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Multiple-allelic incompatibility factors at one locus or at two unlinked loci were reported almost 50 years ago as the typical systems determining self-sterility and the patterns of interstrain mating of the higher Basidiomycetes. 1 2 The concept of multiple series of alleles at one locus or at two independent loci was accepted for almost 30 years, and during this time, the origin of new, nonparental incompatibility factors was attributed to mutations.3 This acceptance was challenged by Papazian,4, 5 whose results, with the A incompatibility factor of S. commune, related the origin of nonparental factors to meiosis by the demonstration that new factors, when crossed, yield among their progeny the original factors at a low frequency. A later study6' 7 showed beyond any doubt that nonparental factors originate through recombination, the nonparental factors of any cross always assignable to two classes, each self-sterile but cross-fertile with the other. The A incompatibility factor was found to be made up of two linked loci, each comprising a series of alleles, with compatibility of two A factors being dependent upon allelic difference(s) at either locus or at both loci. Later studies with Coprinus lagopus8' 9 and Collybia velutipes'0 provided a similar picture.A study of the B factor of S. commune was initiated in 1955 to test the B factor against the basic two-locus model found in the A factor,6 and preliminary results with three B factors showed a high degree of structural similarity between the A and B factors. Analysis of the progency of additional pairings of B factors has brought this generalization into question, however, since (a) recombinants were detected in fewer (7 of 23) random crosses between B factors than was expected, and (b) the interrelations between these factors could not be explained simply on the basis of a two-locus model.'1 A close parallel to this case was found in Pleurotus ostreatus12, 13 and Pleurotus spodolecus.10' 14 Until recently, the further study of the structure of the B factor was impractical because of the low frequency of recombination, in the absence of any closely linked, bracketing markers that could afford some selective enrichment for intrafactor recombinations. The recovery and characterization of a secondary mutation in the Bf3 locus,'5 which gave one mating response when mated with a B factor having the same Ba allele and a different response when mated with a B factor having an unlike Ba allele, provided a new means of discrimination of B-factor structure and stimulated the renewal of the study. The availability and use of this mutant was expected to increase greatly the efficiency of the work, since it should permit the identification of alleles at the Ba locus of the entire collection of B factors.The main objective of this study was to clarify the structure of the B factor and to seek a general model for the structure and function of the factor. Materials and Experimental Procedures.-The strains of S. commune used were either the original strains from a world-wide...