fuzzySim: applying fuzzy logic to binary similarity indices in ecology

Binary similarity indices are widely used in ecology, for example for detecting associations between species occurrence patterns, comparing regional and temporal species assemblages, and assessing beta diversity patterns, including spatial and temporal species loss and turnover. Such indices have widespread applications in biogeography, global change biology and biodiversity conservation. Similarity indices are commonly calculated upon binary presence/absence (or sometimes modelled suitable/unsuitable) data, which are generally incomplete and more categorical than their underlying natural patterns. Probable false absences are disregarded, amplifying the effects of data deficiencies and the scale dependence of the results. Fuzzy occurrence data, with a degree of uncertainty attributed to localities where presence or absence cannot be safely assigned, could better reflect species distributions, compensating for incomplete knowledge and methodological errors. Similarity indices would therefore also benefit from accommodating such fuzzy data directly. This study proposes fuzzy versions of the binary similarity indices most commonly used in ecology, so that they can be directly applied to continuous (fuzzy) rather than binary occurrence values, thus producing more realistic similarity assessments. Fuzzy occurrence can be obtained with several methods, some of which are also provided. The procedure is robust to data source disparities, gaps or other errors in species occurrence records, even for restricted species for which slight inaccuracies can affect substantial parts of their range. The method is implemented in a free and open-source software package, fuzzySim, which is available for the r statistical software and under implementation for the QGIS geographic information system. It is provided with sample data and an illustrated tutorial suitable for non-experienced users.