Title:
A gene-free formulation of classical quantitative genetics used to examine results and interpretations under three standard assumptions.

Abstract:
Quantitative genetics (QG) analyses variation in traits of humans, other animals, or plants in ways that take account of the genealogical relatedness of the individuals whose traits are observed. "Classical" QG, where the analysis of variation does not involve data on measurable genetic or environmental entities or factors, is reformulated in this article using models that are free of hypothetical, idealized versions of such factors, while still allowing for defined degrees of relatedness among kinds of individuals or "varieties." The gene-free formulation encompasses situations encountered in human QG as well as in agricultural QG. This formulation is used to describe three standard assumptions involved in classical QG and provide plausible alternatives. Several concerns about the partitioning of trait variation into components and its interpretation, most of which have a long history of debate, are discussed in light of the gene-free formulation and alternative assumptions. That discussion is at a theoretical level, not dependent on empirical data in any particular situation. Additional lines of work to put the gene-free formulation and alternative assumptions into practice and to assess their empirical consequences are noted, but lie beyond the scope of this article. The three standard QG assumptions examined are: (1) partitioning of trait variation into components requires models of hypothetical, idealized genes with simple Mendelian inheritance and direct contributions to the trait; (2) all other things being equal, similarity in traits for relatives is proportional to the fraction shared by the relatives of all the genes that vary in the population (e.g., fraternal or dizygotic twins share half of the variable genes that identical or monozygotic twins share); (3) in analyses of human data, genotype-environment interaction variance (in the classical QG sense) can be discounted. The concerns about the partitioning of trait variation discussed include: the distinction between traits and underlying measurable factors; the possible heterogeneity in factors underlying the development of a trait; the kinds of data needed to estimate key empirical parameters; and interpretations based on contributions of hypothetical genes; as well as, in human studies, the labeling of residual variance as a non-shared environmental effect; and the importance of estimating interaction variance.