Within-forest stand (or formation, or plot) and between-forest stand (or formation, or plot) biodiversity indices (original) (raw)
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A unified index to measure ecological diversity and species rarity. Ecography 31
2008
Several indices have been created to measure diversity, and the most frequently used are the Shannon-Wiener (H) and Simpson (D) indices along with the number of species (S) and evenness (E). Controversies about which index should be used are common in literature. However, a generalized entropy (Tsallis entropy) has the potential to solve part of these problems. Here we explore a family of diversity indices (S q ; where q is the Tsallis index) and evenness (E q ), based on Tsallis entropy that incorporates the most used indices. It approaches S when q 00, H when q 01 and gives D when q 0 2. In general, varying the value of the Tsallis index (q), S q varies from emphasis on species richness (qB1) to emphasis on dominance (q 1). Similarly, E q also works as a tool to investigate diversity. In particular, for a given community, its minimum value represents the maximum deviation from homogeneity (E q
A unified index to measure ecological diversity and species rarity
Ecography, 2008
Several indices have been created to measure diversity, and the most frequently used are the Shannon-Wiener (H) and Simpson (D) indices along with the number of species (S) and evenness (E). Controversies about which index should be used are common in literature. However, a generalized entropy (Tsallis entropy) has the potential to solve part of these problems. Here we explore a family of diversity indices (S q ; where q is the Tsallis index) and evenness (E q ), based on Tsallis entropy that incorporates the most used indices. It approaches S when q 00, H when q 01 and gives D when q 0 2. In general, varying the value of the Tsallis index (q), S q varies from emphasis on species richness (qB1) to emphasis on dominance (q 1). Similarly, E q also works as a tool to investigate diversity. In particular, for a given community, its minimum value represents the maximum deviation from homogeneity (E q
Revisiting the Relation Between Species Diversity and Information Theory
Acta Biotheoretica, 2008
The Shannon information function (H) has been extensively used in ecology as a statistic of species diversity. Yet, the use of Shannon diversity index has also been criticized, mainly because of its ambiguous ecological interpretation and because of its relatively great sensitivity to the relative abundances of species in the community. In my opinion, the major shortcoming of the traditional perspective (on the possible relation of species diversity with information theory) is that species need for an external receiver (the scientist or ecologist) to exist and transmit information. Because organisms are self-catalized replicating structures that can transmit genotypic information to offspring, it should be evident that any single species has two possible states or alternatives: to be or not to be. In other words, species have no need for an external receiver since they are their own receivers. Therefore, the amount of biological information (at the species scale) in a community with one only species would be $ { \log }_{2} 2^{1} = 1 $ species, and not $ { \log }_{2} 1 = 0 $ bits as in the traditional perspective. Moreover, species diversity appears to be a monotonic increasing function of $ { \log }_{2} 2^{{\text{S}}} $ (or S) when all species are equally probable (S being species richness), and not a function of $ { \log }_{2} {\text{ S}} $ as in the traditional perspective. To avoid the noted shortcoming, we could use 2H (instead of H) for calculating species diversity and species evenness (= 2H/S). However, owing to the relatively great sensitivity of H to the relative abundances of species in the community, the value of species dominance (= 1 − 2H/S) is unreasonably high when differences between dominant and subordinate species are considerable, thereby lowering the value of species evenness and diversity. This unsatisfactory behaviour is even more evident for Simpson index and related algorithms. I propose the use of other statistics for a better analysis of community structure, their relationship being: species evenness + species dominance = 1; species diversity × species uniformity = 1; and species diversity = species richness × species evenness.
Conceptual and statistical problems associated with the use of diversity indices in ecology
Revista de Biología Tropical, 2008
Diversity indices, particularly the Shannon-Wiener index, have extensively been used in analyzing patterns of diversity at different geographic and ecological scales. These indices have serious conceptual and statistical problems which make comparisons of species richness or species abundances across communities nearly impossible. There is often no a single statistical method that retains all information needed to answer even a simple question. However, multivariate analyses could be used instead of diversity indices, such as cluster analyses or multiple regressions. More complex multivariate analyses, such as Canonical Correspondence Analysis, provide very valuable information on environmental variables associated to the presence and abundance of the species in a community. in addition, particular hypotheses associated to changes in species richness across localities, or change in abundance of one, or a group of species can be tested using univariate, bivariate, and/or rarefaction statistical tests. The rarefaction method has proved to be robust to standardize all samples to a common size. Even the simplest method as reporting the number of species per taxonomic category possibly provides more information than a diversity index value. Rev. Biol. Trop. 57 : 451-460. Epub 2009 September 30.
Environmental and Ecological Statistics, 2005
Many methods that study the diversity within hierarchically structured populations have been developed in genetics. Among them, the analysis of molecular variance (AMOVA) (Excoffier et al., 1992) has the advantage of including evolutionary distances between individuals. AMOVA is a special case of a far more general statistical scheme produced by Rao (1982a; 1986) and called the apportionment of quadratic entropy (APQE). It links diversity and dissimilarity and allows the decomposition of diversity according to a given hierarchy. We apply this framework to ecological data showing that APQE may be very useful for studying diversity at various spatial scales. Moreover, the quadratic entropy has a critical advantage over usual diversity indices because it takes into account differences between species. Finally, the differences that can be incorporated in APQE may be either taxonomic or functional (biological traits), which may be of critical interest for ecologists.
Biodiversity and Conservation, 2000
Ideally, the estimates of biological diversity of a community of species in a habitat should refer to the biological variation among the species and not merely to their numbers and frequencies. However, the current estimates of biodiversity incorporate only the latter two components but not the biological differences among the species. Ganeshaiah et al. [(1997) Current Science 73: 128-133] have proposed an estimate called the Avalanche Index (AI) that can incorporate the biological heterogeneity among the species in a habitat. This estimate, besides being methodologically simple, can incorporate any quantifiable differences among the species, information on species richness and their frequencies in the habitat. In this paper we have estimated AI for tree vegetation in 14 forest types across different ecosystems of the world and have compared these estimates with other indices being currently used. Through this we have attempted to analyse the relative utility of AI in discriminating the habitats based on their biological heterogeneity by capturing their intra-community biological variation. We discuss the merits and demerits of the AI as a comprehensive estimate of biological diversity.
Generalized entropy indices to measure α- and β-diversities of macrophytes
Brazilian Journal of Physics, 2009
A family of entropy indices constructed in the framework of Tsallis entropy formalism is used to investigate ecological diversity. It represents a new perspective in ecology because a simple equation can incorporate all aspects of α−diversity, from richness to dominance and can be also related to a measure of species rarity. In addition, a generalized Kullback-Leibler distance, constructed in the framework of a nonextensive formalism, is recalled and used as a measure of β−diversity between two systems. These tools are applied to data relative to the macrophytes collected from two not far apart arms of Itaipu Reservoir, in Paraná River basin.
A conceptual guide to measuring species diversity
Three metrics of species diversity -species richness, the Shannon index and the Simpson index -are still widely used in ecology, despite decades of valid critiques leveled against them. Developing a robust diversity metric has been challenging because, unlike many variables ecologists measure, the diversity of a community often cannot be estimated in an unbiased way based on a random sample from that community. Over the past decade, ecologists have begun to incorporate two important tools for estimating diversity: coverage and Hill diversity. Coverage is a method for equalizing samples that is, on theoretical grounds, preferable to other commonly used methods such as equal-effort sampling, or rarefying datasets to equal sample size. Hill diversity comprises a spectrum of diversity metrics and is based on three key insights. First, species richness and variants of the Shannon and Simpson indices are all special cases of one general equation. Second, richness, Shannon and Simpson can be expressed on the same scale and in units of species. Third, there is no way to eliminate the effect of relative abundance from estimates of any of these diversity metrics, including species richness. Rather, a researcher must choose the relative sensitivity of the metric towards rare and common species, a concept which we describe as 'leverage.' In this paper we explain coverage and Hill diversity, provide guidelines for how to use them together to measure species diversity, and demonstrate their use with examples from our own data. We show why researchers will obtain more robust results when they estimate the Hill diversity of equal-coverage samples, rather than using other methods such as equaleffort sampling or traditional sample rarefaction.