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The several concepts and methods for calculating areas of animal activity are compared. These include minimum home range, circular, mean linear, and median-composite, based on points where individual members of a species were seen. The results with these methods are compared with those based on outlines of home range (or territory) as commonly used for birds. Calculating a home range as circular yields area products close to reality for some sociologic groups of animals but not for most. The minimum-range method yields products smaller than those based on the circular-range method. The median-composite method yields a more compact central area, or core, than do the others but also a progressively wider scattering of isolated points toward the exterior of the composite range. In one case examined (squirrel home ranges), the area which enclosed 75 percent of the points in the core of the median-composite range was about the same as that enclosing 100 percent of the points as commonly used in the minimum home-range method. The shapes of observed home ranges generally change with number of observations and time, but the cores tend to be more stable, and remain more characteristic for different groups, even though also affected by the habitat. Frequency-distribution studies based on the distances of points from the major and minor median axes permit statistical analyses of deviations. Workers in home-range biomass (McNab 1963 and Lewis 1963), home-range area (Dice and Clark 1953 and Sanderson and Sanderson 1964), sociology (Calhoun and Casby 1958:11), parasitology (Milne 1949: 196 and Audy 1961:411), biomass per inhabited area (Odum 1959:152 and Cockrum 1962:154), and other relations of animals to objects in areas of activity are confronted by many methods of delineating home range. All of these delineations are biased according to the means of observation as well as the means of calculating area. Nevertheless, the records bear useful common characteristics which may be enhanced by comparative study. In one study (Stumpf and Mohr 1962) we used mean centers (of Hayne 1949), and axes of individual ranges to construct composite ranges, from which we determined the shape of average areas of activity for various species. Later we found that median centers and axes were more convenient for studying the relation of parasitism to areas of activity (Mohr and Stumpf 1964:74). This median-composite method is applied here to home ranges described in our earlier paper. Results based on livetrapping and retrapping are compared to those based on other methods of observation, direct and indirect, and to other procedures for determining areas of ranges. Thanks to Drs. Deane P. Furman of the Division of Parasitology, Glen C. Sanderson of the Illinois Natural History Survey, Lowell Adams of the George Williams Hooper Foundation, and Ryo Tanaka of the Kochi Women's College, Japan, for reading and discussing various points in our manuscript; to Dr. James N. Layne of Cornell University for lending homerange data on the red squirrel (Tamiasciurus hudsonicus) and to Mrs. Margaret S. Dickinson of Columbia, Missouri, for help with composition in the manuscript.