Schmalhausen and Waddington were perhaps the first to clearly see that epistatic interactions between genes can produce genetic control over genetic variability, and to apprehend the theoretical implications of this (Schmalhausen, 1949; Waddington, 1942). Per definition, epistasis is the influence of the gene at one locus on the effects of alleles at other loci (for a way to measure epistatic effects see Cheverud and Routman, 1995). It thus reflects the fact that the expression of genetic variation is under the influence of other genes. Evidence that variability of phenotypic traits is under genetic control comes from research on the phenomenon of "canalization." The term was first introduced by Waddington (1942) to describe the tendency of development to produce clearly distinguished tissue and organ types. However, the concept had only limited impact on developmental biology, but became important in quantitative genetics. It describes the fact that mutant phenotypes often show much more variation than the wild type phenotype. Some of this variation is genetic variation which was "suppressed" in the wild type genetic background (for a recent review, see Scharloo, 1991). Selection experiments suggested that the sensitivity of a trait to genetic variation can be decreased by artificial stabilizing selection (Rendel, 1967; Scharloo, 1988) or increased by artificial directional selection (Lazebnyi et al., 1991). Recently it has been shown that the average effect of P-element induced mutations on life history traits in Drosophila is negatively correlated with the influence on fitness of the trait. The stronger the impact on fitness the smaller the average effect of a new mutation (Stearns and Kawecki, 1994).
Evidence for genetic control over phenotypic variability is of capital interest to evolutionary theory (Scharloo, 1991). This literature shows that evolution not only produces the fixation of spontaneously generated variation, but it can can also change the "rules" under which heritable phenotypic variation is produced, i.e. the variability of the traits itself can evolve. The genome has control over the "allocation" of genetic variance to phenotypic characters. Some characters that were variable can become fixed (Riedl, 1975, Stebbins, 1974), while others may become integrated into a tightly coupled complex of characters (Stearns, 1993) or others may gain variability after a developmental constraint was broken (Vermeij, 1970, 1973, 1974).
Population genetics has been developed to understand the dynamics of genetic variation. However, the issue here is the evolution of the variability of characters. So the question is how to describe the variability of a trait and its evolution in population genetic terms in order to link the theory of evolvability to the existing apparatus of evolutionary theory. Genetic variability of a character is determined by two factors: the rate of mutation of genes influencing the character and the effect of the mutations on the state of the character. Mutation rate is a standard parameter in population genetic model and there is also theory on the selection forces acting on mutation rate (Eshel, 1973; Altenberg and Feldman, 1987). The effects of mutations can either be arbitrarily assigned to individual alleles, or described as the distribution of mutational effects (Kimura, 1965). Mathematically, the relationship between the genotype and the phenotype is a function f, which assigns to each genotype G the average phenotype P (averaged over so-called 'environmental' variation) 
(or if there is genotype-environment interaction
).
The idea of a genotype-phenotype mapping function has been used in quantitative genetics, for instance in the study of genetic canalization (Rendel, 1967, Scharloo, 1987), multivariate mutation selection balance (Wagner, 1989a), the evolution of pleiotropy (Altenberg, 1995a), the study of epistatic effects (Gimelfarb, 1989, Wagner et al., 1994), and in evolutionary algorithms (for instance: Altenberg, 1994; Banzhaff, 1994; Schwefel, 1981). The genotype-phenotype mapping function describes how genetic variation is translated into phenotypic variation and is thus a way of describing how the phenotype is represented in the genotype. The evolution of genetic representations can thus be modeled as the influence of selection on the genotype-phenotype mapping function.