Optimal Designs for M-Allel Crosses in One and Two-Way Setting

Abstract

Mating design involving multi–allele cross m (≥2) lines play very important role to study the genetic properties of a set of inbred lines in plant breeding experiments. A most common mating design in genetics is the diallel cross which consist ofv=p(p-1)/2 crosses of p inbred lines such that the crosses of the type (i × j) = (j × i) for i,j = 1,2, ..., p.This type of mating design is called complete diallel cross (CDC) method 4 of Griffing[2]. The concept of CDC can be easily extended to double cross designs. A double cross design is obtained by crossing two unrelated F1 hybrids symbolized as (i ×j) and (k × l), where i ≠j≠k ≠l ≠i, are 4 parents and (i× j) and (k × l) are two F1’s[3]. Let nc denote the total number of crosses (experimental units) involved in an m-allele cross experiment, where m=2 or 4. Generally double cross experiments are conducted using a completely randomized design (CRD) or a randomized complete block (RCB) design involving some or all nc crosses as treatments. The number of crosses in such a mating design increases rapidly with increase in the number of lines. It leads to an overall inefficient experiment. It is for this reason that the use of incomplete block design as environment design is needed for double cross experiments [3].