The Application of Neutral Landscape Models inConservation BiologyKIMBERLY A. WITHDepartment of Biological Sciences, Bowli...
1070       Applications of Neutral Landscape Models                                                                      W...
With                                                                            Applications of Neutral Landscape Models  ...
1072       Applications of Neutral Landscape Models                                                                       ...
With                                                                              Applications of Neutral Landscape Models...
1074       Applications of Neutral Landscape Models                                                                       ...
With                                                                                Applications of Neutral Landscape Mode...
1076       Applications of Neutral Landscape Models                                                                     Wi...
With                                                                               Applications of Neutral Landscape Model...
1078       Applications of Neutral Landscape Models                                                                       ...
With                                                                                                Applications of Neutra...
1080       Applications of Neutral Landscape Models                                                                       ...
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1997 with the application of neutral landscape models in conservation biology

  1. 1. The Application of Neutral Landscape Models inConservation BiologyKIMBERLY A. WITHDepartment of Biological Sciences, Bowling Green State University, Bowling Green, OH 43403, U.S.A.,email kwith@bgnet.bgsu.eduAbstract: Neutral landscape models, derived from percolation theory in the field of landscape ecology, aregrid-based maps in which complex habitat distributions are generated by random or fractal algorithms. Thisgrid-based representation of landscape structure is compatible with the raster-based format of geographicalinformation systems (GIS), which facilitates comparisons between theoretical and real landscapes. Neutrallandscape models permit the identification of critical thresholds in connectivity, which can be used to predictwhen landscapes will become fragmented. The coupling of neutral landscape models with generalized popula-tion models, such as metapopulation theory, provides a null model for generating predictions about popula-tion dynamics in fragmented landscapes. Neutral landscape models can contribute to the following applica-tions in conservation: (1) incorporation of complex spatial patterns in (meta)population models; (2)identification of species’ perceptions of landscape structure; (3) determination of landscape connectivity; (4)evaluation of the consequences of habitat fragmentation for population subdivision; (5) identification of thedomain of metapopulation dynamics; (6) prediction of the occurrence of extinction thresholds; (7) determi-nation of the genetic consequences of habitat fragmentation; and (8) reserve design and ecosystem manage-ment. This generalized, spatially explicit framework bridges the gap between spatially implicit, patch-basedmodels and spatially realistic GIS applications which are usually parameterized for a single species in a spe-cific landscape. Development of a generalized, spatially explicit framework is essential in conservation biol-ogy because we will not be able to develop individual models for every species of management concern.Aplicación de Modelos de Paisaje Neutros en la Biología de la ConservaciónResumen: Los modelos de paisajes neutros derivados de la teoría de percolación en el campo de la ecologíade paisaje, consisten en mapas cuadriculados en los que se genera la distribución de hábitats complejos pormedio de algoritmos aleatorios o fractales. Esta representación de la estructura del paisaje es compatible conel formato de los sistemas de información geográfica (SIG) que facilitan la comparación entre paisajes teóri-cos y reales. Los modelos de paisaje neutros permiten la identifición de umbrales críticos de conectividad, quese pueden utilizar para predecir cuando se fragmentarán los paisajes. El acoplamiento de modelos de paisajeneutros con modelos poblacionales generales, por ejemplo la teoría de metapoblaciones, proporciona unmodelo nulo para generar predicciones de la dinámica poblacional en paisajes fragmentados. Los modelosde paisaje neutros tienen la siguiente aplicación en la conservación: (1) incorporación de patrones espacialescomplejos en modelos de (meta) poblaciones; (2) identificación de la percepción de la estructura del paisajepor las especies; (3) determinación de la conectividad del paisaje; (4) evaluación de las consecuencias de lafragmentación del hábitat en la subdivisión de poblaciones; (5) identificación del dominio de la dinámicametapoblacional; predicción de umbrales de extinción; (7)determinación de las consecuencias genéticas de lafragmentación del hábitat y (8) diseño de reservas y manejo de ecosistemas. Este marco de referencia generaly espacialmente explícito llena el vacío entre modelos espacialmente implícitos, basados en parcelas, y aplica-ciones. SIG espacialmente realistas que generalmente consideran a una sola especie en un paisaje específico.El desarrollo de un marco de referencia general y espacialmente explícito es esencial en la biología de la con-servación, ya que no es posible elaborar modelos individuales para cada especie.Paper submitted June 19, 1996; revised manuscript accepted January 21, 1997. 1069 Conservation Biology, Pages 1069–1080 Volume 11, No. 5, October 1997
  2. 2. 1070 Applications of Neutral Landscape Models WithIntroduction cies confined to a newly fragmented habitat do not necessarily function as a metapopulation; poor dispersalHabitat fragmentation is a central issue in conservation abilities may prevent the species from recolonizing habi-biology (Soulé 1986; Rolstad 1991; Harrison 1994; Wiens tat patches following extinction (Hanski & Gilpin 1991).1996) and has been implicated in the greatest extinction “Metapopulation” has become synonymous with anyevent on Earth in over 65 million years (Wilcox & Mur- spatially subdivided population (e.g., Hastings & Harri-phy 1985). Although loss of habitat poses the greatest son 1994), which is a broader definition than originallythreat to maintaining biodiversity, the effects of frag- accommodated by metapopulation theory (Levins 1969;mentation are more insidious. Fragmentation results in 1970). Spatial subdivision is a necessary, but not sufficient,the subdivision and decreased area of habitat, increases condition for metapopulation dynamics. In fact, therethe potential for edge effects, and changes the surround- are several conditions that are necessary for metapopula-ing habitat matrix, all of which may reduce the continuity tion persistence (Hanski et al. 1995). Metapopulationsor connectivity of the landscape and thus threaten the occupy what Wiens (1997b) refers to as the “Goldilockssurvival of sensitive species (Rolstad 1991). Fragmenta- Zone.” The notion is that there is a critical patch geome-tion effects are so evident, so amply documented, that we try and a critical dispersal rate that is neither too muchappear to have overlooked a rather fundamental question: (patches are not too isolated, dispersal is not too fre-when do landscapes become fragmented? This is one of quent) nor too little, but “just right.” Despite its wide-the primary concerns of conservationists; yet, conserva- spread application in conservation, the assumptions ortion biology offers no formal theory to predict when habi- conditions underlying metapopulation theory are rarelytat fragmentation occurs. tested to determine whether the population of manage- Instead, theory focuses on the consequences of spatial ment concern is functioning as a metapopulation (Harri-subdivision for biodiversity and the persistence of popu- son 1991; 1994; Doak & Mills 1994; Hastings & Harrisonlations. Metapopulation theory has become a major the- 1994).oretical underpinning of conservation biology (Hanski & How do we manage populations that are subdividedGilpin 1991; Caughley 1994; Meffe & Carroll 1994; Hanski but are not, strictly speaking, metapopulations? A broader& Simberloff 1997). Metapopulation structure—subdi- modeling framework is needed, one that incorporatesvided populations linked by dispersal that balances ex- landscape complexity beyond simple patch-based mod-tinctions and recolonization of patches—figures promi- els and which can encompass a range of population dy-nently in the design of reserves (Quinn & Hastings 1987) namics including metapopulation structure. Landscapeand in the management of threatened populations (e.g., ecology has emerged as a discipline whose primary focusBeier 1993; LaHaye et al. 1994; Hanski et al. 1995). From a is the analysis of the ecological consequences of envi-conceptual and analytical standpoint, metapopulation ronmental heterogeneity or patchiness (Turner & Gard-models are appealing because they offer a simple way to ner 1991). Given that metapopulation theory and land-view and model a spatially complex world. As a legacy of scape ecology both deal with the consequences ofisland biogeographic theory, metapopulation theory holds patchiness, Hanski and Gilpin (1991) proposed that theto a binary view of the world, of patches embedded “fusion of metapopulation studies and landscape ecol-within an inhospitable, or at least an “ecologically neu- ogy should make for an exciting scientific synthesis.”tral” (Wiens et al. 1993), matrix of non-preferred habitat. Landscape structure may often be an important compo-Because anthropogenic destruction of habitat dramati- nent of metapopulation dynamics (Fahrig & Merriamcally fragments the landscape into small, disconnected 1994; Wiens 1997a). Variation in patch quality, bound-patches of habitat (e.g., Krummel et al. 1987; Gardner et aries between patches, the nature of the mosaic (patchal. 1993), patch-based models would seem apt descriptors context), and overall landscape connectivity may influ-of the resulting population dynamics. ence the dynamics of local populations and the way in The problem is that this patch-based view of the world, which local populations are linked by dispersal (Wiensalthough analytically tractable, does not encompass the 1997a). Dispersal also defines the scale at which individ-full range of spatial complexity inherent in real systems. uals perceive landscape structure and whether a land-Metapopulation models assume populations are contained scape is connected or whether a species is likely to bewithin discrete habitat patches, but this is an over-sim- affected by fragmentation (Wiens & Milne 1989; Wiensplification for most systems where it is difficult to delin- et al. 1993; With 1994; Pearson et al. 1996). Individualeate population boundaries. Habitat patches are not oce- movement is thus the most important unifying theme inanic islands; individuals of many species can move through both metapopulation dynamics and landscape ecologythe habitats that comprise the matrix, which may differ- (Wiens 1997a).entially affect colonization success (e.g., Cummings & Despite the obvious applications of landscape ecologyVessey 1994; Gustafson & Gardner 1996). Habitat frag- for conservation biology, and vice versa, the synthesismentation may or may not produce spatial differentia- between the two disciplines has barely begun (Wienstion in the dynamics of populations (Wiens 1997b). Spe- 1997a ). As a first step toward forging a link between theseConservation BiologyVolume 11, No. 5, October 1997
  3. 3. With Applications of Neutral Landscape Models 1071fields, my objective in this paper is to introduce conser- understand the statistical properties and connectivity ofvation biologists to a recent theoretical development in heterogeneous systems (Feder 1988). For ecological ap-the field of landscape ecology. Neutral landscape models plications, artificial landscapes were conceived as perco-(Gardner et al. 1987; Gardner & O’Neill 1991) show prom- lation maps in which habitat could be assigned to oc-ise of providing a spatially explicit framework for model- cupy some proportion, h, of cells (Gardner et al. 1987;ing (meta)population dynamics. Landscape maps are Gardner & O’Neill 1991). These landscapes are gener-constructed as grids in which cells are identified by hab- ated with analytical algorithms and thus are “neutral” toitat type or some other landscape feature; this raster for- the biological and physical processes that shape realmat is therefore compatible with management applica- landscape patterns. Neutral landscapes provide a usefultions tied to geographical information systems (GIS). model for the study of ecological responses to landscapeNeutral landscapes are constructed with simple algo- patterns because they are based on the movement, flow,rithms that generate complex habitat distributions. When or rate of spread that characterize a diverse array of bi-coupled with generalized population models, such as ological processes (e.g., resource utilization by species,metapopulation theory, neutral landscapes provide a O’Neill et al. 1988; Lavorel et al. 1995; species coexist-spatially explicit framework for modeling population dy- ence, Gardner et al. 1991; Lavorel et al. 1994; Palmer 1992;namics in fragmented landscapes. Currently, population spread of disturbance, Turner et al. 1989). They are thusmodels are coupled with GIS-generated landscapes (spa- well suited for providing a spatially explicit frameworktially “realistic” models, Hanski 1994a) to understand how for modeling population responses to landscape change.actual or projected land-use change affects some threat-ened or endangered species (e.g., Bachman’s Sparrow, Simple Random Landscapes[Aimophila aestivalis]; Pulliam et al. 1992). These spe-cies-specific models are thus a special case of the more The first generation of neutral landscapes were simplegeneral modeling framework I propose; neutral land- random maps created by randomly assigning habitat to ascapes provide null models for predicting when habitat proportion, h, of the grid map (Gardner et al. 1987;fragmentation occurs and is expected to affect popula- Gardner & O’Neill 1991; Fig. 1). The number of availabletion dynamics. The development of a generalized, spa- habitat cells on a particular landscape is thus hm2,tially explicit framework in conservation biology is es- where m is the number of cells along one side of thesential given that we will be unable to develop individual landscape grid (number of rows or columns). Althoughmodels for every species of management concern. I de- patch structure is not explicitly defined in the construc-scribe the different types of neutral landscape models tion of such landscapes, it emerges nonetheless from thethat have been generated and how these have been used aggregation of habitat cells to form clusters or various ecological applications. I then outline a proto- Patches are defined by aggregation size or “neighbor-col for coupling these landscape models with metapopu- hood rule” (Fig. 2). For example, the simplest definitionlation models. Finally, I discuss the implications of neu- of a patch is determined by the “nearest-neighbor rule;”tral landscape models for conservation biology. the neighborhood includes the four adjacent cells (Rule 1, Fig. 2). The “next-nearest neighbor” rule includes the nearest neighbors, plus the four diagonal cells; each cellNeutral Landscape Models thus has eight neighboring cells (Rule 2, Fig. 2). Larger neighborhood rules include cells that are not immedi-Neutral landscape models are derived from percolation ately adjacent, but are still considered part of the “neigh-theory, which developed from the study of the flow of borhood” in defining patch structure (e.g., Rule 3, Fig.liquids through lattices of material aggregates (Orbach 2). The rationale behind this is that highly vagile species1986). Neutral landscape models have been applied to or those with good dispersal abilities are able to cross Figure 1. Examples of neu- tral landscape models. The proportion of available habitat ( h) is 0.33 in all maps (shaded cells). For the hierarchical random map, h varies across three levels as h1 ϭ 0.85, h2 ϭ 0.75, and h3 ϭ 0.50 ( h1 ϫ h2 ϫ h3 ϭ 0.33). Conservation Biology Volume 11, No. 5, October 1997
  4. 4. 1072 Applications of Neutral Landscape Models With Figure 2. Connectivity of a landscape comprised of 35% habitat using differ- ent neighborhood rules. The landscape is con- nected and contains a sin- gle cluster that “perco- lates” across the map only when neighborhood Rule 3 is used as in this example.“gaps” in available habitat and thus might link non-adja- threshold, landscape connectivity is disrupted and thecent cells in a neighborhood of utilized habitat (e.g., landscape is dominated by small, isolated clusters of habi-Dale et al. 1994; With & Crist 1995; Pearson et al. 1996). tat; the landscape is fragmented. The use of neighborhood rules provides a species-cen- The threshold value, and thus whether or not the land-tered definition of landscape structure, permitting patch scape is fragmented, depends upon the scale at whichstructure to be identified at a scale appropriate to the or- species perceive patch structure. Highly vagile speciesganism in question. This is analogous to the concept of are represented with larger neighborhood rules and per-“ecological neighborhoods” (Addicott et al. 1987) and is ceive the landscape as connected across a greater rangebased on dispersal distances, movement rates through of habitat loss (Gardner et al. 1991; With & Crist 1995;habitat, or the “willingness” of individuals to cross gaps Pearson et al. 1996). The critical threshold for these spe-of nonhabitat. This information can be difficult to obtain cies will thus be lower. For example, hcrit ϭ 0.30 for spe-in the field, but neighborhood rules provide a means of cies able to cross gaps of unsuitable habitat (Rule 3);modeling animal movement in a reasonable fashion and such a species would not perceive the landscape as frag-can be used to compare the effects of land-use practices mented until habitat comprised Ͻ30% (Plotnick & Gard-and habitat fragmentation on various groups of species ner 1993).that differ in dispersal ability. Percolation theory strictly deals with binary systems— In discussions of fragmentation effects, it is not clear habitat versus nonhabitat—just like metapopulation the-at what point the landscape became fragmented, partic- ory, thus providing a common framework for linkingularly from the standpoint of the target species. One of these modeling approaches. Neutral landscapes needthe most significant contributions of neutral landscape not be restricted to a single habitat type, however, andmodels has been the identification of critical thresholds proportions of multiple habitat types can be specifiedin landscape connectivity, which defines quantitatively (h1 ϩ h2 ϩ ϭ 1, where n ϭ number of habitat types).the point at which the landscape becomes fragmented. On random maps each habitat will percolate at the cor-Imagine a completely forested landscape. If forest habi- responding hcrit for the specified neighborhood rule.tat is randomly removed a cell at a time, the landscape be- Such heterogeneous landscape maps more closely ap-comes riddled with gaps, but the landscape remains con- proximate environmental complexity (e.g., Fig. 4). Het-nected as long as habitat cells are adjacent (if the nearest- erogeneous landscape maps permit the modeling ofneighbor rule is used) and form a continuous cluster that complex interactions between species characteristics,stretches from one end of the landscape to the other (Fig. such as habitat affinity, and features of the landscape,3). With continued deforestation the removal of a single such as the abundance and quality of different habitatcell is enough to break the continuous cluster into two types (With & Crist 1995; With et al. 1997). Criticalseparate clusters. At this point, the landscape is suddenly thresholds in species’ responses to habitat fragmenta-disconnected. This is the critical threshold (hcrit), which is tion result from the interaction of species characteristicspredicted by percolation theory to occur on a random with landscape structure. For example, habitat special-landscape when h ϭ 0.59 for the nearest-neighbor rule ists, regardless of dispersal abilities, are more likely to be(Fig. 2). Above the threshold, habitat destruction merely affected by loss of habitat than a disruption of landscaperesults in a loss of habitat area (Andrén 1994). Below the connectivity (With & Crist 1995). Simulation experimentsConservation BiologyVolume 11, No. 5, October 1997
  5. 5. With Applications of Neutral Landscape Models 1073 Figure 3. Critical threshold in landscape connectivity. As the proportion of avail- able habitat (shaded cells) is reduced, connectivity— the occurence of a percolat- ing cluster—is disrupted, producing small, isolated clusters of habitat across the landscape. The largest patches (defined by the nearest-neighbor Rule 1, see Fig. 2) are the dense black areas in each land- scape.on neutral landscapes help identify scenarios where Wiens 1990). Natural landscapes exhibit scale-depen-threshold effects could occur for a given species or group dent changes in pattern (Krummel et al. 1987; O’Neill etof species that share similar life-history characteristics or al. 1991). Species may respond to resource distributiondispersal strategies. Simulation experiments, conducted at different levels within the hierarchical patch structureas a factorial design for all levels of the model parame- of the landscape, as determined by their perceptualters, permit the exploration of the model state space and grain—the finest scale at which they respond to hetero-provide a simple means of identifying statistically signifi- geneity—and their spatial extent—the broadest scale atcant factors, or combinations of variables, that affect pop- which the species interacts with heterogeneity, usuallyulation distributions and persistence (With et al. 1997). determined by dispersal distances (Kotliar & WiensThis makes it possible to tease apart the specific land- 1990; With 1994). Thus, it is important to identify thescape features that affect the structure and dynamics of spatial scaling of habitat across the landscape and to de-populations. termine the scales at which species are interacting with landscape structure. For example, habitat fragmentationHierarchical Random Landscapes may have different consequences for biodiversity if it oc- curs at fine versus broad scales. Fine-scale fragmentationMuch of the conceptual appeal of metapopulation the- poses a greater risk to landscape connectivity than theory lies in its recognition of hierarchical structure in nat- same reduction of habitat at a coarser scale (Rolstadural systems (“population of populations,” Levins 1970). 1991; Pearson et al. 1996). Habitat destruction at a broadResources are generally patchy in distribution and this scale obviously produces gaping holes in the landscape,patch structure may be manifested across scales in a but some large, contiguous tracts of habitat are left in-nested hierarchy of patches within patches (Kotliar & tact which helps promote overall landscape connectiv- Figure 4. Application of neutral landscape models to various conservation scenarios. Management of small, discretely patchy populations (“island” pop- ulations) might be mod- eled with simple random maps. For the study of frag- mentation effects or popu- lations that have a spa- tially complex distribution(patchy populations), fractal landscapes provide more appropriate models. Edge effects can also be addressed infractal landscapes by designating a “habitat halo” around the primary habitat. In addition, heterogeneous land-scapes comprised of Ͼ1 habitat type or source/sink population can be modeled with neutral landscapes ( fractallandscape example shown here). Conservation Biology Volume 11, No. 5, October 1997
  6. 6. 1074 Applications of Neutral Landscape Models Withity. Small, isolated “clear cuts” are more insidious be- els of landscape patterns with simple control over spa-cause these whittle away at the percolating cluster. The tial autocorrelation (Petigen & Saupe 1988; Palmer 1992;removal of a single critical cell of habitat breaks the per- With et al. 1997; Fig. 1). Although two-dimensional frac-colating cluster into two separate clusters and results in tals may be generated in various ways, we have used thea disconnected landscape. midpoint displacement algorithm outlined in Saupe Hierarchically structured landscape models reflect the (1988) to generate fractal landscapes. For the purposesinherent patch structure of natural landscapes (O’Neill of this discussion, it will suffice to understand that aet al. 1992; Lavorel et al. 1993; Gardner et al. 1993; Fig. 3-dimensional surface—a topographical map—is created.1). Hierarchical neutral landscapes are generated using a The “ruggedness” of the topography depends upon thefractal algorithm referred to as “curdling” (Mandelbrot degree of correlation among habitat cells, H. The fractal1983). The number of scales across which pattern varies dimension of the landscape is D ϭ 3-H; landscapes withis set by specifying a number of hierarchical levels, L, little spatial autocorrelation (low H) will have an ex-within the map. The proportion of habitat that occurs tremely variable surface (sharp peaks adjacent to deepwithin each level is set independently as h1...hL. This is a valleys) that is more volume-filling and hence D → 3 (Fig.recursive procedure; the availability of habitat at one 5). Extremely complex landscapes can thus be gener-level constrains the availability of habitat at finer scales. ated in a systematic fashion, just by varying H. As a con-For example, 60% of the landscape could be covered by sequence, the effects of habitat fragmentation can be as-forest at the coarsest scale (h1), and 80% of those cells sessed across a gradient of habitat clumping (H) andcould contain forest at an intermediate level (h2), and abundance (h).perhaps 40% of the L2 cells will contain forest at the fin- Habitat is assigned to the continuously varying surfaceest scale (h3). The available habitat across the landscape of fractal landscapes by making slices along an “eleva-is thus the combined probabilities, P ϭ h1 ϫ ...hL; in the tional gradient” and assigning the range of elevationsprevious example, P ϭ 0.6 ϫ 0.8 ϫ 0.4 ϭ 0.192. If habi- (which are the cell values) encompassed by the slice totat is absent at the coarsest scale, it will not be found at a particular habitat type. The proportion of a particularfiner scales either. Subtle patterns of landscape fragmen- habitat represented on the landscape is determined bytation can be created by adding “whey” to the “curds” the range of elevations encompassed in each slice; ifand seeding habitat with a proportion, q, at each of the 40% of the elevational range is captured by the slice,finer levels (Pearson et al. 1996). Available habitat is then 40% of the landscape will be comprised of that hab-now calculated as: itat. This produces a contour map. Habitat is assigned along a gradient and thus certain habitat types will al- P = [ h1 × h2 × h3 ] + [ h1 × ( 1 – h2 ) × q3 ] + ways be adjacent (e.g., habitats 1 and 2, habitats 2 and 3, [ ( 1 – h 1 ) × q 2 × h 3 ] + [ ( 1 – h 1 ) × ( 1 – q 2 ) × q 3 ]. but not habitats 1 and 3). This models the transition of ecotones in natural landscapes or can be used to explore edge effects by designating a small proportion of habitatFractal Landscapes adjacent to a primary habitat (e.g., h2 ϭ 0.05 and h3 ϭThe neutral landscapes assumed complete spatial inde- 0.35 in Fig. 4).pendence among cells; habitat types exhibited no spatial Fractal landscapes have been applied to the conse-autocorrelation, although h obviously affects the proba- quences of fragmentation for biodiversity (Palmer 1992)bility that adjacent cells will be similar. In reality habitat and subdivided populations (With et al. 1997). Scale-is distributed with some degree of spatial contagion across dependent effects on species coexistence were found inlandscapes. Fractal algorithms can generate neutral mod- fractal landscapes. In extremely fragmented landscapes Figure 5. Topography of fractal landscapes. These maps illustrate how chang- ing the spatial autocorrela- tion among habitat cells (H) affects the spatial pat- terning and hence the frac- tal dimension (D) of land- scapes ( D ϭ 3-H).Conservation BiologyVolume 11, No. 5, October 1997
  7. 7. With Applications of Neutral Landscape Models 1075(high D), more plant species were able to coexist at the number of parameters so that the model is analyticallyfinest scale (within individual cells) than in more clumped tractable. With computer-based simulation modeling,landscapes (Palmer 1992). Species richness at the scale the number of parameters under simultaneous consider-of the entire landscape was lower in fragmented than in ation can be greatly increased and more complex prob-clumped landscapes, however. Factors that operate at lems addressed. Metz and Diekmann (1986) character-different scales may affect population distributional pat- ized different population modeling approaches based onterns. Populations were more likely to be subdivided at the “p-state, i-state” framework, one of which they clas-the landscape scale on fractal maps (with intermediate sified as “i-state configuration models,” which refer par-levels of spatial dependence, H ϭ 0.5), and population ticularly to simulation models that take into consider-distributions were determined primarily by species’ hab- ation the life-history characteristics of individuals initat affinities and habitat quality (With et al. 1997). At heterogeneous environments (DeAngelis & Gross 1992).finer scales on fractal landscapes, however, populationstructure was influenced by the relative abundance ofhabitat and the interaction of species’ habitat affinitieswith habitat quality. Coupling Metapopulation Models and Neutral Landscape ModelsA Generalized, Spatially Explicit Framework Lande (1987) adapted the phenomonological metapopu- lation model of Levins (1969) to territorial populationsBecause metapopulation models define a narrow range on a random landscape. This model is spatially implicit;of population dynamics (i.e., the “Goldilocks Zone”), the landscape is assumed to be binary, in which suitableHastings and Harrison (1994) formulated a more general territories of a fixed size are randomly distributed in antheoretical framework called the “p-state, i-state model,” unsuitable matrix. By incorporating demographic parame-which was initially developed by Metz and Diekmann ters and the dispersal range of individuals searching for(1986). Parameters that describe the condition of indi- territories, Lande derived the “demographic potential”viduals (i-state) could be numbers of individuals or allele of the population, a single parameter that described thefrequencies, and the state of the population as a whole maximum occupancy of territories at equilibrium. Terri-(p-states) could be described as the fraction of patches torial populations exhibited extinction thresholds, de-that are in particular i-states. The model is among the termined by their demographic potential and the pro-most general models in population biology—virtually all portion of suitable territories available on the landscape.models in population biology are among its special cases— Species with high demographic potential (good dispers-and the point of defining a model at this level of general- ers, high reproductive output), for example, can with-ity is that it provides a single framework for integrating stand considerable habitat loss before the populationand comparing different population models. Neverthe- crashes. The application for conservation biology is ob-less, this model is spatially implicit; the spatial arrange- vious and Lande’s model has been used to illustrate howment of habitat is ignored, but allows for very general as- habitat fragmentation would impact the Northern Spot-sumptions about patch sizes and dispersal. ted Owl (Strix occidentalis caurina). The population is Conceptually, then, one might extend this framework predicted to go extinct once old-growth forest coversto an “l-state, p-state, i-state” model. In this case, l is a Ͻ20% of the landscape (Lande 1988; Lamberson et al.landscape containing a group of populations under con- 1992).sideration or fraction of landscape in various p-states, p Lande’s model has the basic form of an l-state, p-state,is an individual population (or a local site, such as a grid i-state model, where the equilibrium occupancy of terri-cell) on the landscape, and i is an individual organism. tories (local sites or patches) across the landscape (p*,Functions at higher levels constrain parameter states at an l-state) was determined for a single (meta)population.lower levels (e.g., habitat distribution, an l-state, affects In this application individual territories or “patches” arehabitat of individual cells, a p-state), and patterns at higher p-states that can be occupied by a single breeding pairlevels may be obtained by aggregating information from with proportion p (a p-state). The demographic poten-lower levels. This facilitates the translation of patterns tial of the (meta)population (k, an l-state) is based on in-and processes across levels of organization. In the model, dividual parameters such as the lifetime reproductivefunctions can be derived that describe the relations output of individual females (Ro,’ a function of i-state pa-among l-, p-, and i-states; for example, an l-state describ- rameters such as age-specific birth and death rates, anding the mean population size is a function of a p-state age at first reproduction) and the dispersal range (m, an-variable (number of individuals in each population). The other i-state) of juveniles searching for a suitable, unoc-state parameters specified at each level depend upon cupied territory. Persistence of the population on thethe question of interest. The utility of such a model lies landscape (p*) depends upon the availability of suitablein its versatility. In practice, it is necessary to limit the habitat (h, an l-state) and the demographic potential of Conservation Biology Volume 11, No. 5, October 1997
  8. 8. 1076 Applications of Neutral Landscape Models Withthe population (k). The equilibrium occupancy of suit- Davies 1995). These models however, are typically pa-able habitat is positive ( p* Ͼ 0) only if h exceeds the rameterized for a specific management application (e.g.,threshold value determined by the life-history and dis- LaHaye et al. 1994; Liu et al. 1995; Hanski et al. 1995;persal abilities of the species. The extinction threshold Hanski et al. 1996), which may ultimately limit their gen-is the minimum proportion of suitable habitat required erality in other systems or even other species within thefor population persistence on the landscape; below this, same system (e.g., Liu et al. 1995). The coupling of (meta)the population goes extinct. Species with low reproduc- population models with neutral landscape models showstive output and poor dispersal abilities (low k) are pre- promise of providing a generalized, spatially explicit frame-dicted to go extinct much sooner (at higher values of h) work, thus cultivating the synthesis envisioned by Han-than species with high demographic potentials. For ex- ski and Gilpin (1991). Neutral landscape models canample, a species with k ϭ 0.2 is only able to occupy 20% contribute to the following applications in conservationof habitat patches even when the landscape is entirely biology.suitable (h ϭ 1.0). Such a species is predicted to go ex-tinct when 20% of the landscape has been destroyed (h ϭ0.8). A species with k ϭ 0.6, on the other hand, would Representation of Complex Spatial Patterns inpersist on the landscape until h ϭ 0.4. (Meta)Population Models This model, while analytically tractable, can not dealwith the spatial complexity of real systems. Thus, Lande Algorithms used to generate artificial landscapes providesuggested that “the prediction of extinction thresholds a simple means of generating environmental complexityfor real populations may be most accurately accom- in a number of ways (e.g., Figs. 1 and 4). Neutral land-plished by incorporating these principles into computer scape models enable one to vary systematically aspectsmodels that explicitly account for habitat quality and of landscape structure such as relative habitat abun-spatial distribution and the influence of these factors on dance, spatial contagion (“clumping” of pattern and thusthe dispersal behavior and life history parameters of indi- patch-size distributions), or amount of edge. This per-viduals” (Lande 1987:634). We are now in the process of mits the exploration of the effects of fragmentation acrosslinking neutral landscapes and metapopulation models a range of severity and spatial complexity. Neutral land-(K. A. With and A. W. King, unpublished data). Because scapes offer a more holistic view of landscape structurelandscape structure affects dispersal success (the prob- by dealing with the intact landscape (Pearson et al.ability of successfully colonizing unoccupied habitat 1996). Landscapes are not dissected into discrete ele-patches or territories in Lande’s model), the introduc- ments such as patches, matrix, and corridors. Rather, patchtion of spatial complexity (e.g., a function of h and H for structure emerges from the interaction (e.g., movementfractal landscapes; Fig. 5) should affect the predicted responses) of organisms with environmental complexity,value of extinction thresholds. Preliminary results sug- enabling “species’ perceptions” of landscape structure.gest that populations persist longer on fractal landscapesthan predicted by Lande’s model. Fractal landscapes areinherently more clumped than random landscapes and Identification of Species’ Perceptions of Landscape Structurethus remain connected across a greater range of habitatloss. Dispersal success is thus higher on fractal land- The patch-structure of the landscape is defined by spe-scapes, even when habitat is scarce, and populations are cies’ area requirements and their propensity for move-able to persist across across a greater range of habitat ment (Wiens et al. 1993; Dale et al. 1994; With & Cristloss than populations on random landscapes. 1995; Pearson et al. 1996). This permits an organism-cen- tered definition of landscape structure, which is necessary if we are to adopt meaningful and effective conservation strategies (Hansen & Urban 1992). The consequences ofApplications for Conservation Biology land-use change and fragmentation can be simulta- neously addressed on the same landscape for a multi-What new insights can be gained by developing a syn- tude of species with different dispersal capabilities andthesis between conservation biology and landscape ecol- life-history traits. For example, Dale et al. (1994) identi-ogy? The importance of landscape pattern and connec- fied species likely to be extirpated following forest frag-tivity in structuring metapopulation dynamics suggests mentation in the tropics based on the area requirementsthat current metapopulation theory could be enhanced and the “gap-crossing” ability of these species (i.e., theirby incorporating spatially explicit theory from landscape willingness to cross areas of unsuitable habitat). Not onlyecology (Wiens 1996). The challenge of modeling meta- can the effects on target species be addressed, but itpopulation dynamics in a spatially complex environment might then be possible to identify the circumstances un-has been tackled by a variety of modeling approaches, der which other populations, not currently of manage-(e.g., Wu & Levin 1994; Hanski 1994b; Possingham & ment concern, become threatened.Conservation BiologyVolume 11, No. 5, October 1997
  9. 9. With Applications of Neutral Landscape Models 1077Determination of Landscape Connectivity landscape may function as a single population, in which case, metapopulation theory is no longer relevant (WiensThe key to metapopulation persistence is to maintain 1997a). At the other extreme, if the landscape is highlylandscape connectivity, a functional cohesion among hab- fragmented and populations are subdivided, it may beitat patches across the landscape. Neutral landscape possible to treat each patch as a separate unit (e.g., indi-models predict the occurrence of critical thresholds in vidual reserves). Thus, the domain of metapopulationhabitat fragmentation, abrupt transition ranges where dynamics may fall somewhere in the vicinity of the per-small losses of habitat have dramatic, and potentially colation threshold, where the explicit spatial arrange-dire, ecological consequences (Gardner et al. 1993; With ment of patches and inter-patch movements are most& Crist 1995; Pearson et al. 1996). Threshold effects are important.“a major unsolved problem facing conservationists” (Pul-liam & Dunning 1994:193). The potential for thresholdeffects should be a principal concern in the evaluation Prediction of Extinction Thresholdsof management strategies in fragmented landscapes. Far from enhancing population persistence, spatial sub- division may drive some species to extinction if they doEvaluation of the Consequences of Habitat Fragmentation for not have the demographic potential and dispersal abili-Population Subdivision ties to exploit patchy habitats. Extinction thresholds are determined by the interaction between landscape struc-Habitat fragmentation does not always produce meta- ture, demography, and dispersal; it is not yet clear topopulation structure, but may nevertheless have impor- what extent extinction thresholds are related to criticaltant implications for the spatial structure of populations. thresholds in landscape structure and population subdi-The most obvious effects of landscape structure are on vision. The ability to predict which species will go ex-dispersal among habitat patches. Dispersal affects colo- tinct, and when, under various scenarios of land-usenization rates, whether patches are connected, and thus change may ultimately be the most critical application ofwhether subpopulations function as a metapopulation. neutral landscape models in conservation. As outlinedThus, predicting “exactly how the translation from indi- previously, this can be accomplished by coupling neu-vidual movements to population distribution and inter- tral landscapes with metapopulation models, such asactions should be accomplished is one of the most vex- that derived by Lande (1987) for territorial problems confronting a metapopulation-landscapesynthesis” (Wiens 1997a:52–53). We have modeled indi- Determination of the Genetic Consequences of Habitatvidual movement in heterogeneous, simple random land- Fragmentationscapes (i.e., mosaics of three habitats) as a percolationprocess to identify the point at which populations be- Dispersal is not the only process affected by landscapecame subdivided (With & Crist 1995). The results of this structure. As individuals move, they take their genessimulation exercise demonstrated that this “threshold” with them and thus ultimately gene flow among popula-between continuously distributed and patchy populations tions can be affected by habitat fragmentation. Greendepended upon the relative abundance of preferred habi- (1994) used a simple random landscape to demonstratetat, the relative habitat affinities of species (e.g., whether that genetic variability within a population was highlya habitat generalist or specialist), and the dispersal range sensitive to changes in landscape connectivity. Belowof the species. Subsequent modeling work on heteroge- the critical threshold, a regional population became sub-neous fractal landscapes, with habitats of varying quality, divided and genetic drift increased genetic variabilityindicated that different factors may simultaneously oper- among populations. Again, the critical region where thisate at both fine and broad scales that affect population occurred depended upon the neighborhood functiondistributional patterns (With et al. 1997). It is important (area of gene flow) and pattern of remember that patchiness does not always matter, par-ticularly if habitat is abundant, dispersal distances are Guide Reserve Design and Ecosystem Managementgreater than the scale of fragmentation, the species is ageneralist, the species has a myopic view of the landscape At the landscape scale, patch-based theory (i.e., theoryand can only detect patches over short distances, or if of island biogeography) is being used to design reservehabitat patches are ephemeral (Fahrig 1988; With & Crist networks and in the management of entire ecosystems.1995; Wiens 1997b). Corridors have been implemented as an obvious solu- tion to the problem of maintaining connectivity in an in-Identification of the Domain of Metapopulation Dynamics creasingly fragmented world. Why then have corridors become one of the most hotly debated issues in conser-Where is the “Goldilocks Zone?” In highly connected vation (Mann & Plummer 1995)? Although habitat corri-landscapes (e.g., above the critical threshold), the entire dors linking populations or individual reserves may facil- Conservation Biology Volume 11, No. 5, October 1997
  10. 10. 1078 Applications of Neutral Landscape Models Withitate the dispersal of some species (e.g., large carnivores the grid cells to be square or hexagonal?), and what theor ungulates), the presumed effectiveness of corridors underlying assumptions are regarding movement thatremains controversial (Hobbs 1992). The notion of land- are ultimately used to define landscape structure. For ex-scape connectivity is perhaps being taken too literally. ample, determination of the critical threshold dependsConnectivity need not entail physical linkages between on the lattice geometry of the neutral landscape (Plot-patches; it is the functional connectivity—patches linked nick & Gardner 1993), the specific algorithm used toby dispersal—that is ultimately important. In a patch- generate the landscape (random vs fractal; With et al.based view of the world, corridors are appealing because 1997), and the way dispersal is modeled (e.g., differentthey provide a physical bridge linking habitat islands neighborhood rules; Plotnick & Gardner 1993; With &across a matrix sea. Given that landscapes are habitat Crist 1995; Pearson et al. 1996). These assumptions allmosaics and that species can traverse the “matrix,” corri- have the potential to affect one’s assessment of the con-dors may not be discrete structures. Gustafson and Gard- sequences of habitat fragmentation for populations. Thener (1996) used hierarchical random neutral landscapes best application is to make “comparative and qualitativeto model the effects of dispersal on patch colonization statements about the likely population responses to a setrates across heterogeneous landscapes. Areas that facili- of potential or real landscape alterations” (Dunning et al.tated movement, and thus functioned effectively as cor- 1995:9). Although we still may be unable to make quan-ridors, tended to be diffuse and difficult to identify from titative predictions about the effects of landscapestructural features of the landscape. Another holdover change on populations, the development of a general-from patch-based theory is the assumption that flows be- ized spatially explicit framework by integrating metapo-tween patches are linear and symmetrical. Spatial com- pulation theory with neutral landscape models may leadplexity may reduce colonization success when individu- to new insights in the conservation management ofals must follow convoluted pathways or are trapped in threatened populations.“cul-de-sacs” (Gustafson & Gardner 1996). Asymmetry indispersal between patches arises because of patch con-text; an isolated patch may have a high proportion of dis- Acknowledgmentspersers which successfully reach a neighboring patch,but if the neighbor is part of a network of patches, only a Final drafting of the paper has been facilitated by a grantsmall fraction of dispersers from this neighboring patch from the Faculty Research Committee at Bowling Greenmay reach the more isolated one. These applications from State University and by NSF grant DEB-9532079. I thankneutral landscape models underscore the importance of L. Fahrig, J. Day, and two anonymous reviewers, whoseelaborating reserve design from the standpoint of overall comments on the initial version have vastly improvedlandscape connectivity and within the context of entire the presentation of this paper.landscape mosaics rather than isolated patches (Presseyet al. 1993; Hobbs et al. 1993). Literature CitedConclusions Addicott, J. F., J. M. Aho, M. F. Antonlin, D. 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