Relationship of cyst nematode gene frequencies to soybean resistance

Soybean (S, Glycine max (L.) Merr.) lines with relatively few cysts of soybean cyst nematode (CN, Heterodera glycines Ichinohe) populations are usually called CN-resistant. The phenotype of number of cysts per plant is of the CN-S (Cyst Nematode-Soybean) association and determined by the interactions of genes for avirulence-resistance. The acronym "alins" was proposed for these alleles for incompatibility, with "xalin" representing the interaction X of one microsymbiont malin with its host h-alin. These alins are dominant in the gene-for-gene model but may be mostly recessive with CN-S. Definitive genetic studies have been hindered by the heterogeneity of sexually reproducing CN populations and lack of the appropriate genetic models. Loegering's abstract interorganismal genetic model was modified so that one model represented all four possible interactions of dominant-recessive alins for an incompatible phenotype. This involved redefining the Boolean algebra symbol 1 to represent both the alins AND their frequencies. The model was used to derive the relationship: {ie893-01} where the expectation E of cysts (of any CN-S combination, as proportion of number of cysts on a check cultivar) is proportional to the product Π of CN genotypic frequencies expressed as functions of m-alin frequencies. Each m-alin is at a different locus, i.e., {ie893-02}. The number of terms multiplied for each CN-S is equal to the number of alins in the S line (or F2 plant). There are too many unknowns in the equation to solve for any of them. The relationship does explain the continuous distributions of phenotypes that were nearly always observed. Basic genetic principles were used to concurrently derive the models and to obtain discontinuous distributions of numbers of cyst phenotypes in segregating generations due to one recessive alin in a CN-"susceptible" soybean line.