Objective, empirical measures of overlap between samples of items distributed proportionally into various qualitative categories are presented and reviewed. These indices of overlap, derived from either probability or information theory, should prove useful to the ecologist in comparative studies of diet, habitat preference, seasonal patterns of abundance, faunal lists, or similar data.

Measurement of "overlap" in comparative ecological studies

Spatial distribution is one of the most characteristic ecological properties of species. Unlike rates of growth and reproduction, which often vary more between generations within a species than they do between species, spatial distribution yields characteristics parameters that segregate species. These parameters are the population expression of the individual behavior defined by the ethologist and observed by the naturalist. They determine the spatial distribution of temporal dynamic change. Starlings flock, herrings school, and deer herd together, while eagles, sharks, and tigers hunt alone. This behavior determines their spatial patterns. The spatial patterns of insects are no less specific. Interest in this characteristic of species is both applied and fundamental. Most of the sound data available for analysis were collected by applied entomologists and hydrobiologists. Large mammals are rarely available in the numbers and species necessary for comparative analysis, although there are good data for birds. Insects are especially suitable for investigation because of the large numbers of individuals and species. Expermentation is difficult because, if the population is constrained, the natural distribution is destroyed. Hence, fundamental interest tends to be theoretical, rather than practical, or directed to behavioral response rather than to spatial pattern. Applied interest centers on formalizing systems of sampling.

Assessing and Interpreting the Spatial Distributions of Insect Populations

Spatial pattern analysis based on Ripley's K-func- tion is a second-order analysis of point patterns in a two- dimensional space. The method is increasingly used in studies of spatial distribution patterns of plant communities, but the statistical methods involved are sometimes poorly understood or have been modified without evaluating the effects on re- sults. The procedures of field data acquisition, statistical analy- sis, and the test for the null hypothesis of complete spatial randomness are described and the presentation of results is discussed. Different methods of edge correction were tested on a computer-generated random pattern and a mapped distri- bution of a Mediterranean shrubland. The inclusion of buffer zones around mapped plots describes the spatial pattern most accurately, but may not warrant the additional labour in- volved. Three variations of the weighted edge correction yielded comparable results for the distribution patterns tested. The toroidal edge correction may give biased results for non- random patterns. Recommendations for standardisation of the statistical procedures and data presentation are given.

Spatial pattern analysis in ecology based on Ripley's K-function: introduction and methods of edge correction.

Lacunarity analysis is a multi-scaled method of determining the texture associated with patterns of spatial dispersion (i.e., habitat types or species locations) for one-, two-, and three-dimensional data. Lacunarity provides a parsimonious analysis of the overall fraction of a map or transect covered by the attribute of interest, the degree of contagion, the presence of self-similarity, the presence and scale of randomness, and the existence of hierarchical structure. For self-similar patterns, it can be used to determine the fractal dimension. The method is easily implemented on the computer and provides readily interpretable graphic results. Differences in pattern can be detected even among very sparsely occupied maps.

Lacunarity indices as measures of landscape texture

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Papers

Measuring of dispersion of individuals and analysis of the distributional patterns.