Alternative spatial resolutions and estimation of carbon flux over a managed forest landscape in Western Oregon

Spatially-distributed estimates of biologically-driven CO₂ flux are of interest in relation to understanding the global carbon cycle. Global coverage by satellite sensors offers an opportunity to assess terrestrial carbon (C) flux using a variety of approaches and corresponding spatial resolutions. An important consideration in evaluating the approaches concerns the scale of the spatial heterogeneity in land cover over the domain being studied. In the Pacific Northwest region of the United States, forests are highly fragmented with respect to stand age class and hence C flux. In this study, the effects of spatial resolution on estimates of total annual net primary production (NPP) and net ecosystem production (NEP) for a 96 km² area in the central Cascades Mountains of western Oregon were examined. The scaling approach was a simple `measure and multiply' algorithm. At the highest spatial resolution (25 m), a stand age map derived from Landsat Thematic Mapper imagery provided the area for each of six forest age classes. The products of area for each age class and its respective NPP or NEP were summed for the area wide estimates. In order to evaluate potential errors at coarser resolutions, the stand age map was resampled to grain sizes of 100, 250, 500 and 1000 m using a majority filter reclassification. Local variance in near-infrared (NIR) band digital number at successively coarser grain sizes was also examined to characterize the scale of the heterogeneity in the scene. For this managed forest landscape, proportional estimation error in land cover classification at the coarsest resolution varied from –1.0 to +0.6 depending on the initial representation and the spatial distribution of the age class. The overall accuracy of the 1000 m resolution map was 42% with respect to the 25 m map. Analysis of local variance in NIR digital number suggested a patch size on the order of 100–500 m on a side. Total estimated NPP was 12% lower and total estimated NEP was 4% lower at 1000 m compared to 25 m. Carbon flux estimates based on quantifying differences in total biomass stored on the landscape at two points in time might be affected more strongly by a coarse resolution analysis because the differences among classes in biomass are more extreme than the differences in C flux and because the additional steps in the flux algorithm would contribute to error propagation. Scaling exercises involving reclassification of fine scale imagery over a range of grain sizes may be a useful screening tool for stratifying regions of the terrestrial surface relative to optimizing the spatial resolution for C flux estimation purposes.     

Impact of data integration technique on historical land-use/land-cover change: Comparing historical maps with remote sensing data in the Belgian Ardennes

Historical reconstructions of land-use/cover change often require comparing maps derived from different sources. The objective of this study was to measure land-use/cover changes over the last 225 years at the scale of a Belgian landscape, Lierneux in Ardennes, on the basis of a heterogeneous time series of land cover data. The comparability between the land-cover maps was increased following a method of data integration by map generalisation. Two types of time series were built by integrating the maps either by reference to the initial map of the time series or by pair of successive maps. Land-cover change detection was performed on the initial time series without data integration and on the two types of integrated time series. Results reveal that land cover and landscape structure have been subject to profound changes in Lierneux since 1775, with an annual rate of change at the landscape level of up to 1.40%. The major land-cover change processes observed are expansion of grasslands-croplands and reforestation with coniferous species, leading to amore fragmented landscape structure. The annual rates of land-cover change estimated from integrated data are significantly different from the annual rates of change estimated without a prior integration of the data. There is a trade-off between going as far back in time as possibleversus performing change detection as accurately as possible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of changing spatial scale on the analysis of landscape pattern

The purpose of this study was to observe the effects of changing the grain (the first level of spatial resolution possible with a given data set) and extent (the total area of the study) of landscape data on observed spatial patterns and to identify some general rules for comparing measures obtained at different scales. Simple random maps, maps with contagion (i.e., clusters of the same land cover type), and actual landscape data from USGS land use (LUDA) data maps were used in the analyses. Landscape patterns were compared using indices measuring diversity (H), dominance (D) and contagion (C). Rare land cover types were lost as grain became coarser. This loss could be predicted analytically for random maps with two land cover types, and it was observed in actual landscapes as grain was increased experimentally. However, the rate of loss was influenced by the spatial pattern. Land cover types that were clumped disappeared slowly or were retained with increasing grain, whereas cover types that were dispersed were lost rapidly. The diversity index decreased linearly with increasing grain size, but dominance and contagion did not show a linear relationship. The indices D and C increased with increasing extent, but H exhibited a variable response. The indices were sensitive to the number (m) of cover types observed in the data set and the fraction of the landscape occupied by each cover type (P _k); both m and P _kvaried with grain and extent. Qualitative and quantitative changes in measurements across spatial scales will differ depending on how scale is defined. Characterizing the relationships between ecological measurements and the grain or extent of the data may make it possible to predict or correct for the loss of information with changes in spatial scale.     

A multi-scale analysis of landscape statistics

It is now feasible to monitor some aspects of landscapeecological condition nationwide using remotely-sensed imagery andindicators of land cover pattern. Previous research showedredundancies among many reported pattern indicators andidentified six unique dimensions of land cover pattern. Thisstudy tested the stability of those dimensions and representativepattern indicators across different types of land cover maps. Themaps were derived from Landsat Thematic Mapper images of theTennessee River and Chesapeake Bay watersheds, and they differedin resolution, number of attributes, and method of delineatinglandscape unit boundaries. A multivariate analysis of patternmetrics was conducted separately for each map, and the resultswere then compared among types of maps. Measures of land coverdiversity, texture, and fractal dimension were more consistentthan measures of average patch shape or compaction among the landcover maps.     

An investigation of uncertainty in field habitat mapping and the implications for detecting land cover change

Land cover data for landscape ecological studies are frequently obtained by field survey. In the United Kingdom, temporally separated field surveys have been used to identify the locations and magnitudes of recent changes in land cover. However, such map data contain errors which may seriously hinder the identification of land cover change and the extent and locations of rare landscape features. This paper investigates the extent of the differences between two sets of maps derived from field surveys within the Northumberland National Park in 1991 and 1992. The method used in each survey was the Phase 1 approach of the Nature Conservancy Council of Great Britain. Differences between maps were greatest for the land cover types with the smallest areas. Overall spatial correspondence between maps was found to be only 44.4%. A maximum of 14.4% of the total area surveyed was found to have undergone genuine land cover change. The remaining discrepancies, equivalent to 41.2% of the total survey area, were attributed primarily to differences of land cover interpretation between surveyors (classification error). Differences in boundary locations (positional error) were also noted, but were found to be a relatively minor source of error. The implications for the detection of land cover change and habitat mapping are discussed.     

The use of remotely-sensed satellite imagery for landscape classification in Wales (U.K.)

Remotely-sensed satellite data from Landsat TM and MSS were processed digitally to make landscape classifications of three study areas of south east Wales. The classifications were constructed by classifying major variations in land cover mosaics within the areas, and using these data to group the 1 km × 1 km cells of the National Grid into landscape classes according to the combination of cover types found within them. The TWINSPAN algorithm, which is a polythetic, divisive classification method, was used as the basis of the study.The results showed that while satellite imagery could only be used to extract information about land cover, the close association betwen landscape, land cover and terrain meant that the major physical divisions in the study area could also be detected in the landscape classification. The landscape types recognised in the study were found to be consistent with those indicated in other independent data which relate to the areas. These data included the ITE Land Classes for Great Britain, and the Agricultural (June) Census statistics for England and Wales.The approach to landscape classification described allows landscape classifications to be made rapidly. These classifications can provide a sampling frameworks for landscape survey in areas where basic map data are lacking or resources for field survey are limited. The landscape classifications can also assist in making landscape evaluations since they allow different landscape types to be compared in respect of such properties such as their typicalness, rarity, naturalness and position on a geographical or ecological gradient.     

Presettlement landscape heterogeneity: Evaluating grain of resolution using General Land Office Survey data

General Land Office Survey (GLOS) records from the A.D. 1840s provide data for quantitative characterization of presettlement vegetation across western Mackinac County, Michigan, located within the mixed conifer-northern hardwoods forest region. We analyzed data from land survey plat maps and 1958 bearing, witness, and line trees from 162 surveyed section and quarter-section corners in order to map vegatation cover types at a level of spatial resolution appropriate for characterizing landscape heterogeneity using standard landscape ecological metrics. As also demonstrated by a number of both classic and contemporary plant-ecological studies, the distribution of landforms, soils properties, hydrology, and location of fire breaks all contribute to the heterogeneity in vegetation observed at a landscape scale in the region. Through a series of spatial landscape analyses with differing grain of resolution, in this study we determine that a grid cell size of 65 ha (0.5 mi×0.5 mi or 0.25 mi²) to 259 ha (1 mi²) gives a conservative characterization of landscape heterogeneity using standard metrics and is therefore appropriate for use of GLOS data to study historical landscape changes.     

Effects of changing landscape pattern and U. S. G. S. land cover data variability on ecoregion discrimination across a forest-agriculture gradient

We examined the use of coarse resolution land cover data (USGS LUDA) to accurately discriminate ecoregions and landscape-scale features important to biodiversity monitoring and management. We used land cover composition and landscape indices, correlation and principal components analysis, and comparison with finer-grained Landsat TM data, to assess how well LUDA data discriminate changing patterns across an agriculture-forest gradient in Minnesota, U.S.A. We found LUDA data to be most accurate at general class levels of agriculture and forest dominance (Anderson Level I), but in consistent and limited in ecotonal areas of the gradient and within forested portions of the study region at finer classes (Anderson Level II). We expected LUDA to over-represent major (matrix) cover types and under-represent minor types, but this was not consistent with all classes. 1) Land cover types respond individualistically across the gradient, changing landscape grain as well as their spatial distribution and abundance. 2) Agriculture is not over-represented where it is the dominant land cover type, but forest is over-represented where it is dominant. 3) Individual forest types are under-represented in an open land matrix. 4) Within forested areas, mixed deciduous-coniferous forest is over-represented by several orders of magnitude and the separate conifer and hardwood types under-represented. Across gradual, transitional agriculture-forest areas, LUDA cover class dominance changes abruptly in a stair-step fashion. In general, rare cover types that are discrete, such as forest in agriculture or wetlands or water in forest, are more accurately represented than cover classes having lower contrast with the matrix. Northward across the gradient, important changes in the proportions of conifer and deciduous forest mixtures occur at scales not discriminated by LUDA data. Results suggest that finer-grained data are needed to map within-state ecoregions and discriminate important landscape characteristics. LUDA data, or similar coarse resolution data sources, should be used with caution and the biases fully understood before being applied in regional landscape management. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stochastic generating models for simulating hierarchically structured multi-cover landscapes

For simulating hierarchically structured raster maps of landscapes that consist of multiple land cover types, we extend the concept of neutral landscape models to provide a general Markovian model. A stochastic transition matrix provides the probability rules that govern landscape fragmentation processes by assigning finer resolution land cover categories, given coarser resolution categories. This matrix can either be changed or remain the same at different resolutions. The probability rules may be defined for simulating properties of an actual landscape or they may be specified in a truly neutral manner to evaluate the effects of particular transition probability rules.For illustration, model parameters are defined heuristically to simulate properites of actual watershed-delineated landscapes in Pennsylvania. Three landscapes were chosen; one is mostly forested, one is in a transitional state between mostly forested and a mixture of agriculture, urban and suburban land, while the third is fully developed with only remnant forest patches that are small and disconnected. For each landscape type, a small sample of raster maps are simulated in a Monte Carlo fashion to illustrate how an empirical distribution of landscape measurements can be obtained.     

The influence of patch-delineation mismatches on multi-temporal landscape pattern analysis

Investigations of land-cover change often employ metrics designed to quantify changes in landscape structure through time, using analyses of land cover maps derived from the classification of remote sensing images from two or more time periods. Unfortunately, the validity of these landscape pattern analyses (LPA) can be compromised by the presence of spurious change, i.e., differences between map products caused by classification error rather than real changes on the ground. To reduce this problem, multi-temporal time series of land-cover maps can be constructed by updating (projecting forward in time) and backdating (projecting backward in time) an existing reference map, wherein regions of change are delineated through bi-temporal change analysis and overlaid onto the reference map. However, this procedure itself creates challenges, because sliver patches can occur in cases where the boundaries of the change regions do not exactly match the land-cover patches in the reference map. In this paper, we describe how sliver patches can inadvertently be created through the backdating and updating of land-cover maps, and document their impact on the magnitude and trajectory of four popular landscape metrics: number of patches (NP), edge density (ED), mean patch size (MPS), and mean shape index (MSI). In our findings, sliver patches led to significant distortions in both the value and temporal behaviour of metrics. In backdated maps, these distortions caused metric trajectories to appear more conservative, suggesting lower rates of change for ED and inverse trajectories for NP, MPS and MSI. In updated maps, slivers caused metric trajectories to appear more extreme and exaggerated, suggesting higher rates of change for all four metrics. Our research underscores the need to eliminate sliver patches from any study dealing with multi-temporal LPA.     

Effects of stream map resolution on measures of riparian buffer distribution and nutrient retention potential

Riparian ecosystems are interfaces between aquatic and terrestrial environments recognized for their nutrient interception potential in agricultural landscapes. Stream network maps from a broad range of map resolutions have been employed in watershed studies of riparian areas. However, map resolution may affect important attributes of riparian buffers, such as the connectivity between source lands and small stream channels missing in coarse resolution maps. We sought to understand the influence of changing stream map resolution on measures of the river network, near-stream land cover, and riparian metrics. Our objectives were: (1) to evaluate the influence of stream map resolution on measures of the stream network, the character and extent of near-stream zones, and riparian metrics; (2) to compare patterns of variation among different physiographic provinces; and (3) to explore how predictions of nutrient retention potential might be affected by the resolution of a stream map. We found that using fine resolution stream maps significantly increased our estimates of stream order, drainage density, and the proportion of watershed area occurring near a stream. Increasing stream map resolution reduced the mean distance to source areas as well as mean buffer width and increased the frequency of buffer gaps. Measures of percent land cover within 100 m of streams were less sensitive to stream map resolution. Overall, increasing stream map resolution led to reduced estimates of nutrient retention potential in riparian buffers. In some watersheds, switching from a coarse resolution to a fine resolution stream map completely changed our perception of a stream network from well buffered to largely unbuffered. Because previous, broad-scale analyses of riparian buffers used coarse-resolution stream maps, those studies may have overestimated landscape-level buffer prevalence and effectiveness. We present a case study of three watersheds to demonstrate that interactions among stream map resolution and land cover patterns make a dramatic difference in the perceived ability of riparian buffers to ameliorate effects of agricultural activities across whole watersheds. Moreover, stream map resolution affects inferences about whether retention occurs in streams or riparian zones.     

Modeling scale-dependent landscape pattern,dispersal, and connectivity from the perspective of the organism

Understanding the impacts of habitat fragmentation on dispersal is an important issue in landscape and conservation ecology. Here I examine the effects of fine- to broad-scale patterns in landscape structure on dispersal success of organisms with differing life-history traits. An individual-based model was used to simulate dispersal of amphibian-like species whose movements were driven by land cover and moisture conditions. To systematically control spatial pattern, a landscape model was created by merging simulated land cover maps with synthetic topographic surfaces. Landscapes varied in topographic roughness and spatial contagion in agriculture and urban land cover. Simulations included three different species types that varied in their maximum potential dispersal distances by 1-, 2-, or 4-fold. Two sets of simulations addressed effects of varying aspects of landscape structure on dispersal success. In the first set of simulations, which incorporated variable distances between breeding patches, dispersal success was lowest for all species types when anthropogenic cover was patchily distributed. In the second set, with interpatch distances held constant as landscape composition varied, dispersal success decreased as anthropogenic cover became spatially contagious. Both sets revealed strong main effects of species characteristics, interpatch distances and landscape composition on dispersal success; furthermore, scale-dependent patterns in land cover and moisture gradients had a stronger effect on longer- than shorter-ranging species types. Taken together, these simulations suggest that heuristic conservation strategies could potentially be developed based on important but limited life history information.     

Impacts of road corridors on urban landscape pattern: a gradient analysis with changing grain size in Shanghai, China

Urbanization is one of the most important driving forces for land use and land cover change. Quantifying urban landscape pattern and its change is fundamental for monitoring and assessing ecological and socioeconomic consequences of urbanization. As the largest city in the country, Shanghai is now the fastest growing city in China. Using land use data set of 2002 and combining gradient analysis with landscape metrics, we analyzed landscape pattern of Shanghai with increasing grain size to study the impacts of road corridors on urban landscape pattern. Landscape metrics were computed along a 51×9 km² transect cutting across Shanghai with a moving window. The results showed that the urban landscape pattern of Shanghai was greatly changed when road corridors were merged with urban patches and the variation of patch density would alter when grain size changed. As a linear land use type, road corridors exhibited a different spatial signature comparing with other land use types and distinctive behavior with increasing grain size. Merging road and urban patches resulted in a sharp reduction in patch density, mainly caused by segmentation of roads corridors. The results suggested that grain size around 7.5 m might be optimal for urban landscape analysis. Landscape patch density is significantly correlated with road percent coverage and the most important effect of road corridors in urban landscape is increased habitat fragmentation.     

Old-growth forest landscape transitions from pre-European settlement to present

We conducted a multi-temporal spatial analysis of forest cover for a 9600 ha landscape in northern Wisconsin, U.S.A., using data from pre-European settlement (1860s), post-settlement (1931), and current (1989) periods. Using GIS we have shown forest landscape changes and trajectories that have been generally described in aggregate for the norther Great Lake States region. We created the pre-European settlement map from the witness tree data of the original federal General Land Office survey notes. The 1931 cover was produced from the Wisconsin Land Economic Inventory, and the 1989 cover map was based on color infrared photography. We used GIS to analyze 1) land area occupied by different forest types at different dates, 2) temporal transitions between dates and their driving proceses, and 3) successional trajectories with landforms and spatial associations of forest types. Over the 120 year period, forest cover has changed from a landscape dominated by old-growth hemlock (Tsuga canadensis) and hardwood forests (Acer saccharum, Betula alleghaniensis) to largely second-growth hardwoods and conifers. The former dominant hemlock is largely eliminated from the landscape. From 1860 to 1931, large-scale disturbances associated with logging were the dominant processes on the landscape. Early successional forest types covered much of the landscape by the 1930s. From 1931 to 1989, succession was the dominant process driving forest transitions as forest types succeeded to a diverse group of upland hardwood and conifer forest types. If successional trajectories continue, a more homogeneous landscape may develop comprised of both a northern hardwood type dominated by sugar maple, and a boreal conifer/hardwood forest.     

Estimates of dryland degradation in Argentina with Fourier signatures from low-altitude monochromatic images with high spatial resolution

Most world drylands are used as graziny lands and undergo degradation of their vegetation cover. The plant cover is typically structured in patchy arrangements, inducing fertility islands critical to maintenance of ecosystem properties. The characteristics of patch structure (size of patches, connectivity-continuity of patch units, etc.) are indicators of the degree of dryland deterioration. We characterized changes in patch structure induced by sheep grazing at a landscape scale using monochromatic low-altitude imagery digitized to a spatial resolution of about 1 m with standard techniques of harmonic analysis applied to develop Fourier signatures. The signatures developed on image line transects were tested with ground samples and mathematical models of plant cover in several dryland fields where spatial deterioration gradients existed. The sensitivity and errors associated to long-wave noise introduced by the geometry of the camera-field-sun spatial arrangement and to high frequency noise introduced by the digitizing process were evaluated by applying suitable filters in the frequency domain. Fourier signatures developed on monochromatic low-altitude imagery proved to be indicative of changes in the patching arrangements of plant cover. We concluded that adequately filtered, high spatial resolution monochromatic images can be used to evaluate the degree of deterioration of dryland landscapes through the computation of selected Fourier signatures in their frequency domain. At comparable cost, aerial photography allows inspecting the landscape at higher spatial resolutions than those attainable with satellite imagery. Also, aerial photos of many areas are available for earlier dates than images from remote sensors, which would allow better inspection of long-term ecosystem changes.This revised version was published online in May 2005 with corrections to the Cover Date.     

Characterizing watershed-delineated landscapes in Pennsylvania using conditional entropy profiles

When the objective is to characterize landscapes with respect to relative degree and type of forest (or other critical habitat) fragmentation, it is difficult to decide which variables to measure and what type of discriminatory analysis to apply. It is also desirable to incorporate multiple measurement scales. In response, a new method has been developed that responds to changes in both the marginal and spatial distributions of land cover in a raster map. Multiscale features of the map are captured in a sequence of successively coarsened resolutions based on the random filter for degrading raster map resolutions. Basically, the entropy of spatial pattern associated with a particular pixel resolution is calculated, conditional on the pattern of the next coarser parent resolution. When the entropy is plotted as a function of changing resolution, we obtain a simple two-dimensional graph called a conditional entropy profile, thus providing a graphical visualization of multi-scale fragmentation patterns.Using eight-category raster maps derived from 30-meter resolution LANDSAT Thematic Mapper images, the conditional entropy profile was obtained for each of 102 watersheds covering the state of Pennsylvania (USA). A suite of more conventional single-resolution landscape measurements was also obtained for each watershed using the FRAGSTATS program. After dividing the watersheds into three major physiographic provinces, cluster analysis was performed within each province using various combinations of the FRAGSTATS variables, land cover proportions and variables describing the conditional entropy profiles. Measurements of both spatial pattern and marginal land cover proportions were necessary to clearly discriminate the watersheds into distinct clusters for most of the state; however, the Piedmont province essentially only required the land cover proportions. In addition to land cover proportions, only the variables describing a conditional entropy profile appeared to be necessary for the Ridge and Valley province, whereas only the FRAGSTATS variables appeared to be necessary for the Appalachian Plateaus province. Meanwhile, the graphical representation of conditional entropy profiles provided a visualization of multi-scale fragmentation that was quite sensitive to changing pattern.     

CORINE-based landscape indices weakly correlate with plant species richness in a northern European landscape transect

We present the results of one of the few available tests of how CORINE (CLC2000) is likely to perform as a basis for the calculation of landscape indices, for environmental monitoring over large areas. This paper investigates to what extent landscape structural indices based on this widely used European land cover database can be used to predict plant species richness in a 2,000 km² transect in the northeast of Scotland. We investigate both statistical and map resolution issues by comparing the performance of CORINE-based common landscape indices with the same indices derived from a much more detailed geographic data set. In our case study, only shape-related indices show correlation with species richness, but effect size, important for monitoring, is small. The results highlight the area-specific and map specific nature of the performance of landscape indices for protecting plant diversity. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Influence of high-resolution data on the assessment of forest fragmentation

Context

Remote sensing has been a foundation of landscape ecology. The spatial resolution (pixel size) of remotely sensed land cover products has improved since the introduction of landscape ecology in the United States. Because patterns depend on spatial resolution, emerging improvements in the spatial resolution of land cover may lead to new insights about the scaling of landscape patterns.

Objective

We compared forest fragmentation measures derived from very high resolution (1 m²) data with the same measures derived from the commonly used (30 m?×??30 m; 900 m²) Landsat-based data.

Methods

We applied area-density scaling to binary (forest; non-forest) maps for both sources to derive source-specific estimates of dominant (density ≥?60%), interior (≥?90%), and intact (100%) forest.

Results

Switching from low- to high-resolution data produced statistical and geographic shifts in forest spatial patterns. Forest and non-forest features that were “invisible” at low resolution but identifiable at high resolution resulted in higher estimates of dominant and interior forest but lower estimates of intact forest from the high-resolution source. Overall, the high-resolution data detected more forest that was more contagiously distributed even at larger spatial scales.

Conclusion

We anticipate that improvements in the spatial resolution of remotely sensed land cover products will advance landscape ecology through re-interpretations of patterns and scaling, by fostering new landscape pattern measurements, and by testing new spatial pattern-ecological process hypotheses.

     

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.     

Neutral models for the analysis of broad-scale landscape pattern

The relationship between a landscape process and observed patterns can be rigorously tested only if the expected pattern in the absence of the process is known. We used methods derived from percolation theory to construct neutral landscape models,i.e., models lacking effects due to topography, contagion, disturbance history, and related ecological processes. This paper analyzes the patterns generated by these models, and compares the results with observed landscape patterns. The analysis shows that number, size, and shape of patches changes as a function of p, the fraction of the landscape occupied by the habitat type of interest, and m, the linear dimension of the map. The adaptation of percolation theory to finite scales provides a baseline for statistical comparison with landscape data. When USGS land use data (LUDA) maps are compared to random maps produced by percolation models, significant differences in the number, size distribution, and the area/perimeter (fractal dimension) indices of patches were found. These results make it possible to define the appropriate scales at which disturbance and landscape processes interact to affect landscape patterns.