OnomasticDiversity (version 0.1)

fGeometricMean: Calculate the Geometric Mean

Description

This function obtains the geometric mean introduced by Stephen Terrence Buckland and coauthors. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.

Usage

fGeometricMean(x, pki, pki0, s, location)

Value

A dataframe containing the following components:

location

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

geometricMean

the value of geometric mean.

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).

pki

name of a variable which represents the relative frequency for each species.

pki0

name of a variable which represents the relative frequency for each species at initial time point.

s

vector which represents total number of species.

location

represents the grouping element.

Author

Maria Jose Ginzo Villamayor

Details

For a community \(i\), the geometric mean of relative abundances is defined by \(G_t = \exp \left(\frac{1}{S_i} \sum_{k\in S_i} \log \frac{N_{ki}^t}{N_{ki}^{t_0}}\right)\), where \(N_{ki}^t\) denotes the number of individuals of species \(k\) at times $t$, \(t_0\) is the baseline year and \(S_i\) are all species at the community, species richness.

In onomastic context, \(N_{ki}^t\) denotes the absolute frequency of surname \(k\) in region (\(\approx\) community diversity context) \(i\) at times \(t\).

References

Buckland, S.T., Studeny, A.C., Magurran, A.E., Illian, J.B., & Newson, S.E. (2011). The geometric mean of relative abundance indices: a biodiversity measure with a difference. Ecosphere, 2(9), art.100.

Studeny, A.C. (2012). Quantifying Biodiversity Trends in Time and Space. PhD thesis, University of St Andrews.

van Strien, A.J., Soldaat, L.L., & Gregory, R.D. (2012). Desirable mathematical properties of indicators for biodiversity change. Ecological Indicators, 14, 202--208.

See Also

fMargalef, fMenhinick, fPielou, fShannon, fSheldon, fSimpson, fSimpsonInf, fGeneralisedMean, fHeip

Examples

library(sqldf)
data(surnamesgal14)
loc <- length(unique(surnamesgal14$muni))

apes2=sqldf('select  muni, count(surname) as ni,
sum(number) as population from surnamesgal14
group by muni;')
surnamesgal14$pki0 <- surnamesgal14$pki

result = fGeometricMean (x= surnamesgal14[surnamesgal14$number != 0,],
pki="pki", pki0="pki0" , location  = "muni",
s = apes2$ni[1:loc])
result

data(namesmengal16)
loc <- length(unique(namesmengal16$muni))

names2=sqldf('select  muni, count(name) as ni,
sum(number) as population from namesmengal16
group by muni;')

namesmengal16$pki <- (namesmengal16$number /
namesmengal16$population)
namesmengal16$pki0 <- namesmengal16$pki

result = fGeometricMean (x= namesmengal16[namesmengal16$number != 0,],
pki="pki", pki0="pki0" , location  = "muni",
s = names2$ni[1:loc])
result

data(nameswomengal16)
loc <- length(unique(nameswomengal16$muni))

names2=sqldf('select  muni, count(name) as ni,
sum(number) as population from nameswomengal16
group by muni;')

nameswomengal16$pki <- (nameswomengal16$number /
nameswomengal16$population)
nameswomengal16$pki0 <- nameswomengal16$pki

result = fGeometricMean (x= nameswomengal16[nameswomengal16$number != 0,], 
pki = "pki", pki0 = "pki0", location  = "muni", 
s = names2$ni[1:loc])
result