fSimpson: Calculate the Simpson's diversity index

In OnomasticDiversity: Onomastic Diversity Measures

Calculate the Simpson's diversity index

Description

This function obtains the Simpson's diversity index and the inverse introduced by Edward Hugh Simpson. It was the first index used in ecology. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

fSimpson(x, k, n, location)

Arguments

x	dataframe of the data values for each species.
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 Simpson's diversity index is defined by D_{S_i} = \sum \limits_{k\in S_i} p_{ki}^2, 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. The Simpson index tends to be smaller when the community is more diverse.

In onomastic context, p_{ki} denotes the relative frequency of surname k in region (\approx community diversity context) i, i.e., Simpson's diversity index is equivalent to the concept of isonymy..

Value

A dataframe containing the following components:

location	represents the grouping element, for example the communities / regions.
simpson	the value of the Simpson's diversity index.
divSimpson	the value of the inverse Simpson's diversity index.

Author(s)

Maria Jose Ginzo Villamayor

References

Simpson (1949) Measurement of diversity. Nature, 163.

See Also

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

Examples

data(surnamesgal14)
result = fSimpson (x= surnamesgal14, k="number",
n="population", location  = "muni" )
result

data(namesmengal16)
result = fSimpson (x= namesmengal16, k="number",
n="population", location  = "muni" )
result

data(nameswomengal16)
result = fSimpson (x= nameswomengal16, k="number",
n="population", location  = "muni" )
result

OnomasticDiversity documentation built on May 29, 2024, 1:32 a.m.