GENERAL AND EXACT INBREEDING COEFFICIENT OF MAIZE SYNTHETICS DERIVED FROM DOUBLE CROSSES.

Abstract

Developing synthetic varieties (VS’s) using traditional methods is a difficult task. Even using few potential parents, the possible VS’s would be too many to form and evaluate. Hybrid parents can be used to find a solution for this problem. In this research, the use of d double crosses (CD’s) as parents of a VS (SinCD) was evaluated, instead of using 4d lines (SinL) to generate synthetics. Inbreeding coefficients (CE’s) have been derived from SinCD (FSinCD’s); however, their accuracy and generality degree have not been established. The hypothesis of this study was that the current FSinCD’s are restricted and inaccurate. Because the performance of synthetics is related to their CE, the objective of this study was to derive a general and exact FSinCD. It was assumed that the initial 4d lines were not relatives and that their CE (F) was 0?F?1. The sample of each double cross (m plants) was initially visualized as a “large” series of x groups of 16 plants each (16 genotypes of the genotypic array of the respective CD). As a result of the random mating that generates a SinCD, each CD produces: 1) 16x?m selfpollinations; 2) (15)(16)x?15m direct and reciprocal crosses; and 3) 256x(x?1)?m(m?16) crosses between the x groups. The CE’s of these three sets are 1/2, (3?4F)/30, and (1?F)/8, respectively, and it was concluded that the exact CE for “large” m is FSinCD?(1?F)/8d. Based on these results, the general and exact FSinCD was derived for any value of m.