Для популяционных генетиков...

Интересный набор инструментов для анализа генетических данных от лаборатории биометрии и эволюционной биологии (Biometry and Evolutionary Biology Lab (UMR 5558)) Лионского университета (Lyon University).

The software "ade4" is for R and can be characterized by:

- the implementation of graphical and statistical functions
- the availability of numerical data
- the redaction of technical and thematic documentation
- the inclusion of bibliographic references

Also, the GUI is available to facilitate multivariate data analysis through "ade4" library from R.
For me, the possibility to calculate genetic distances by dist.genet() function is most of importance. To get this point, a researcher can use 5 types of distances.

Sources:
http://pbil.univ-lyon1.fr/ade4TkGUI/home.php?lang=eng
http://pbil.univ-lyon1.fr/ade4html/dist.genet.html

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The syntax is as follows:

dist.genet(genet, method = 1, diag = FALSE, upper = FALSE)

Arguments:
genet a list of class genet
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

Details on methods:
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 <=q i <=q t, 1 <=q j <=q nu, 1 <=q k <=q 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+}^+=tnu

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|