Quantitative genetic analysis of characters in wheat using crosses of chromosome substitution lines (theoretical considerations).

COMPARED to studies based on ordinary homozygous varieties, the use of chromosome substitution lines obtained by means of aneuploid series in Triticum uestiuum L. (SEARS 1944, 1953; UNRAU, PERSON and KUSPIRA 1956; PERSON 1956) permits a more complete, detailed and reliable analysis of the genetic structure of hexaploid wheats (KUSPIRA and UNRAU 1957; SEARS, LOEGERING and RODENHISER 1957; LOEGERING and SEARS 1966). The present paper attempts to show the development of a quantitative genetic analysis of characters in common wheat using triparental groups consisting of three parents, of which one or two are disomic substitution lines, and of the corresponding crosses and some of the backcrosses. The analysis basically follows the scaling test pattern (MATHER 1949) , the obtained genotypic values representing the interaction effects of sets of genes at the level of homologous and/or nonhomologous chromosomes. A preliminary section under the heading Definitions and Concepts is intended to provide the formulation of the simple theoretical foundations underlying the analyses. The symbols of set theory are used in this section, and partly in the subsequent sections (e.g. see KEMENY, SNELL and THOMPSON 1957; LIPSCHUTZ 1964; HALMOS 1965).