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dist.genet 67
Let P the table of general term p k ij
p + ij = ∑ m(j)
k=1 pk ij = 1, p+ i+ = ∑ ν
j=1 p+ ij = ν, p+ ++ = ∑ ν
j=1 p+ i+ = tν
The option method computes the distance matrices between populations using the frequencies p k ij .
Value
1. Nei’s distance:
D 1 (a, b) = − ln(
√ ∑ν
k=1
∑ ν
∑ m(k)
k=1 j=1 pk aj pk bj
∑ )
m(k)
j=1 (pk bj )2
∑ m(k)
j=1 (pk aj )2 √ ∑ν
k=1
2. Angular distance √ or Edwards’ distance:
D 2 (a, b) =
1 − 1 ν
∑ ν
k=1
∑ m(k)
j=1
√
p k aj pk bj
3. Coancestrality coefficient or Reynolds’ distance:
D 3 (a, b) =
√ ∑ν ∑ m(k)
∑ k=1 j=1 (pk aj −pk bj )2
ν
2 (1−∑ m(k)
k=1 j=1 pk aj pk bj )
4. Classical Euclidean distance or Rogers’ distance:
D 4 (a, b) = 1 ∑ ν ∑ m(k)
ν k=1 j=1 (pk aj − pk bj )2
√
1
2
5. Absolute genetics distance or Provesti ’s distance:
D 5 (a, b) = 1 ∑ ν ∑ m(k)
2ν k=1 j=1 |pk aj − pk bj |
returns a distance matrix of class dist between the rows of the data frame
Author(s)
Daniel Chessel
Anne B Dufour 〈dufour@biomserv.univ-lyon1.fr〉
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.