Scaling simulation models for spatially heterogeneous ecosystems with diffusive transportation

The behavioral dependence of vegetation simulation models for spatially heterogeneous grasslands on simulation resolution was investigated. The dependence can be largely attributed to the non-linearity of the models. We showed that increasing scale or decreasing spatial resolution tended to overestimate the changing rate of an ecosystem using our landscape simulation model for alkaline grasslands in northeast China. A technique for scaling up simulation models with diffusive transportation was developed in this study by means of expanding the nonlinear driving functions in the model. The analysis showed that a simulation model for spatially heterogeneous landscapes might necessitate modification of both its mathematical structure and parameterization when applied to different scales. The scaling coefficients derived in this study were shown to be proportional to the variances or covariance of the spatially referenced variables, and can be estimated by running the model at a fine resolution for selected samples of the coarser grid cells. The technique was applied to a grassland landscape in northeast China and the results were compared with five-year observations on community succession. The comparison indicated that the proposed technique could effectively reduce overall scaling error of the model by as much as 80%, depending on the scaling difference between the fine and the coarse resolutions as well as the sampling scheme used.     

Analysis of fine-scale spatial pattern of a grassland from remotely-sensed imagery and field collected data

An important practical problem in the analysis of spatial pattern in ecological systems is that requires spatially-intensive data, with both fine resolution and large extent. Such information is often difficult to obtain from field-measured variables. Digital imagery can offer a valuable, alternative source of information in the analysis of ecological pattern. In the present paper, we use remotely-sensed imagery to provide a link between field-based information and spatially-explicit modeling of ecological processes. We analyzed one digitized color infrared aerial photograph of a serpentine grassland to develop a detailed digital map of land cover categories (31.24 m × 50.04 m of extent and 135 mm of resolution), and an image of vegetation index (proportional to the amount of green biomass cover in the field). We conducted a variogram analysis of the spatial pattern of both field-measured (microtopography, soil depth) and image-derived (land cover map, vegetation index, gopher disturbance) landscape variables, and used a statistical simulation method to produce random realizations of the image of vegetation index based upon our characterization of its spatial structure. The analysis revealed strong relationships in the spatial distribution of the ecological variables (e.g., gopher mounds and perennial grasses are found primarily on deeper soils) and a non-fractal nested spatial pattern in the distribution of green biomass as measured by the vegetation index. The spatial pattern of the vegetation index was composed of three basic components: an exponential trend from 0 m to 4 m, which is related to local ecological processes, a linear trend at broader scales, which is related to a general change in topography across the study site, and a superimposed periodic structure, which is related to the regular spacing of deeper soils within the study site. Simulations of the image of vegetation index confirmed our interpretation of the variograms. The simulations also illustrated the limits of statistical analysis and interpolations based solely on the semivariogram, because they cannot adequately characterize spatial discontinuities.     

Identifying structural self-similarity in mountainous landscapes

Digital elevation model data were used to partition a mountainous landscape (northwestern Montana, USA) into watershed/hillslope terrain units at several different spatial scales. Fractal analysis of the perimeter to area relationships of the resulting partition polygons identified statistical self-similarity across a range of spatial scales (approximately four orders of magnitude in partition area). The fractal dimension was higher for a relatively complex fluvially-dominated terrain than for a structurally simpler glacially-dominated terrain (1.23 vs. 1.02, respectively). The structural self-similarity exhibited by this landscape has direct implications in scaling up ecosystem process models for landscape to regional simulations.     

Does the scale of our observational window affect our conclusions about correlations between endangered salmon populations and their habitat?

Differences in the strength of species-habitat relationships across scales provide insights into the mechanisms that drive these relationships and guidance for designing in situ monitoring programs, conservation efforts and mechanistic studies. The scale of our observation can also impact the strength of perceived relationships between animals and habitat conditions. We examined the relationship between geographic information system (GIS)-based landscape data and Endangered Species Act-listed anadromous Pacific salmon (Oncorhynchus spp.) populations in three subbasins of the Columbia River basin, USA. We characterized the landscape data and ran our models at three spatial scales: local (stream reach), intermediate (6th field hydrologic units directly in contact with a given reach) and catchment (entire drainage basin). We addressed three questions about the effect of scale on relationships between salmon and GIS representations of landscape conditions: (1) at which scale does each predictor best correlate with salmon redd density, (2) at which scale is overall model fit maximized, and (3) how does a mixed-scale model compare with single scale models (mixed-scale meaning models that contain variables characterized at different spatial scales)? We developed mixed models to identify relationships between redd density and candidate explanatory variables at each of these spatial scales. Predictor variables had the strongest relationships with redd density when they were summarized over the catchment scale. Meanwhile strong models could be developed using landscape variables summarized at only the local scale. Model performance did not improve when we used suites of potential predictors summarized over multiple scales. Relationships between species abundance and land use or intrinsic habitat suitability detected at one scale cannot necessarily be extrapolated to other scales. Therefore, habitat restoration efforts should take place in the context of conditions found in the associated watershed or landscape.     

Shifts in bat community structure related to evolved traits and features of human-altered landscapes

Population declines for many bat species are associated with rapid, human-induced ecosystem changes. In this context, the available species pool is determined in part by historical adaptation to the native ecosystem, but the resulting community structure may be determined principally by the ability of evolved traits to function in the novel context of a human-dominated ecosystem. To investigate the role of human disturbance as a determinant of bat communities, we surveyed assemblages and species occurrence rates in 27 agriculturally dominated landscapes exhibiting a gradient of human-induced forest fragmentation in Indiana, USA. We used multiple linear regression to explore the relationship of landscape environmental variables to species diversity. We then examined the relationship between community structure, evolved species traits and fragmentation conditions across a landscape using RLQ analysis. Overall, species diversity was positively related to the amount of forest and negatively correlated with amount of urban development in a landscape. We also observed a significant relationship between evolved species traits and landscape-level variables that is consistent with globally anticipated trends for bat species extinction risk. Our findings suggest that responses of bat species to human modification of ecosystems on the scale of a few kilometers could drive distributional dynamics at larger spatial and longer temporal scales.     

Predicting land use change: comparison of models based on landowner surveys and historical land cover trends

To make informed planning decisions, community leaders, elected officials, scientists, and natural resource managers must be able to evaluate potential effects of policies on land use change. Many land use change models use remotely-sensed images to make predictions based on historical trends. One alternative is a survey-based approach in which landowners’ stated intentions are modeled. The objectives of our research were to: (1) develop a survey-based landowner decision model (SBM) to simulate future land use changes, (2) compare projections from the SBM with those from a trend-based model (TBM), and (3) demonstrate how two alternative policy scenarios can be incorporated into the SBM and compared. We modeled relationships between land management decisions, collected from a mail survey of private landowners, and the landscape, using remotely-sensed imagery and ownership parcel data. We found that SBM projections were within the range of TBM projections and that the SBM was less affected by errors in image classification. Our analysis of alternative policies demonstrates the importance of understanding potential effects of targeted land use policies. While policies oriented toward increasing enrollment in the Conservation Reserve Program (CRP) resulted in a large (11–13%) increase in CRP lands, policies targeting increased forest thinning on private non-industrial lands increased low-density forest projections by only 1%. The SBM approach is particularly appropriate for landscapes including many landowners, because it reflects the decision-making of the landowners whose individual actions will result in collective landscape change.     

Remote sensing for the assessment of ecosystem services provided by urban vegetation: A review of the methods applied

The study and assessment of ecosystem services through remote sensing has increased substantially over the last two decades, as evidenced by the publication of studies that have applied it. The technological development of satellite images has improved in terms of spatial, spectral, radiometric, and temporal resolution, allowing the space-time observation, classification and monitoring of vegetation on the surface of the Earth. However, there are remaining methodological challenges for assessing ecosystem services due to the diversity of applications, the resources used, and its study in complex environments such as cities. This systematic review is based on identifying and analysing the variety of methods concerning the application of remote sensing for the assessment of ecosystem services provided by vegetation in cities, through a classification of these methods according to the data collection source (passive sensors, passive and active sensors and the fusion of other data sources with sensors). The classification of methods has been applied to a selection of existing articles in indexed scientific databases based on a non-statistical meta-analysis that make a direct reference to the topic of interest. The results show the approaches found in every method classified, their relationships with the geographical scale and the image resolutions used, and the advantages and limitations from the data processes that comprise remote sensing. We conclude from this analysis with three key factors to consider in the selection of remote sensing methods for the assessment of ecosystem services provided by urban vegetation: the definition of the approach(es), the urban scale to be assessed, and the image resolution available.     

Effects of changing spatial resolution on the results of landscape pattern analysis using spatial autocorrelation indices

Understanding the relationship between pattern and scale is a central issue in landscape ecology. Pattern analysis is necessarily a critical step to achieve this understanding. Pattern and scale are inseparable in theory and in reality. Pattern occurs on different scales, and scale affects pattern to be observed. The objective of our study is to investigate how changing scale might affect the results of landscape pattern analysis using three commonly adopted spatial autocorrelation indices,i.e., Moran Coefficient, Geary Ratio, and Cliff-Ord statistic. The data sets used in this study are spatially referenced digital data sets of topography and biomass in 1972 of Peninsular Malaysia. Our results show that all three autocorrelation indices were scale-dependent. In other words, the degree of spatial autocorrelation measured by these indices vary with the spatial scale on which analysis was performed. While all the data sets show a positive spatial autocorrelation across a range of scales, Moran coefficient and Cliff-Ord statistic decrease and Geary Ratio increases with increasing grain size, indicating an overall decline in the degree of spatial autocorrelation with scale. The effect of changing scale varies in their magnitude and rate of change when different types of landscape data are used. We have also explored why this could happen by examining the formulation of the Moran coefficient. The pattern of change in spatial autocorrelation with scale exhibits threshold behavior,i.e., scale effects fade away after certain spatial scales are reached (for elevation). We recommend that multiple methods be used for pattern analysis whenever feasible, and that scale effects must be taken into account in all spatial analysis.     

Quantifying the effect of grazing and shrub-clearing on small scale spatial pattern of vegetation

Disturbances such as grazing, invading species, and clear-cutting, often act at small spatial scales, and means for quantifying their impact on fine scale vegetation patterns are generally lacking. Here we adopt a set of landscape metrics, commonly used for quantifying coarse scale fragmentation, to quantify fine scale fragmentation, namely the fine scale vegetation structure. At this scale, patches often consist of individual plants smaller than 1 m², requiring the grain of the analysis to be much smaller. We used balloon aerial photographs to map fine details of Mediterranean vegetation (pixel size <0.04 m) in experimental plots subjected to grazing and clear-cutting and in undisturbed plots. Landscape metrics are sensitive to scale. Therefore, we aggregated the vegetation map into four coarser scales, up to a resolution of 1 m, and analyzed the effect of scale on the metrics and their ability to distinguish between different disturbances. At the finest scale, six of the seven landscape metrics we evaluated revealed significant differences between treated and undisturbed plots. Four metrics revealed differences between grazed and control plots, and six metrics revealed differences between cleared and control plots. The majority of metrics exhibited scaling relations. Aggregation had mixed effects on the differences between metric values for different disturbances. The control plots were the most sensitive to scale, followed by grazing and clearing. We conclude that landscape metrics are useful for quantifying the very fine scale impact of disturbance on woody vegetation, assuming that the analysis is based on sufficiently high spatial resolution data.     

Scale detection in real and artificial landscapes using semivariance analysis

Semivariance analysis is potentially useful to landscape ecologists for detecting scales of variability in spatial data. We used semivariance analysis to compare spatial patterns of winter foraging by large ungulates with those of environmental variables that influence forage availability in northern Yellowstone National Park, Wyoming. In addition, we evaluated (1) the ability of semivariograms to detect known scales of variability in artificial maps with one or more distinct scales of pattern, and (2) the influence of the amount and spatial distribution of absent data on semivariogram results and interpretation. Semivariograms of environmental data sets (aspect, elevation, habitat type, and slope) for the entire northern Yellowstone landscape clearly identified the dominant scale of variability in each map layer, while semivariograms of ungulate foraging data from discontinuous study areas were difficult to interpret. Semivariograms of binary maps composed of a single scale of pattern showed clear and interpretable results: the range accurately reflected the size of the blocks of which the maps were constructed. Semivariograms of multiple scale maps and hierarchical maps exhibited pronounced inflections which could be used to distinguish two or three distinct scales of pattern. To assess the sensitivity of semivariance analysis to absent data, often the product of cloud interference or incomplete data collection, we deliberately masked (deleted) portions of continuous northern Yellowstone map layers, using single scale artificial maps as masks. The sensitivity of semivariance analysis to random deletions from the data was related to both the size of the deleted blocks, and the total proportion of the original data set that was removed. Small blocks could be deleted in very high proportions without degrading the semivariogram results. When the size of deleted blocks was large relative to the size of the map, the corresponding variograms became sensitive to the total proportion of data removed: variograms were difficult or impossible to interpret when the proportion of data deleted was high. Despite success with artificial maps, standard semivariance analysis is unlikely to detect multiple scales of pattern in real ecological data. Semivariance analysis is recommended as an effective technique for quantifying some spatial characteristics of ecological data, and may provide insight into the scales of processes that structure landscapes.     

Taxon-dependent Scaling: Beetles,Birds, and Vegetation at Four North American Grassland Sites

Because organisms respond to the environment at different scales, it is important to develop ways of determining the appropriate scales for a specific ecological process and organism. We consider whether the relative importance of different scales is associated with organism mobility, and whether this relationship is independent of landscape characteristics. We observed abundances of particular species for vascular plants, ground-dwelling beetles and breeding birds along eight 2-km transects of 40 sampling stations each, distributed over four sites along the regional gradient from shortgrass steppe in central Colorado to tallgrass prairie in central Kansas. For each transect and taxonomic group, the relative importance of factors measured at the trap scale (1 m; soil texture and hardness, vegetation height, bare ground), at the local scale (10 m; density of shrubs and cacti) and at the landscape scale (30 m; Landsat 7 TM spectral bands, slope and elevation) was assessed using hierarchical canonical variance partitioning with forward selection of explanatory variables. Plant, beetle and bird community composition was explained by environmental factors measured at all three scales. Factor influence was more consistent between transects and between plants and beetles for the more homogeneous landscapes of the shortgrass steppe than for the more heterogeneous landscapes of the tallgrass prairie. We conclude that, independent of the mobility of a taxonomic group, factors at several scales are important in explaining community composition. The importance of different scales shifts along a regional gradient, and the variability between sites is high even for nearby sites.     

Influences of scale on bat habitat relationships in a forested landscape in Nicaragua

Context

Scale dependence of bat habitat selection is poorly known with few studies evaluating relationships among landscape metrics such as class versus landscape, or metrics that measure composition or configuration. This knowledge can inform conservation approaches to mitigate habitat loss and fragmentation.

Objectives

We evaluated scale dependence of habitat associations and scaling patterns of landscape metrics in relation to bat occurrence or capture rate in forests of southwestern Nicaragua.

Methods

We captured 1537 bats at 35 locations and measured landscape and class metrics across 10 spatial scales (100–1000 m) surrounding capture locations. We conducted univariate scaling across the 10 scales and identified scales and variables most related to bat occurrence or capture rate.

Results

Edge and patch density, at both landscape and class levels, were the most important variables across species. Feeding guilds varied in their response to metrics. Certain landscape and configuration metrics were most influential at fine (100 m) and/or broad (1000 m) spatial scales while most class and composition metrics were influential at intermediate scales.

Conclusions

These results provide insight into the scale dependence of habitat associations of bat species and the influence of fine and broad scales on habitat associations. The effects of scale, examined in our study and others from fine (100 m) to broad (5 km) indicate habitat relationships for bats may be more informative at larger scales. Our results suggest there could be general differences in scale relationships for different groups of landscape metrics, which deserves further evaluation in other taxonomic groups.

     

Patterns and scale relations among urbanization measures in Stockholm,Sweden

In this study we measure urbanization based on a diverse set of 21 variables ranging from landscape indices to demographic factors such as income and land ownership using data from Stockholm, Sweden. The primary aims were to test how the variables behaved in relation to each other and if these patterns were consistent across scales. The variables were mostly identified from the literature and limited to the kind of data that was readily accessible. We used GIS to sample the variables and then principal component analyses to search for patterns among them, repeating the sampling and analysis at four different scales (250 × 250, 750 × 750, 1,250 × 1,250 and 1,750 × 1,750, all in meters). At the smallest scale most variables seemed to be roughly structured along two axes, one with landscape indices and one mainly with demographic factors but also impervious surface and coniferous forest. The other land-cover types did not align very well with these two axes. When increasing the scale this pattern was not as obvious, instead the variables separated into several smaller bundles of highly correlated variables. Some pairs or bundles of variables were correlated on all scales and thus interchangeable while other associations changed with scale. This is important to keep in mind when one chooses measures of urbanization, especially if the measures are indices based on several variables. Comparing our results with the findings from other cities, we argue that universal gradients will be difficult to find since city shape and size, as well as available information, differ greatly. We also believe that a multivariate gradient is needed if you wish not only to compare cities but also ask questions about how urbanization influences the ecological character in different parts of a city.     

Hierarchical relationships between landscape structure and temperature in a managed forest landscape

Management may influence abiotic environments differently across time and spatial scale, greatly influencing perceptions of fragmentation of the landscape. It is vital to consider a priori the spatial scales that are most relevant to an investigation, and to reflect on the influence that scale may have on conclusions. While the importance of scale in understanding ecological patterns and processes has been widely recognized, few researchers have investigated how the relationships between pattern and process change across spatial and temporal scales. We used wavelet analysis to examine the multiscale structure of surface and soil temperature, measured every 5 m across a 3820 m transect within a national forest in northern Wisconsin. Temperature functioned as an indicator – or end product – of processes associated with energy budget dynamics, such as radiative inputs, evapotranspiration and convective losses across the landscape. We hoped to determine whether functional relationships between landscape structure and temperature could be generalized, by examining patterns and relationships at multiple spatial scales and time periods during the day. The pattern of temperature varied between surface and soil temperature and among daily time periods. Wavelet variances indicated that no single scale dominated the pattern in temperature at any time, though values were highest at finest scales and at midday. Using general linear models, we explained 38% to 60% of the variation in temperature along the transect. Broad categorical variables describing the vegetation patch in which a point was located and the closest vegetation patch of a different type (landscape context) were important in models of both surface and soil temperature across time periods. Variables associated with slope and microtopography were more commonly incorporated into models explaining variation in soil temperature, whereas variables associated with vegetation or ground cover explained more variation in surface temperature. We examined correlations between wavelet transforms of temperature and vegetation (i.e., structural) pattern to determine whether these associations occurred at predictable scales or were consistent across time. Correlations between transforms characteristically had two peaks; one at finer scales of 100 to 150 m and one at broader scales of ^>300 m. These scales differed among times of day and between surface and soil temperatures. Our results indicate that temperature structure is distinct from vegetation structure and is spatially and temporally dynamic. There did not appear to be any single scale at which it was more relevant to study temperature or this pattern-process relationship, although the strongest relationships between vegetation structure and temperature occurred within a predictable range of scales. Forest managers and conservation biologists must recognize the dynamic relationship between temperature and structure across landscapes and incorporate the landscape elements created by temperature-structure interactions into management decisions.     

Textural Ordination Based on Fourier Spectral Decomposition: A Method to Analyze and Compare Landscape Patterns

We propose an approach to texture characterization and comparison that directly uses the information of digital images of the earth surface without requesting a prior distinction of structural ‘patches’. Digital images are partitioned into square ‘windows’ that define the scale of the analysis and which are submitted to the two-dimensional Fourier transform for extraction of a simplified textural characterization (in terms of coarseness) via the computation of a ‘radial’ power spectrum. Spectra computed from many images of the same size are systematically compared by means of a principal component analysis (PCA), which provides an ordination along a limited number of coarseness vs. fineness gradients. As an illustration, we applied this approach to digitized panchromatic air photos depicting various types of land cover in a semiarid landscape of northern Cameroon. We performed ‘textural ordinations’ at several scales by using square windows with sides ranging from 120 m to 1 km. At all scales, we found two coarseness gradients (PCA axes) based on the relative importance in the spectrum of large (> 50 km⁻¹), intermediate (30–50 km⁻¹), small (10–25 km⁻¹) and very small (<10 km⁻¹) spatial frequencies. Textural ordination based on Fourier spectra provides a powerful and consistent framework to identifying prominent scales of landscape patterns and to compare scaling properties across landscapes.     

Impact of scale on morphological spatial pattern of forest

Assessing and monitoring landscape pattern structure from multi-scale land-cover maps can utilize morphological spatial pattern analysis (MSPA), only if various influences of scale are known and taken into account. This paper lays part of the foundation for applying MSPA analysis in landscape monitoring by quantifying scale effects on six classes of spatial patterns called: core, edge, perforation, branch, connector and islet. Four forest maps were selected with different forest composition and configuration. The sensitivity of MSPA to scale was studied by comparing frequencies of pattern classes in total forest area for various combinations of pixel size (P) and size parameter (S). It was found that the quantification of forest pattern with MSPA is sensitive to scale. Differences in initial composition and configuration influence the amount but not the general tendencies of the variations of morphological spatial pattern (MSP) class proportions with scale. Increase of P led to data generalization resulting in either a removal of the small size features or their potential transformation into other non-core MSP classes, while an increase of S decreases the MSP core area and this process may transform small core areas into the MSP class islet. We established that the behavior of the MSPA classes with changing scale can be categorized as consistent and robust scaling relations in the forms of linear, power, or logarithmic functions over a range of scales.     

Scaling patterns of biomass and soil properties: an empirical analysis

We argue that studies at multiple scales must necessarilychange the extent of measurements, not just the spacing, in order toeffectivelycapture information regarding processes at multiple scales. We have implementeda multi-scale sampling scheme using transects of 10 cm, 1m, 10 m, 100 m, and 1 km ateach of four sites along an elevational gradient from dry foothills forest toalpine tundra in the Front Range of Colorado; these four sites form anadditional transect of 22 km. Along each of these transects wetookten equally spaced soil cores and measured variables important in determiningboth microbial and plant community structure: soil water content, organicmattercontent, pH, and total soil biomass. With this sampling scheme we are able totreat scale as an independent variable in our analyses, and our data show thatboth particular sites and particular variables can determine whether estimatesof mean values are scale-dependent or not. A geostatistical analysis using allof our data shows common relationships between scales across ecologicallydiverse sites; biomass shows the most complex pattern of distribution acrossscales, as measured by fractal dimension. Our analyses also reveal theinadequacy of several standard geostatistical models when applied to data frommultiple scales of measurement – we recommend the use of the boundedpowerlaw model in such cases. We hypothesize that because biological communitiesmustrespond simultaneously to multiple variables with differing patterns of spatialvariation, the spatial variation of biological communities will be at least ascomplex as the most complex environmental variable at any given site.This revised version was published online in May 2005 with corrections to the Cover Date.     

Detecting dominant landscape objects through multiple scales: An integration of object-specific methods and watershed segmentation

Complex systems, such as landscapes, are composed of different critical levels of organization where interactions are stronger within levels than among levels, and where each level operates at relatively distinct time and spatial scales. To detect significant features occurring at specific levels of organization in a landscape, two steps are required. First, a multiscale dataset must be generated from which these features can emerge. Second, a procedure must be developed to delineate individual image-objects and identify them as they change through scale. In this paper, we introduce a framework for the automatic definition of multiscale landscape features using object-specific techniques and marker-controlled watershed segmentation. By applying this framework to a high-resolution satellite scene, image-objects of varying size and shape can be delineated and studied individually at their characteristic scale of expression. This framework involves three main steps: 1) multiscale dataset generation using an object-specific analysis and upscaling technique, 2) marker-controlled watershed transformation to automatically delineate individual image-objects as they evolve through scale, and 3) landscape feature identification to assess the significance of these image-objects in terms of meaningful landscape features. This study was conducted on an agro-forested region in southwest Quebec, Canada, using IKONOS satellite data. Results show that image-objects tend to persist within one or two scale domains, and then suddenly disappear at the next, while new image-objects emerge at coarser scale domains. We suggest that these patterns are associated to sudden shifts in the entire image structure at certain scale domains, which may correspond to critical landscape thresholds.This revised version was published online in May 2005 with corrections to the Cover Date.