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Can we trust the chord (and the Hellinger) distance?
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To avoid the problems associated with the Euclidean distance for the calculation of plot-to-plot dissimilarity, a variety of alternative measures have been proposed. Among them, the chord and the Hellinger distances are both obtained by first transforming separately the species abundances in each plot vector and then by calculating the Euclidean distance on the chord-transformed or the Hellinger-transformed data. However, although both measures are routinely used by ecologists as substitutes for the Euclidean distance, they have very different properties. In this paper, using a modified version of Dalton's principle of transfers, I will show that, unlike the Euclidean distance, the chord and the Hellinger distances are not monotonic to changes in absolute abundances. Therefore, they are not interchangeable with the Euclidean distance. The moral of this story is that although dissimilarity may appear an intuitively simple concept, the properties of even the best-known indices are not fully understood. Therefore, a clear understanding of old and new coefficients is needed to evaluate their ability to highlight relevant aspects of compositional dissimilarity among plots
A new look at functional beta diversity
Full text linkThe variability in species composition among a set of sampling sites, or beta diversity, is considered a key signature of the ecological processes that shape the spatial structure of species assemblages. In this paper, we propose to decompose this variability into three additive components: i) the standard similarity in the (relative) abundances of species among sites, ii) the degree of functional dissimilarity between individuals of distinct species among sites, and iii) the degree of functional similarity between individuals of distinct species among sites, or beta redundancy. These three components can be used to portray the functional resemblance among sites on a ternary diagram. With the resulting ternary diagram of ‘functional resemblance’ we can relate various aspects of taxonomic and functional variability among sites to community assembly processes more completely than just looking at individual components. The potential of this method is shown with real data on the functional turnover of Alpine species along a primary succession on glacial deposits in northern Italy
A new parametric measure of functional dissimilarity. Bridging the gap between the Bray-Curtis dissimilarity and the Euclidean distance
No full textCommunity ecologists usually consider the Euclidean distance inappropriate to explore the multivariate structure of species abundance data. This is because the Euclidean distance may lead to the counterintuitive result for which two sample plots with no species in common may be more similar to each other than two plots that share the same species list. To overcome this paradoxical situation, the species abundances need to be normalized in some way. Among the many coefficients used by ecologists for the analysis of assemblage data, the Bray-Curtis dissimilarity is certainly the most commonly used. This measure entails normalization of species-wise differences between two plots by the total species abundance in both plots. By highlighting the relationship between the Bray-Curtis dissimilarity and the Euclidean distance, we propose a parametric dissimilarity measure that is appropriate for handling data on community composition. We also show how the new parametric measure can be generalized to the measurement of functional dissimilarity between two plots. A small dataset on the species functional turnover along a chronosequence on Alpine grasslands is used to illustrate the behavior of the proposed measure
Identifying functionally distinctive and threatened species
No full textFunctional traits determine species' responses to environmental change and/or determine species' effects on ecosystem functions. When species with distinctive functional traits are threatened, there is a risk that ecosystem properties are also threatened. This is because functionally distinctive species may be those that have irreplaceable roles in an ecosystem and/or those that would be able to survive unusual environmental disturbances. To include functional distinctiveness as a criterion in conservation strategies, we need formal quantification of species' degree of distinctiveness while incorporating extinction risk. Based on previously developed quantitative methods, we develop a framework that links different metrics of functional distinctiveness and accounts for all species' extinction probabilities. Our framework is particularly relevant at the local scale, where species extinctions impact ecosystem functioning and where conservation policies are developed. As a case study, we thus applied our framework to the mammals of Indian dry forests known to be threatened with a drastic decrease in functional diversity and identified top-priority species as the threatened, most functionally distinctive species. We notably highlight that although some of the top-priority species we identified are charismatic and targeted by conservation actions, others are not. On the basis of this case study, we note that less charismatic, less known species that may be key for ecosystems could be revealed by applying our framework to a range of ecosystems and taxa
Hill numbers everywhere. Does it make ecological sense?
Full text linkA supposed weakness of most diversity measures is their non-linearity with respect to species addition. Even for a community where all species have equal abundance, each added species usually leads to a smaller increment in the diversity measure than the species added before it. A recent proposal to solve this problem was to transform classical diversity measures to ‘effective numbers of species’ or ‘Hill numbers.’ For any community with diversity D, the effective number of species N is the number of equally abundant species that is needed to get a diversity value equal to D. The conversion of classical diversity measures to Hill numbers makes them linear with respect to species addition such that, given two equally large and completely distinct communities, each with diversity D, if these communities are pooled, the diversity of the pooled communities is 2D. According to this proposal, Hill numbers have been widely adopted in ecological literature as the ultimate solution for diversity analysis regardless of the scientific question at hand. In contrast, we believe that assuming a non-linear response of diversity measures to species addition is more suitable for many ecological questions. Building on this idea, we have introduced a typification of diversity measures based on how quickly diversity increases as species are added
Una misura di entropia per la stima dell'impatto antropico in un'area forestale dell'Italia Centrale
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