fShannon {OnomasticDiversity}

Calculate the Shannon-Weaver diversity index

Description

This function obtains the Shannon-Weaver diversity index introduced by Claude Elwood Shannon. This diversity measure came from information theory and measures the order (or disorder) observed within a particular system. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

 fShannon(x, k, n, location)

Arguments

x

dataframe of the data values for each species not null (because if you have a sample, there might be species that are not represented)..

k

name of a variable which represents absolute frequency for each species.

n

name of a variable which represents total number of individuals.

location

represents the grouping element.

Details

For a community i, the index of Shannon-Weaver is defined by the expression H^{\prime} = -\sum\limits_{k\in S_i} (p_{ki} \log_2 p_{ki}), where p_{ki} represents the relative frequency of species k, because p_{ki} = \frac{N_{ki}}{N_i}, (where N_{ki} denotes the number of individuals of species k and N_i total number of individuals in all S_i species at the community, species richness. This index is related to the weighted geometric mean of the proportional abundances of the types.

In onomastic context, p_{ki} denotes the relative frequency of surname k in region (\approx community diversity context) i and S_i are all surnames in region i.

Value

A dataframe containing the following components:

location

represents the grouping element, for example the communities / regions.

shannon

the value of the Shannon-Weaver diversity index.

Author(s)

Maria Jose Ginzo Villamayor

References

Shannon C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.

Shannon C.E., Weaver W. (1949). The Mathematical Theory of Communication. Urbana: University of Illinois Press. USA, 96. pp. 117.

See Also

fMargalef, fMenhinick, fPielou, fSheldon, fSimpson, fSimpsonInf, fGeneralisedMean, fGeometricMean, fHeip.

Examples

data(surnamesgal14)
result = fShannon (x= surnamesgal14[surnamesgal14$number != 0,],
k="number", n="population", location  = "muni" )
result

data(namesmengal16)
result = fShannon (x= namesmengal16[namesmengal16$number != 0,],
k="number", n="population", location  = "muni" )
result

data(nameswomengal16)
result = fShannon (x= nameswomengal16[nameswomengal16$number != 0,],
k="number", n="population", location  = "muni" )
result