![]() ![]() Let ℓ 1, ℓ 2, …, ℓ S be the species in a community, and let p s be the proportion of individuals belonging to species ℓ s. Finally, we compare it to HCDT entropy and Hurlbert’s index on a real-world example of under-sampled tropical forest to illustrate its decisive advantage when applied to this type of data. After this, we derive a simple formula for the corresponding effective number of species and discuss its estimation. We then show how to estimate ζ r with no bias and how to construct confidence intervals, which can be used to compare the diversities of different communities. We show that ζ r is a valid measure of diversity, satisfying the axioms established in the literature. It has a simple interpretation, specifically, in a species accumulation curve, ζ r is the probability that the individual sampled at rank r + 1 belongs to a new species. The generalized Simpson’s entropy ζ r is parameterized: increasing its parameter r gives more relative importance to rare species. We introduce generalized Simpson’s entropy as a measure of diversity for its particular performance when it is used to estimate the diversity of small samples from hyper-diverse communities. ![]() Hurlbert’s index has a simple and practical interpretation and can be estimated with no bias, but only up to when its parameter is strictly less than the sample size. Its properties are very similar and, hence, it will not be treated here. Rényi’s entropy is related to HCDT entropy by a straightforward transformation: the natural logarithm of the deformed exponential. HCDT entropy has many desirable properties but, despite recent progress, it cannot be accurately estimated when the communities are insufficiently sampled. If the profiles do not cross, one community can be declared to be more diverse than the other. The profiles of two communities can be compared to provide a partial order of their diversity. These indices can be used to estimate the diversity of a community and then to plot their values against the parameter, which controls the weight of rare species, to obtain a diversity profile. Among the most popular indices of this type are HCDT entropy (which includes richness, Simpson’s index, and Shannon’s entropy as special cases), Rényi’s entropy, and the less-used Hurlbert’s index. Further, they can be expressed as an effective number of species, which allows for an easy interpretation of their values. Since one index is generally insufficient to fully capture the diversity of a community, modern measures of diversity are parameterizable, allowing the user to give more or less relative importance to rare versus frequent species. Classical measures of this type include richness (the number of species), Shannon’s entropy, and Simpson’s index. butterflies) or, more loosely, to a meaningful group (e.g. a subset of species in the community under study that belong to the same taxon (e.g. Such measures only make sense when applied to a single taxocene, i.e. the diversity of the distribution of species, ignoring their features. We focus on species-neutral diversity, i.e. Indeed, measuring diversity requires both a robust theoretical framework and empirical techniques to effectively estimate it. Many indices of biodiversity have been proposed based on different definitions of diversity and different visions of the biological aspects to address. ![]()
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