Anthropogenic fragmentation of landscapes is known as a major reason for the loss of species in industrialized countries. Landscape fragmentation caused by roads, railway lines, extension of settlement areas, etc., further enhances the dispersion of pollutants and acoustic emissions and affects local climatic conditions, water balance, scenery, and land use. In this study, three new measures of fragmentation are introduced: degree of landscape division (D), splitting index (S), and effective mesh size (m). They characterize the anthropogenic penetration of landscapes from a geometric point of view and are calculated from the distribution function of the remaining patch sizes. First, D, S, and m are defined, their mathematical properties are discussed, and their reactions to the six fragmentation phases of perforation, incision, dissection, dissipation, shrinkage, and attrition are analysed. Then they are compared with five other known fragmentation indices with respect to nine suitability criteria such as intuitive interpretation, low sensivity to very small patches, monotonous reaction to different fragmentation phases, and detection of structural differences. Their ability to distinguish spatial patterns is illustrated by means of two series of model patterns. In particular, the effective mesh size (m), representing an intensive and area-proportionately additive measure, proves to be well suited for comparing the fragmentation of regions with differing total size.
