Biological diversity would apparently seem the most intuitive and easily studied of all the ecological concepts. However, in practice biodiversity has suffered from great number of definitions that vary with the specific needs of the different researchers, thus making it extremely confusing as an ecological concept. In this paper, I shortly review the concept of biodiversity showing that there exists a substantial ambiguity among ecologists as far as biodiversity conceptualization and evaluation is concerned. I conclude that, due to this major (...) disagreement on its very nature, biodiversity may be defined simply as a set of multivariate summary statistics for quantifying different characteristics of community structure. (shrink)

The degree to which abundances are divided equitably among community species or evenness is a basic property of any biological community. Several evenness indices have been proposed to summarize community structure. However, despite their potential applicability in ecological research, none seems to be generally preferred. In this paper we show that, unlike other evenness indices without any clear information-theoretical meaning, Hill's parametric diversity measure E ,0 has an immediate relation to Rényi's generalized information. Therefore, E ,0 might be adequate for (...) summarizing community structure within the context of a general theoretical framework of diversity analysis based on information theory. (shrink)

Traditional diversity indices are computed from the abundances of species present and are insensitive to taxonomic differences between species. However, a community in which most species belong to the same genus is intuitively less diverse than another community with a similar number of species distributed more evenly between genera. In this paper, we propose an information-theoretical measure of taxonomic diversity that reflects both the abundances and taxonomic distinctness of the species. Unlike previous measures of taxonomic diversity, such as Rao's quadratic (...) entropy, in this new measure the analyzed taxonomic properties are associated with the single species instead of species pairs. (shrink)

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon''s entropy H or Simpson''s index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot (...) diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy''s generalized entropy of type . In this way, a parametric measure of -diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker''s -diversity for data on species relative abundances. (shrink)

The degree to which abundances are evenly divided among the species of a given community is a basic property of any biological community. Several evenness indices have thus far been proposed in ecological literature. However, despite their vast potential applicability in ecological research, none seems to be generally preferred. In this paper, I first summarize the basic requirements that evenness measures should meet to adequately behave in ecological studies. Then, I discuss the major drawbacks of these requirements and propose an (...) alternative family of measures that are based on the notion of specificity used in fuzzy set theory for measuring the uncertainty associated with a fuzzy set. (shrink)

Community diversity has been studied extensively in relation to its effects on ecosystem functioning. Testing the consequences of diversity on ecosystem processes will require measures to be available based on a rigorous conceptualization of their very meaning. In the last decades, literally dozens of measures of diversity have been proposed. However, rather than using unrelated metrics, we need to identify their separate components so that possible links between them and ecosystem functioning can be examined using an agreed-upon language. In this (...) paper, first, a short overview on new and old measures of community diversity is presented. Next, I propose a general framework in which most of the existing measures of diversity are sorted into four interrelated semantic classes: richness, abundance-weighted diversity, evenness and divergence. In this view, this paper constitutes an attempt to organize the very large number of existing diversity measures avoiding ambiguities in the meaning of the different facets of community diversity. (shrink)

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total information content as (...) special cases of this more general function. (shrink)

This reply paper includes two brief remarks in rejoinder to the commentary papers of Myers and Patil, Podani, and Sarkar. The first observation concerns the fundamental nature of ecological diversity measures, while the second one specifically addresses some interesting mathematical connections between α- and β-diversity.