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

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’.

Seasonal variability in the Macroinvertebrate Community Index: Are seasonal correction factors required?

“…We then calculated the relative abundance of traits at each site by multiplying the proportion of each category per trait by the relative abundances of species at the site. The resulting trait-by-site array contained the relative abundance of each trait category at each site (for further details see Chevenet et al 1994). These data were compared with SQMCI values.…”

Influence of vegetation cover on the biological traits of pond invertebrate communities

“…Ecological (e.g., functional feeding group, aquatic stage) and physiological (e.g., respiration) traits were obtained from Tachet et al (2000). Species traits information was then structured using a fuzzy-coding technique (Chevenet et al 1994): scores ranged from '0', indicating 'no affinity' to '5', indicating 'high affinity' for a given species traits category. Note that some taxa were not concerned by all biological traits (e.g., crustaceans are not concerned by "emergence period").…”

“…In this case, a '0' score was given to the corresponding trait categories. Here, the discriminative weight of the taxa for this particular variable is zero (see also Chevenet et al 1994, Usseglio-Polatera et al 2000. This matrix was studied by a 'Fuzzy Correspondence Analysis' (FCA) (Chevenet et al 1994).…”

“…Invertebrate biomasses were first recorded in the various mesohabitat types of each pond over a one-year period (biomass matrix), then species traits were described using a fuzzy-coding method (species traits matrix). A simultaneous analysis of the two matrices performed through a co-inertia analysis was used to investigate changes in species traits combinations (Chevenet et al 1994) according to the type and extent of the pond vegetation.…”

Effects of vineyard coverage and extent on benthic macroinvertebrates in streams of Northern California

“…The traits for all taxa present in each sample and the proportional representation of each trait category were determined based on descriptions used by Beˆche et al (2006). Because the fuzzy-coding approach was used (Chevenet et al, 1994), each taxon could be described using a fractional composition of multiple trait categories. For example, a taxon could be described as 0.4 semivoltine and 0.6 bi-voltine, with the fractions summing to 1.0, which would indicate that this taxon has partial semi-voltine and partial bi-voltine characteristics, and be expressed in terms of relative abundance.…”