How many tough-rachis mutants gave rise to domesticated barley?

It is commonly agreed that cultivation of wild barley preceded the selection of the domesticated, non-brittle spike type. However, how common was wild barley cultivation before domestication and how many domesticated mutants gave rise to the barley crop could not be inferred from botanical and archaeological evidence. Some clues, nevertheless, can be obtained from the pattern of allozyme diversity in wild and cultivated barley obtained by Kahler and Allard (1981). Parallel variation, in terms of number of alleles per locus and frequency of the various alleles, was found in wild and domesticated barley. This similarity has been taken as an indication of multiple domestications and the frequency of the rarest alleles has been used to estimate that about 100 tough-rachis different mutants were necessary for the inclusion of the allozyme diversity of the wild barley in the domesticated crop. Assuming mutation rate of 10^-6 in the locus governing tough rachis, the plant population required to generate these 100 mutants in one year would extend over about 200 hectares, or 10 hectares if the 100 mutants have been formed over a period of 20 years. The simplified calculations suggest that prior to domestication cultivation of wild barley was not a common practice.