OPTION 6  Fst and other correlations
(adapted from the original Genepop v3.1c documentation)

 These options compute estimates of Fis, Fit and Fst or analogous correlations for allele size, either for each pair of sample (sub-options 2 and 4) or a single measure for all samples (sub-options 1 and 3). Fst is estimated by a " weighted " analysis of variance (Cockerham, 1973 ; Weir and Cockerham, 1984), and the analogous measure of correlation in allele size (rho_st, see Rousset, 1996) is estimated by the same technique (Michalakis and Excoffier, 1996). Multilocus estimates are computed as in Weir and Cockerham (1984). Refer to Appendix 2 and Appendix3 for more information.

In options 2 and 4 (pairs of samples), single locus and multilocus estimates are written to the output file.

Sub-options 3 and 4 : using allele sizes for intra class correlation.

 The web version of Genepop assumes that allele size corresponds to the allele entries in the data file, ie the entry for each allele will correspond to its size (e. g. allele designated by < 61 > has a length of 61 units (units = nucleotides, kilobases, etc.)). As two-digit coding is insufficient in most cases for microsatellite loci, Genepop allows you to use data files with three-digit entries (e.g. allele designated by < 155 > has a length of 155 units. The only restriction is that there should be no more than 99 unique alleles in the data file for any locus.

Results are returned via your web browser which you can then save to your local machine. You may also choose to have them emailed to you.

Sub-option 5: Analysis of isolation by distance between individuals

Sub-option 5 allows analysis of isolation by distance between pairs of individuals as described in Rousset (2000). It computes estimates â of the a parameters described there, which are somewhat analogous to Fst/(1-Fst) estimates, and generate a *.MIG output file which is directly used by the ISOLDE program. To that aim a more specific format must be followed for the Genepop input file. The position of individuals must be specified as two coordinates standing for their name (i.e. before the comma on the line for each individual), and since each individual is considered as a "sample", it must be separated by a "Pop". An example of such input file is given below: The first individual is located at the point x = 0, y = 15, the second at the point x = 0, y   =30, etc.

________ the file starts below this line _____________

Title line: "Vines in la Grange des Peres vineyard"
0 15,   0201 0303 0102 0302 1011
0 30,   0202 0301 0102 0303 1111
0 45,   0102 0401 0202 0102 1010
0 60,   0103 0202 0101 0202 1011
0 75,   0203 0204 0101 0102 1010
15 15,  0102 0202 0201 0405 0807
15 30,   0102 0201 0201 0405 0307
15 45,   0201 0203 0101 0505 0402
15 60,   0201 0303 0301 0303 0603
15 75,   0101 0201 0301 0505 0807

_________ the file ends above this line ___________

This sub-option automatically writes the *.MIG file with the genetic and geographic distance matrices and runs the ISOLDE program.

This sub-option automatically writes a file with the genetic and geographic distance matrices and runs the ISOLDE program. F statistics will NOT be converted to F/(1-F) statistics, so you can safely ignore this Isolde parameter, but must provide values for the others. The result returned is the output from Isolde.

Sub-option 6: Analysis of isolation by distance between groups

Sub-option 6 allows analysis of isolation by distance between pairs of groups. Proceed as for sub-option 5 except that at least one population must have more than one individual.

Sub-option 9 : Analysis of isolation by distance
Sub-option 7 (or 8) computes a semi matrix of Fst (or Rho_st) estimates and returns it via the web browser. To do an analysis of isolation by distance, you have to write a semi matrix of geographical distances at the end of this file, using a text editor or word processor. Note that the half matrix has another format than in some previous versions of Genepop. The format of the file is given below :
___________________File starts below this line___________________________________
From file : bidon                   <------anything (comments)
8 (an example)                      <---# of samples (comments ignored)
Theta:                              <---anything (comments)
 0.18 0.107
 0.19 0.068  0.011
 0.20 0.664  0.665 0.009
 0.21 0.098  0.058  0.673  0.675
 0.22 0.048  0.682  0.683  0.017  0.001
0.23 0.715  0.721  0.666  0.666  0.037 0.006
distances:                          <---anything (comments)
 158.0 1215.0
 158.1 1213.0 2300.0
 158.2 2300.0    2.0 1057.0
 158.3 1055.0 2525.0 2525.0 1000.0
 158.4 1057.0 1055.0 2525.0 2525.0 1000.0
   8.0 3582.0 3582.0 3582.0 3582.0    1.0 2.222
Anything after the second half matrix       <----as it says is ignored
__________________File ends above this line_____________________________________

After creating the matrix file, copy and paste the data into the input window on the Genepop form. Choose sub-option 9 to run the Isolde program, fill in the parameters and submit for processing.

Program ISOLDE. This program does three things when run on an appropriate matrix file :

  1.  It computes a regression of Fst or Fst/(1-Fst) estimates to either geographic distances or its natural logarithm. The interpretation of regressions of Fst/(1-Fst) is discussed in Rousset (1997). As detailed there, samples at small geographic distances are not expected to follow a simple general theory, so the program asks for a minimum geographical distance. Pairwise comparisons of samples at larger distances only are used to estimate the regression coefficient.
  2.  it computes "Mantel's tests" (Mantel, 1967). Three aspects of such tests must be distinguished: the permutation procedure which is used to determine the distribution of the test statistics, the test statistics itself, and the definition of the rejection zone. (i) The principle of Mantel permutation procedure is to permute lines (or columns) of the (semi) matrix. This program does such permutations, which can provide the distribution of any statistics under the null hypothesis of independence between the two variables (here, genotype counts and geographic location). Whatever the statistics used, the test will be "exact" if its distribution is determined in this way. (ii) Mantel considered a particular statistics "Z" and approximations for its distribution. Instead, this program uses a rank correlation coefficient and no approximation. The rank correlation may be more "robust" - however, no study has compared such statistics for detecting isolation by distance. (iii) Isolation by distance will generate positive correlations between geographic distance and estimates of Fst/(1-Fst) or of Fst. But the ISOLDE program can be used to compute other Mantel tests where the alternative hypothesis of interest is likely to generate a negative correlation. Hence the results of two one-sided tests are provided.
  3.  It writes the result of the analyses in an " output " format and in a "graphic" format. The latter contains the data in the following tabular format: 

    1   0.001   <-- first pair of samples
  4. 2   0.001   <-- second pair of samples
    50  0.009   <-- and so on
    the first column containing geographic distance or their logarithm, the second Fst/(1-Fst) or Fst estimates. This "graphic" file can be used as input file by other programs such as EXCEL or Mathematica to plot the results of the analyses. You can also use EXCEL and this input file if you want to plot "Log M" estimates against Log distance as in Slatkin (1993) since  M=(1-Fst)/(2 Fst).

The ISOLDE program can obviously be run on other kinds of matrices provided Mantel's permutations are appropriate. Do not use the "logarithm" option if some values in the second semi matrix are negative or null. Do not use the Fst/(1-Fst) option if you use ISOLDE for a Mantel test not related to isolation by distance. In any cases, you just have to follow format given above.

Last Modified on December 1, 2020 by Eleanor Morgan
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