adegenet (version 1.0-0)

dist.genpop: Genetic distances between populations

Description

This function computes measures of genetic distances between populations using a genpop object. Currently, five distances are available, some of which are euclidian (see details). A non-euclidian distance can be transformed into an Euclidian one using quasieuclid in order to perform a Principal Coordinate Analysis dudi.pco (both functions in ade4). The function dist.genpop is based on former dist.genet function of ade4 package.

Usage

dist.genpop(x, method = 1, diag = FALSE, upper = FALSE)

Arguments

x

a list of class genpop

method

an integer between 1 and 5. See details

diag

a logical value indicating whether the diagonal of the distance matrix should be printed by print.dist

upper

a logical value indicating whether the upper triangle of the distance matrix should be printed by print.dist

Value

• returns a distance matrix of class dist between the rows of the data frame

Details

Let A a table containing allelic frequencies with t populations (rows) and m alleles (columns). Let $\nu$ the number of loci. The locus j gets m(j) alleles. $m=\sum_{j=1}^{\nu} m(j)$ For the row i and the modality k of the variable j, notice the value $a_{ij}^k$ ($1 \leq i \leq t$, $1 \leq j \leq \nu$, $1 \leq k \leq m(j)$) the value of the initial table. $a_{ij}^+=\sum_{k=1}^{m(j)}a_{ij}^k$ and $p_{ij}^k=\frac{a_{ij}^k}{a_{ij}^+}$ Let P the table of general term $p_{ij}^k$ $p_{ij}^+=\sum_{k=1}^{m(j)}p_{ij}^k=1$, $p_{i+}^+=\sum_{j=1}^{\nu}p_{ij}^+=\nu$, $p_{++}^+=\sum_{j=1}^{\nu}p_{i+}^+=t\nu$ The option method computes the distance matrices between populations using the frequencies $p_{ij}^k$. 1. Nei's distance (not Euclidian): $D_1(a,b)=- \ln(\frac{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} p_{aj}^k p_{bj}^k}{\sqrt{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} {(p_{aj}^k) }^2}\sqrt{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} {(p_{bj}^k)}^2}})$ 2. Angular distance or Edwards' distance (Euclidian): $D_2(a,b)=\sqrt{1-\frac{1}{\nu} \sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} \sqrt{p_{aj}^k p_{bj}^k}}$ 3. Coancestrality coefficient or Reynolds' distance (Euclidian): $D_3(a,b)=\sqrt{\frac{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)}{(p_{aj}^k - p_{bj}^k)}^2}{2 \sum_{k=1}^{\nu} (1- \sum_{j=1}^{m(k)}p_{aj}^k p_{bj}^k)}}$ 4. Classical Euclidean distance or Rogers' distance (Euclidian): $D_4(a,b)=\frac{1}{\nu} \sum_{k=1}^{\nu} \sqrt{\frac{1}{2} \sum_{j=1}^{m(k)}{(p_{aj}^k - p_{bj}^k)}^2}$ 5. Absolute genetics distance or Provesti 's distance (not Euclidian): $D_5(a,b)=\frac{1}{2{\nu}} \sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} |p_{aj}^k - p_{bj}^k|$

References

To complete informations about distances: Distance 1: Nei, M. (1972) Genetic distances between populations. American Naturalist, 106, 283--292. Nei M. (1978) Estimation of average heterozygosity and genetic distance from a small number of individuals. Genetics, 23, 341--369. Avise, J. C. (1994) Molecular markers, natural history and evolution. Chapman & Hall, London.

Distance 2: Edwards, A.W.F. (1971) Distance between populations on the basis of gene frequencies. Biometrics, 27, 873--881. Cavalli-Sforza L.L. and Edwards A.W.F. (1967) Phylogenetic analysis: models and estimation procedures. Evolution, 32, 550--570. Hartl, D.L. and Clark, A.G. (1989) Principles of population genetics. Sinauer Associates, Sunderland, Massachussetts (p. 303).

Distance 3: Reynolds, J. B., B. S. Weir, and C. C. Cockerham. (1983) Estimation of the coancestry coefficient: basis for a short-term genetic distance. Genetics, 105, 767--779.

Distance 4: Rogers, J.S. (1972) Measures of genetic similarity and genetic distances. Studies in Genetics, Univ. Texas Publ., 7213, 145--153. Avise, J. C. (1994) Molecular markers, natural history and evolution. Chapman & Hall, London.

Distance 5: Prevosti A. (1974) La distancia gen�tica entre poblaciones. Miscellanea Alcob�, 68, 109--118. Prevosti A., Oca~na J. and Alonso G. (1975) Distances between populations of Drosophila subobscura, based on chromosome arrangements frequencies. Theoretical and Applied Genetics, 45, 231--241. For more information on dissimilarity indexes: Gower J. and Legendre P. (1986) Metric and Euclidian properties of dissimilarity coefficients. Journal of Classification, 3, 5--48 Legendre P. and Legendre L. (1998) Numerical Ecology, Elsevier Science B.V. 20, pp274--288.

See Also

quasieuclid,dudi.pco

Examples

if(require(ade4)){
data(microsatt)
obj <- as.genpop(microsatt$tab)

listDist <- lapply(1:5, function(i) quasieuclid(dist.genpop(obj,met=i)))
for(i in 1:5) {attr(listDist[[i]],"Labels") <- obj$pop.names}
listPco <- lapply(listDist, dudi.pco,scannf=FALSE)

par(mfrow=c(2,3))
for(i in 1:5) {scatter(listPco[[i]],sub=paste("Dist:", i))}
}