To accommodate a discussion of genetic representations in the language of evolutionary biology it is essential to clearly distinguish between variation and variability, even if these terms are often used synonymous in the scientific literature. The term variation refers to the actually present differences among the individuals in a population or a sample, or between the species in a clade. Variation can be directly observed as a property of a collection of items. In contrast variability is a term that describes the potential or the propensity to vary. Variability thus belongs to the group of "dispositional" concepts, like solubility (Goodman, 1955). Solubility does not describe an actual state of a substance, say sodium chloride, but its expected behavior if brought into contact with a sufficient amount of solvent, for instance water. Similarly, variability of a phenotypic trait describes its propensity to change in response to environmental and genetic influences. The representation problem is thus about the variability of the phenotype and not directly about the genetic variation within populations. And the concept of developmental constraints (sensu Maynard-Smith et al. 1985) is about the limits of variability of traits caused by the way they are "coded" in the genome.
As a directly observable property, variation is comparatively easy to measure. Genetic variation in a population is measured by the heterozygosity or the degree of polymorphism. Quantitative phenotypic variation is measured by the phenotypic, genetic and environmental variance or any other statistical measure of dispersion. In contrast, variability is much harder to measure. Genetic variability at the molecular level is measured as mutation rate. Genetic variability of quantitative phenotypic traits is measured by the mutational variance Vm, the average additive genetic variance produced per generation by mutations, or in the case of more than one trait, by the mutational covariance matrix, M. Each of these quantities requires elaborate experimental designs to be estimated.
The relationship between variation and variability is conditional. Clearly, if there is variation in a character it has to be variable, but the reverse is not true. Therefore the study of natural variation can give hints on the pattern of variability as for instance the study of osteological variation suggests the existence of constraints (Alberch, 1983; Rienesl and Wagner, 1992), but it is at best a surrogate of variability.
The genetic variance of a trait, i.e. the raw material of evolution, is a fairly ephemeral property. It depends on the complement of genes currently segregating in the population, the effect of the alleles present and their frequencies. Whenever an allele changes its frequency or gets fixed the genetic variance of the character may change (Bürger Wagner Stettinger, 1989; Turelli, 1988). The same is true for genetic correlations, which not only depend on the alleles segregating but also on the linkage disequilibrium among them (Bulmer, 1980). On the other hand the genetic variability of a character is a property of the genome. It remains the same as long as the complement of loci and the mutation rate is the same and as long as no epistatic mutations have been substituted. However, variability is under genetic control and may thus evolve.
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 (1957) 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 to genetic variation of a trait can be decreased by artificial stabilizing selection (Rendel, 1967; Scharloo, 1988). Most 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 et al., 1995).
Evidence for genetic control over phenotypic variability is of capital interest to evolutionary theory (Sharloo, 1991). This literature shows that evolution by fixation of spontaneously generated variation does not just happen, but that evolution can also change the "rules" under which heritable variation is produced, i.e. the variability of the traits itself can evolve. 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). Perhaps Schmalhausen was the first to clearly see the theoretical implications of a genetic control of variability (Schmalhausen, 1949). His key observations of abundant epistatic effects among mutations is just another way of observing that the genetic variability of a trait is under genetic control. Per definition, epistasis is the influence of the locus at one locus on the effects of alleles at other loci. It thus reflects the fact that the expression of genetic variation is under the influence of other genes.
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 a theory on the selection forces acting on mutation rate (Altenberg and Feldman, 1987). The effect of a mutation can either be arbitrarily assigned to individual alleles, or described as the variance of the distribution of mutational effects. 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).
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) and 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.