A fuzzy coding approach for the analysis of long‐term ecological data

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Abstract
SUMMARY: We present an unconventional procedure (fuzzy coding) to structure biological and environmental information, which uses positive scores to describe the affinity of a species for different modalities (i.e. categories) of a given variable. Fuzzy coding is essential for the synthesis of long‐term ecological data because it enables analysis of diverse kinds of biological information derived from a variety of sources (e.g. samples, literature). A fuzzy coded table can be processed by correspondence analysis. An example using aquatic beetles illustrates the properties of such a fuzzy correspondence analysis. Fuzzy coded tables were used in all articles of this issue to examine relationships between spatial‐temporal habitat variability and species traits, which were obtained from a long‐term study of the Upper Rhône River, France. Fuzzy correspondence analysis can be programmed with the equations given in this paper or can be performed using ADE (Environmental Data Analysis) software that has been adapted to analyse such long‐term ecological data. On Macintosh AppleTM computers, ADE performs simple linear ordination, more recently developed methods (e.g. principal component analysis with respect to instrumental variables, canonical correspondence analysis, co‐inertia analysis, local and spatial analyses), and provides a graphical display of results of these and other types of analysis (e.g. biplot, mapping, modelling curves). ADE consists of a program library that exploits the potential of the HyperCardTM interface. ADE in an open system, which offers the user a variety of facilities to create a specific sequence of programs. The mathematical background of ADE is supported by the algebraic model known as ‘duality diagram’.