Biometrical Parameters of Self-fertilizing Diploid Populations1

HE theoretical aspects of diploid populations where all reproduction is by self-fertilization have been considered by several workers (ANDERSON and KEMPTHORNE 1954; COCKERHAM 1954,1963 ; HORNER, COMSTOCK and ROBINSON 1954; DEMPSTER 1955; KEMPTHORNE 1956, 1957, 1963; HORNER and WEBER 1956; GATES, COMSTOCK and ROBINSON 1957; HANSON and WEBER 1961). Several of these papers have indicated parametric representations of the biometrical aspects of quantitative traits of such populations. The purpose of the present paper is to study the biometrical aspects of self-fertilizing populations by an approach suggested by DEMPSTER (1955). The parametrizations obtained will be somewhat more general than results obtained previously. Of the work mentioned previously, only GATES et al. (1957) considered in a detailed way the consequences of the genetic phenomenon of linkage. The present work will have one weakness in common with the remainder of the previous work cited. in that linkage will be ignored. Bnsic notation: When all reproduction is by self-fertilization with no selection, a population can be considered as an aggregate of sub-populations with each subpopulation including all the progeny of one individual in a certain generation. Thus, we will consider initially a subpopulation originating from a single individual in generation zero, and later the overall population will be considered. A diploid genotype involving n loci may be symbolized as