This function is deprecated. See the dist.genpop function in the package adegenet.
This program computes any one of five measures of genetic distance from a set of gene frequencies in different populations with several loci.
dist.genet(genet, method = 1, diag = FALSE, upper = FALSE)a list of class genet
an integer between 1 and 5. See details
a logical value indicating whether the diagonal of the distance matrix should be printed by print.dist
a logical value indicating whether the upper triangle of the distance matrix should be printed by print.dist
returns a distance matrix of class dist between the rows of the data frame
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: \(D_1(a,b)=- \ln(\frac{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} p_{aj}^k p_{bj}^k}{\sqrt{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} {(p_{aj}^k) }^2}\sqrt{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} {(p_{bj}^k)}^2}})\)
2. Angular distance or Edwards' distance: \(D_2(a,b)=\sqrt{1-\frac{1}{\nu} \sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} \sqrt{p_{aj}^k p_{bj}^k}}\)
3. Coancestrality coefficient or Reynolds' distance: \(D_3(a,b)=\sqrt{\frac{\sum_{k=1}^{\nu} \sum_{j=1}^{m(k)}{(p_{aj}^k - p_{bj}^k)}^2}{2 \sum_{k=1}^{\nu} (1- \sum_{j=1}^{m(k)}p_{aj}^k p_{bj}^k)}}\)
4. Classical Euclidean distance or Rogers' distance: \(D_4(a,b)=\frac{1}{\nu} \sum_{k=1}^{\nu} \sqrt{\frac{1}{2} \sum_{j=1}^{m(k)}{(p_{aj}^k - p_{bj}^k)}^2}\)
5. Absolute genetics distance or Provesti 's distance: \(D_5(a,b)=\frac{1}{2{\nu}} \sum_{k=1}^{\nu} \sum_{j=1}^{m(k)} |p_{aj}^k - p_{bj}^k|\)
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<U+00E9>tica entre poblaciones. Miscellanea Alcob<U+00E9>, 68, 109--118. Prevosti A., Oca<U+00F1>a J. and Alonso G. (1975) Distances between populations of Drosophila subobscura, based on chromosome arrangements frequencies. Theoretical and Applied Genetics, 45, 231--241.
To find some useful explanations: Sanchez-Mazas A. (2003) Cours de G<U+00E9>n<U+00E9>tique Mol<U+00E9>culaire des Populations. Cours VIII Distances g<U+00E9>n<U+00E9>tiques - Repr<U+00E9>sentation des populations. http://anthro.unige.ch/GMDP/Alicia/GMDP_dist.htm
# NOT RUN {
data(casitas)
casi.genet <- char2genet(casitas,
as.factor(rep(c("dome", "cast", "musc", "casi"), c(24,11,9,30))))
ldist <- lapply(1:5, function(method) dist.genet(casi.genet,method))
ldist
unlist(lapply(ldist, is.euclid))
kdist(ldist)
# }
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