Genetical Interference in Maize

Abstract

BACK-CROSS linkage data in maize involving three or more genes have been analysed to examine them from the point of view of consistency with Owen's theory^1–3 of genetical recombination. As a measure of interference, the Kosambi coefficient³ K has been used. In a back-cross experiment involving two segments AB and BD, let y ₁, y ₂ be the recombination values for each segment, y ₁₊₂ the recombination value for the entire segment AD, and y ₁₂ the frequency of simultaneous recombination in both segments, then K is given by y ₁₂/2y ₁ y ₂ y ₁₊₂. Kosambi⁴ has proposed the relation 2y = tanh(2x) to relate the map distance x and the recombination fraction y between two loci. When K = 1, Kosambi's relation is satisfied. Owen^1–3 has expressed x and y in terms of a metric u in which interference is uniform, and has postulated the interference function f(u) = 4u exp(−2u) as an adequate fit to the observed data. Assuming this form for the interference function, K = 1 at the metrical mid-arm of long chromosome arms (≥ 40 cM.). The map-length of a segment from centromere to mid-arm is then given by where T is metrical arm-length¹.