Constitutional Of Partial Thrale Cross Designs And Their Analysis

Construction of Partial triallel cross designs and their analysis.rnAddisu Jember.rnTwo new methods of construction of mating designs for partial triallel cross for p > 3 lines arernproposed. In the first method we have used a Latin square of order 𝑝, where 𝑝 a prime or powerrnof a prime is, then bordered rows and columns of the Latin square by the directrix of the Latinrnsquare. Each cell together with border elements gives a design for Partial triallel cross afterrneliminating the elements of directrix. In the second method, first we obtain initial blocks and thenrndevelop cyclically mod (p) these initial blocks, we get block designs for partial triallel cross.rnThese designs are found to be optimal in the sense of Das and Gupta (1997). Diallel matingrndesigns are useful in estimating the additive and dominance genetic variances only under thernabsence of epistatic effects. If epistatic effects are present the variance component due torninteraction between additive and additive (𝜎𝐴𝐴rn2), additive and dominance (𝜎𝐴𝐷rn2) and dominancernand dominance (𝜎𝐷𝐷rn2) can be estimated by raising only Triallel Crosses. However, the numberrnof all possible three way crosses would be unmanageable even for a moderate number of lines 𝑝.rnTo handle this situation, we are giving here two new methods of constructing mating design forrnpartial triallel cross. A method of analysis of these mating designs is also shown by numericalrnexample.rnKeywords: directrix of Latin squares, mating designs, triallel cross, partial triallel cross,rngeneral effects of first kind, general effects of second kind

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