Bootstrapping: Resampling of Alleles or Genotypes Using a Bootstrap Method

Description

To be able to test the null hypothesis of absence of genetic differentiation between populations, a bootstrap method is performed. Thereby, alleles (or genotypes) of the same locus are randomly allocated over the populations. The obtained range of D, Dest, Dest.Chao, Gst or Gst.est (refer to Jost, 2008) values from the reallocated data sets is used to define the 95% bootstrap confidence interval and can be further used to calculate p-values using the function p.val.

Usage

Bootstrapping.D(tab, bt=1000)
Bootstrapping.Dest(tab, bt=1000)
Bootstrapping.Chao(tab, bt=1000)
Bootstrapping.Gst(tab, bt=1000)
Bootstrapping.Gst.est(tab, bt=1000)

Arguments

tab

A data table that equals the output of the function inputformat (see the section 'value' in the description of this function). A different input format can be used by transforming the table

This is a numeric argument (default=1000) that defines the times of bootstrap-resampling, that the p-values and the 95% confidence intervals are based on.

Value

The following objects are both printed and assigned to the R workspace (.GlobalEnv).
D.means, Dest.means, Dest.Chao.means, Gst.means, Gst.est.meansA vector of 1000 (default) bootstrap values characterizing the average genetic differentiation over all loci.
D.loci, Dest.loci, Dest.Chao.loci, Gst.loci, Gst.est.lociA vector of 1000 (default) bootstrap values characterizing the genetic differentiation for each locus separately.
confidence.limitsA list that contains (1) confidence.limits.per.locus: A data frame listing the lower and upper 95% confidence limits of the genetic differentiation for each locus separately; (2) confidence.limit.over.all.loci: Lower and upper 95% confidence limits of the genetic differentiation averaged over all loci.

Details

The function Hardy.Weinberg that is included in this package, delivers the output Hardy Weinberg Equilibrium = FALSE/TRUE. If all of the populations compared are in Hardy Weinberg Equilibrium (Hardy Weinberg Equilibrium = TRUE), the alleles that were found in each population for a single locus, are randomly allocated over all populations. If alleles are not inherited independently from each other (Hardy Weinberg Equilibrium = FALSE) genotypes are randomly allocated (Goudet, 1996). By the reallocation of alleles or genotypes, all populations share a common gene pool and are not differentiated. The range of D, Dest, Dest.Chao, Gst or Gst.est values calculated from these data tables give examples of the degree of differentiation that not actually exists but could have arisen by chance alone due to a bias in the sample of the real population.

If the empirical value of D, Dest, Dest.Chao, Gst or Gst.est is larger than 95% of the values obtained by bootstrapping, the populations can be regarded as being significantly differentiated with a significance level of 0.05. The p-value can be calculated using the function p.val. 95% standard bootstrap confidence intervals are calculated automatically using the method given by Manly (1997, eqn. 3.1, p.35):

Estimate +(-) 1.96*(Bootstrap standard deviation)

Estimate stands for the empirical D, Dest, Dest.Chao, Gst or Gst.est value that has been obtained.

References

Goudet, J., Raymond, M., deMeeues, T. and Rousset, F. 1996 Testing differentiation in diploid populations. Genetics 144, 4, p. 1933--1940.

Jost, L. 2008 Gst and its relatives do not measure differentiation. Molecular Ecology 17, 18, p. 4015--4026.

Manly, B. F. J. 1997 Randomization, Bootstrap and Monte Carlo Methods in Biology Chapman & Hall, London.

Examples

Run this code

data(Example.transformed)

Example1 <- Example.transformed

Bootstrapping.Dest(Example1, bt=10)
confidence.limits

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