Allopolyploidy is a major force in evolution. It is often assumed that if two congeneric species hybridize, there is the potential for allopolyploid formation. We propose a “compatibility hypothesis” which may play a major role in allopolyploidization—that is, only a subset of the many constituent genotypes of two congeners (referred to here as compatible genotypes) are actually able to cross and form a viable hybrid that may lead to an allopolyploid, while other genotype combinations are incompatible and cannot produce viable hybrids. There is considerable evidence for variability in the success of homoploid hybrids based on the parental genotypes; here, we extend the role of the compatibility of parental genotypes to allopolyploid formation. We provide evidence that the compatibility model has played a significant role in allopolyploid formation in natural allopolyploids in Tragopogon (Compositae) and pose the question: is the model more widely applicable to other allopolyploids, including natural formations as well as those produced in agricultural and horticultural systems? There are noteworthy implications of the model; for example, if only a few parental genotypic combinations will yield an allopolyploid, the genetic diversity in a repeatedly formed natural allopolyploid would paradoxically be limited.