# HELP WITH GENEPOP

## OPTION 3 - Population differentiation

(adapted from the original Genepop 4.0 documentation written by Francois Rousset)

All tests are based on Markov chain algorithms. The Markov chain parameters are controlled exactly as in option 1.

### Suboptions 1 or 2 - (genic differentiation)

These are concerned with the distribution of alleles in the various samples. The null hypothesis tested is Ho: 'alleles are drawn from the same distribution in all populations'. For each locus, the test is performed on a contingency table like this one:

```
Sub-Pop.  Alleles
1    2   Total
_______
1        14   46   60
2        6    76   82
3        10   74   84
4        4    58   62
_______
Total     34   254  288

```

For each locus, an unbiased estimate of the P-value is computed. The test statistic is either the probability of the sample conditional on marginal values, or the G log likelihood ratio. In the first case, the test is Fisher's exact probability test, and the algorithm is described in Raymond & Rousset (1995a). A simple modification of this algorithm is used for the exact G test. Genepop's default is now the G test.

For sub-option 2, the tests are the same, but they are performed for all pairs of samples for all loci.

### Sub-options 3 or 4 (genotypic differentiation)

These are concerned with the distribution of diploid genotypes in the various populations. The null hypothesis tested is Ho: "genotypes are drawn from the same distribution in
all populations". For each locus, the test is performed on a contingency table like this one:

```                  Genotypes:
-------------------------
1    1   2   1   2   3
Pop:     1    2   2   3   3   3   All
----
Pop1     142  27  0   13  1   0   183
Pop2     149  20  0   11  0   4   184
Pop3     131  12  0   9   0   1   153
Pop4     119  22  1   10  0   0   152
Pop5     120  17  1   10  1   0   149
Pop6     134  18  2   15  0   0   169
Pop7     116  15  1   10  1   1   144
Pop8     214  41  3   14  2   1   275
Pop9     84   17  0   7   2   0   110
Pop10    107  18  0   15  3   0   143
Pop11    134  32  1   21  4   0   192
Pop12    105  26  1   11  1   4   148
Pop13    97   19  2   23  4   0   145
Pop14    95   28  3   19  3   1   149

All:     1747 312 15  188 22  12  2296

```

An unbiased estimate of the P-value of a log-likelihood (G) based exact test is performed (Goudet et al. 1996). For this test, the statistic defining the rejection zone is the G value computed on the genic table derived from the genotypic one (see Goudet et al., 1996 for the choice of this statistic), so that the rejection zone is defined as the sum of the probabilities of all tables (with the same marginal genotypic values as the observed one) having a G value computed on the derived genic table higher than or equal to the observed G value.

For sub-option 4, the test is the same but is performed automatically for all pairs of populations for all loci.

### OUTPUT

Results are returned via your web browser if you select the HTML option for Output Delivery. You can also have the results emailed to you if you choose this option (which is advisable for datafiles with 1) numerous loci or 2) numerous unique alleles for each locus or 3) increased Markov chain parameters). All contingency tables are saved in the output file. Two intractable situations are indicated: empty tables or tables with one row or one column only ('No table'), and tables for which all rows or all columns marginal sums are 1 ('No information'). Estimates of P-values are given, as well as (for sub-options 1 and 3) a combination of all test results (Fisher's method), which assumes a statistical independence across loci. For sub-options 2 and 4, this combination of all tests across loci (Fisher's method) is performed for each sample pair. The result Highly sign.[ificant] is reported when at least one of the individual tests being combined yielded a zero P-value estimate.

Last Modified on December 1, 2020 by Eleanor Morgan

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