The theory of linkage in polysomic inheritance

Abstract

The paper is concerned with the combinatorial and statistical problems arising in the theoretical analysis of linkage in polysomic inheritance. The second section gives a method of enumerating the heterogenic genotypes capable of being composed with given numbers of genes. In the third section these are classified in isomorphic sets, which correspond with the partitions in two or more dimensions of the numbers 4 and 6. The members of an isomorphic set can be generated by systematic gene substitution from any member of the set, and in consequence yield populations of gametes with equivalent frequencies. An aspect of the subject which has escaped attention is the multiplicity of the modes of gamete formation. Their enumeration is discussed in §4, and leads to the specification in §5 of the gametic matrices for the 16 sets or pairs of isomorphic sets arising in tetrasomics with two linked loci. In most cases the rank of the matrix is less than 11, so that the gametic series from the genotype concerned is deficient in respect of some of the information sought. Different sets of genotypes may be used to supplement one another’s information. The final section discusses in outline the statistical problem of estimating the frequencies of modes of gamete formation from observed gametic series.