been several synthetic studies of scalingwith models. King (1991, see also King et al. 1991)and Rastetter et al. (1992) considered several methodsfor extending models across scales. Levin and Pacala(1997) emphasized methods to simplify models in scal-ing, noting that, while direct extrapolation to largescales might provide a wealth of model output, it wouldnot necessarily provide any greater insight into the sys-

tem. Urban et al. (1999) considered the relative meritsof sampling approaches (i.e., distributed models),‘‘brute force’’ model extensions (i.e., use a bigger com-puter), and alternative scaling methods (see below).Rastetter et al. (2003) illustrated model-based extrap-olations based on the rich data infrastructure of theLong-term Ecological Research (LTER) network. Mill-er et al. (2004) reviewed model-based extrapolationswith an emphasis on species distributional (e.g., hab-itat) models. They addressed the statistics of extrapo-lation, including an emphasis on the propagation ofuncertainty in model-based extrapolation. Wu et al. (inpress) directly addressed uncertainty issues in scaling.

Peters et al. (2004) focused on the role of ‘‘space’’in model-based extrapolation, considering a range ofecological applications that would seem to require anexplicitly spatial model. They distinguished amongnonspatial models, implicitly spatial models in whichthe model is nonspatial but the data that drive it arespatially structured, and explicitly spatial models thatdirectly simulate neighborhood interactions or conta-gious processes. While noting that many ecological ap-plications can be addressed with simple models (non-spatial or implicitly spatial, see also Roughgarden1997), several instances seem to require explicitly spa-tial approaches (see also Strayer et al. 2003). Thesesituations include nonlinearities and thresholds, timelags and system-level feedbacks, and neighborhood in-fluences or contagious processes. These situations, ofcourse, are precisely the cases that make landscapes sointeresting!

In all of this, an underlying motivation is the implicittrade-off between model complexity—its ‘‘realism’’—and its tractability or reliability. Making a model morerealistic might make it more accurate (given sufficientunderstanding and data to implement it), but this de-creases its precision because of the error associatedwith its estimation (Rastetter et al. 1992). This trade-off, sometimes posed as a tension between sins of omis-sion and sins of commission (Peters et al. 2004), mo-tivates the goal of simplifying a fine-scale model toprovide larger-scale extrapolations.

An alternative to a computationally demanding,brute-force model extension is to simplify a model atcoarse scale and large extent, reformulating it explicitlyin terms of fine-scale processes—an approach we mightterm ‘‘elegant force.’’ Methods for reformulating mod-els include moment closure methods, compelling be-cause they can yield a larger-scale expression of theinitial model in closed form solution (e.g., Rastetter etal. 1992, Dieckmann et al. 2000). Similarly, Moorcroftet al. (2001) were able to extend a stochastic forest gapmodel to very large scales by deriving a size- and age-structured (SAS) approximation of the mean behaviorof the gap model. Alternatively, in a Bayesian approach(Ellison 2004), detailed models might be used to pro-vide informative priors for a coarse-grain, large-scalemodel—given some data to fit the coarse-scale model.

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1998 DEAN L. URBAN Ecology, Vol. 86, No. 8

In a hierarchical Bayesian approach, a large-scale mod-el can be assembled directly from nested models at finerscales (e.g., Wikle et al. 1998, Clark 2003). Here, Iillustrate another approach in which a fine-scale modelis used to parameterize a larger-scale abstraction of thefine-scale model. The abstraction is essentially a modelof the finer-scale simulator, a meta-model. This ap-proach is amenable to any simulation model (see Wil-liams et al. 1997 for an example using a soil–plant–atmosphere model), but is especially compelling forcomplicated, unwieldy simulators.

CASE STUDIES: SCALING FROM INDIVIDUALS

TO LANDSCAPES

A natural starting point for scaling from individualsto landscapes is individual-based simulation models(e.g., Dunning et al. 1995). Given object-based pro-gramming languages and software tools, this is an in-creasingly easy way to encode and implement the nat-ural history and ‘‘ecological first principles’’ of indi-viduals, integrating these to the population, commu-nity, or ecosystem level (DeAngelis and Gross 1992,DeAngelis and Mooij 2003).

Two case studies illustrate how these models can bescaled to a much larger extent. The first case is con-cerned with extending forest gap dynamics to verylarge spatial scales, while the second aims to extendforest bird behavior and demography to regional meta-populations. In both cases, a detailed, fine-scale modelis used to inform a larger-scale model that is faithfulto the details but still manageable at very large scales.

Scaling forest dynamics from trees to landscapes

The essence of the ecological scaling dilemma inforest ecology is this: we know a lot about trees, a fairbit about forest stands, but not very much about for-ested landscapes or regions; yet it is at these largerscales that management and policy apply.

Two kinds of forest models are especially well de-veloped. Gap models simulate individual trees and theirinteractions to generate aggregate stand-level behavior(e.g., Shugart 1984, Botkin 1993). Stand models sim-ulate the behavior of a stand directly, with the standsummarized in terms of average stature, compositionaltype, size distribution, or some other aggregate mea-sure. These include Markov processes, stage (age orsize class) transition models, regression-based modelssuch as yield tables, and so on. At the landscape scale,many models are extended versions of stand models(Weinstein and Shugart 1983, Baker 1989, Mladenoffand Baker 1999).

In a first-order Markovian forest model, the state ofthe system comprises a vector x summarizing the dis-tribution (area or proportions) of the study area in eachof i 5 1, m forest types, and an m 3 m matrix P oftransition probabilities or rates pij. The models are ap-pealing because of their versatility and tractability(Usher 1992, Urban and Wallin 2002), yet they can be

difficult to parameterize. For example, Horn (1975) es-timated transition probabilities by observing the inci-dence of seedlings of various species under the cano-pies of full-size trees; the assumption was that eventualtree replacement patterns could be inferred from rel-ative stem densities under each tree. Of course, dif-ferences in growth and survival related to toleranceand episodic vagaries of nature render such assump-tions overly simplistic; yet direct empirical estimatesof transitions that take place over decades are wellbeyond the scope of most field studies. Over largerscales encompassing a variety of stand types and en-vironmental settings, the empirical task becomes evenmore daunting.

Acevedo et al. (1995, 1996) developed an alternativeapproach. They began by using a gap model to simulatethe establishment, annual diameter growth, and even-tual mortality of each tree on the plot (tens to thousandsof stems) subject to a variety of species- and size-specific functions (Shugart 1984, Urban and Shugart1992). In the model, they classified each model plot (a10 3 10 m grid cell) to a discrete forest type, definedon species composition and size structure. At each timestep, each plot was reclassified and instances were tal-lied when a plot changed from one type to another.Accrued over a long simulation (e.g., 10 000 yr), thesetallies summarize the transitions that define a Markovprocess (see Allen and Shugart 1983 for an illustration).The resulting Markov model is thus parameterized ina way that is faithful to our best understanding of forestprocess as implemented in the fine-scale model, but ina form that can be applied at much larger scales. Inparticular, ecological processes such as facilitation andinhibition can be calibrated into the meta-model, to theextent that the gap model can generate these (see Hus-ton and Smith [1987] and Smith and Huston [1989] forillustrations).

Acevedo et al. (1995, 1996) actually used the tran-sition tallies to estimate a semi-Markovian simulatorthat incorporated fixed lags and distributed transitionsthat more realistically reflected the successional tran-sients, an extension that only slightly complicates theparameterization. Acevedo et al. (1995) used a similarapproach to develop a model that could simulate forestsuccession over an elevation gradient. In this, the gapmodel was run in Monte Carlo fashion over a range ofelevations, and semi-Markovian transition probabilitieswere modeled in terms of current state, time, and el-evation (a proxy for temperature, via lapse rates).

More generally, Urban et al. (1999) illustrated thatthis approach could be used to generate a variety ofcoarser resolution meta-models. For example, theyused the same gap model (based on Urban et al. 1993)to develop a cellular automaton, a semi-Markov model,and a stage-based transition model framed in terms oftree diameter classes per species (see also Garman2004). Each of these model forms had particularstrengths and weaknesses. The cellular automaton was


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especially effective in modeling spatial processes (firespread, seed dispersal) while providing only crude suc-cessional transients. The semi-Markov model providedmuch more realistic transients, but ignored spatial pro-cesses. The stage-based model was especially amenableto exploring timber-management scenarios, as thesetreatments are framed in terms of species and diameterselections. Urban et al. (1999) suggested that this sameapproach could be generalized to derive a wide rangeof application-specific meta-models. That is, particulardetails can be abstracted into meta-models of variousforms, depending on the application. Acevedo et al.(2001) have simplified this approach by largely auto-mating the model estimation process, from initial gap-model simulations to final calibration of the meta-model.

Thus far, relatively little has been done with thesemeta-models to gain a more compact understanding ofor more general predictions about landscapes. But thereis plenty of raw material available. The cellular autom-aton meta-model MetaFor (Urban et al. 1999) providesan illustration. MetaFor incorporates the basic agentsof pattern formation in forested landscapes (Urban etal. 1987, 2000): the physical template, expressed inthis case as gradients in temperature and soil moistureover a range of elevation; biotic processes, representedby successional relationships mediated by species tol-erances to cold and drought, as well as local seed dis-persal; and disturbance, here as contagious fire, rep-resented by fire spread conditioned on forest age (fuelload) and soil (fuel) moisture. The meta-model wasbuilt from and calibrated to a more complicated gapmodel implemented and tested for Sierran mixed-co-nifer forests (Miller and Urban 1999, Urban 2000, Ur-ban et al. 2000).

As a tutorial on landscape pattern evolution, MetaForwas run in a factorial design on a hypothetical land-scape with/without an environmental gradient and with/without local seed dispersal. Three representative spe-cies were included: ponderosa pine (Pinus ponderosa),white fir (Abies concolor), and lodgepole pine (P. con-torta). White fir grows faster than either pine. Impor-tantly, each species grows best at mid-elevations.Through competition, ponderosa pine is displaced tolower elevations due to its lower growth rate but highertolerance to drought (which increases at lower eleva-tions). Lodgepole pine is displaced to higher elevationsdue to its slower growth but better cold tolerance (itis also least tolerant of drought). This result is as sim-ulated by the gap model and is consistent with thegeneral patterns suggested by Smith and Huston(1989). The factorial model experiment illustrates nice-ly the implications of interactions among competition,gradient response, and local dispersal in generatingspatial pattern (Fig. 1) as well as relative abundancepatterns (Fig. 2). In particular, in the ‘‘gradient 1 localdispersal’’ case (lower right panel in Figs. 1 and 2),the effects of competition and mass effects are both

apparent: each of the species occupies its ‘‘character-istic’’ elevation range, dominance within these zonesis amplified by mass effects, and the ecotones are re-inforced by local dispersal.

While simple and intuitive when presented in thisway, this illustration also has a more profound impli-cation for large-scale studies of forests. Given com-petitive hierarchies and local dispersal, in general it isnot possible to infer the environmental tolerances of aspecies from observations of its abundance. That is,the environmental mode for a species need not (andgenerally does not) occur where the species achievesits best demographic performance. At a fine scale, wealready know this; this is a key distinction in the Hutch-insonion concept of the fundamental as compared torealized niche. Despite this, we often use species abun-dances at larger scales to estimate environmental tol-erances (e.g., Iverson and Prasad 1998). Somewhatironically, this result, illustrated so nicely with gapmodels, also invalidates the scheme by which mostearly gap models were parameterized from speciesrange data (e.g., Botkin et al. 1972, Shugart 1984).

The meta-modeling approach is not a panacea forlandscape-scale applications. Because it is defined toreproduce selected behaviors of the fine-scale model,the meta-model can only be as good as the originalmodel. Thus, for a fine-scale model that is not wellvalidated, the meta-model extension represents thelarge-scale implications of a working hypothesis ascompared to a specific prediction. In trade, the simplermeta-model might yield new insights into large-scalebehaviors of the system, simply by jettisoning the over-whelming detail of the fine-scale model. Indeed, forsome forms of meta-models there can be an analyticsolution (e.g., Acevedo et al. 1996).

If a model is a simplification of a real system thena meta-model is doubly simplified, in that only selectedfeatures are abstracted to the meta-model. Urban et al.(1999) recommended using the models in combination:the detailed model is used to derive a meta-model, themeta-model is used to pose hypotheses or explore im-plications at large scale and coarse resolution, but thedetailed model is retained to examine special cases(e.g., conditions near thresholds, complicated transientbehaviors).

There is much to explore in this realm. For example,we know that the fine-scale details of dispersal can havequalitative implications for forest dynamics (e.g., viafat-tailed dispersal kernels; Clark et al. 1998, 1999).Intriguingly, tree dispersal kernels are scaled similarlyto topographic pattern (Urban et al. 2000), inviting thepossibility for interference or resonance between de-mographic process and environmental constraints.Likewise, details about species-specific or size-specificgrowth and mortality rates are important in gap modelsfor which these field measurements are available (e.g.,Pacala et al. 1993, 1996). Thus, it is crucial that larger-scale models incorporate the fine-scale details that mat-

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FIG. 1. Illustration of feedbacks between gradient response and seed dispersal in a competition-mediated cellular autom-aton, called MetaFor. In the lower panels, the gradient runs from hot/dry to cold/wet from bottom to top of the figure. Inthe right panels, dispersal is implemented as a cellular automaton with eight-cell neighborhoods. Species are ponderosa pine(orange), white fir (green), and lodgepole pine (blue). Species ranks: for growth rates, white fir . ponderosa pine ø lodgepolepine; for drought tolerance, ponderosa pine . white fir . lodgepole pine; for cold tolerance, lodgepole pine . white fir .ponderosa pine. Maps are snapshots at year 1000 of a simulation from random initial conditions.

ter while also broaching new constraints and interac-tions that emerge at larger scales.

Extending bird demography to regionalmetapopulations

There are many approaches to modeling metapop-ulations, including patch-centered vs. landscape ap-proaches (so-called ‘‘island’’ vs. ‘‘mosaic’’ models),and there is a range of opinions about how the detailsof these systems should be represented (see Belisle2005). Here, I use one approach, an individual-based

‘‘island’’ model, to illustrate another example of meta-modeling.

Urban and Shugart (1986) developed an individual-based metapopulation simulator at a time when this taskwas near the limits of computational feasibility. Today,there is much less computational constraint on the lim-its to the ecological richness that might be implementedinto a spatially explicit, individual-based model(DeAngelis and Mooij 2003). Still, the large scale ofconservation planning can make such models cumber-some in application. More importantly, the data needed


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FIG. 2. Species abundance patterns for the panels shown in Fig. 1. Abundances are tallied by rows, then plotted againstthe elevation gradient. These are rotated from Fig. 1 for clarity; thus, abundances along the gradient (bottom to top in Fig.1) are plotted right to left in Fig. 2. Species are ponderosa pine (orange), white fir (green), and lodgepole pine (blue).

to parameterize such models confidently are often lim-ited, especially over large scales. This motivates asearch for more macroscopic approaches that can beapplied over very large scales, with rather limited fine-scale data, and yet provide useful predictions aboutmetapopulation dynamics and their conservation im-plications (Keitt et al. 1997).

Urban and Keitt (2001) turned to graph theory (Har-ary 1969) as a more general framework in which toexamine patterns of connectivity in landscapes. Agraph is a set of nodes (points; here, as centroids ofhabitat patches) and edges (lines connecting twonodes if the patches are functionally connected, e.g.,by dispersal). Graphs are used routinely in other dis-ciplines to model networks of various sorts: trans-portation, communication, computer networks, etc.(Hayes 2000a, b); in biology, graphs are used in sys-

tematics and food webs. Graph theory is extremelywell developed as a ‘‘pure math’’ discipline as wellas in practical applications (e.g., Gross and Yellen1999, Wallis 2000).

In modeling landscapes as graphs, Urban and Keitt(2001) illustrated how basic graph operations such asshortest paths and minimum spanning trees could pro-vide useful insights into landscape connectivity. Im-portantly, while graph models appear quite simple vi-sually, they nonetheless can incorporate a wealth ofecological information about habitat suitability and dis-persal behavior. For example, Bunn et al. (2000) fol-lowed the protocol of Urban and Keitt (2001) but re-fined the model by using resistance-weighted dispersaldistances to define graph edges. In this, actual distancesare replaced by functional distances estimated to reflectbarriers or resistance to dispersal of each cover type

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within the landscape. Similarly, information about hab-itat patches can be incorporated into the graph nodes.For example, E. S. Minor, R. I. McDonald, E. A. Treml,and D. L. Urban (unpublished manuscript) adjustedpatch area to reflect habitat quality, in effect reducingcarrying capacity and recruitment potential in marginalhabitat patches. Other details on habitat quality or de-mographic behavior can be incorporated into the graphdepending on available data.

E. S. Minor and D. L. Urban (unpublished manu-script) explicitly compared assessments based on agraph model with the predictions of a spatially explicit,individual-based metapopulation model (updated fromUrban and Shugart [1986]). They used Landsat The-matic Mapper imagery and ground vegetation samplesto classify forests as potential habitat for the WoodThrush (Hylocichla mustelina), a neotropical migrantof some concern to conservationists. They constructeda graph model for the species, covering a broad regionin the North Carolina Piedmont centered on the citiesof Durham, Chapel Hill, and Raleigh (the Triangle).The study area includes on the order of 10 000 forestpatches, making direct simulation with the metapop-ulation model rather cumbersome. Their approach wasto use the simulation model to establish the corre-spondence between the detailed simulator and the graphmodel, then use the graph model for regional assess-ments.

The metapopulation simulator tracks each bird (ter-ritorial breeders and nonterritorial floaters) in each hab-itat patch of the landscape mosaic. Each year, eachbreeder attempts a species-specific number of broods,each with a typical clutch size. Breeding attemptsfledge young stochastically and each attempt may bereduced by brood parasitism by cowbirds (Molothrusater) or lost to nest predation. Parasitism and predationare edge effects in that their incidence (probability)increases with proximity to a nonforest edge. Fledg-lings disperse stochastically in search of unoccupiedbreeding habitat; carrying capacity for each patch isdefined in terms of territory size for the species. Dis-persal probabilities are based on between-patch dis-tances, assuming a negative-exponential dispersal ker-nel estimated from published banding studies (see Han-ski and Ovaskainen [2000] and Ovaskainen and Hanksi[2001] for a similar approach).

While the metapopulation simulator is quite com-plicated in terms of its demographic bookkeeping, thesimulator and graph model use exactly the same inputin terms of habitat descriptions and dispersal proba-bilities; the habitat patches become graph nodes andthe dispersal probabilities are used to define graph edg-es. Thus, the graph becomes a meta-model by incor-porating the essential details of the simulator. Thegraph analysis, however, can be extended to habitatmosaics that are orders of magnitude larger than canbe simulated with the detailed model.

E. S. Minor and D. L. Urban (unpublished manu-script) found general agreement between the detailedsimulator and the graph model, in that the two modelsidentified most of the same patches as being importantto regional metapopulation persistence (Fig. 3). Thissuggests that the graph model, defined in terms of rel-evant ecological details, can be used to extrapolatethese details over much larger scales. Minor is currentlyconducting field surveys to confirm that the predictionsof both models are supported by census data. In thisvalidation effort, the graph model also serves as a sam-pling template, providing a vehicle for selecting fieldsites to test the model efficiently (Urban 2000, 2002).That is, candidate sites for field censuses are selectedfrom the landscape by stratifying sites over a range ofsize and connectivity as defined by the graph model.

Graph-theoretic models seem quite promising for ap-plications couched in metapopulation theory: basicgraph operations can address both source-sink (Pulliam1988) and spreading-of-risk (Levins 1969) conceptualmodels (Urban and Keitt 2001). Yet we have onlyscratched the surface of available theory. For example,Franc (2004) explored metapopulation dynamics as ep-idemiological contact processes on graphs, and high-lighted key results in connectivity that depend only onthe degree distribution of the graph. The degree of anode is the number of edges connected to it, and thefrequency distribution of degrees for a graph can, insome cases, index the behavior of the graph indepen-dently of the graph’s actual topology; sometimes themean degree is sufficient. Such relationships have re-ceived considerable attention in network analysis, forexample, in analyzing how computer viruses spread onthe Internet (Strogatz 2001). These studies focus onhow the structure of the graph predicts its dynamicalbehavior and resilience to node loss; again, the parallelto conservation applications couched in metapopula-tion theory is quite clear.

A graph-theoretic perspective might provide usefulinsight in reconciling ‘‘patch-based’’ and ‘‘landscape-scale’’ assessments in metapopulation or landscapestudies (e.g., Lee et al. 2002). In the former, the goalis to predict species occurrence, abundance, or diversityin terms of patch-level descriptors such as size (area),shape (edge/area ratio), or isolation (measured in var-ious ways). In the latter approach, average or syntheticindices at the landscape scale are used to predict overallabundance, persistence or diversity; examples includethe predictions of neutral-model landscapes framed interms of habitat amount ( p) and contagion (H ) (Gard-ner et al. 1987, With and King 1997, King and With2002). In a graph, levels of organization can be definedas separate subgraphs (i.e., connected components, Fig.3 top), based on a specified threshold distance (Urbanand Keitt 2001). If these components are scaled ap-propriately to dispersal, patches in the same componentshould behave similarly over time compared to patchesin different components. Thus, graph components pre-


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FIG. 3. Correspondence between results of an individual-based, spatially explicit metapopulation simulator and macro-scopic graph-theoretic assessment of the same landscape. Patches are contiguous cells of potential habitat, as classified fromThematic Mapper imagery. Top panel: graph of the landscape, with nodes at patch centroids and edges drawn for thosepatches within 2500 m distance. While this graph is largely connected, note locations (red arrows) where loss of a nodewould cut the graph into separate components. Darker patches are more important to population persistence. Lower panel:patches shaded similarly, based on their importance estimated with an individual-based, spatially explicit simulator.

sent themselves as natural levels of analysis for land-scapes. This perspective is easily reconciled withpatch-level analyses: the component to which eachpatch belongs could be entered into a regression as adummy variable; a significant effect for this dummyvariable would indicate higher-level organization than

the patch scale. (Reciprocally, this same result, ifstrong, would suggest that patches in the same com-ponent were pseudoreplicated in that their populationswould not be strictly independent.) Importantly, thegraph model provides a rigorous framework withinwhich the node (patch), component, and graph (land-

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scape) levels can be reconciled explicitly. By exten-sion, if one were to define graph components over arange of threshold distances (see Urban and Keitt 2001for an illustration), this dummy-variable testing ap-proach could be used to infer which distance bestmatches the data, and by implication, best reflects thenatural scaling of the species relative to landscape pat-tern.

CONCLUSIONS AND PROSPECTUS

While we have had some success in extending de-tailed models to larger scales, we have made less pro-gress in generating useful insights at these larger scales.Many applications have been concerned with simply‘‘filling in the map’’ (a single prediction), rather thananalyzing the model to discover general insights arisingfrom the fine-scale processes. At the same time, mod-eling applications concerned with general theory oftenhave been quite abstract, divorced from the rich naturalhistory and complicated pattern of real species on reallandscapes. Our challenge is to reconcile these ap-proaches, to generate theory based on the implicationsof natural history and fine-scale processes as these areexpressed at larger scales.

Testing this theory will pose a challenge. The meta-modeling approach implies three levels of tests: vali-dating the detailed, fine-scale model, verifying that themeta-model faithfully matches the detailed model, andvalidating the meta-model over larger scales. Garman(2004) illustrates several such tests. While we are be-coming more sophisticated about model testing in gen-eral (e.g., Canham et al. 2003), the lack of detailed dataover large scales will continue to be an issue. Oneapproach to testing the theory will be to use the modelsthemselves as sampling frames, so that field data canbe collected as efficiently as possible and with maxi-mum information for model tests (Urban 2000, 2002).

Another compelling challenge is to determine whichfine-scale details actually matter at larger scales. In this,the compact efficiency of simplified models such asmeta-models provides a useful approach. By abstract-ing different details into a series of meta-models, wecan generate competing models that can be evaluatedagainst the same data. The model-selection processthen becomes a means of determining which details aremost important at the larger scale. For example, theforest patterns generated by four versions of MetaFor(Figs. 1 and 2) might be compared to patterns censusedin the field or mapped from high-resolution imagery.Similarly, competing graph models (Fig. 3) could begenerated by making different assumptions about dis-persal capabilities, and tested against census data tac-tically collected over a range of (modeled) connectiv-ity. This competing (meta)-model strategy would seemto offer a way to push our theory to larger scales withstatistical rigor and efficiency.

I have pointed to a few alternative approaches tomodel scaling, from elegantly analytic (e.g., moment

closure methods) to less elegant but more generallyaccessible meta-modeling techniques; other approachessuch as hierarchical Bayesian models are also prom-ising. Regardless of the approach, the challenge cur-rently is to find useful generalizations at the landscapescale, general insights phrased in macroscopic termswhile still respecting the ecological details we celebrateat finer scales.

ACKNOWLEDGMENTS

My work with forest meta-models was initiated under NSFgrant DBI-96-30606; the Sierran forest study has been sup-ported by USGS/BRD Coop. Agreement 99WRA0019 andNSF grants IBN-96-52656 and DEB-01-08191. The TriangleLandscape Change project, including the bird metapopulationstudy, has been supported by NSF grant SBR-98-17755. Mi-guel Acevedo has been the driving force behind our workwith meta-models of forests; my foray into graph theory hasbeen guided by Tim Keitt. Emily Minor and Marie-JoseeFortin provided helpful reviews of an earlier draft of thismanuscript.

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MANAGING LANDSCAPES FOR CONSERVATION UNDER UNCERTAINTY

M. A. BURGMAN,1,3 D. B. LINDENMAYER,2 AND J. ELITH1

1School of Botany, University of Melbourne, Parkville 3010 Australia2Centre for Resource and Environmental Studies, Australian National University, ACT 0200 Australia

Abstract. In ecology, populations may be linked conceptually with landscapes throughhabitat and spatial population models. Usually, these models deal with single species andtreat a range of uncertainties implicitly and explicitly. They assist managers in testingdifferent management scenarios and making strategic decisions. Landscape pattern analysiswas the first attempt to deal with multiple species, and it led to a range of landscapemanagement strategies. Advances in landscape ecology, driven largely by the pragmaticneeds of conservation, are building approaches to multispecies management that havestronger ecological foundations. However, their treatment of uncertainty is in its infancy.In this paper, we provide examples to illustrate some of these issues. We conclude that oneof the most important sources of uncertainty is the choice of the modeling frame. Werecommend that landscape planners use different kinds of models, identify important sourcesof uncertainty that may affect planning decisions, and seek options that are likely to resultin tolerable outcomes, despite uncertainty.

Key words: decision theory; focal species; habitat maps; landscape ecology; metapopulations;nested subsets; reserve design; spatial pattern.

INTRODUCTION

Habitat loss causes losses of biodiversity worldwide(Fahrig 2003, Hobbs and Yates 2003). Forman (1995,Forman and Godron 1986) sparked conservation in-terest in landscape ecology by predicting that speciesand ecological systems may be conserved by managinglandscape-scale patterns and processes. Hanski andGilpin (1991) predicted the merger of ideas in land-scape ecology, community ecology, and metapopula-tion theory. A synthesis has not yet occurred, in partbecause they employ different jargon and use differentanalytical tools (Moilanen and Hanski 2001). In fact,perspectives have become more divergent. The rangeof tools has multiplied without a critical evaluation oftheir role in the broader context of making decisionsto conserve landscapes.

The objectives of this paper are to outline approachesto modeling in landscape ecology, to document theiruncertainties, and to evaluate ways of using them tomake decisions under uncertainty. In particular, we willpoint towards new developments that might improvethe ways in which uncertainty is acknowledged andincluded in decision making. This topic is importantbecause unacknowledged uncertainty leads to optimis-tic expectations that cannot be satisfied, to the misdi-rection of scarce conservation resources, and to actionsthat are blind to substantial qualitative and quantitativeuncertainties that, if they were apparent, would lead todifferent decisions.

Manuscript received 2 June 2004; revised 21 September 2004;accepted 21 September 2004. Corresponding Editor: M. Fortin.For reprints of this Special Feature, see footnote 1, p. 1965.


In the first part of this paper, we outline briefly thebroad conceptual frameworks for linking species withtheir landscapes, namely habitat models and spatialpopulation models, and examine how they deal withuncertainty. In the second part, we explore conceptualresponses to the more difficult issue of managing mul-tiple species, and how these concepts are translated intopractical management tools. Last, we evaluate synthe-ses emerging in practical applications, how they areused to conserve species at a landscape scale, and howthey deal with uncertainty.

LINKING SINGLE SPECIES TO A LANDSCAPE

In broad terms, landscape managers create concep-tual and quantitative models to simplify problems andguide decisions, usually employing a specific set ofskills that result from training and context. A conse-quence is that the choice of a kind of model (heretermed the ‘‘modeling frame’’) brings with it an un-acknowledged set of biases and assumptions. Land-scape ecology focuses on the link between the spatialpattern of a landscape and the dynamics of the speciesit supports. There are many ways to explore and char-acterize this link. Commonly, the first step is to acquireknowledge about the link through experiment or fieldobservation. To achieve this, landscape modelers needto work with field ecologists to develop a sense of thescale and context of practical problems. Models canthen be developed, often focusing on one species at atime. These are usually habitat models or spatially ex-plicit population models. The following section out-lines the essential features of these modeling approach-es, the conventions they have adopted for representing

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2008 M. A. BURGMAN ET AL. Ecology, Vol. 86, No. 8

TABLE 1. Habitat modeling methods arranged by their demands for data (after Elith and Burgman 2003).

Type of habitat model Data References

Habitat suitability index Map(s) of variables and experts U.S. Fish and Wildlife Service (1980), Burg-man et al. (2001)

Minimum convex polygons, al-pha hulls, kernels

Locations only Ostro et al. (1999), Burgman and Fox (2003)

Climate envelopes, multivariatedistance methods

Locations and maps of variables Nix (1986), Carpenter et al. (1993), Hirzel etal. (2001)

Resource selection functions Locations, random (available) loca-tions, and maps of variables

Manly et al. (2002)

Generalized linear models(GLMs; logistic regression),generalized additive models(GAMs), canonical correlationanalysis

Presence/absence (where absence isunused locations or pseudo-ab-sence) and maps of variables

McCullagh and Nelder (1989), Hastie and Tib-shriani (1990), Austin (2002), Zaniewski etal. (2002), ter Braak (1986)

GLMs or GAMs (Poisson re-gression)

Abundance and maps of variables McCullagh and Nelder (1989), Hastie and Tib-shriani (1990)

Decision trees, multivariateadaptive regression splines(MARS), machine learningmethods (e.g., neural net-works, genetic algorithms)

In theory, many of these can beadapted to any data.

Breiman et al. (1984), Stockwell and Peters(1999), Moisen and Frescino (2002)

FIG. 1. Habitat models for Leptospermum grandifolium inCentral Highlands, Victoria, Australia. (a) An ‘‘average’’ hab-itat model: a Bayesian model average (BMA) prediction forthe habitat of Leptospermum grandifolium. (b) Upper and (c)lower 95% confidence intervals for the predicted probabilitiesbased on a generalized linear model. (d) A habitat modelbased on DOMAIN, a multivariate distance method (Carpen-ter et al. 1993).

uncertainty, and how the choice of a modeling framemay affect landscape management decisions.

Habitat models

Habitat models link the distribution of a species di-rectly to environmental variables, taking on a landscapecontext when mapped in geographic space. Habitatmodeling methods suit a variety of data, contexts, andskills. They include expert habitat suitability indices,

envelope methods, multivariate and statistical models,and machine learning methods (Table 1). All can pro-vide predictions of species distributions across a land-scape, if the necessary data are available in a spatialform at an appropriate scale. Fig. 1a provides an ex-ample of a statistical model for a rare plant in southernAustralia, based on presence–absence records and spa-tial environmental data (Elith 2000, Elith and Burgman2003). Such models are used to guide biological sur-veys, design reserves and set resource management pri-orities.

Habitat maps usually are presented, used, and eval-uated as if they were certain. In reality, there are nu-merous sources of uncertainty. For instance, modelstructure (choice of relevant variables, response shapes,methods for combining and weighting variables andaccounting for spatial autocorrelation) is uncertain.Habitat models are sensitive to uncertainty in the un-derlying data layers and to the number, bias, accuracy,and representativeness of species records. Disturbanceand other temporal dynamics make habitat maps un-certain. Most habitat maps take a static view of therelationship between a species and its environment, ig-noring changes over time with ecological successionand disturbance. Maps are empirical and based on cor-relations and do not easily include causality. All ofthese sources of uncertainty, and others, are present inmost habitat maps and should be recognized if we areto identify problems, correct errors and account for theuncertainty in predictions.

Elith et al. (2002) outlined a classification of uncer-tainties in habitat models. At the highest level, it dis-tinguished between epistemic uncertainty (uncertaintyin knowledge about facts) and linguistic uncertainty(uncertainty based on language). It recognized mea-surement error, bias, natural variation, model uncer-tainty, and subjective uncertainty as forms of epistemic


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TABLE 2. Spatial population modeling methods.

Type of model Data References

Stochastic patch occupancymodels

Patch structure, occupancy, recolonization, andextinction rates

Hanski (1994), Ovaskainen andHanski (2004), Moilanen (2004)

Frequency (population) model Patch structure, population sizes, dispersal, fe-cundity, survival, carrying capacity, levelsof variation

Akcakaya and Ferson (1992), Ak-cakaya (2001)

Cellular automata Grid-based environmental data, dispersal char-acteristics, carrying capacity

Hogeweg (1988), Gaylord andNishidate (1996)

Continuous habitat quality meta-population model

Each cell has habitat quality that affects ex-tinction and colonization rates.

Gu et al. (2002)

Agent-based model Grid-based environmental data, behavioralrules

Topping et al. (2003)

Individual-based model Distributions of individuals, high-resolutionhabitat suitability data, behavioral rules

DeAngelis and Gross (1992),Grimm (1999), Wiegand et al.(2003)

uncertainty. Linguistic sources included vagueness (na-ture and language have gradual boundaries), ambiguity(words have more than one meaning) and underspe-cificity (unwanted generality in data).

Many habitat modeling methods, such as climate andgeographic envelopes, have no formal means of rep-resenting uncertainty. Some methods are available todeal with uncertainty explicitly, but different methodsreflect very different aspects. For instance, subjectiveand linguistic uncertainties may be represented in hab-itat suitability maps with fuzzy numbers (Burgman etal. 2001). In contrast, parameter uncertainty in statis-tical models may be represented with confidence in-tervals. Fig. 1b and c show the 95% confidence inter-vals for the ‘‘best estimate’’ of a regression model. Thebounds encapsulate parameter uncertainty and some ofthe uncertainties in the input data. Often, several al-ternative habitat models are plausible (e.g., Wintle etal. 2004). Model uncertainty may be represented byintervals that encompass several statistical models(Burnham and Anderson 2002) or reduced by usingrobust methods for model building (e.g., lasso, ridgeregression, boosting; see Hastie et al. 2001). Bias andimprecision may be estimated by evaluating maps withnew field data (Elith and Burgman 2003) or exploredby simulating likely errors. Established methods char-acterize how uncertainty propagates through models(e.g., Heuvelink 1998). Whilst there are many tech-niques for exploring, characterizing and reducing un-certainty, most modelers fail to use any of them. Wesuggest that the only way to broaden our understandingof error and uncertainty and its impact on planningdecisions is to incorporate analyses of uncertainty inmodeling routinely.

Further, the decision to use a particular modelingframe brings with it inherent uncertainties. For in-stance, envelope methods based on climate variablestend to overpredict habitat. Geographic envelopesbased on small samples tend to underpredict habitat(Burgman and Fox 2003). Models that do not incor-porate complex responses to environments, interac-tions, or competition may be ecologically unrealistic

(Leathwick and Austin 2001, Austin 2002). We addmodeling frame uncertainty to Elith et al.’s (2002) tax-onomy, a form of uncertainty in which the choice of amodeling frame leads us to ignore a subset of the fullsuite of epistemic and linguistic uncertainties.

The choice of a habitat modeling frame is usuallydetermined by available data and relevant skills. Rarelyis more than one frame applied, even though predic-tions may be substantially different (e.g., Thuiller2003). Thus, Fig. 1d represents a different, plausibleprediction for the distribution for the rare plant basedon multivariate distances, clearly outside the 95% con-fidence intervals of the statistical model. The only wayto explore the impact of this kind of uncertainty is totry different modeling frames. If the results lead todifferent management decisions, the planner should ex-plore the biological basis for the modeling frames, orchoose an option that gives a reasonable outcome, ir-respective of which habitat model is right. We alsosuggest that there should be a strong imperative formodelers to understand and report the tendencies andlikely shortcomings of the modeling frame that theyuse, rather than publish results that imply that theirpreferred method is best and free of biases and errors.All models are false, and understanding their strengthsand weaknesses will encourage informed use.

Spatial population models

Most habitat maps link presence or abundance toenvironmental data but, as Van Horne (1983) pointedout, the links between habitat occupancy, density anddemographic success are not necessarily close. Spatialpopulation models provide a bridge between habitatmaps and the demography and ecology of a species(Fahrig 2003, in press).

Spatial population models encompass multiple mod-eling frames. These include incidence functions, sto-chastic patch occupancy models, frequency models,agent-based models, cellular automata, and individualbased models (see Table 2 for references and exam-ples). Metapopulation models assume more or less dis-crete local populations that interact by migration and

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FIG. 2. (a) The ‘‘biodiversity spine’’ (black), a planning option for forest destined for harvesting and plantation conversionin northeast Tasmania. The spine was designed around the idea of maintaining a spatial pattern that would facilitate dispersaland a source of individuals for recolonization of disturbed patches in a forested landscape. It forms links with existingreserves (gray). Biodiversity spines will be disturbed by forest operations but are intended to be managed for flora and faunavalues more intensively than the remaining landscape. (b) The probability of decline of Simson’s stag beetle (Hoplogonussimsoni) in northeast Tasmania, with and without the biodiversity spine shown in (a). The lines are the cumulative probabilitiesof falling below the specified threshold population size at least once in the next 100 years. The dotted lines show 95%confidence intervals for the risk curves (Akcakaya 2001).

gene flow (Hanski and Gaggiotti 2004). All are drivenby some kind of spatial representation of a species’habitat. However, the ways the models use spatial hab-itat information are very different. Some incidencefunctions and frequency models simplify the landscapeinto habitat, nonhabitat, and dispersal pathways. Forinstance, Akcakaya and Ferson (1992, Akcakaya 2001)developed a spatial algorithm to interpret the size andlocation of subpopulations and the connections be-tween them, based on a habitat quality threshold andneighborhood size. Thus, patch size and connectionsmay be conditioned by knowledge of a species’ be-havior, social structure, and dispersal ability. In con-trast, most cellular automata and individual-based mod-els use spatial environmental data or habitat modelsmore directly. For example, Gu et al. (2002) developeda spatial incidence function metapopulation model thatused habitat maps, regional (spatially autocorrelated)disturbance, dispersal, connectivity, and local extinc-tions.

Spatial population models deal explicitly with sev-eral aspects of uncertainty. Population models typicallyinclude natural variation with time-dependent modelparameters. Parameter uncertainty may be incorporatedin random samples of initial conditions. Many frame-works model spatially explicit disturbances and chang-es in habitat quality over time (Possingham 1996, Ak-cakaya et al. 2004). The uncertain outcomes of alter-native management options can be explored by rep-resenting them as different model structures andassumptions. The importance of changes in parametersmay be evaluated by comparing model outcomes with

those that result from models that are unchanged, theusual focus of formal sensitivity analysis. For example,Fig. 2a shows a planning option for forests in an areaof northeast Tasmania. The biodiversity spine is a plan-ning concept based on landscape-planning principles.The efficacy of this option in reducing the risk of pop-ulation decline for Simson’s Stag Beetle was evaluatedwith a frequency-based metapopulation model (Fig.2b). A range of such options may be ranked in termsof costs and benefits.

Parameter uncertainty alone may be large enough toaffect decisions based on population models (Taylor1995, Beissinger and Westphal 1998, Ludwig 1999,Reed et al. 2002). The choice of a population dynamicmodeling frame carries with it additional embeddedassumptions and simplifications, many of which are notquestioned closely in routine applications because theyare conventionally acceptable (cf., Brigham and Thom-son 2003). Building models in different frames andexamining the consequences will test the importanceof these assumptions. For example, Mooij and De-Angelis (2003) explored the propagation of uncertaintyin animal dispersal models in three modeling frames.They concluded that building ecological realism intocomplex models provides insurance against compound-ing errors. In addition to simulation approaches, thereare likely to be theoretical and analytical solutions tothe problem of assessing the errors associated with amodel frame and this work would represent an excitingnew research direction.

Even within a given modeling frame, usually thereare alternative plausible models. Structural (model) un-


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TABLE 3. Landscape pattern models.

Type of landscapepattern model Data Ecological considerations References

Island habitat/nonhabitat (forall species)

Sharp discontinuities, uninhabitablematrix, habitat is static and iden-tical for all species

MacArthur and Wilson(1967), Rosenzweig(1995)

Patch-matrix-corridor habitat/nonhabitat, dis-persal pathways (forall species)

Sharp discontinuities, uninhabitablematrix, habitat is static and iden-tical for all species

Forman (1995)

Habitat variegation grades of habitat suit-ability, dispersal path-ways

Habitat is static and identical for allspecies.

McIntyre and Hobbs(1999)

Gradient concept environmental data,knowledge of speciesresponse to environ-ment

Species respond to environment aspattern gradients at different in-tensities (resolutions).

McGarigal and Cushman(2005)

Environmental domains ecologically relevant en-vironmental variables

Habitat is determined by definedcombinations of environmentaldrivers.

Leathwick et al. (2003)

certainty is rarely considered (cf., Pascual et al. 1997).They can be evaluated by changing model structuresand dependencies, re-estimating parameters and reas-sessing management options. If alternative structureslead to different decisions, then landscape plannersmay choose among or average over alternatives (e.g.,Fig. 1a), or take decisions that lead to acceptable out-comes, irrespective of which model is correct.

While the potential for relatively comprehensive ex-amination of uncertainty exists in most populationmodeling frames, in many applications, such analysesare cursory or entirely absent. For instance, spatial pop-ulation models do not account for the range of uncer-tainties in the underlying habitat maps outlined above.Until recently, most have ignored temporal habitat dy-namics, interactions between multiple species and cor-relations in environmental conditions between spatiallyseparate patches of habitat. Population modeling wouldbe strengthened by new research on these issues.

Like habitat models, the choice of a modeling frameshould not depend on the availability of relevant skillsbut in practice, it often does. Perhaps the most difficultissue of all is that spatial population models treat singlespecies. Few applications support analyses of multipleinteracting species in dynamic landscapes. Spatial pop-ulation models provide managers with a tool for ex-ploring the trade-offs and assumptions surroundingmanagement alternatives. Their detail and spatial scaleare flexible and can be modified to suit case-specificquestions. However, as long as they remain focused onsingle species, their utility will remain limited to solv-ing iconic and economically important problems. Ad-vances in methods for considering multiple specieswould be particularly useful.

LINKING MANY SPECIES TO A LANDSCAPE THROUGH

PATTERN ANALYSIS

Forman’s (1995) concept of landscape pattern wasan attempt to reconcile the absence of direct infor-mation about the majority of species with the need to

make decisions about how to manage landscapes. Land-scape pattern models characterize the size, shape andarrangement of elements in a landscape and relate themto environmental variables that maintain species di-versity and ecological processes. They include the is-land model (MacArthur and Wilson 1967; see reviewby Haila 2002), Forman’s (1995) patch-corridor-matrixmosaic, and models that focus more on gradients suchas habitat variegation, the gradient concept and envi-ronmental domains (Table 3). Landscape patterns de-fined by these models may be quantified with patternindices that measure heterogeneity, spatial contagion,fractal dimension, connectivity and so on (e.g., O’Neillet al. 1988, Li and Reynolds 1994), although attributesrelevant for a specific question, and the scale at whichthey should be evaluated, need to be defined in termsof the organisms’ characteristics (Lindenmayer et al.2002, Moilanen and Nieminen 2002, With 2004,McGarigal and Cushman 2005).

In general, landscape pattern models ignore uncer-tainty. Indices of spatial pattern are uncertain becausehabitat quality is heterogeneous within patches, andgradients vary with different stages of an organism’slife history, with ecological succession and followingdisturbance (Whittaker et al. 1973, Austin 1999, Foxand Fox 2000). Different species use landscapes dif-ferently and at different scales, making it difficult toabstract landscape properties in a way that makes sensefor all, or even for most, species (Wiens 1994, Manninget al. 2004). For example, Fig. 3 illustrates habitat pat-terns for a bird, a mammal, and a beetle in northeastTasmania: species that use the landscape at differentspatial scales. Some of these uncertainties are quanti-tative and others are qualitative and subjective, makingit difficult to represent them all with a single reliabilitymeasure. However, the ecological reasons for choosingan index often are not provided, few measures are usedconsistently in different studies, many are scale de-pendent and they provide no measures of uncertainty

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FIG. 3. Habitat maps for three species: (a)Yellow-tailed Black Cockatoo (Calptorhynchusfunereus), (b) spotted-tailed quoll (Dasyurusmaculatus), and (c) Simson’s stag beetle (Ho-plogonus simsoni); and (d) a landscape contourmap, based on the habitat maps for the samethree species. Contours are constructed by over-laying habitat suitability maps for individualspecies. Darker regions are relatively suitablefor many species. The maps are a 4 3 3.5 kmsection of the region in Fig. 2, in northeast Tas-mania.

(Cale and Hobbs 1994, Moilanen and Hanski 2001,Dungan et al. 2002, Lindenmayer et al. 2002, Wu2004).

One problem with several of the landscape patternmethods is that they present maps with hard bound-aries. In reality, transition zones in nature are not usu-ally sharp. One way of dealing with uncertainty inboundaries is to avoid creating them, instead viewingpatterns in biodiversity as a continuum (Ferrier 2002,Faith 2003, McGarigal and Cushman 2005). Fuzzy settheory can address intermediate classes and indeter-minate boundaries in maps (Arnot et al. 2004). Nev-ertheless, uncertainties in pattern maps usually are notcommunicated (cf., Elith et al. 2002) and rarely con-tribute to decision making.

The choice of a modeling frame within which torepresent landscape pattern carries with it many as-sumptions about the grain and extent of the landscapeand the ways in which species respond to landscapemanagement (Dungan et al. 2002, McGarigal and Cush-man 2005). Like habitat and population models, thechoice of the modeling frame should not depend onconventional acceptability or the availability of rele-vant skills but in practice, it often does. The importanceof the choice may be explored by characterizing a land-scape within two or more frames and examining if thechoice makes a difference to management decisions. Ifit does, the landscape planner is obliged to explorefurther the ecological foundation for the choice, or tomake decisions that deliver acceptable outcomes, ir-respective of the choice of a frame.

MANAGING LANDSCAPES

Landscape managers are aware that explicit singleand multiple species models do not deal explicitly withmost things of value in a landscape. Managers make

decisions, despite the complexities of ecosystems.These circumstances have precipitated a scramble ofideas to assist managers to make decisions with at leastsome ecological support. Several of these approachesare outlined below, each of which carries assumptionsabout habitat, population dynamics, and ecological re-sponses to change.

Ideas about landscape pattern have contributed tostrategies for management. The island model suggestsreserves close together are better than reserves farapart, and the patch-corridor-matrix model further sug-gests that reserves connected by a corridor are betterthan isolated reserves (see reviews and critiques byGilbert 1980, Burgman et al. 1988, Simberloff 1988,Doak and Mills 1994, Haila 2002, Manning et al. 2004).However, it is difficult to find simple guidelines builton these concepts that result in effective conservationstrategies in a variety of circumstances for a range ofspecies. Empirical research shows that the beneficialeffects of corridors depend on their width, length, lo-cation in the landscape, the extent to which the matrixis used by species of interest, and the type and patternof land use in the matrix (Hobbs 1992, Lindenmayerand Possingham 1996, Rosenberg et al. 1997, Beierand Noss 1998, Bennett 1998). On the negative side,corridors may exacerbate the spread of weeds, pest an-imals, diseases, and fires, and connect high-quality hab-itat patches to population ‘‘sinks’’ (Harrison and Bruna2000).

The island model led to the premise that species-poor, small, habitat patches support subsets of assem-blages from larger, species-rich patches, termed nestedsubset theory (see Table 3 for references; see Fischerand Lindenmayer 2002). This theory leads to a focuson large patches, at the expense of smaller and moreisolated patches. Nested subset theory and island the-


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ory focus on collective measures (assemblage com-position and species diversity respectively), ignoringspecies-specific information on dispersal, interactions,recolonization, and the ability of populations to recoverfrom disturbance.

A common way to manage landscapes is to manip-ulate the spatial pattern. For example, the planning op-tion in Fig. 2 was devised by forest managers to con-form with Forman’s (1995) patch-matrix-corridor mod-el. Landscapes that retain corridors are assumed to bemore likely to maintain species because subpopulationscan recolonize empty habitat patches and exchange in-dividuals and genes (Brown and Kodric-Brown 1977,Haddad and Baum 1999). Reserves in Fig. 2 were con-sidered to be refugia for many species. The ‘‘matrix’’of relatively unsuitable habitat included areas destinedfor harvesting and regeneration or conversion to plan-tations, along with patches that were not scheduled forharvesting. The spines provided connections, corridors,and dispersal pathways between patches.

Another way to manage landscapes is to manipulatespatial and temporal disturbances to mimic those of‘‘natural’’ disturbance regimes (e.g., Hunter 1993, At-tiwill 1994). This approach has many of the same as-sumptions and uncertainties as the landscape patternmodels outlined above but it adds a temporal dimensionto account for dynamic change. Spatial dynamics suchas disturbance and vegetation succession have beenincluded in spatial population models by making patchqualities and carrying capacities change over time(Possingham and Davies 1995, Akcakaya 2001). Suchmodels have been further developed to include dynam-ics such as fire explicitly (e.g., see examples in Ak-cakaya et al. 2004). Uncertainty arises because thecharacteristics of a natural disturbance regime can bedifficult to estimate and fire regimes are difficult tomanage (Burgman 1996, Richards et al. 1999).

Focal species are an attempt to provide landscapemanagers with a direct link between landscape patternsand the ecology of species. A ‘‘focal’’ species, the mostsusceptible, is identified for each landscape attributesuch as patch size, connectedness and disturbance in-tensity and frequency. It is the species that is likely toexperience the largest increase in extinction risk whenthe attribute changes. Together, focal species have eco-logical requirements that define the attributes (spatialpatterns) that meet the needs of the biota (Lambeck1997). This definition uses the concept of ‘‘umbrella’’species, whose protection will result in the protectionof most other species (see Fleishman et al. 2000). Whileit is difficult to know which species are most sensitiveto each attribute (e.g., Brooker and Brooker 2002; seeLindenmayer and Fischer 2003) and empirical evidenceis equivocal (Andelman and Fagan 2000), the methodprovides a more concrete template for designing min-imal landscape requirements for species persistencethan using spatial pattern alone. Assumptions could beexplored with empirical data and population models.

Habitat models provide decision support for singlespecies, whereas most real contexts demand judgmentsfor many species. The landscape-contour model is adifferent attempt to link the ecological attributes ofmany species to landscape patterns. Landscape con-tours are composed of overlays of habitat suitabilitycontours for different species (see Fischer et al. 2004).The spatial grain (Dungan et al. 2002) at which speciesrespond to their environment is reflected in differentcontour densities (Wiens 1995). Fig. 3d provides anexample of a landscape-contour model for the threespecies habitat models in Fig. 3a–c. As such, it rep-resents a kind of a spatial average over species.

A common approach to managing biodiversity is toprotect species-rich hotspots (Mittermeier et al. 1998)and other areas that contain unique assemblages ofplants and animals. Reserve design algorithms seekcomprehensive reserve systems, those that include acomplete array of known biodiversity (Pressey 1994,Pressey and Cowling 2001). ‘‘Adequate’’ reserves aimto support viable populations. Spatial population mod-els and habitat models have been used to evaluate re-serve design options (e.g., Armbruster and Lande 1993,Moilanen and Cabeza 2002). Faith et al. (2003) de-scribed ‘‘biodiversity viability analysis’’ in which theyestimated gains and losses in persistence of all species.Desmet et al. (2002) addressed the need to design re-serves to account for spatial and evolutionary pro-cesses.

Because there are many species, and few data onmost of them, it is impossible to model a substantialor representative set of species. This problem promptedFerrier et al. (2002) to develop generalized dissimilar-ity modeling (GDM) to model the collective propertiesof the biota through the compositional dissimilarity(the b and g diversity) of sites. GDM combines bioticsamples and environmental data in a matrix regression-based approach to predict compositional dissimilaritiesbetween grid cells. Predictions from GDM can be usedto guide environmental classifications and to set pri-orities for conservation areas (Ferrier 2002). The ap-proach is particularly useful in highly diverse, rela-tively data-poor regions, going beyond a few flagshiptaxa to a more comprehensive consideration of thebiota.

The gaps between spatial population models andlandscape models are apparent to managers involvedin day-to-day decision making. Landscape models suchas Forman’s patch-corridor-matrix model lack explicitecological support. Habitat and spatial population mod-els provide information on only one or a few species.These concerns have led to the development of manyof the innovations outlined above. However, there isno explicit recognition of uncertainty in corridor de-sign, nested subsets, disturbance management, focalspecies, landscape contours, reserve design algorithms,or generalized dissimilarity modeling. Thus, eventhough some inroads have been made into modeling

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uncertainty in habitat models, spatial population mod-els and landscape pattern models, these developmentshave not yet found their way into new, pragmatic man-agement tools. And like the development of modelingframes for habitats, populations and landscapes, thechoice of a landscape management model from amongthose outlined above usually is determined by conven-tion and available skills. Decisions in many contextswill be sensitive to the choice, making it necessary forthe planner to justify the choice on ecological groundsor to make decisions that give reasonable outcomes,no matter which frame is adopted.

DISCUSSION

Uncertainty is pervasive in all levels of landscapemanagement for conservation. The importance of un-certainty depends on the context of a decision and in-creases with larger landscapes and longer time hori-zons. Yet many forms of uncertainty are not acknowl-edged in the models that support decisions. In somecases, uncertainty is ignored altogether. One of the mostimportant and least recognized forms is the choice ofa modeling frame. It exists at all operational levels andat all scales of ecological resolution, from single-spe-cies habitat modeling to landscape management. Thequestion then arises, how can pervasive and unac-knowledged uncertainty be embraced in landscapemanagement for conservation?

Uncertainties may be assessed through careful eval-uation of model predictions. Models are useful thatpredict accurately and precisely at a scale that makesoperational sense. Monitoring can track the conse-quences of management decisions, so that the weightgiven to predictions from a model that is routinelywrong declines as experience accumulates. A more ex-plicit approach is to adopt procedures that account foras many forms of uncertainty as possible (such as errorpropagation and sensitivity analyses) and to use severalmodeling frames and examine if the choice makes adifference to management decisions. If it does, thelandscape planner may explore further the ecologicaland statistical foundation for the choice.

In general, decision strategies for landscape man-agement try to maximize performance (e.g., Weitzman1998, Possingham et al. 2002a, b, Westphal and Pos-singham 2003). An alternative path, to which we al-luded several times above, is to make decisions thatmaximize the chance of a tolerable outcome, despitewhat is unknown and irrespective of the choice of aframe. There is a firm theoretical foundation for thisstrategy. Decision strategies should seek robust out-comes that are acceptable to the stakeholders who carrythe burden of the risks (Ben-Haim 2001, Burgman2005). Landscape planners should not focus on findinga true model, but rather should explore models andmodeling frames that lead them to consider robust, sat-isfactory alternatives.

A model structure and its level of detail will be de-termined by the kind of decision one needs to make.For example, a very simple model may be sufficient,even when data are abundant, if it can be shown thatthe simple model subsumes or bounds more complexinterpretations of the data or if the decision is invariantto the model detail. If the decision context is known,then decision theory (Ben-Haim 2001, Possingham etal. 2002b) may provide means for combining evidenceand arbitrating between alternatives to maximize ro-bustness to uncertainty.

Often, modelers feel compelled to try to make betterpredictions, without considering the context in whichtheir predictions will be used. Good decision makingprobes uncertainty (Edwards and Fortin 2001), leadingto a better understanding of the role uncertainty playsin managing a landscape. Better decisions may not nec-essarily depend on better models or more precise sci-entific predictions, but on a better understanding of thedecision context and the social imperatives that driveit (Pielke 2003).

The model we use to represent landscapes affects theway we subsequently interpret the effects of changeand look for options that mitigate risks. In the past,landscape management has been governed by eitherlandscape pattern or the considerations of individualspecies. However, syntheses are emerging in applica-tions. While there is some recognition of uncertaintyin spatial pattern models, habitat models and spatialpopulation models, it is little considered in the decisiondomain. Landscape managers are responsible for manyspecies. The new challenge is to develop decision sup-port systems in which ecologically-based, multi-spe-cies predictions are cast in a form that is useful forconservation managers and that provides informationon uncertainty so that managers may make risk-baseddecisions. The foundations for these advances lie indecision theory (see Ben-Haim 2001) and research intorobust decision making for multispecies managementis urgently required.

ACKNOWLEDGMENTS

We thank Lenore Fahrig, Nicolas Ray, Atte Moilanen, An-urag Agrawal, Marie-Josee Fortin, and two anonymous re-viewers for their comments on drafts of the manuscript. JeffMeggs, Simon Grove, and others at Forestry Tasmania, whichinitiated the northeast Tasmanian project, supplied data andadvice, and gave permission for us to use the data in Figs. 2and 3.

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ecol 86 815.1965 1966 - Ecology & Evolutionary Biology at ... · ﬁeld internationally. Today, the concepts of landscape ecology (e.g., patch dynamics, metapop-ulation theory, hierarchical