A mathematical comment on the formulae for the aggregation index and the shape index

Ina recent paper [Landscape Ecol. 15: 591–601 (2000)] He et al. describedanaggregation index AI _i to measure pixelaggregation within a single class i. We show that thecommonly used shape index SI _i is related to theproposed aggregation metric as SI _i =(A _i) +AI _i(1 –(A _i)), with(A _i) dependent on class areaA _i only. Moreover, it is shown that thenormalized shape index, SI _i ^*,equals (1 – AI _i). We conclude thatAI _i does not provide any information notprovided by SI _i, orSI _i ^*.This revised version was published online in May 2005 with corrections to the Cover Date.     

Linking greenhouse gas emissions to urban landscape structure: the relevance of spatial and thematic resolutions of land use/cover data

Context

Emissions of greenhouse gases in urban areas play an important role in climate change. Increasing attention has been given to urban landscape structure–emission relationships (SERs). However, it remains unknown if and to what extent SERs are dependent on observational scale.

Objective

To assess how changing observational scales (in terms of spatial and thematic resolutions) of urban landscape structure affect SERs.

Methods

We examined correlations between 16 landscape metrics and greenhouse gas emissions across 52 European cities, through (1) systematic manipulation of spatial and thematic resolutions of the urban land use/cover (ULUC) dataset, and (2) comparison between available standard ULUC datasets with different spatial resolutions.

Results

Our analyses showed that the observed SERs significantly depend on both thematic and spatial resolutions of the ULUC data. For the 16 landscape metrics, we found diverse spatial/thematic scaling relations exhibiting monotonic, hump-shaped or scale-invariant trends. For different landscape metrics, the SERs were strongest at different spatial scales, suggesting that there is no consistent scaling relation over those observational scales.

Conclusions

SERs are highly sensitive to spatial and thematic resolutions of landscape data. To avoid the problem of ‘ecological fallacy,’ important caveats should be taken for interpretations based on single landscape metrics. Particular consideration should be paid to metrics that are easily interpretable, predictable in scaling behaviors, and important for shaping SERs, such as PLAND, ED, and LPI. Systematic investigations on scaling behaviors of SERs over well-defined scale domains are encouraged in future studies linking greenhouse gas emissions and urban landscape structure.

     

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.     

Effects of remote sensor spatial resolution and data aggregation on selected fragmentation indices

Analyzing the effect of scale on landscape pattern indices has been a key research topic in landscape ecology. The lack of comparability of fragmentation indices across spatial resolutions seriously limits their usefulness while multi-scale remotely sensed data are becoming increasingly available. In this paper, we examine the effect of spatial resolution on six common fragmentation indices that are being used within the Third Spanish National Forest Inventory. We analyse categorical data derived from simultaneously gathered Landsat-TM and IRS-WiFS satellite images, as well as TM patterns aggregated to coarser resolutions through majority rules. In general, majority rules tend to produce more fragmented patterns than actual sensor ones. It is suggested that sensor point spread function should be specifically considered to improve comparability among satellite images of varying pixel sizes. Power scaling-laws were found between spatial resolution and several fragmentation indices, with mean prediction errors under 10% for number of patches and mean patch size and under 5% for edge length. All metrics but patch cohesion indicate lower fragmentation at coarser spatial resolutions. In fact, an arbitrarily large value of patch cohesion can be obtained by resampling the pattern to smaller pixel sizes. An explanation and simple solution for correcting this undesired behaviour is provided. Landscape division and largest patch index were found to be the least sensitive indices to spatial resolution effects. This revised version was published online in May 2005 with corrections to the Cover Date. This revised version was published online in July 2006 with corrections to the Cover Date.     

Landscape patterns from mathematical morphology on maps with contagion

The perceived realism of simulated maps with contagion (spatial autocorrelation) has led to their use for comparing landscape pattern metrics and as habitat maps for modeling organism movement across landscapes. The objective of this study was to conduct a neutral model analysis of pattern metrics defined by morphological spatial pattern analysis (MSPA) on maps with contagion, with comparisons to phase transitions (abrupt changes) of patterns on simple random maps. Using MSPA, each focal class pixel on a neutral map was assigned to one of six pattern classes—core, edge, perforated, connector, branch, or islet—depending on MSPA rules for connectivity and edge width. As the density of the focal class (P) was increased on simple random maps, the proportions of pixels in different pattern classes exhibited two types of phase transitions at threshold densities (0.41 ≤ P ≤ 0.99) that were predicted by percolation theory after taking into account the MSPA rules for connectivity and edge width. While there was no evidence of phase transitions on maps with contagion, the general trends of pattern metrics in relation to P were similar to simple random maps. Using an index P for comparisons, the effect of increasing contagion was opposite that of increasing edge width.     

Sensitivity and effectiveness and of landscape metric scalograms in determining the characteristic scale of a hierarchically structured landscape

Landscape metric scalograms (the response curves of landscape metrics to changing grain size) have been used to illustrate the scale effects of metrics for real landscapes. However, whether they detect the characteristic scale of hierarchically structured landscapes remains uncertain. To address this question, the scalograms of 26 class-level metrics were systematically examined for a simple random landscape, seven hierarchical neutral landscapes, and the real landscape of the Xilin River Basin of Inner Mongolia, China. The results show that when the fraction of the focal patch type (P) is below a critical value (P _c), most metric scalograms are sensitive to change in single-scale and lower-level hierarchical structure and insensitive to change in higher-level hierarchical structure. The scalograms of only a few metrics measuring spatial aggregation and connectedness are sensitive to change in intermediate-level hierarchical structure. Most metric scalograms explicitly identify the characteristic scale of a single-scale landscape and fine or intermediate characteristic scales of a multi-scale landscape for both simulated and real landscapes. When P exceeds P _c, only some metrics detect scale and change in structure. The scalograms of total class area and Euclidean nearest-neighbor distance cannot detect scale or change in structure in either case. Landscape metric scalograms are useful for addressing scale issues, including illustrating the scale effects of spatial patterns, detecting multi-scale patterns, and developing possible scaling relations.

     

A new data aggregation technique to improve landscape metric downscaling

Scale is a fundamental concept in landscape ecology and considerable attention has been given to the scale-dependent relationships of landscape metrics. Many metrics have been found to exhibit very consistent scaling relationships as map resolution (i.e., pixel or grain size) is increased. However, these scaling relationships tend to break down when attempting to ‘downscale’ them, and the scaling function is often unable to accurately predict metric values for finer resolutions than the original data. The reasons for this breakdown are not well understood. This research examines the downscaling behavior of metrics using various data aggregation techniques in an attempt to better understand the characteristics of metric scaling behavior. First, downscaling performance is examined using the traditional method of aggregation known as ‘majority rules’. Second, a new data aggregation technique is introduced that utilizes fractional land cover abundances obtained from sub-pixel remote sensing classifications in order to capture a greater amount of the spatial heterogeneity present in the landscape. The goal of this new aggregation technique is to produce a more accurate scaling relationship that can be downscaled to predict metric values at fine resolutions. Results indicate that sub-pixel classifications have the potential to transform data aggregation to allow more accurate downscaling for certain landscapes, but accuracy is linked to the spatial heterogeneity of the landscape.     

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.     

Sensitivity of resource selection and connectivity models to landscape definition

Context

The definition of the geospatial landscape is the underlying basis for species-habitat models, yet sensitivity of habitat use inference, predicted probability surfaces, and connectivity models to landscape definition has received little attention.

Objectives

We evaluated the sensitivity of resource selection and connectivity models to four landscape definition choices including (1) the type of geospatial layers used, (2) layer source, (3) thematic resolution, and (4) spatial grain.

Methods

We used GPS telemetry data from pumas (Puma concolor) in southern California to create multi-scale path selection function models (PathSFs) across landscapes with 2500 unique landscape definitions. To create the landscape definitions, we identified seven geospatial layers that have been shown to influence puma habitat use. We then varied the number, sources, spatial grain, and thematic resolutions of these layers to create our suite of plausible landscape definitions. We assessed how PathSF model performance (based on AIC) was affected by landscape definition and examined variability among the predicted probability of movement surfaces, connectivity models, and road crossing locations.

Results

We found model performance was extremely sensitive to landscape definition and identified only seven top models out of our suite of definitions (<1%). Spatial grain and the number of geospatial layers selected for a landscape definition significantly affected model performance measures, with finer grains and greater numbers of layers increasing model performance.

Conclusions

Given the sensitivity of habitat use inference, predicted probability surfaces, and connectivity models to landscape definition, out results indicate the need for increased attention to landscape definition in future studies.

     

The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system

Geographical information systems (GIS) are well suited to the spatial analysis of landscape data, but generally lack programs for calculating traditional measures of landscape structure (e.g., fractal dimension). Standalone programs for calculating landscape structure measures do exist, but these programs do not enable the user to take advantage of GIS facilities for manipulating and analyzing landscape data. Moreover, these programs lack capabilities for analysis with sampling areas of different size (multiscale analysis) and also lack some needed measures of landscape structure (e.g., texture).We have developed the r.le programs for analyzing landscape structure using the GRASS GIS. The programs can be used to calculate over sixty measures of landscape structure (e.g., distance, size, shape, fractal dimension, perimeters, diversity, texture, juxtaposition, edges) within sampling areas of several sizes simultaneously. Also possible are moving window analyses, which enable the production of new maps of the landscape structure within windows of a particular size. These new maps can then be used in other analyses with the GIS.     

Scale problems in reporting landscape pattern at the regional scale

Remotely sensed data for Southeastern United States (Standard Federal Region 4) are used to examine the scale problems involved in reporting landscape pattern for a large, heterogeneous region. Frequency distributions of landscape indices illustrate problems associated with the grain or resolution of the data. Grain should be 2 to 5 times smaller than the spatial features of interest. The analyses also reveal that the indices are sensitive to the calculation scale,i.e., the unit area or extent over which the index is computed. This “sample area” must be 2 to 5 times larger than landscape patches to avoid bias in calculating the indices. Research sponsored by the Office of Research and Development, U.S. Environmental Protection Agency under IAG DW89934440-6 and DW89936104-01 with the U.S. Department of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc.     

Spatial scale and pattern dependences of aboveground biomass estimation from satellite images: a case study of the Sierra National Forest,California

Context

Spatial scale and pattern play important roles in forest aboveground biomass (AGB) estimation in remote sensing. Changes in the accuracy of satellite images-estimated forest AGBs against spatial scales and pixel distribution patterns has not been evaluated, because it requires ground-truth AGBs of fine resolution over a large extent, and such data are difficult to obtain using traditional ground surveying methods.

Objectives

We intend to quantify the accuracy of AGB estimation from satellite images on changing spatial scales and varying pixel distribution patterns, in a typical mixed coniferous forest in Sierra Nevada mountains, California.

Methods

A forest AGB map of a 143 km² area was created using small-footprint light detection and ranging. Landsat Thematic Mapper images were chosen as typical examples of satellite images, and resampled to successively coarser resolutions. At each spatial scale, pixels forming random, uniform, and clustered spatial patterns were then sampled. The accuracies of the AGB estimation based on Landsat images associated with varying spatial scales and patterns were finally quantified.

Results

The changes in the accuracy of AGB estimation from Landsat images are not monotonic, but increase up to 60–90 m in spatial scale, and then decrease. Random and uniform spatial patterns of pixel distributions yield better accuracy for AGB estimation than clustered spatial patterns. The corrected NDVI (NDVIc) was the best predictor of AGB estimation.

Conclusions

A spatial scale of 60–90 m is recommended for forest AGB estimation at the Sierra Nevada mountains using Landsat images and those with similar spectral resolutions.

     

Is bird incidence in Atlantic forest fragments influenced by landscape patterns at multiple scales?

The degree to which habitat fragmentation affects bird incidence is species specific and may depend on varying spatial scales. Selecting the correct scale of measurement is essential to appropriately assess the effects of habitat fragmentation on bird occurrence. Our objective was to determine which spatial scale of landscape measurement best describes the incidence of three bird species (Pyriglena leucoptera, Xiphorhynchus fuscus and Chiroxiphia caudata) in the fragmented Brazilian Atlantic forest and test if multi-scalar models perform better than single-scalar ones. Bird incidence was assessed in 80 forest fragments. The surrounding landscape structure was described with four indices measured at four spatial scales (400-, 600-, 800- and 1,000-m buffers around the sample points). The explanatory power of each scale in predicting bird incidence was assessed using logistic regression, bootstrapped with 1,000 repetitions. The best results varied between species (1,000-m radius for P. leucoptera; 800-m for X. fuscus and 600-m for C. caudata), probably due to their distinct feeding habits and foraging strategies. Multi-scale models always resulted in better predictions than single-scale models, suggesting that different aspects of the landscape structure are related to different ecological processes influencing bird incidence. In particular, our results suggest that local extinction and (re)colonisation processes might simultaneously act at different scales. Thus, single-scale models may not be good enough to properly describe complex pattern–process relationships. Selecting variables at multiple ecologically relevant scales is a reasonable procedure to optimise the accuracy of species incidence models.     

Ground cover increases spatial aggregation and association of insect herbivores and their predators in an agricultural landscape

Context

Enhancing ground cover vegetation is an important agricultural practice that regulates herbivore and predator insects in agricultural landscapes. However, the effects of ground cover on the spatial distributions of these organisms have scarcely been explored.

Objectives

Our goal was to measure the effects of ground cover on the spatial aggregation and association of insect herbivores and predators, which might contribute to the control of herbivorous pests.

Methods

We conducted our experiments in peach orchards at two sites in eastern China. The two sites have experimental units with ground cover treatments that created a heterogeneous landscape. We conducted a 2-year experiment to investigate the abundance and distribution of herbivores (leafhoppers) and predators (ladybirds), using geostatistics to analyze their spatial aggregation and association.

Results

The abundance of predators increased and that of herbivores decreased in ground cover orchards compared to control orchards without ground cover. The proportion of spatial structure was greater than 0.75 for both herbivores and predators in the control orchards, indicating a lack of spatial aggregation, and less than 0.75 in peach orchards with ground cover, indicating spatial aggregation. The correlation of spatial aggregation between herbivores and predators was significantly positive in the ground cover treatment, indicating association of the two insect guilds. In control orchards, on the other hand, this was not significant.

Conclusions

The presence of ground cover increased predator abundance, spatial aggregation of herbivores and predators as well as their spatial association, suggesting a mechanism for more efficient control of herbivorous pests in peach orchards.

     

Streambed landscapes: evidence that stream invertebrates respond to the type and spatial arrangement of patches

The availability and spatial arrangement of habitat patches are known to strongly influence fauna in terrestrial ecosystems. The importance of patch arrangement is not well-studied within running-water systems where flow-induced movements of patches and of fauna could decouple habitat characteristics and faunal habitat preferences. Using small, stream-dwelling invertebrates, we asked if fauna in such systems can distinguish among patch types and if patch arrangement at their `landscape scale' (i.e., within a streambed across which they move and forage) can be linked to faunal abundance. We quantified the spatial distribution of sand and leaf patches at multiple sites on a streambed at regular intervals over a 1 yr period, estimated faunal abundance in the two patch types, and experimentally determined if faunal colonization varied among leaf patches that were similar structurally but differed in their potential microbial food resources. We show that despite their small size and limited swimming abilities, these stream invertebrates did respond to patch type, that specific characteristics of an individual patch influenced faunal colonization, and that the spatial arrangement of patches on the streambed was linked to field abundances. Larval chironomids and adult copepods were more abundant in leaves than in sand and preferentially colonized leaf patches made with rapidly decomposing leaves that harbored higher microbial (bacteria and fungi) abundances over leaf patches with more refractory leaves and lower microbial abundances. Further, statistical models that included spatially-explicit data on patch arrangement (e.g., patch contagion, distance between patches) explained significantly more variation in faunal abundance, than models that included only nonspatial information (e.g., date, time since last flood). Despite the fact that these fauna live in a highly dynamic environment with variable flow rates during the year, unstable patch configurations, and seasonal changes in total abundance, our findings suggest a need for aquatic ecologists to test the hypothesis that small-scale landscape attributes within streams (e.g., leaf patch aggregation) may be important to faunal dynamics. If patch aggregation has negative consequences for stream biota, streambed `landscapes' may be fundamentally different from many terrestrial landscapes due to the inherent connectivity provided by the water and the over-riding importance of patch edges. Regardless of these differences, our findings suggest that the spatial configuration of patches in a landscape may have consequences for fauna even in highly dynamic systems, in which patches move and fauna periodically experience high levels of passive dispersal.     

Relationships between landcover proportion and indices of landscape spatial pattern

Recent studies have related percolation theory and critical phenomena to the spatial pattern of landscapes. We generated simulated landscapes of forest and non-forest landcover to investigate the relationship between the proportion of forest (P_i) and indices of patch spatial pattern. One set of landscapes was generated by randomly assigning each pixel independently of other pixels, and a second set was generated by randomly assigning rectilinear clumps of pixels. Indices of spatial pattern were calculated and plotted against P_i. The random-clump landscapes were also compared with real agricultural landscapes. The results support the use of percolation models as neutral models in landscape ecology, and the performance of the indices studied with these neutral models can be used to help interpret those indices calculated for real landscapes.     

Linking macrodetritivore distribution to desiccation resistance in small forest fragments embedded in agricultural landscapes in Europe

Purpose

Most of the agricultural landscape in Europe, and elsewhere, consists of mosaics with scattered fragments of semi-natural habitat like small forest fragments. Mutual interactions between forest fragments and agricultural areas influence ecosystem processes such as nutrient cycling, a process strongly mediated by the macrodetritivore community, which is however, poorly studied. We investigated macrodetritivore distribution patterns at local and landscape-level and used a key functional trait (desiccation resistance) to gain mechanistic insights of the putative drivers.

Methods

Macrodetritivores were sampled in forest edges-centres of 224 European forest fragments across 14 landscapes opposing in land use intensity. We used a multilevel analysis of variance to assess the relative contribution of different spatial scales in explaining activity-density and Shannon-diversity of woodlice and millipedes, together with a model-based analysis of the multivariate activity-density data testing the effect on species composition. Secondly, we tested if desiccation resistance of macrodetritivores varied across communities at different spatial scales using linear mixed effect models.

Results

Forest edge-centre and landscape use intensity determined activity-density and community composition of macrodetritivores in forest fragments, while fragment characteristics like size and continuity were relatively unimportant. Forest edges and higher intensity landscapes supported higher activity-density of macrodetritivores and determined species composition. Forest edges sustained woodlouse communities dominated by more drought tolerant species.

Conclusions

Landscape use intensity and forest edges are main drivers in macrodetritivore distribution in forest fragments with desiccation resistance a good predictor of macrodetritivore distribution. Key functional traits can help us to predict changes in community structure in changing landscapes.

     

A new contagion index to quantify spatial patterns of landscapes

A contagion index was proposed by O'Neill et al. (1988) to quantify spatial patterns of landscapes. However, this index is insensitive to changes in spatial pattern. We present a new contagion index that corrects an error in the mathematical formulation of the original contagion index. The error is identified mathematically. The contagion indices (both original and new) are then evaluated against simulated landscapes.