dist.genpop | R Documentation |
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 Euclidean one
using cailliez
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.
dist.genpop(x, method = 1, diag = FALSE, upper = FALSE)
x |
a list of class |
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 |
upper |
a logical value indicating whether the upper triangle of the distance matrix should be printed by |
Let A a table containing allelic frequencies with t populations (rows) and m alleles (columns).
Let ν the number of loci. The locus j gets m(j) alleles.
m=∑_{j=1}^{ν} m(j)
For the row i and the modality k of the variable j, notice the value a_{ij}^k (1 ≤q i ≤q t, 1 ≤q j ≤q ν,
1 ≤q k ≤q m(j)) the value of the initial table.
a_{ij}^+=∑_{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}^+=∑_{k=1}^{m(j)}p_{ij}^k=1, p_{i+}^+=∑_{j=1}^{ν}p_{ij}^+=ν, p_{++}^+=∑_{j=1}^{ν}p_{i+}^+=tν
The option method
computes the distance matrices between populations using the frequencies p_{ij}^k.
1. Nei's distance (not Euclidean):
D_1(a,b)=- \ln(\frac{∑_{k=1}^{ν} ∑_{j=1}^{m(k)}
p_{aj}^k p_{bj}^k}{√{∑_{k=1}^{ν} ∑_{j=1}^{m(k)}
{(p_{aj}^k) }^2}√{∑_{k=1}^{ν} ∑_{j=1}^{m(k)}
{(p_{bj}^k)}^2}})
2. Angular distance or Edwards' distance (Euclidean):
D_2(a,b)=√{1-\frac{1}{ν} ∑_{k=1}^{ν}
∑_{j=1}^{m(k)} √{p_{aj}^k p_{bj}^k}}
3. Coancestrality coefficient or Reynolds' distance (Eucledian):
D_3(a,b)=√{\frac{∑_{k=1}^{ν}
∑_{j=1}^{m(k)}{(p_{aj}^k - p_{bj}^k)}^2}{2 ∑_{k=1}^{ν} (1-
∑_{j=1}^{m(k)}p_{aj}^k p_{bj}^k)}}
4. Classical Euclidean distance or Rogers' distance (Eucledian):
D_4(a,b)=\frac{1}{ν} ∑_{k=1}^{ν} √{\frac{1}{2}
∑_{j=1}^{m(k)}{(p_{aj}^k - p_{bj}^k)}^2}
5. Absolute genetics distance or Provesti 's distance (not Euclidean):
D_5(a,b)=\frac{1}{2{ν}} ∑_{k=1}^{ν} ∑_{j=1}^{m(k)}
|p_{aj}^k - p_{bj}^k|
returns a distance matrix of class dist
between the rows of the data frame
Thibaut Jombart t.jombart@imperial.ac.uk
Former dist.genet code by Daniel Chessel chessel@biomserv.univ-lyon1.fr
and documentation by Anne B. Dufour dufour@biomserv.univ-lyon1.fr
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 genetica entre poblaciones. Miscellanea Alcobe, 68, 109–118.
Prevosti A., Ocaña 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 Euclidean 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.
cailliez
,dudi.pco
## Not run: data(microsatt) obj <- as.genpop(microsatt$tab) listDist <- lapply(1:5, function(i) cailliez(dist.genpop(obj,met=i))) for(i in 1:5) {attr(listDist[[i]],"Labels") <- popNames(obj)} listPco <- lapply(listDist, dudi.pco,scannf=FALSE) par(mfrow=c(2,3)) for(i in 1:5) {scatter(listPco[[i]],sub=paste("Dist:", i))} ## End(Not run)
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