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The Shannon index is the most commonly used way to quantitatively determine species diversity, H, as modeled by the following equation: = = The Shannon index factors in both species evenness and species richness, as represented by the variables p i and s, respectively. The lowest possible value of H is zero, and the higher a community’s H ...
The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", [2] [3] and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem ...
A diversity index is a method of measuring how many different types (e.g. species) there are in a dataset (e.g. a community).Diversity indices are statistical representations of different aspects of biodiversity (e.g. richness, evenness, and dominance), which are useful simplifications for comparing different communities or sites.
There are many ways to measure biodiversity within a given ecosystem. However, the two most popular are Shannon-Weaver diversity index, [4] commonly referred to as Shannon diversity index, and the other is Simpsons diversity index. [5] Although many scientists prefer to use Shannon's diversity index simply because it takes into account species ...
The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.
A rank abundance curve. A rank abundance curve or Whittaker plot is a chart used by ecologists to display relative species abundance, a component of biodiversity.It can also be used to visualize species richness and species evenness.
The first approach is to calculate a weighted generalized mean of the within-subunit species proportional abundances, and then take the inverse of this mean. The second approach is to calculate the species diversity for each subunit separately, and then take a weighted generalized mean of these. [4] [13] If the first approach is used, the ...
The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information , where it can be used as a measure of entanglement . In the Heisenberg XY spin chain model, the Rényi entropy as a function of α can be calculated explicitly because it is an automorphic function with ...