The Heritability of All-or-None Traits: Viability of Poultry.

N E of the fundamental steps in any analysis of the inheritance of quan0 titative characters is the partitioning of the total phenotypic variance of the trait under study into it; genetic and environmental portions. The various techniques for this purpose for characters showing continuous or graded types of variation are well known (see WHATLEY 1942). They are based on methods of variance and correlation analysis derived in the main from the studies of WRIGHT (1921), although many phases of the general problem were attacked earlier by WRIGHT (1917) and several other investigators (among them WEINBERG 1909; FISHER 1918 et d.). In the case of characters whose phenotype is expressed in an all-or-none manner these methods do not directly apply. However, special techniques based on the inverse probability transformation have been used in this connection by WRIGHT (1934a, 1934b, 1943), while more recently LUSH, LAMOREUX and HAZEL (1948) considered the problem in a more direct relationship to applied animal breeding practice. Reference to the methodology and results of this investigation will be made in the course of discussion. It may also be noted that a t least one other attempt a t what may be interpreted as the estimation of heritability of an allor-none trait (multiple births in cattle) is on record, an attempt which, however, did not consider fully the difficulties of application of the analysis of variance to binomial data ( KORKMAN 1948). I t is actually possible to derive a simple technique for dealing with all-ornone data by considering certain properties of the “degree of heritability,” which for quantitative characters may be defined as the proportion of the phenotypic variance due to additively genetic differences between individuals. The purpose of this communication is to describe a method of approximate determination of the degree of heritability of traits expressed in an all-or-none manner, and to discuss briefly the significance of the results obtained. The derivation presented is applied to raw percentage data as contrasted with similar formulas developed by WRIGHT (Zoc. cit.) and applied to transformed data. The problem was suggested by the junior author who also supplied the material, the general solution and actual analysis having been carried out by the senior author, while the responsibility for the presentation and discussion is shared by both.