이면교배에 있어서 블록계획에 관한 연구 : 결측치가 있는 경우

Abstract

Diallel crosses as mating designs are commonly used to study the genetic properties of inbred lines in animal and plant breeding experiments. Suppose there are inbred lines and let a cross between lines and be denoted by Let denote the total number of distinct crosses in the experiment. Our interest lies in comparing the parents with respect to their general combining ability(gca) parameters. The complete diallel cross(CDC) involves all possible crosses among the parental lines with . Sometimes tends to be large resulting in a large number of crosses, and it becomes impractical to carry out even one replication of the diallel cross. In such situations a partial diallel cross(PDC) may be used for carrying out the experiment. The patial diallel cross(PDC) is often used , , distinct crosses where is the constant number of other lines each line is crossed with. Diallel crosses in completely randomized designs have been discussed by several authors, e.g. Kempthorne and Currow(1961), Singh and Hinkelmann and Kempthorne(1963), Hinkelmann(1975), Singh and Hinkelmann(1990). Optimal block designs for complete diallel crosses have been considered by Gupta and Kageyama(1994), Dey and Midha(1996), and Das, Dey and Dean(1998). Singh and Hinkelmann(1995) gave efficient block designs for partial diallel crosses using partially balanced incomplete block designs. Orthogonal blocking of partial diallel crosses was considered by Gupta, Das and Kageyama (1995). When a complete design is used, situations sometimes arise when one or two observations are lost for some reason not necessarily associated with either the response or the particular lines involved in the crosses. Here, we investigate the effects of missing observations randomly scattered throughout the design, on or two observations missing in certain classes of CDC designs. Consider the situation where crosses scattered throughout the initial diallel cross design become unavailable for analysis. The number of distinct configurations of missing crosses and the properties of the resulting designs will depend on the particular diallel cross design under consideration. The line effect comparisons will depend on which crosses are lost, the number of replicates of these crosses in the initial design and the number of crosses common to the blocks affected by the missing observations. In the paper, we derive theoretical results for the loss of one cross from CDC designs based on nested balanced incomplete block designs. We consider the losses in efficiency for a range of such designs and show that, even for these CDC designs, three differences need to be determined. there are several situations to consider when determining the variance of the differences between the pairs of line effects. Different variances are given for pairs of lines consisting of : (1) the two lines in the missing cross (2) one of the lines in the missing cross (3) two lines not in the missing cross. These are listed for a wide range of CDC designs belonging to this class. For other CDC designs, we evaluate the average and maximum variances of pairwise line differences numerically to explore the effects of losing one or two crosses from the initial design. The efficiencies of these comparisons are listed for some of the examples of CDC designs given previously, and it is show that, although overall these designs are fairly robust to losing observations, some specific comparisons may be seriously affected by missing data, particularly in the PDC designs where some crosses do not appear in the initial design structure. In this paper, We studies robustness of optimal block designs for estimating general combining ability() effects against loss of observations in diallel cross. To illustrate the process of examining the effects of losing observations from a diallel cross design. we shall consider the situation where crosses are lost from the optimal CDC block designs.