Variance components for statistical genetics: applications in medical research to characteristics related to human diseases and health.

RA Fisher introduced variance components in 1918. He synthesized Mendelian inheritance with Darwin's theory of evolution by showing that the genetic variance of a continuous trait could be decomposed into additive and non-additive components. The model can be extended to include environmental factors, interactions, covariation, and non-random mating. Identifiability depends critically on design. Methods of analysis include modelling the mean squares from a fixed effects analysis of variance, and covariance structure modelling, which can be extended to multivariate traits and has been used to study ordinal traits by reference to postulated, unmeasured, latent 'liabilities'. These methods operate on dependent observations within independent groups of the same size and structure, and therefore require balanced designs ('regular' pedigrees). A multivariate normal model handles data in its generic form, utilizes data efficiently from all members of pedigrees of unequal size or varying structure, accommodates individuals missing at random, and allows flexible modelling with tests of distributional assumptions and fit. Most analytical methods use least squares or maximum likelihood under normal theory. Robust methods, scale transformation, ascertainment, path diagrams and correlational path models (popular in behavioural genetics through addressing nonrandom mating and social interactions), 'heritability', and the contribution and limitations of statistical modelling to the 'nature-nurture' debate, are discussed.