Diversity index#Shannon index

The Shannon index (often Shannon-Wiener or Shannon -Weaver index) is a mathematical quantity in biometrics for the description of diversity ( cf. biodiversity) is employed. It describes the variety considered one data taking into account both the number of different categories of data (eg the number of species ) and abundance (number of individuals per species).

Definition

Shannon index H ' of a population consisting of S N individuals in different species, each of which belong to a species,

Pi is the proportion of each species i in the total number N, that is, the relative abundance of each species. ( Instead of the natural logarithm ln is also the base-2 logarithm, log2 is used. )

If the number of species S is specified, the Shannon index reaches its maximum when all species are equally occupied, and then has the value.

Connection with information theory

The Shannon index corresponds to the entropy H of a discrete memoryless source ( discrete random variable) X over a finite alphabet, which is defined as follows: It assigns to each probability of an event to its information content. Then, the entropy of a character is defined as the expected value of the information content, wherein the probability at which the i- th character of the alphabet occurs zi.

The Shannon -Weaver and Shannon-Wiener Debate

Both the name " Shannon -Weaver index " and the name " Shannon -Wiener index " is misleading. Warren Weaver was co-author and popularizer of the bound " A Mathematical Theory of Communication ," Claude Elwood Shannon in his theory that had previously already laid down in two essays published. Norbert Wiener presented the probabilistic calculation methods available, which was based on Shannon's elaboration. His other research in the context of cybernetics built on the Shannon information theory. The development of the index, however, is solely attributable to Shannon.