Generalized entropy indices to measure α- and β-diversities of macrophytes (original) (raw)
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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.
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
Comparison of diversity indices applied to macrophyte incidence-based data
Brazilian Archives of Biology and Technology, 2012
In this work, a recently proposed diversity index based on Patil and Taillie parametric diversity measure (or Tsallis entropy), S q* , was applied to samples (presence-absence data) of macrophytes from the Itaipu Reservoir, Brazil. This new index was the value of the family of indices S q for a specific evenness of a sample. Results demonstrated that the Shannon index and species richness showed expressively high correlation with the S q* ; however, the evenness had low correlation coefficients with the index S q* , indicating that S q* was particularly sensitive to rarity and species richness. On the other hand, the weak correlations of this index with evenness demonstrated that it was less sensitive to species relative abundances.
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
Acta Oecologica, 2004
A desirable property of a diversity index is the so-called sum property. For a diversity index that possesses the sum property, such as species richness N, Shannon's entropy H or Simpson's index 1/D, the community diversity is decomposable into species-level patterns and the sum of single species diversities gives the pooled diversity of the species collection. In this paper, parametric diversity of type a is used to quantify how fertilizer applied to soil affects the relative contribution of species endemic or preferential to serpentine soils within a garigue plant community in Tuscany (Italy). Soil fertilizer significantly improved the biomass production of the original species pool without any significant colonization by alien species. However, the major biomass increments were experienced by species that are not exclusive to serpentine soils. In this view, the reduced abundance of species endemic or preferential to serpentine soils can be interpreted as a loss of 'ecological quality' of the analyzed community.
MethodsX
The idea of entropy, which has its roots in information theory and proposes that one may measure the degree of uncertainty associated with the prediction of bits and pieces of information, has been widely used by biologists and ecologists for decades to define biological diversity. For ecologists, the core of the issue is whether or not two species' distribution taken from the same habitat are the same or distinct. The Shannon index and Simpson diversity are well-known in ecology; however, the non-linearity of these indices may cause a misinterpretation of the underlying diversity, as shown by Lou Jost (2006) and others. Applying the proposed template, one can: • calculate several biodiversity indices, • compare two different forest stands (or formations, or plots), or two different profiles in two different times, for the same forest stand (or formation, or plot), in terms of biodiversity.
Towards a sounder interpretation of entropy-based indicators in ecological network analysis
Ecological Indicators, 2017
Various indicators rooted in the concepts of information and entropy have been proposed to be used for ecological network analysis. They are theoretically well grounded and widely used in the literature, but have always been difficult to interpret due to an apparent lack of strict relations with node and link weight. We generated several sets of 10,000 networks in order to explore such relations and work towards a sounder interpretation. The indices we explored are based on network composition (i.e., type and importance of network compartments), or network flows (i.e., type and importance of flows among compartments), including Structural Information (SI), Total System Throughput (TST), Average Mutual Information (AMI), Flow Diversity (H), and Ascendency (ASC). A correlation analysis revealed a lack of strict relationships among the responses of the investigated indicators within the simulated space of variability of the networks. However, fairly coherent patterns of response were revealed when networks were sorted by following a "bottom-up" criterion, i.e. by increasing the dominance of the large-sized top predator in the network. This ranking is reminiscent of ecosystem succession, along which the prominence of higher trophic level organisms progressively increases. In particular, the results show that a simple increase in organisms having large size and low consumption rates is potentially able to simultaneously lead to an increase of different types of information (as SI, H and AMI), thus also emphasizing the importance of bionomic traits related to body size in affecting information-related properties in a trophically connected community. The observed trends suffer from a certain dispersion of data, which was diminished by imposing specific and ecologically meaningful constraints, such as mass balancing and restriction to certain range of the ratio A/C, an index related to the viability of ecological networks. These results suggest that the identification of a set of effective constraints may help to identify improved conditions for applicability of the investigated flow-based indicators, and also provide indication on how to normalise them with respect to meaningful network properties or reference states. Thus, in order to increase confidence in the derived network metrics describing a particular ecosystem state, and thus increase their applicability, it is advisable to construct replicate networks by taking the variability of input data into account, and by applying uncertainty and sensitivity analyses.
Computing β-diversity with Rao's quadratic entropy: a change of perspective
Diversity and Distributions, 2007
Ecologists have traditionally viewed β-diversity as the ratio between γ-diversity and average α-diversity. More recently, an alternative way of partitioning diversity has been proposed for which β-diversity is obtained as the difference between γ-diversity and average α-diversity. Although this additive model of diversity decomposition is generally considered superior to its multiplicative counterpart, in both models βdiversity is a formally derived quantity without any self-contained ecological meaning; it simply quantifies the diversity excess of γ-diversity with respect to average α-diversity. Taking this excess as an index of β-diversity is a questionable operation. In this paper, we show that a particular family of α-diversity measures, the most celebrated of which is Rao's quadratic entropy, can be adequately used for summarizing βdiversity. Our proposal naturally leads to a new additive model of diversity for which, given two or more sets of plots, overall plot-to-plot species variability can be additively partitioned into two non-negative components: average variability in species composition within each set of plots and the species variability between the set of plots. For conservation purposes, the suggested change of perspective in the summarization of β-diversity allows for a flexible analysis of spatial heterogeneity in ecological diversity so that different hierarchical levels of biotic relevance (i.e. from the genetic to the landscape level) can be expressed in a significant and consistent way.