Variation in community composition and species turnover are different types of beta diversity, expressing non-directional and directional changes, respectively. While directional changes (e.g. turnover) along geographic gradients can be studied in any direction depending on the hypothesis of interest to researchers, temporal changes can only be meaningfully studied from past to present. Although a wide variety of methods exist for partitioning variation and related community-level phenomena such as similarity, richness difference and nestedness, approaches evaluating species turnover along geographic or temporal gradients, based on an analogous conceptual framework, are rare. We therefore look into the possibilities for examining different aspects of directional changes along a gradient when presence-absence community data are available. Measures of community overlap, as well as species loss and gain from one sampling unit to another along a gradient are combined to define a variety of turnover and nestedness concepts and to derive functions for their quantification. Each concept represents an ecological phenomenon to be indicated (indicandum), whereas measures (indicators) quantify relevant properties of these concepts. The measures use the raw number of species as well as relativized forms in accordance with the well-known Jaccard and Sørensen indices. The main innovation is the development of new measures of directional community change. We demonstrate differences between traditional non-directional and the new directional measures and use several examples to show that actual communities display directional responses to a particular ecological gradient. The new measures therefore reveal an uncovered aspect of community ecology.
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