Ecosystems (2007) 10: 846–853 DOI: 10.1007/s10021-007-9062-7
Spatial Heterogeneity in Habitat Quality and Cross-Scale Interactions in Metapopulations Robert L. Schooley,1,* and Lyn C. Branch2 1 Department of Natural Resources and Environmental Sciences and Program in Ecology and Evolutionary Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; 2Department of Wildlife Ecology and Conservation, University of Florida, Gainesville, Florida 32611, USA
ABSTRACT Integration of habitat heterogeneity into spatially realistic metapopulation approaches reveals the potential for key cross-scale interactions. Broadscale environmental gradients and land-use practices can create autocorrelation of habitat quality of suitable patches at intermediate spatial scales. Patch occupancy then depends not only on habitat quality at the patch scale but also on feedbacks from surrounding neighborhoods of autocorrelated patches. Metapopulation dynamics emerge from how demographic and dispersal processes interact with relevant habitat heterogeneity. We provide an empirical example from a metapopulation of round-tailed muskrats (Neofiber alleni) in which habitat quality of suitable patches was spatially autocorrelated most strongly within 1,000 m, which was within the expected dispersal range of
the species. After controlling for factors typically considered in metapopulation studies—patch size, local patch quality, patch connectivity—we use a cross-variogram analysis to demonstrate that patch occupancy by muskrats was correlated with habitat quality across scales £ 1,171 m. We also discuss general consequences of spatial heterogeneity of habitat quality for metapopulations related to potential cross-scale interactions. We focus on spatially correlated extinctions and metapopulation persistence, hierarchical scaling of source–sink dynamics, and dispersal decisions by individuals in relation to information constraints.
INTRODUCTION
ecology and landscape ecology, which stresses effects of landscape structure on ecological processes, has been a surprisingly sluggish endeavor (Wiens 1997; Hanski and Gaggiotti 2004; With 2004; Armstrong 2005). Merging these two branches of spatial ecology is important for understanding cross-scale interactions induced by habitat pattern. Cross-scale interactions refer to processes at one spatial or temporal scale interacting with processes at another scale (Peters and others 2004; Peters and others, this issue). With spatial crossscale interactions, broad-scale drivers interact with fine-scale processes to shape system dynamics or fine-scale processes influence a broad spatial extent.
Key words: dispersal; habitat heterogeneity; metapopulation; source-sink; spatial autocorrelation.
Metapopulation theory embraces dynamics from patch to landscape scales and has become the dominant paradigm for conservation of species in fragmented landscapes (Hanski and Gaggiotti 2004). Historically, metapopulation theory developed within a patch-matrix framework and spatial heterogeneity of habitat was deemphasized (but see Thomas 1994). Integration of metapopulation
Received 15 May 2007; accepted 25 May 2007; published online 10 July 2007. *Corresponding author; e-mail:
[email protected]
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Spatial Heterogeneity in Habitat Quality Cross-scale interactions can produce threshold responses due to nonlinear dynamics (Peters and others 2004; Peters and others, this issue). Spatial heterogeneity in habitat is relevant to metapopulations at several levels (Thomas and Hanski 2004). First, a metapopulation approach is useful only if one initially can dichotomize habitat into suitable patches and intervening matrix. Second, matrix heterogeneity can affect dispersal success and recolonization of patches following local extinctions (Ricketts 2001; Revilla and others 2004). Third, the degree of habitat heterogeneity within suitable patches can influence temporal variability of population size and extinction risk (Kindvall 1996). Fourth, variation in habitat quality among suitable patches can be a main driver of occupancy patterns (Dennis and Eales 1997; Hokit and others 1999; Fleishman and others 2002; Franken and Hik 2004; Schooley and Wiens 2005). Our focus is on this last level—spatial heterogeneity in patch quality. Specifically, we explore potential consequences of spatial autocorrelation of patch quality for metapopulation dynamics. Spatial correlation of demographics and site occupancy has received attention (for example, Harrison and Quinn 1989; Smith and Gilpin 1997; McCarthy and Lindenmayer 2000; Knapp and others 2003; Johnson 2005), but autocorrelation of habitat variables rarely has been explicitly considered in empirical metapopulation studies (but see Trenham and others 2001; Gonza´lez-Megı´as and others 2005). Metapopulation models have evolved toward ‘‘spatially realistic approaches‘‘ (Hanski 1994; Hanski and Gaggiotti 2004) that are spatially explicit in that actual patch locations are considered when estimating patch connectivity and modeling turnover and occupancy. However, most metapopulation approaches have been spatially implicit in terms of habitat quality of patches, and only have emphasized quality effects at the local, patch scale. Spatial autocorrelation of habitat quality creates the opportunity for neighborhood effects and crossscale interactions not captured by simple area-isolation conceptualizations of metapopulations (Pellet and others 2007). Broad-scale drivers (for example, environmental gradients and land use) that determine patch quality across the landscape interact with local processes of extinction and recolonization to produce regional patterns of occupancy and metapopulation dynamics. In particular, the likelihood that a patch is rescued from extinction (Brown and Kodric-Brown 1977) or recolonized after a local extinction will depend on habitat quality of patches within dispersal distance as well as size and connectivity of surrounding source patches (Hanski
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1994). Emergent metapopulation dynamics depend on how demographic and dispersal processes interact with habitat heterogeneity. Cross-scale linkages are modified by habitat pattern. Many modeling studies have demonstrated the possibility of nonlinear behavior of metapopulations including extinction thresholds related to habitat loss and fragmentation (for example, Bascompte and Sole´ 1998; Hanski and Ovaskainen 2000; Fahrig 2002; Ovaskainen and others 2002). Similar thresholds related to changes in habitat quality are possible but have been relatively neglected. Our objective is to highlight the potential importance of habitat heterogeneity for metapopulations within the general framework of crossscale interactions. First, we provide an empirical example for a metapopulation of round-tailed muskrats (Neofiber alleni) in which we quantify spatial patterns of patch occupancy and habitat quality using spatial statistics and geostatistics. We evaluate whether habitat quality of suitable patches is spatially autocorrelated, and then we examine cross-scale relations between patch occupancy and habitat quality for evidence that occupancy by muskrats depends on habitat conditions of surrounding wetlands within dispersal range. Second, we discuss general consequences of spatial autocorrelation of habitat quality for metapopulation dynamics. We consider correlated patch extinctions, spatial scaling of source–sink dynamics, and dispersal decisions by individuals related to information constraints. These general issues arise due to the habitat patterning at intermediate scales that underlies crucial cross-scale interactions.
METHODS Study System The round-tailed muskrat is a small (adults 250 g), nocturnal, semi-aquatic herbivore that has been proposed as a species of special concern due to its rarity and to extensive habitat loss (Lefebvre and Tilmant 1992). The round-tailed muskrat represents a monotypic genus with a restricted geographic range limited to Florida and southern Georgia (Lefebvre and Tilmant 1992; Bergstrom and others 2000). Our research on spatial dynamics of round-tailed muskrats was conducted on a 19,500-ha site in the southern half of Avon Park Air Force Range in central Florida (15 km east of Avon Park). Suitable habitat for muskrats consisted of small (median = 0.9 ha), isolated (mean nearestneighbor distance = 312 m) depression marshes surrounded by a diverse terrestrial matrix.
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We surveyed 457 wetlands for presence–absence of muskrats during fall-winter in each of 2 years (2002–2003 and 2003–2004). Patch occupancy was determined reliably based on presence of lodges constructed by muskrats (Schooley and Branch 2005). Active lodges usually can be distinguished from recently abandoned lodges because an active lodge has a solid structure with a well-formed interior chamber, fresh plant clippings, or nearby feeding platforms. Our survival study of marked lodges (Schooley and Branch 2005) indicated that all lodges (active or recently abandoned) were constructed during the current hydrological year (June–May), so we used all muskrat lodges for determining occupancy of wetlands. For each wetland, we recorded cover and density of maidencane grass (Panicum hemitomon) and then calculated a maidencane index that ranged from 0 (no maidencane) to 1 (pure maidencane with an estimated cover of 81–100%). We refer to the maidencane index, averaged for the two years, more generally as ‘‘habitat quality‘‘ hereafter because the diet of round-tailed muskrats in central Florida is primarily maidencane stems and roots (Birkenholz 1963), muskrats typically occur within maidencane zones within wetlands and often use maidencane to build lodges (Birkenholz 1963; Branch and Schooley 2005), and rates of local extinction and colonization within wetlands are related to maidencane cover (Branch and Schooley 2005). Empirical evidence indicates that round-tailed muskrats displayed metapopulation dynamics (Hanski 1994) across the naturally fragmented landscape. First, suitable marshland habitat occurred in discrete patches that covered less than 5% of the landscape. Second, small wetlands can support subpopulations of round-tailed muskrats because of their small home-range sizes (1,263– 2,071 m2, Schooley and Branch 2006). Third, muskrats occupied 26% of the 457 wetlands in each of 2 years but exhibited substantial turnover among wetland patches with local extinctions balanced by recolonizations (Branch and Schooley 2005). Fourth, extinction risk was related negatively to patch size. Fifth, colonization probability was related positively to a spatial connectivity metric developed for metapopulations (Hanski 1994; Branch and Schooley 2005).
Autocorrelation of Habitat Quality We quantified the spatial pattern of habitat quality with a Moran‘s I correlogram. Moran‘s I coefficient is a measure of spatial autocorrelation that usually ranges from )1 to 1 (Fortin and Dale 2005).
Positive values of Moran‘s I indicate positive autocorrelation, negative values indicate negative autocorrelation, and the expected value is near 0 when spatial autocorrelation is absent. To test for significance of Moran‘s I values at particular lag distances, we calculated P values using a Monte Carlo randomization procedure with 999 permutations (Sawada 1999), and then adjusted P values to account for multiple testing using a progressive Bonferroni correction (Fortin and Dale 2005) with an initial probability level of a equal to 0.05. We also estimated the range of spatial dependence in habitat quality by constructing an experimental variogram (Rossi and others 1992; Gamma Design Software 2004; Fortin and Dale 2005). A variogram is the plot of semivariance (half the average squared difference between pairs of values) versus lag distance and includes three relevant parameters: nugget (c0), spatial range (a), and sill (c0 + c, where c is the structural variance). The nugget represents spatial variability at short distances due to local random effects or measurement errors (Fortin and Dale 2005). The range indicates the maximum distance of spatial autocorrelation. The sill is the value at which the semivariance levels off once the range is exceeded.
Cross-Scale Relations: Patch Occupancy and Habitat Quality If the quality of surrounding wetlands influences the number of dispersers into wetlands dependent on demographic rescue or recolonization, then local patch occupancy should be correlated with habitat quality at the landscape scale. To evaluate these cross-scale correlations between patch occupancy by muskrats and landscape-scale habitat quality, we initially conducted a logistic regression analysis that included occupancy as the response variable and three key predictor variables typical for metapopulation models: patch size, local habitat quality, and spatial connectivity. Then, we evaluated whether the residuals from this regression model were correlated with habitat quality of patches across broader scales using geostatistics. For the logistic regression model (PROC GENMOD, SAS Institute 2002), wetlands were considered occupied if muskrats were present in 1 year or more and unoccupied if muskrats were absent in both years. We used a spatial connectivity metric typical of the incidence function model (Hanski 1994; Moilanen and Nieminen 2002) that integrates distances to and sizes of potential source populations. We considered only source patches within a specified buffer radius from each target
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Figure 1. Map of spatial distribution of habitat quality of 457 depression marshes at Avon Park Air Force Range, Florida, that represented suitable habitat patches for a metapopulation of round-tailed muskrats. Symbol size reflects habitat quality, which was an index of cover and density of maidencane grass in wetlands averaged over 2 years. Wetlands were geographically isolated even though some symbols overlap.
patch because our study area was not an isolated patch network, and thus an edge adjustment was necessary (see Branch and Schooley 2005; Schooley and Wiens 2005). We used a buffer radius of 2 km because only 2% of vacant wetlands located more than 2 km from a source population (n = 50) were colonized between years (Branch and Schooley 2005). Connectivity (Si) of patch i included a negative exponential dispersal kernel and was defined as X pj expðadij ÞAbj Si ¼ ð1Þ j6¼i
where pj is the likelihood that patch j was occupied and could serve as a source patch, a is a parameter that scales the effect of distance on dispersal, dij is the distance (km) between centers of patches i and j (for dij £ 2 km), Aj is the area of patch j, and b is a scaling parameter relating abundance to patch area. We set pj equal to 0 for patches unoccupied in both years, pj equal to 0.5 for patches occupied in 1 year, and pj equal to 1 for patches occupied in both years. We estimated a as 0.5 by using logistic regression to model colonization of patches in 2003–2004 as a function of expðadÞ; where d was the distance to the nearest potential source patch, and selecting the value of a that minimized the deviance of the model fit (Hokit and others 2001). Abundance and emigration are unlikely to scale linearly with patch area (Moilanen and Nieminen 2002; Schooley and Wiens 2005), so we assumed
that the relationship was nonlinear and used a value of 0.5 for b (see Moilanen and Nieminen 2002). After running the logistic regression model (occupancy = intercept + patch size + patch quality + connectivity), we saved the deviance residuals and then constructed a cross-variogram between the residuals and habitat quality (Rossi and others 1992; Gamma Design Software 2004; Fortin and Dale 2005). Cross-variograms are similar to variograms except that cross-variograms model the spatial covariation between two variables. Cross-variograms can be positive or negative depending on how the variables are related (Rossi and others 1992).
RESULTS Habitat quality of wetlands was heterogeneous in space (Figure 1) and exhibited positive spatial autocorrelation up to 6,000 m (Figure 2). However, Moran‘s I coefficients were strongest at moderate distances ( £ 1,000 m) and relatively weak beyond 3,000 m (Figure 2). Spatial patterns of habitat quality also were well described by a theoretical spherical variogram model (R2 = 0.87, sill = 0.02312, nugget = 0.01151) with an estimated range of 3,000 m. Round-tailed muskrats were present in 35.7% of the 457 wetlands in either 1 or 2 years. The logistic regression model of patch occupancy (R2 = 0.41)
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Figure 2. Moran‘s I spatial correlogram of habitat quality of wetlands. Solid circles indicate significant spatial autocorrelation; open circles indicate non-significant values. Significance of I for each lag distance was determined with a Monte Carlo randomization test (a = 0.05 with a progressive Bonferroni correction).
indicated that patch size (P < 0.0001, Wald v2 = 19.48, d.f. = 1), wetland quality (P < 0.0001, v2 = 45.22, d.f. = 1), and spatial connectivity (P < 0.0001, v2 = 39.17, d.f. = 1) were important predictors. The experimental cross-variogram between the regression residuals and habitat quality was well matched (R2 = 0.72) by a theoretical spherical model that included a small nugget variance (Figure 3). The residuals and habitat quality were correlated positively up to a range of 1,171 m (Figure 3). The ratio c/(c0 + c) varies between 0 and 1 and reflects the proportion of sample variance that is explained by spatially structured variance (Crist 1998; Gamma Design Software 2004). For our cross-variogram, c/(c0 + c) = 0.935.
DISCUSSION Empirical Cross-Scale Interactions Habitat quality of suitable patches was spatially autocorrelated for round-tailed muskrats in a naturally fragmented landscape. The intensity of the positive autocorrelation decayed with distance and was strongest for lags up to 1 km, which is similar to expected scales of dispersal for muskrats (Schooley and Branch 2006). Spatial autocorrelation in habitat quality was likely due to multiple drivers. Occurrence and density of maidencane grass is sensitive to inundation frequencies and water depths (David 1999). Hydroperiods for the shallow, seasonal marshes at our site are related to local topography and to regional rainfall patterns.
Figure 3. Isotropic cross-variogram demonstrating crossscale correlation between patch occupancy by roundtailed muskrats and habitat quality of suitable patches. The occupancy variable represented residuals from a logistic regression model that controlled for factors known to affect patch occupancy in metapopulations (patch size, local habitat quality, and spatial connectivity). Filled circles represent the experimental cross-variogram. The solid line represents the best-fitting theoretical cross-variogram, which is a spherical model.
Also, cattle grazing can affect habitat quality of wetlands for muskrats because cattle prefer maidencane and reduce its abundance in freshwater marshes (Kalmbacher and others 1984). Cattle grazing was managed at the pasture scale (50– 2,500 ha), and wetland quality was related negatively to grazing intensity (Branch and Schooley 2005). Autocorrelation of patch quality created neighborhoods of high-quality and low-quality patches across the landscape, with these neighborhoods characterized by different levels of patch occupancy and capacities for demographic rescue and recolonization. Patch-level processes and patterns scale up to broader distribution patterns, which then generate positive feedbacks by affecting the abundance of future colonists in neighborhoods. Our cross-variogram analysis quantified the spatial scale at which occupancy was related to habitat quality, independent of patch-level traits and isolation, which represents an insight not normally revealed by metapopulation studies. Furthermore, the bestfitting theoretical cross-variogram was a spherical model that included a sill, unlike linear or exponential models without sills (Fortin and Dale 2005). This outcome indicates that the relationship between fine-scale site occupancy and intermediate-scale habitat heterogeneity was nonlinear in the sense that the range represents a threshold. Beyond approximately 1.2 km, the cross-scale interaction degraded quickly, probably because the
Spatial Heterogeneity in Habitat Quality typical dispersal distance of potential immigrants was exceeded.
Broader Consequences of Autocorrelated Habitat Quality Metapopulation persistence is promoted by relatively asynchronous population dynamics among patches (Harrison and Quinn 1989; McCarthy and Lindenmayer 2000). Spatially correlated local extinctions (Smith and Gilpin 1997) can reduce long-term viability of metapopulations because a patch with a declining population is less likely to be rescued from extinction (Brown and Kodric-Brown 1977) or recolonized after extinction when it is surrounded by patches that are going extinct concurrently. Correlation of extinctions often is discussed in terms of effects of weather, disturbance, and predators (Harrison and Quinn 1989; Smith and Gilpin 1997; McCarthy and Lindenmayer 2000; Johst and Drechsler 2003). Spatial heterogeneity of habitat quality also can create a template that favors spatially correlated extinctions, whether the spatial patterning of habitat is related to anthropogenic disturbance or to ‘‘natural‘‘ environmental gradients and patchiness. Low-quality sites should contain small populations that are more prone to demographic stochasticity, less resistant to environmental stochasticity, and more likely to go extinct. For instance, weather effects such as drought or flooding that occur across regional scales could interact with habitat quality to create spatially correlated extinctions for roundtailed muskrats at finer scales. Moreover, autocorrelation of patch quality should reduce the likelihood of the rescue effect operating within lowquality patch clusters. Pulliam (1988) formalized the concept of source– sink dynamics for populations in spatially heterogeneous environments. Habitat quality is at the core of source–sink dynamics in that high-quality habitat functions as a source in which births exceed deaths, and emigration outweighs immigration; whereas low-quality habitat functions as a sink in which deaths exceed births, and immigration outweighs emigration (Pulliam 1988). For source–sink systems, patch quality usually is treated as a binary variable (Pulliam 1988; Boughton 1999; Kreuzer and Huntly 2003; Kawecki 2004). Habitat quality often is continuous in nature (Figure 1), however, and individuals and populations frequently are exposed to habitat gradients (Kristan 2003). In source–sink metapopulations, dynamics typically are modeled and investigated at the patch scale (Boughton 1999; Kawecki 2004). If there is spatial
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autocorrelation in habitat quality and local population dynamics, however, then clusters of patches could act collectively as source or sink habitat. Aggregate vital rates and emigration-immigration balances at this intermediate, patch-cluster level could have overriding importance to occupancy dynamics, cross-scale feedbacks, and regional persistence of metapopulations. Dispersal is the key transfer process (Peters and others, this issue) that links dynamics across spatial scales in metapopulations. For animal species with active dispersal, individuals must decide whether to disperse and where to settle. Such dispersal decisions can depend on many factors (Ims and Hjermann 2001) including habitat quality of the current site and that of other potential settlement sites. Expectations of whether dispersal patterns should follow source–sink or balanced dispersal models (Diffendorfer 1998) depend in part on the ability of individuals to assess habitat quality. Optimal decisions regarding dispersal and habitat selection are unlikely in fragmented landscapes in which information about neighborhood patches is limited (Lima and Zollner 1996; Ranta and others 1999). How can individuals conduct a cost-benefit analysis of dispersal when benefits of other patches are unknown and sampling habitat patches is costly? For species that evolved in environments with autocorrelated habitat quality, the spatial patterning of habitat is a source of landscape information that could be used by potential dispersers. Individuals born in high-quality patches can be expected to encounter other high-quality patches nearby and short-distance dispersal might be a good option, whereas individuals born in lowquality patches are likely to be surrounded by other low-quality patches and long-distance dispersal might be required. Although costs of moving through the matrix and densities of conspecifics in other patches remain unknowns, autocorrelation reduces information constraints regarding habitat quality. Reliability of this type of landscape information depends on autocorrelation strength within dispersal range (Ims and Hjermann 2001), and on temporal stability of the patterns of habitat heterogeneity. For round-tailed muskrats, habitat quality is correlated within dispersal range (Figure 2), but spatial patterns might vary over relevant time scales due to changing land-use practices.
CONCLUSIONS Metapopulation ecology inherently integrates patterns and processes across multiple scales from patches to patch clusters to entire patch networks.
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As ecologists continue to merge habitat heterogeneity with spatially realistic metapopulation approaches, explicit spatial patterning of habitat quality and potential for cross-scale interactions and neighborhood feedbacks should be considered. Autocorrelation of patch quality at intermediate scales has consequences for dispersal decisions by individuals and for spatially dependent population dynamics. Finally, most models that investigate extinction thresholds for complete metapopulations focus on habitat loss with ‘‘spatially correlated landscapes‘‘ referring solely to spatial clustering of suitable habitat patches (for example, Ovaskainen and others 2002). Incorporating autocorrelation of habitat quality of patches into extinction-threshold models would further bridge the gap between theory and many real landscapes.
ACKNOWLEDGMENTS Our research on metapopulation ecology of roundtailed muskrats was funded by a grant from the US Department of Defense. We thank J. Bridges, P. Ebersbach, P. Margosian, and P. Walsh for facilitating our study at Avon Park Air Force Range. We are grateful to J. Christopoulos, L. Showen, S. Cardiff, B. Gilbreath, M. McDermott, A. Pries, M. Shumar, and C. Wolf for assistance with fieldwork. B. Bestelmeyer, D. Peters and M. Turner provided helpful comments on earlier drafts of the manuscript.
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