basic.stats {hierfstat}

Basic diversity and differentiation statistics

Description

Estimates individual counts, allelic frequencies, observed heterozygosities and genetic diversities per locus and population. Also Estimates mean observed heterozygosities, mean gene diversities within population Hs, Gene diversities overall Ht and corrected Htp, and Dst, Dstp. Finally, estimates Fst and Fstp as well as Fis following Nei (1987) per locus and overall loci

Usage

basic.stats(data,diploid=TRUE,digits=4)

## S3 method for class 'basic.stats'
print(x,...)

Hs(data,...)

Ho(data,...)

Arguments

data

a data frame where the first column contains the population to which the different individuals belong, and the following columns contain the genotype of the individuals -one locus per column-

diploid

Whether individuals are diploids (default) or haploids

digits

how many digits to print out in the output (default is 4)

x

an object of class basic.stats

...

further arguments to pass to print.bas.stats

Value

n.ind.samp

A table –with np (number of populations) columns and nl (number of loci) rows– of genotype counts

pop.freq

A list containing allele frequencies. Each element of the list is one locus. For each locus, Populations are in columns and alleles in rows

Ho

A table –with np (number of populations) columns and nl (number of loci) rows– of observed heterozygosities

Hs

A table –with np (number of populations) columns and nl (number of loci) rows– of observed gene diversities

Fis

A table –with np (number of populations) columns and nl (number of loci) rows–of observed Fis

perloc

A table –with as many rows as loci– containing basic statistics Ho, Hs, Ht, Dst, Ht', Dst', Fst, Fst' ,Fis, Dest

overall

Basic statistics averaged over loci

Note

For the perloc and overall tables (see value section), the following statistics, defined in eq.7.38– 7.43 pp.164–5 of Nei (1987) are estimated:

The observed heterozygosity

Ho= 1-\sum_k \sum_i Pkii/np,

where Pkii represents the proportion of homozygote i in sample k and np the number of samples.

The within population gene diversity (sometimes misleadingly called expected heterozygosity):

Hs=\tilde{n}/(\tilde{n}-1)[1-\sum_i\bar{p_i^2}-Ho/2\tilde{n}],

where \tilde{n}=np/\sum_k 1/n_k and \bar{p_i^2}=\sum_k p_{ki}^2/np

The overall gene diversity

Ht= 1-\sum_i\bar{p_i}^2+Hs/(\tilde{n} np)-Ho/(2\tilde{n} np),

where \bar{p_i}=\sum_kp_{ki}/np.

The amount of gene diversity among samples Dst=Ht-Hs

Dst'=np/(np-1)Dst

Ht'=Hs+Dst'

Fst=Dst/Ht.(This is not the same as Nei's Gst, Nei's Gst is an estimator of Fst based on allele frequencies only)

Fst'=Dst'/Ht'

Fis=1-Ho/Hs

Last, Dest=np/(np-1) (Ht'-Hs)/(1-Hs) a measure of population differentiation as defined by Jost (2008) is also given

Here, the p_{ki} are unweighted by sample size. These statistics are estimated for each locus and an overall loci estimates is also given, as the unweighted average of the per locus estimates. In this way, monomorphic loci are accounted for (with estimated value of 0) in the overall estimates.

Note that the equations used here all rely on genotypic rather than allelic number and are corrected for heterozygosity.

Author(s)

Jerome Goudet [e-mail]

References

Nei M. (1987) Molecular Evolutionary Genetics. Columbia University Press

Jost L (2008) GST and its relatives do not measure differentiation. Molecular Ecology, 17, 4015-4026.

Nei M, Chesser R (1983) Estimation of fixation indexes and gene diversities. Annals of Human Genetics, 47, 253-259.

See Also

ind.count,pop.freq.

Examples

data(gtrunchier)
basic.stats(gtrunchier[,-1])
Hs(gtrunchier[,-2])
Ho(gtrunchier[,-2])