Abstract
The use of the evenness (E(λ)) of the eigenvalues of similarity matrices corresponding to different hierarchical levels of ecosystem classifications, is suggested to test correlation (or predictivity) between biological communities and environmental factors as one alternative of analysis of variance (parametric or non-parametric). The advantage over traditional methods is the fact that similarity matrices can be obtained from any kind of data (mixed and missing data) by indices such as those of Goodall and Gower. The significance of E(λ) is calculated by permutation techniques. One example of application of E(λ) is given by a data set describing plant community types (beech forests of the Italian peninsula).
Highlights
The separation between the classes of a classification in terms of the features used for the classification itself or in terms of features not used for the classification, can be evaluated by parametric methods based on simple or multivariate analysis of variance (ANOVA or MANOVA) [1,2] and by nonparametric ones [3]
In 1988, Biondini et al [5] proposed to test the separation between classes by an index based on Euclidean metric that uses the average within class sum of squares (δ) by introducing the methods known as multiple response permutation procedure (MRPP) and its randomized block design analogue (MRBP)
In the present paper we suggest using E(λ) to test if the k classes of a given classification are significantly separated when they are described by a space defined by environmental factors (set B) of external features, i.e., features that have not been used to obtain T
Summary
The separation between the classes of a classification in terms of the features used for the classification itself or in terms of features not used for the classification, can be evaluated by parametric methods based on simple or multivariate analysis of variance (ANOVA or MANOVA) [1,2] and by nonparametric ones [3]. Clark and Anderson proposed, respectively the methods known as Analysis Of SIMilarity (ANOSIM) [6] and PERmutational Multivariate ANalysis Of Variance (PERMANOVA) [7] in which the ratio between and within dissimilarity averages or “between (or among)/within (residual) sum of squares” can be based on any kind of similarity functions as suggested in [4]. In all these methods the significance of the class separation is tested by permutation techniques [8,9]. The advantage of ANOSIM and PERMANOVA with respect the method of Biondini et al [5] relies on the fact that both can be applied to any kind of data (mixed and missing data) if similarity is measured by suitable functions, e.g., the one of Gower or Goodall [1,2]
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