Onomastic Diversity Measures

Description

Different measures which can be used to quantify similarities between regions. These measures are isonymy, isonymy between, Lasker distance, coefficients of Hedrick and Nei. In addition, it calculates biodiversity indices such as Margalef, Menhinick, Simpson, Shannon, Shannon-Wiener, Sheldon, Heip, Hill Numbers, Geometric Mean and Cressie and Read statistics.

Details

The DESCRIPTION file:

Index of help topics:

OnomasticDiversity-package
                        Onomastic Diversity Measures
fCressieRead            Cressie and Read
fGeneralisedMean        Calculate the Generalised Mean
fGeometricMean          Calculate the Geometric Mean
fHeip                   Calculate the Heip's diversity index
fHill                   Calculate the Hill's diversity numbers
fIsonymy                Calculate the Isonymy within a region
fIsonymyAll             Calculate the Isonymy, Isonymy between regions,
                        Lasker distances, Euclidean distance and Nei's
                        distances
fMargalef               Calculate the Margalef's diversity index
fMenhinick              Calculate the Menhinick's diversity index
fPielou                 Calculate the Pielou's diversity index
fShannon                Calculate the Shannon-Weaver diversity index
fSheldon                Calculate the Sheldon's diversity index
fSimpson                Calculate the Simpson's diversity index
fSimpsonInf             Calculate the Simpson's diversity index and the
                        inverse
namesmengal16           namesmengal16 data
nameswomengal16         nameswomengal16 data
surnamesgal14           surnamesgal14 data

This package computes the different measures which can be used to quantify similarities between regions. These measures are isonymy, isonymy between, Lasker distance, coefficients of Hedrick and Nei. A diversity index is a numerical measure of how many different types (such as species) are present in a dataset (a community), as well as the evolutionary relationships among the individuals distributed throughout those types, such as richness, divergence, and evenness. These indicators are numerical representations of biodiversity in several dimensions (richness, evenness, and dominance). Then, this package calculates biodiversity indices such as Margalef, Menhinick, Simpson, Shannon, Shannon-Wiener Sheldon, Heip, Hill Numbers, Geometric Mean and Cressie and Read statistics.

Author(s)

Maria Jose Ginzo Villamayor [aut, cre]

Maintainer: Maria Jose Ginzo Villamayor <mariajose.ginzo@usc.es>

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. <https://doi.org/10.1890/ES11-00186.1>

Cressie, Noel and Read, Timothy RC (1984) Multinomial goodness-of-fit tests. Computational Statistics and Data Analysis, 46(3), 440–464. <http://www.jstor.org/stable/2345686>

Sheldon, A. L. (1969). Equitability indices: dependence on the species count. Ecology, 50, 466–467. <https://doi.org/10.2307/1933900>

Simpson (1949) Measurement of diversity. Nature, 163. <https://doi.org/10.1038/163688a0>

Studeny, A.C. (2012). Quantifying Biodiversity Trends in Time and Space. PhD thesis, University of St Andrews. <https://research-repository.st-andrews.ac.uk/bitstream/handle/10023/3414/AngelikaStudenyPhDThesis.pdf?sequence=3&isAllowed=y>

van Strien, A.J., Soldaat, L.L., & Gregory, R.D. (2012). Desirable mathematical properties of indicators for biodiversity change. Ecological Indicators, 14, 202–208. <https://doi.org/10.1016/j.ecolind.2011.07.007>

See Also

fCressieRead, fGeneralisedMean, fGeometricMean, fHeip, fHill, fIsonymy, fIsonymyAll, fMargalef, fMenhinick, fPielou, fShannon, fSheldon, fSimpson, fSimpsonInf, fGeneralisedMean, fHeip

Cressie and Read

Description

This function obtains the Cressie and Read statistics introduced by Noel Cressie and Timothy Read. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

fCressieRead(x, number, population, ni, location, lambda)

Arguments

Details

For a community i, Cressie and Read (1984) introduced the following parametric form for a generalised statistic I_n (\lambda) = \frac{2}{\lambda(\lambda+1)} \sum_{k\in S_i} { n_{ki} \left[ \left(\frac{n_{ki}}{n/S_i}\right)^\lambda-1\right]}, where n_{ki} represents the number of individuals of species k in a sample (in the population is N_{ki}), S_i represents all species at the community, species richness, and \lambda is a free parameter.

Varying the value of \lambda gets different statistics. If \lambda= -1 and \lambda= 0, I_n(\lambda) is not defined, but in any case, limits \lambda = -1 and \lambda = 0 can be taken.

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

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Cressie, Noel and Read, Timothy RC (1984) Multinomial goodness-of-fit tests. Computational Statistics and Data Analysis, 46(3), 440–464.

See Also

fHill

Examples

data(surnamesgal14)
result = fCressieRead(x= surnamesgal14 , number="number",
population="population", location = "muni", ni="ni",
lambda = 2)
result

Calculate the Generalised Mean

Description

This function obtains the generalised mean of relative abundances for a collection of species introduced by Angelika C. Studeny. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

fGeneralisedMean (x, pki, pki0, s, location, lambda)

Arguments

Details

For a community i, the generalised mean of relative abundances is defined by M_t (\lambda) = \left[\frac{1}{S_i} \sum_{k\in S_i} \left(\frac{N_{ki}^t}{N_{ki}^{t0}}\right)^\lambda\right]^{\frac{1}{\lambda}}, where N_{ki}^t denotes the number of individuals of species k at times t, t0 is the baseline year and S_i are all species at the community, species richness, and \lambda can be any non-zero real number.

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

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

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

See Also

fMargalef, fMenhinick, fPielou, fShannon, fSheldon, fSimpson, fSimpsonInf, fGeometricMean, 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;')

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

data(namesmengal16)

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

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

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

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

data(nameswomengal16)

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

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

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

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

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)

Arguments

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.

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

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

Calculate the Heip's diversity index

Description

This function obtains the Heip's diversity index introduced by Carlo H. R. Heip. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.

Usage

fHeip (x, k, n, location, s)

Arguments

Details

For a community i, the Heip's diversity index is defined by E_{He} = \frac{2^{H^{\prime}}-1}{S_i-1} where H^{\prime} is the Shannon diversity index and S_i are all species at the community, species richness. This index varies from 0 to 1 and measures how equally the species richness contributes to the total abundance of the community.

In onomastic context, S_i are all surnames in region (\approx community diversity context) i.

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Heip, C. (1974). A New Index Measuring Evenness. Journal of the Marine Biological Association of the United Kingdom, 54(3), 555–557.

See Also

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

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;')


result = fHeip (x= surnamesgal14[surnamesgal14$number != 0,],
k="number", n="population", location  = "muni",
s = apes2$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;')


result = fHeip (x= namesmengal16[namesmengal16$number != 0,],
k="number", n="population", location  = "muni",
s = names2$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;')


result = fHeip (x= nameswomengal16[nameswomengal16$number != 0,],
k="number", n="population", location  = "muni",
s = names2$ni[1:loc] )
result

Calculate the Hill's diversity numbers

Description

This function obtains the Hill's diversity numbers introduced by M. O. Hill. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.

Usage

fHill(x, k, n, location, lambda)

Arguments

Details

For a community i, the Hill's diversity numbers are defined by the expression J(\lambda) = \left(\sum \limits_{k\in S_i} p_{ki}^\lambda\right)^{\frac{1}{1-\lambda}} with the restriction \lambda \geq 0 where p_{ki} represents the relative frequency of species k and S_i are all species at the community, species richness, and \lambda is a free parameter. (This is equivalent to the exponential of Renyi's generalised entropy). The Renyi entropy of order \lambda, where \lambda \geq 0 and \lambda \neq 1, is defined as \mathrm{H}_{\lambda}(X)=\frac{1}{1-\lambda} \log \left(\sum \limits_{i=1}^{n} p_{i}^{\lambda}\right) Here, X is a discrete random variable with possible outcomes in the set \mathcal{A}=\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} and corresponding probabilities p_{i} \doteq \operatorname{Pr}\left(X=x_{i}\right) for i=1, \ldots, n. The logarithm is conventionally taken to be base 2, especially in the context of information theory where bits are used. If the probabilities are p_{i}=1 / n for all i=1, \ldots, n, then all the Renyi entropies of the distribution are equal: \mathrm{H}_{\lambda}(X)=\log n. In general, for all discrete random variables X, \mathrm{H}_{\lambda}(X) is a non-increasing function in \lambda..

Particular cases of \lambda values: \lambda = 0, J(0)=S_i, it corresponds species richness; \lambda = 1, J(1)=e^{H_{t}}, it corresponds the exponential of Shannon's entropy; and \lambda = 2, J(2)= D_{S_i}, it corresponds the 'inverse' Simpson index.

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:

Author(s)

Maria Jose Ginzo Villamayor

References

Hill, M. O. (1973). Diversity and Evenness: a unifying notation and its consequences. Ecology, 54, 427–32.

See Also

fCressieRead.

Examples

data(surnamesgal14)
result = fHill (x= surnamesgal14, k="number", n="population",
location  = "muni", lambda= 0)
result

data(namesmengal16)
result = fHill (x= namesmengal16, k="number", n="population",
location  = "muni", lambda= 0)
result

data(nameswomengal16)
result = fHill (x= nameswomengal16, k="number", n="population",
location  = "muni", lambda= 0)
result

Calculate the Isonymy within a region

Description

This function obtains the isonymy within a region i which has an associated collection S_i of surnames.

Usage

fIsonymy(x, category)

Arguments

Details

Isonymy is defined as I_i=\sum\limits_{k\in S_i}p_{ki}^2 where p_{ki} denotes the relative frequency of surname k in region i.

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

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Crow J.F. and Mange A.P., (1965). Measurement of inbreeding from the frequency of marriages between persons of the same surname. Eugenics Quarterly, 12(4), 199–203.

Barrai, I., Scapoli, C., Beretta, M., Nesti, C., Mamolini, E., and Rodriguez–Larralde, A., (1996). Isonymy and the genetic structure of Switzerland. I: The distributions of surnames. Annals of Human Biology, 23, 431–455.

See Also

fIsonymyAll.

Examples

data(surnamesgal14)
surnamesgal14$pki2 <- (surnamesgal14$number / surnamesgal14$population)^2
result = fIsonymy(surnamesgal14$pki2, surnamesgal14$namuni)
result

data(namesmengal16)
namesmengal16$pki2 <- (namesmengal16$number / namesmengal16$population)^2
result = fIsonymy(namesmengal16$pki2, namesmengal16$namuni)
result

data(nameswomengal16)
nameswomengal16$pki2 <- (nameswomengal16$number / nameswomengal16$population)^2
result = fIsonymy(nameswomengal16$pki2, nameswomengal16$namuni)
result

Calculate the Isonymy, Isonymy between regions, Lasker distances, Euclidean distance and Nei's distances

Description

This function obtains the Isonymy, Isonymy between regions, Lasker distance, Euclidean distance and Nei's distances and Hedrick's coefficient.

Usage

fIsonymyAll (x, n, location, union, measure)

Arguments

Details

Values of Isonymy, Isonymy between regions, Lasker distance, Euclidean distance and Nei's distances and Hedrick's coefficient.

Surname (dis)similarity among regions can be quantified by different measures. Consider index i=1,\ldots,n for denoting a certain geographical region (for two regions, (i,j)). Each region has an associated collection S_i of surnames, and for a pair of regions, the collection of all the surnames in them is denoted by S_{ij} (S_{ij}=S_i\cup S_j). The total number of surnames in a certain region i is denoted by n_i. Surnames will be denoted by indices k and l.

Isonymy is defined as I_i=\sum \limits _{k\in S_i}p_{ki}^2 where p_{ki} denotes the relative frequency of surname k in region i. Isonymy can be also extended as a measure of population similarities between groups. Under the assumption of a common origin, isonymy between two regions i and j is defined as I_{ij}=\sum \limits_{k\in S_{ij}}p_{k_i}p_{k_j}.

Other different measures of the isonymic distance between a pair of locations can be derived from isonymy between. For instance, the Lasker distance is given by L = -\log(I_{ij}).

Lasker distance can be interpreted as a measure of similarity between to areas, where large distance indicate less similarity in surname composition. Nevertheless, Lasker distance is not the only option to quantify surname similarity. Other common coefficients are the Euclidean distance and Nei's distance, both of them given by E = \sqrt{1-\sum_{k\in S_{ij}}{\sqrt{p_{ki}p_{kj}}}}\quad\mbox{and}\quad N = -\log\left(\frac{I_{ij}}{\sqrt{I_iI_j}}\right), respectively. Finally, Hedrick's coefficient gives a standardized measure of isonymy using a procedure similar to that utilized in the calculation of a correlation coefficient. Specifically: H_{ij} = \frac{ 2 \sum \limits_{k \in S_{ij}} p_{ki} p_{kj}}{ \left(\sum \limits_{k \in S_{ij}} p_{ki}^2 + \sum \limits_{k \in S_{ij}} p_{kj}^2 \right) } \mbox{, with } i,j=1\ldots,n.

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

Value

A list containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Barrai, I., Scapoli, C., Beretta, M., Nesti, C., Mamolini, E., and Rodriguez–Larralde, A., (1996) Isonymy and the genetic structure of Switzerland. I: The distributions of surnames. Annals of Human Biology, 23, 431–455.

Cavalli-Sforza, L. L., and Edwards, A. W. F., (1967), Phylogenetic analysis models and estimation procedures. American Journal of Human Genetics, 19, 233 257.

Hedrick, P. W. (1971), A new approach to measuring genetic similarity. Evolution, 25: 276–280.

Lasker, G. W. (1977) A coefficicnt of relationship by isonymy: a method for estimating the genetic relationship between populations. Human Biology, 49, 489–493.

Mikerezi, I., Shina, E. Scapoli, C., Barbujani, G. Mamolini, E., Sandri, M., Carrieri, A., Rodriguez–Larralde, A. and Barrai, I. (2013). Surnames in Albania: a study of the population of Albania through isonymy. Annals of Human Genetics, 77, 232–243.

Nei, M.(1973). The theory and estimation of genetic distance. In Genetic Structure of Populations, edited by N. E. Morton, (Honolulu: University Press of Hawaii), 45–54.

Weiss, V. 1980. Inbreeding and genetic distance between hierarchically structured populations measured by surname frequencies. Mankind Quarterly, 21, 135–149.

See Also

fIsonymy.

Examples

data(surnamesgal14)
result = fIsonymyAll (x= surnamesgal14, n= 314, location = 'muni',
union = 'surname', measure = 'pki')
result

data(namesmengal16)
namesmengal16$pki <- (namesmengal16$number /
namesmengal16$population)
result = fIsonymyAll (x= namesmengal16, n= 313, location = 'muni',
union = 'name', measure = 'pki')
result

data(nameswomengal16)
nameswomengal16$pki <- (nameswomengal16$number /
nameswomengal16$population)
result = fIsonymyAll (x= nameswomengal16, n= 313, location = 'muni',
union = 'name', measure = 'pki')
result

Calculate the Margalef's diversity index

Description

This function obtains the Margalef's diversity index which is a species diversity index developed by Ramon Margalef Lopez during the 1950s. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.

Usage

fMargalef(x, s, n, location)

Arguments

Details

For a community i, the Margalef's diversity index is defined by R_1 = \frac{S_i-1}{\ln(N_i)}, where S_i represents the number of species (richness) and N_i represents the total number of individuals in all S_i.

In onomastic context, N_i denotes the number of individuals in region (\approx community diversity context) i and S_i represents the total number of surnames.

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Margalef D.R., (1958), Information theory in ecology. International Journal of General Systems, 3, 36–71.

See Also

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

Examples

library(sqldf)
data(surnamesgal14)

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

result = fMargalef (x= apes2, s="ni", n="population", location  = "muni")
result

data(namesmengal16)

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

result = fMargalef (x= names2, s="ni", n="population", location  = "muni")
result

data(nameswomengal16)

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

result = fMargalef (x= names2, s="ni", n="population", location  = "muni")
result

Calculate the Menhinick's diversity index

Description

This function obtains the Menhinick's diversity index introduced by Edward F. Menhinick. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.

Usage

fMenhinick(x, s, n, location)

Arguments

Details

For a community i, the Menhinick's diversity index is defined by R_2 = \frac{s_i}{\sqrt{N_i}}, where s_i represents the number of species (richness) and N_i represents the total number of individuals in all s_i.

In onomastic context, N_i denotes the number of individuals in region (\approx community diversity context) i and s_i represents the total number of surnames.

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Menhinick E.F. (1964) A comparison of some species-individuals diversity indices applied to samples of field insects. Ecology, 45, 859–861.

See Also

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

Examples

library(sqldf)
data(surnamesgal14)

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

result = fMenhinick(x= apes2, s="ni", n="population",
location  = "muni")
result

data(namesmengal16)

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

result = fMenhinick(x= names2, s="ni", n="population",
location  = "muni")
result

data(nameswomengal16)

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

result = fMenhinick(x= names2, s="ni", n="population",
location  = "muni")
result

Calculate the Pielou's diversity index

Description

This function obtains the Pielou's diversity index which is an index that measures diversity along with species richness introduced by Evelyn Chrystalla Pielou. It is a method for quantifying species biodiversity that can be adapted to the context of onomastic.

Usage

fPielou(x, k, n, location, s)

Arguments

Details

For a community i, the Pielou's diversity index is defined by J^{\prime} = \frac{H^{\prime}}{\log_2S_i}, where H^{\prime} denotes the Shannon-Wiener index and \log_2S_i denotes the maximum diversity H^{\prime}_{\max}. Pielou's index is the Shannon-Weiner index computed for the sample S_i and represents a measure of Evenness of the community. If all species are represented in equal numbers in the sample, then J^{\prime} = 1. If one species strongly dominates J^{\prime} is close to zero.

In onomastic context, S_i are all surnames in region (\approx community diversity context) i.

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Pielou, E. C. (1966) The measurement of diversity in different types of biological collections. Journal of Theoretical Biology, 13, 131-144.

See Also

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

Examples

library(sqldf)
data(surnamesgal14)

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

result = fPielou (x= surnamesgal14[surnamesgal14$number != 0,],
k="number", n="population", location  = "muni", s = apes2$ni )
result

data(namesmengal16)

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

result = fPielou (x= namesmengal16[namesmengal16$number != 0,],
k="number", n="population", location  = "muni", s = names2$ni )
result

data(nameswomengal16)

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

result = fPielou (x= nameswomengal16[nameswomengal16$number != 0,],
k="number", n="population", location  = "muni", s = names2$ni )
result

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

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:

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

Calculate the Sheldon's diversity index

Description

This function obtains the Sheldon's diversity index introduced by A. L. Sheldon. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

fSheldon (x, k, n, location, s)

Arguments

Details

For a community i, the Sheldon's diversity index is defined by E_{She} = \frac{2^{H^{\prime}}}{S_i}, where H^{\prime} denotes the Shannon-Wiener index and S_i represents the number of species (richness).

In onomastic context, S_i are all surnames in region (\approx community diversity context) i.

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

Sheldon, A. L. (1969). Equitability indices: dependence on the species count. Ecology, 50, 466–467.

See Also

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

Examples

library(sqldf)
data(surnamesgal14)
apes2=sqldf('select  muni, count(surname) as ni,
sum(number) as population from surnamesgal14
group by muni;')

result = fSheldon (x= surnamesgal14[surnamesgal14$number != 0,],
k="number", n="population", location  = "muni",
s = apes2$ni)
result

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

result = fSheldon (x= namesmengal16[namesmengal16$number != 0,],
k="number", n="population", location  = "muni",
s = names2$ni)
result

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

result = fSheldon (x= nameswomengal16[nameswomengal16$number != 0,],
k="number", n="population", location  = "muni",
s = names2$ni)
result

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

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:

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

Calculate the Simpson's diversity index and the inverse

Description

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

Usage

fSimpsonInf(x, k, n, location)

Arguments

Details

For a community i, the Simpson (when N_i is not finite, data are assumed to come from a sample of size N_i) diversity index is defined by D^{\prime}_{S_i} = \sum \limits_{k\in S_i} \frac{n_{ki}(n_{ki}-1)}{n_i(n_i-1)}, where n_{ki} represents the number of individuals of species k in a sample (in the total is N_{ki}) and S_i represents all species at the community, species richness.

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

Value

A dataframe containing the following components:

Author(s)

Maria Jose Ginzo Villamayor

References

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

See Also

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

Examples

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

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

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

namesmengal16 data

Description

This dataset corresponds to 25 most frequent men's names by municipality in Galicia in 2016.

Usage

data(namesmengal16)

Format

namesmengal16 is a data frame with men's names from Galicia in 2016

Source

The data corresponds to 25 most frequent men's names by municipality in Galicia in 2016. The dataset contains 6 columns, prov: the province, muni: the municipality, namuni: the name of the municipality, name: the name, number: the number of people with that name and population: the total population considered by municipality.

These data have been extracted from the website of the Galician Institute of Statistics (IGE). The IGE offers information on the surnames and names of the population whose residence is in the Autonomous Community of Galicia. The base information for the elaboration data is the file of the Municipal Register of inhabitants of 2014 that the National Institute of Statistics (INE) provides to the IGE.

References

Galician Institute of Statistics (IGE), https://www.ige.eu/

Examples

data(namesmengal16)

nameswomengal16 data

Description

This dataset corresponds to 25 most frequent women's names by municipality in Galicia in 2016.

Usage

data(nameswomengal16)

Format

nameswomengal16 is a data frame with women's names from Galicia in 2016.

Source

The data corresponds to 25 most frequent women's names by municipality in Galicia in 2016. The dataset contains 6 columns, prov: the province, muni: the municipality, namuni: the name of the municipality, name: the name, number: the number of people with that name and population: the total population considered by municipality.

These data have been extracted from the website of the Galician Institute of Statistics (IGE). The IGE offers information on the surnames and names of the population whose residence is in the Autonomous Community of Galicia. The base information for the elaboration data is the file of the Municipal Register of inhabitants of 2014 that the National Institute of Statistics (INE) provides to the IGE.

References

Galician Institute of Statistics (IGE), https://www.ige.eu/

Examples

data(nameswomengal16)

surnamesgal14 data

Description

This dataset corresponds to 25 most frequent surnames by municipality in Galicia in 2014.

Usage

data(surnamesgal14)

Format

surnamesgal14 is a data frame with surnames from Galicia in 2014.

Source

The data corresponds to 25 most frequent surnames by municipality in Galicia in 2014. The dataset contains 8 columns, prov: the province, muni: the municipality, namuni: the name of the municipality, surname: the surname, number: the number of people with that surname, population: the total population considered by municipality, ni: the number of surnames considered and p_{ki} which is the frequency of surname k in municipality i.

These data have been extracted from the website of the Galician Institute of Statistics (IGE). The IGE offers information on the surnames and names of the population whose residence is in the Autonomous Community of Galicia. The base information for the elaboration data is the file of the Municipal Register of inhabitants of 2014 that the National Institute of Statistics (INE) provides to the IGE.

References

Galician Institute of Statistics (IGE), https://www.ige.eu/

Examples

data(surnamesgal14)