In this the first of an anticipated four paper series, fundamental results of quantitative genetics are presented from a first principles approach. While none of these results are in any sense new, they are presented in extended detail to precisely distinguish between definition and assumption, with a further emphasis on distinguishing quantities from their usual approximations. Terminology frequently encountered in the field of human genetic disease studies will be defined in terms of their quantitive genetics form. Methods for estimation of both quantitative genetics and the related human genetics quantities will be demonstrated. The principal target audience for this work is trainees reasonably familiar with population genetics theory, but with less experience in its application to human disease studies. We introduce much of this formalism because in later papers in this series, we demonstrate that common areas of confusion in human disease studies can be resolved be appealing directly to these formal definitions. The second paper in this series will discuss polygenic risk scores. The third paper will concern the question of “missing” heritability and the role interactions may play. The fourth paper will discuss sexually dimorphic disease and the potential role of the X chromosome.

Background: With over a hundred years of history, most fundamental results in quantitative genetics are well known to most population genetics students, yet there is often considerable confusion concerning precise definitions and assumptions, particularly when interactions may exist. The connections between quantitative genetics and human disease genetics can be obscure to many.

Methods: Fundamental quantitative genetics quantities are derived as conditional expectations of phenotype. Genetic, environmental, additive, dominance and interaction effects and their associated variances are defined, with key results explicitly derived. The effects of linkage disequilibrium and methods to account for it are examined. Methods to estimate and interpret heritability are discussed.

Results: Application of quantitative genetics quantities are extended to binary traits with special emphasis on translation between commonly estimated human disease genetics quantities and their corresponding quantitative genetics representations.

Conclusions: The distinction between modeling definitions and assumptions is made clear. Methods to unite human disease genetics and quantitative genetics are elucidated. Methods to account for linkage disequilibrium and other forms of interaction are described.

quantitative genetics, human disease, linkage disequilibrium, liability model, genetic interaction