(adapted from the original Genepop v4.0 documentation written by Francois Rousset)

This sub-option allows estimation of gene frequencies when a null allele is present. Different methods are available: maximum likelihood, maximum likelihood with genotyping failure, and Brookfield's (1996) estimator, which differences are explained in Appendix 1.

Genepop takes the allele with the highest number for a given locus across all populations as the null allele.20 For example, if you have 4 alleles plus a null allele, a null homozygote individual should be indicated as e.g. 0505 or 9999 in the input file.

The default estimation method is maximum likelihood, using the EM algorithm of Dempster et al. (1977). Apparent null genotypes may also be due to nonspecific genotyping failures. Joint maximum likelihood estimation of such failure rate ('b') and of allele frequencies is available by selecting the appropriate option on the input form. The estimator of Brookfield is also available for selection on the input form. Confidence intervals for null allele frequencies are computed for each locus in each population. Their coverage probability cannot be modified on the web version, however it is possible to alter these confidence intervals using the PC version of Genepop available from http://kimura.univ-montp2.fr/~rousset/Genepop.htm.

The output file for this option may contain:

- For the maximum likelihood methods, estimated allelic frequencies and predicted numbers of homozygotes and of heterozygotes with a null allele. For example, in an output such as

of the seven (2.7046 + 4.2954) apparent homozygotes for allele 1, it is predicted that 4.2954 are actually heterozygotes for allele 1 and for the null

allele. This predicted value is the expected, or average, number of such heterozygotes over different samples with the same number of apparent genotypes,

under the assumptions of the model. - a summary locus-by-population table of estimates of null allele frequencies.
- a summary locus-by-population table of estimates of genotyping failure frequencies ('beta'), if applicable.
- A table of confidence intervals for estimates of null allele frequencies.

Note that there may be insuffcient information to compute estimates and/or confidence intervals: not enough alleles in the sample, for example. These are indicated by the message No information. Sometimes the point estimate can formally be computed but the computed CI is not meaningful. This happens for example in case of heterozygote excess, and generates a (No info for CI) warning (if all pseudo-samples generated by some resampling technique show an heterozygote excess, all pseudo-estimates of null allele frequency will be zero and there is no information to construct a non-null CI from this distribution).

This sub-option "diploidizes" an haploid data set. For example, the line

popul 1, 01
02 10 00

of an haploid dataset with 4 loci, will become

popul 1, 0101 0202 1010 0000

Only haploid data are thus modified in a mixed haploid/diploid datafile. The new data set is returned via the web browser (or email) which you can save as a text file.

Note that there may no longer be any need for this option for further analyses with Genepop (except perhaps as a preliminary to le conversions, option 7), since Genepop 4.0 now performs analyses on haploid data without such prior 'diploidization'.

correspondence between the old and the new numbering is indicated in the returned file above the new dataset.This option was originally introduced in Genepop because for some options, the memory space required depends on the highest allele number. I don't expect this to be a cause of concern now. However, it may be necessary to use this option to convert data before using the Linkdos program.

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

**Please report any problems or bugs that you encounter with the web version
of this option to
Eleanor Morgan**

*Last Modified on
September 24, 2009
by Eleanor Morgan*