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.     

Measuring boundary convexity at multiple spatial scales using a linear “moving window” analysis: an application to coastal river otter habitat selection

Landscape metrics have been used to quantify ecological patterns and to evaluate relationships between animal presence/abundance and habitat at multiple spatial scales. However, many ecological flows occur in linear systems such as streams, or across patch/landscape boundaries (ecotones). Some organisms and flows may depend on the boundary shape, but metrics for defining linear boundary characteristics are scarce. While sinuosity and fractal dimension address some elements of shape, they fail to specify the dominate shape direction (convexity/concavity). We propose a method for measuring boundary convexity and assess its utility, along with sinuosity and fractal dimension, for predicting site selection by coastal river otters. First, we evaluate the characteristics of boundary convexity using a hypothetical boundary. Second, to compare convexity with other linear metrics boundary convexity, sinuosity and fractal dimension were calculated for the coastline of a set of islands in Prince William Sound, AK. Finally, we use logistic regression in an information-theoretic framework to assess site selection of river otters as a function of these linear metrics. Boundary convexity, fractal dimension and sinuosity are relatively uncorrelated at all scales. Otter latrine sites occurred at significantly more convex locations on the coastline than random sites. Using logistic regression and convexity values at the 100 m window-size, 69.5% of the latrine sites were correctly classified. Coastal terrestrial convexity appears to be a promising landscape-scale metric for predicting otter latrine sites. We suggest that boundary convexity may be an important landscape metric for describing species use or ecological flows at ecotones.     

Indices of landscape pattern

Landscape ecology deals with the patterning of ecosystems in space. Methods are needed to quantify aspects of spatial pattern that can be correlated with ecological processes. The present paper develops three indices of pattern derived from information theory and fractal geometry. Using digitized maps, the indices are calculated for 94 quadrangles covering most of the eastern United States. The indices are shown to be reasonably independent of each other and to capture major features of landscape pattern. One of the indices, the fractal dimension, is shown to be correlated with the degree of human manipulation of the landscape.     

Fractal dimension estimates of a fragmented landscape: sources of variability

Although often seen as a scale-independent measure, we show that the fractal dimension of the forest cover of the Cazaville Region changes with spatial scale. Sources of variability in the estimation of fractal dimensions are multiple. First, the measured phenomenon does not always show the properties of a pure fractal for all scales, but rather exhibits local self-similarity within certain scale ranges. Moreover, some sampling components such as area of sampling unit, the use of a transect in the estimation of the variability of a plane, the location, and the orientation of a transect all affect, to different degrees, the estimation of the fractal dimension. This paper assesses the relative importance of these components in the estimation of the fractal dimension of the spatial distribution of woodlots in a fragmented landscape. Results show that different sources of variability should be considered when comparing fractal dimensions from different studies or regions.     

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.     

Multiscale sources of variation in ecological variables: modeling spatial dispersion,elaborating sampling designs

Detection of structured spatial variation and identification of spatial scales are important aspects of ecological studies. Spatial structures can correspond to physical features of the environment or to intrinsic characteristics of ecological processes and phenomena. Spatial variability has been approached through several techniques such as classical analysis of variance, or the calculation of fractal dimensions, correlograms or variograms. Under certain assumptions, these techniques are all closely related to one another and represent equivalent tools to characterize spatial structures.Our perception of ecological variables and processes depends on the scale at which variables are measured. We propose simple nested sampling designs enabling the detection of a wide range of spatial structures that show the relationships among nested spatial scales. When it is known that the phenomenon under study is structured as a nested series of spatial scales, this provides useful information to estimate suitable sampling intervals, which are essential to establish the relationships between spatial patterns and ecological phenomena. The use of nested sampling designs helps in choosing the most suitable solutions to reduce the amount of random variation resulting from a survey. These designs are obtained by increasing the sampling intensity to detect a wider spectrum of frequencies, or by revisiting the sampling technique to select more representative sampling units.     

Spatial pattern analysis of pre- and post-hurricane forest canopy structure in North Carolina,USA

Existing spatial patterns of a forest are in part a product of its disturbance history. Using laser altimetry and field measures of canopy top height to represent pre- and post-hurricane canopy topography, respectively, we measured changes in spatial patterns of stand structure of a United States southern mixed coniferous-deciduous for est. Autocorrelative and fractal properties were measured in this opportunistic study to quantify changes in canopy architecture along twelve, 190-250 m transects that were subjected to moderate to high levels of wind disturbance. Prior to the hurricane, canopy heights were autocorrelated at scales <40 m with an average fractal dimension of 1.71. After the disturbance, autocorrelation disappeared; the average fractal dimension rose to 1.94. This shift towards spatial randomness illustrates part of the cyclical nature of ecosystem development. It shows how a catastrophic collapse of biomass accumulation corresponds to a decrease in ecosystem organization across a landscape. This revised version was published online in July 2006 with corrections to the Cover Date.     

How key habitat features influence large terrestrial carnivore movements: waterholes and African lions in a semi-arid savanna of north-western Zimbabwe

Within a landscape where prey has an aggregated distribution, predators can take advantage of the spatial autocorrelation of prey density and intensify their search effort in areas of high prey density by using area-restricted search behaviour. In African arid and semi-arid savannas, large herbivores tend to aggregate around scarce water sources. We tested the hypothesis that water sources are a key determinant of habitat selection and movement patterns of large free-ranging predators in such savannas, using the example of the African lion. We used data from 19 GPS radio-collared lions in Hwange National Park, Zimbabwe. Maps of lions’ trajectories showed that waterholes are key loci on the lions’ route-maps. Compositional analyses revealed that lions significantly selected for areas located within 2 km of a waterhole. In addition, analysis of lions’ night paths showed that when lions are close to a waterhole (<2 km), they move at lower speed, cover shorter distances per night (both path length and net displacement) and follow a more tortuous path (higher turning angle, lower straightness index and higher fractal dimension) than when they are further from a waterhole. Hence, our results strongly suggest that lions adopt area-restricted searching in the vicinity of waterholes, and reduce their search effort to minimize the time spent far from a waterhole. They provide an illustration of how key habitat features that determine the dispersion of prey (e.g. waterholes in this study) have an influence on the spatial ecology and movement patterns of terrestrial predators.     

Conservation management of complex natural forest and plantation edge effects

Timber plantation forestry is a major threat to indigenous grassland biodiversity, with ecological networks (ENs) currently being used to mitigate this threat. Being composed mostly of linear corridors, ENs create more edge than would occur naturally. To determine the minimum width of corridors for maximising biodiversity conservation, we need first to establish the extent of edge effects from plantation blocks into corridors. We compared arthropod diversity along transects that ran from within plantation blocks into grassland corridors. We also studied the edge effects of natural forest adjacent to natural grasslands within ENs. Sites in grasslands of neighbouring protected areas acted as natural reference sites against which the biodiversity of the EN transects were compared. Two types of exotic plantation trees and various tree age classes were studied. We found a 32 m edge zone from plantation blocks into grassland corridors. Few significant edge effects from plantation blocks occurred at greater distances than this, which suggested that grassland corridors with a width <64 m are essentially all edge. However, and importantly, this situation was complex, as different arthropod taxonomic groups responded differently to edges of plantation blocks and natural forest patches. Natural forest supported many additional species, not just within the forest, but also in associated grassland corridors. This means that maintaining natural forest imbedded within the ENs will protect both indigenous grassland and indigenous forest species as well as help maintain biodiversity across this timber production landscape.     

Fractal characteristics of two-dimensional images of ‘Fuji’ apple trees trained to two tree configurations after their winter pruning

The structural diagrams of apple trees are the comprehensive reflection of the effects of their training and pruning as well as their physiological and ecological characteristics and yield. However, there have been few research reports on the characteristics of the structural diagrams of apple trees. The study investigated the fractal dimension numbers and fractal characteristics of the two-dimensional images of 5-year-old and 10-year-old ‘Fuji’ apple trees trained to the tall spindle configuration and the open-center configuration employing box-counting in combination with the image processing technology of the Photoshop. The two-dimensional images of apple trees with the different configurations differed and varied with their ages. The fractal dimension numbers of the two-dimensional images of the 10-year-old apple trees with the tall spindle configuration and with the open-center configuration were 1.6625 and 1.6531 respectively while the fractal dimension numbers of the two-dimensional images of the 5-year-old apple trees with the tall spindle configuration and with the open-center configuration were 1.6429 and 1.6377 respectively. As the age of the apple trees increased, the spatial quantities and distributions of trunks and branches got slightly intensified, and the fractal dimension numbers of their two-dimensional images and the apple yield increased correspondingly. The comparison of the fractal characteristics of the apple trees with the same age, which were trained to the different configurations, revealed that under the same age, the branch quantities and the apple yield of the apple trees with the tall spindle configuration were higher than those with the open-center configuration, so that under the same age the fractal dimension numbers with the tall spindle configuration were higher than those with the open-center configuration. These results showed that the fractal dimension number of the two-dimensional images of apple trees depended upon their trunk and bough distribution and at the same time it increased with their apple yield as well. Therefore, the fractal dimension numbers of the two-dimensional images of apple trees could be employed as an indicator for assessing training and pruning effects on apple trees and their fruit yield.     

Large-scale effects on the spatial distribution of seabirds in the Northwest Atlantic

Scale questions are particularly important for organisms which range over large areas, as pelagic seabirds do. The investigations of scale are of practical importance for describing patch size of predator and prey, determining the appropriate scale of study and correcting survey transects. We conducted this study in order to explore a substantially wider diversity of spatial scales than has previously been attempted in the pelagic bird literature. As an example of large monitoring datasets dealing with seabirds, we use the PIROP (Programme intégré pour le recherche des oiseaux pélagiques) data set to investigate relevant large scale issues for these species in the Northwestern Atlantic. We analyzed autocorrelation within selected winter and summer transects, and for 1 degree analysis units (‘bins’) for data collected June–August 1966–1992. We also investigated effects of the analysis unit on counting results and on the links between seabirds and their environment (depth, sea surface salinity and temperature). We selected scales of 1, 2, 5 and 10 degrees analysis units; an ecological mapping scale (‘Banks’ not deeper than 200 m) and a political scale (management convention zones of the North Atlantic Fisheries Organization, NAFO) were also included. Using ‘binning’ of various scales, our results show that the Coefficient of Variation for seabird abundances varies among aggregation scales, and that seabird associations with their environment can show scale effects. Autocorrelation of analysis units indicated some distinct larger scale patch sizes for particular species during the breeding season.     

The fractal shape of riparian forest patches

Remnant patches of a forest corridor were examined along the Iowa and Cedar Rivers, Iowa. A fractal dimension was found for these patches which was incorporated with the perimeter:area ratio in an index of shape. This index was then regressed on 5 hydrogeomorphic variables hypothesized to represent processes which might control patch dimensions, plus a variable to represent human impact. The hydrogeomorphic variables were derived from topographic maps; the impact variable used was the proportion of perimeter that was occupied by a road, railroad, transmission line, urban or other built area, or a straight line judged to be agricultural. Three variables remained significant in a reduced model: human impact, valley width, and stream sinuosity, but together the three accounted for only 24% of the variance in patch shape. The fractal perimeter:area ratio increased with human impact, probably because of reduced area, and decreased with valley width, which allowed more extensive forest on wide floodplains, and with sinuosity, which resulted in small patches isolated on the interior of meanders. These results indicate that in this landscape the hydrogeomorphic structures play a role, but that human impact is more significant in its effect on the shape of remnant forest patches. Other structures, such as the regional topography, may account for the unexplained variance. The index of shape used here may be useful as an independent variable in studies of ecological processes affected by patch shape and form and as a guide to conservation.     

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.     

Generating confidence intervals for composition-based landscape indexes

Many landscape indexes with ecological relevance have been proposed, including diversity indexes, dominance, fractal dimension, and patch size distribution. Classified land cover data in a geographic information system (GIS) are frequently used to calculate these indexes. However, a lack of methods for quantifying uncertainty in these measures makes it difficult to test hypothesized relations among landscape indexes and ecological processes. One source of uncertainty in landscape indexes is classification error in land cover data, which can be reported in the form of an error matrix. Some researchers have used error matrices to adjust extent estimates derived from classified land cover data. Because landscape diversity indexes depend only on landscape composition – the extent of each cover in a landscape – adjusted extent estimates may be used to calculate diversity indexes. We used a bootstrap procedure to extend this approach and generate confidence intervals for diversity indexes. Bootstrapping is a technique that allows one to estimate sample variability by resampling from the empirical probability distribution defined by a single sample. Using the empirical distribution defined by an error matrix, we generated a bootstrap sample of error matrixes. The sample of error matrixes was used to generate a sample of adjusted diversity indexes from which estimated confidence intervals for the diversity indexes were calculated. We also note that present methods for accuracy assessment are not sufficient for quantifying the uncertainty in landscape indexes that are sensitive to the size, shape, and spatial arrangement of patches. More information about the spatial structure of error is needed to calculate uncertainty for these indexes. Alternative approaches should be considered, including combining traditional accuracy assessments with other probability data generated during the classification procedure.     

Human-carnivore coexistence in a traditional rural landscape

Facilitating human-carnivore coexistence is a major conservation concern in human-dominated landscapes worldwide. Useful insights could be gained by studying and understanding the dynamics of human-carnivore coexistence in landscapes in which carnivores and humans have coexisted for a long time. We used a two-pronged approach combining ecological and social data to study coexistence of the brown bear (Ursus arctos) and humans in Transylvania, Romania. First, we surveyed 554 km of walking transects to estimate activity via a bear sign index, namely the proportion of anthills disturbed by bears, and used spatially explicit predictive models to test which biophysical and anthropogenic variables influenced bear activity. Second, we interviewed 86 shepherds and 359 villagers and community representatives to assess conflicts with bears and attitudes of shepherds towards bears. Our interdisciplinary study showed that bears and humans coexisted relatively peacefully despite occasional conflicts. Coexistence appeared to be facilitated by: (1) the availability of large forest blocks that are connected to the source population of bears in the Carpathian Mountains; (2) the use of traditional livestock management to minimize damage from bears; and (3) some tolerance among shepherds to occasional conflict with bears. In contrast, bear activity was unrelated to human settlements, and compensation for livestock losses did not influence people’s attitudes toward bears. Our study shows that coexistence of humans and carnivores is possible, even without direct economic incentives. A key challenge for settings with a discontinuous history of human-carnivore coexistence is to reinstate both practices and attitudes that facilitate coexistence.     

The VFractal: a new estimator for fractal dimension of animal movement paths

Fractal measurements of animal movement paths have been used to analyze how animals view habitats at different spatial scales. One problem has been the absence of error estimates for fractal d estimators. To address this weakness, I present and test 4 new estimators for measuring fractal dimension at different spatial scales, along with estimates of their variation. The estimators are based on dividing the movement path into pairs of steps, forming V's, and then estimating various statistics from each V.I measured the performance of these estimators by comparing them to the traditional divider d method, using data generated by two different animal movement models. The estimator based on the net distance between the two steps and the cos turning angle was most accurate, giving estimates similar to those of the traditionally-used divider d method. Precision increased with longer and straighter paths.Strengths of this new estimator are that it can estimate fractal d at different spatial scales, give an estimate of variation, and combine data from many separate path segments which have been gathered at various spatial scales.     

Phase coupling and spatial synchrony of subpopulations of an endangered dune lizard

Examining demographic phase coupling and spatial synchrony is important for understanding complicated spatiotemporal population dynamics. It is also necessary for protecting rare and endangered species; populations whose dynamics are controlled by resource flux will face increased extinction risk if environmental conditions that drive those resources become spatially synchronized. In this study, we studied the spatial synchrony of subpopulations of the threatened Coachella Valley fringe-toed lizard (Uma inornata), on its remaining sand dune habitat in the Coachella Valley of California. Our results indicated that there is a high level of spatial synchrony between lizard density and their mean reproductive effort for two subpopulations separated by a relatively short distance. High levels of spatial synchrony also exist between the mean lizards’ reproductive effort and annual precipitation. We measured spatial synchrony using four separate methods; using different methods allows understanding of complicated ecological interactions.     

A fractal model of vegetation complexity in Alaska

A methodology using fractals to measure vegetation complexity in three regions of Alaska is presented. Subjective, binomial (0 = simple, 1 = complex) classifications of the complexity of mapped vegetation polygon patterns within continuous forest inventory plots measured in the regions were made by interpreters of aerial photographs. The fractal dimensions of the vegetation patterns within the plots then were estimated. Subsequently, the subjective classifications of the photo-interpreted plots were regressed against fractal dimension by using logistic regression.Assessment of interobserver agreement among the aerial photo interpreters, by using estimated unweighted Kappa coefficients, indicated substantial classification agreement among observers.Examination of general versus regional applicability of the logistic models provided strong support for applicability of a single model to all three regions. The logistic model provides numerical identification of the division between simple and complex patterns. Possible applications beyond the needs of the study are discussed.     

A new approach for rescaling land cover data

The resolution of satellite imagery must often be increased or decreased to fill data gaps or match preexisting project requirements. It is well known that a change in resolution introduces systematic errors of size, shape, location and amount of contiguous land cover types. Nevertheless, robust methods for rescaling landscape data are frequently required to assess patterns of landscape change through time and over large areas. We developed a new method for rescaling spatial data that allows map resolution (grain size) to be either increased or decreased while holding the total proportion of land cover types constant. The method uses a weighted sampling net of variable resolution to sample an existing map and then randomly selects from the frequency of cover types derived from this sample to assign the cover type for the corresponding location in the rescaled map. The properties of the sampling net had a variable effect on measures of landscape pattern with the characteristic patch size (S) the most robust metric and the number of clusters (A) the most variable. A comparison of up-scaled and down-scaled maps showed that this process is not symmetrical, producing different errors for increases versus decreases in grain size. Rescaling Landsat (30 m) imagery to the 10 m resolution of SPOT imagery for four National Park units within Maryland and Virginia resulted in errors due to rescaling that were small (1–2%) relative to the total error (∼11%) associated with these images. The new rescaling method is general because it provides a single method for increasing or decreasing resolution, can be applied to maps with multiple land cover types, allows grid geometry to be transformed (i.e., square to hexagonal grids), and provide a more consistent basis for landscape comparisons when maps must be derived from multiple sources of classified imagery.     

Geometry of Large Woodland Remnants and its Influence on Avifaunal Distributions

In fragmented landscapes, remnant vegetation almost always occurs as irregular shapes and frequently with peninsulas or lobes of habitat extending into the surrounding agricultural matrix. Historical time-series of many landscapes indicate that such lobes tend to be lost through time, making remnants more regularly shaped as more habitat is lost. Although the biogeographic peninsular effect suggests that the biodiversity value of lobes should be less than remnant interiors, R.T.T. Forman has suggested that lobes in fragmented, human-dominated landscapes may provide positive ecological functions. We considered the distribution and occurrence of birds in medium-sized (ca. 2000 ha) remnants of the box-ironbark forests of central Victoria, Australia. We compared transects placed in the interiors, along edges and in lobes, finding that in general woodland-dependent species occurred throughout lobes and edges in densities substantially greater than the interiors of the remnants (often ca. 2 km from edges). We conducted analyses that weighted speciesȁ9 predilections to occupy the centres of large woodland areas using independent data. We found that: (1) species favouring centres of large woodland areas (measured using independent data) were distributed evenly throughout our study remnants; and (2) species capable of occupying smaller remnants (≤80 ha) were more prevalent in lobes and along the straight edges of remnants. These results indicate that preservation of lobes is likely to be important for maintaining avian biodiversity in fragmented landscapes, and that the addition of lobes in reconstructing landscapes through revegetation may favour birds.