Bruce T. Milne

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.

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 (Pk); both m and Pkvaried 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.

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.

Scaling of 'landscapes' in landscape ecology, or, landscape ecology from a beetle's perspective

Research performed on microlandscapes embodies the essence of landscape ecology by focusing on the ecological consequences of the mosaic structure of different landscape elements. As an illustration, observations and simulations were used to test whether the fractal structure of grassland microlandscapes affected the movement patterns of tenebrionid beeetles in natural environments. The significant tendency of beetles to avoid 1 m2 cells with fractal dimensions of 1.85 to 1.89 (indicating the area-filling tendency of bare ground) demonstrated the role of landscape structure as a modifier of beetle movements or diffusion in heterogeneous landscapes. Experiments in microlandscapes may accelerate the development of quantitative conceptual frameworks applicable to landscapes at all scales.

Animal movements and population dynamics in heterogeneous landscapes

Organisms respond to environmental heterogeneity at different scales and in different ways. These differences are consequences of how the movement characteristics of animals—their movement rates, directionality, turning frequencies, and turning angles—interact with patch and boundary features in landscape mosaics. The interactions of movement patterns with landscape features in turn produce spatial patterns in individual space-use, population dynamics and dispersion, gene flow, and the redistribution of nutrients and other materials. We describe several theoretical approaches for modeling the diffusion, foraging behavior, and population dynamics of animals in heterogeneous landscapes, including: (1) scaling relationships derived from percolation theory and fractal geometry, (2) extensions of traditional patch-based metapopulation models, and (3) individual-based, spatially explicit models governed by local rules. We conclude by emphasizing the need to couple theoretical models with empirical studies and the usefulness of ‘microlandscape’ investigations.

Animal movement in heterogeneous landscapes : an experiment with Eleodes beetles in shortgrass prairie

The role of small-scale vegetation heterogeneity in determining the movement characteristics of darkling beetles was studied in a semi-arid grassland. We tracked the movements of 75 individuals of three Eleodes spp. in small plots representing different vegetation cover types and grazing intensities. Beetle movements were strongly influenced by vegetation structure, with net displacements highest in bare ground and grass cover types and lowest in cactus and shrub. The three beetle species responded differently to grazing intensity

Resource utilization scales and landscape pattern

The spatial patterning of resources constrains the movement of consumers on the landscape. Percolation theory predicts that an organism can move freely if its critical resource or habitat occupies 59.28% of the landscape. Sparse resources require an organism to operate on larger resource utilization scales. Multiple critical resources necessitate larger scales, while substitutable resources ease the scale requirements. Contagious spatial patterns require larger scales to permit movement between resource clusters. The study indicates a strong link between spatial pattern and ecological processes on a landscape.

The complex structure of hunter–gatherer social networks

In nature, many different types of complex system form hierarchical, self-similar or fractal-like structures that have evolved to maximize internal efficiency. In this paper, we ask whether hunter-gatherer societies show similar structural properties. We use fractal network theory to analyse the statistical structure of 1189 social groups in 339 hunter-gatherer societies from a published compilation of ethnographies. We show that population structure is indeed self-similar or fractal-like with the number of individuals or groups belonging to each successively higher level of organization exhibiting a constant ratio close to 4. Further, despite the wide ecological, cultural and historical diversity of hunter-gatherer societies, this remarkable self-similarity holds both within and across cultures and continents. We show that the branching ratio is related to density-dependent reproduction in complex environments and hypothesize that the general pattern of hierarchical organization reflects the self-similar properties of the networks and the underlying cohesive and disruptive forces that govern the flow of material resources, genes and non-genetic information within and between social groups. Our results offer insight into the energetics of human sociality and suggest that human social networks self-organize in response to similar optimization principles found behind the formation of many complex systems in nature.

Frontiers of Ecology

integration and collaboration as we meet the challenge of understanding the great complexity of biological systems. Ecological subdisciplines are rapidly combining and incorporating other biological, physical, mathematical, and sociological disciplines. The burgeoning base of theoretical and empirical work, made possible by new methods, technologies, and funding opportunities, is providing the opportunity to reach robust answers to major ecological questions. In December 1999 the National Science Foundation convened a white paper committee to evaluate what we know and do not know about important ecological processes, what hurdles currently hamper our progress, and what intellectual and conceptual interfaces need to be encouraged. The committee distilled the discussion into four frontiers in research on the ecological structure of the earth’s biological diversity and the ways in which ecological processes continuously shape that structure (i.e., ecological dynamics). This article summarizes the discussions of those frontiers and explains why they are crucial to our understanding of how ecological processes shape patterns and dynamics of global biocomplexity. The frontiers are 1. Dynamics of coalescence in complex communities 2. Evolutionary and historical determinants of ecological processes: The role of ecological memory 3. Emergent properties of complex systems: Biophysical constraints and evolutionary attractors 4. Ecological topology: Defining the spatiotemporal domains of causality for ecological structure and processes Each of the four research frontiers takes a different approach to the overall ecological dynamics of biocomplexity, and all require integration and collaboration among those approaches. These overlapping frontiers themselves are not necessarily new. Within each frontier, however, are emerging questions and approaches that will help us understand how ecological processes are interconnected over multiple spatial and temporal scales, from local community structure to global patterns.

Fractal Patterns of Insect Movement in Microlandscape Mosaics

How individuals move, whether in short-term searching behavior or long-term dispersal influences the probability that individuals will experience physiological stress or encounter appropriate habitat, potential mates, prey, or predators. Because of variety and complexity, it is often difficult to make sense of movements. Because the fractal dimension of a movement pathway is scale independent, however, it may provide a useful measure for comparing dissimilar taxa. The authors use fractal measures to compare the movement pathways of individual beetles occupying semiarid shortgrass steppe in north-central Colorado. 20 refs., 1 fig., 1 tab.