next up previous
Next: Genetic Control of Up: No Title Previous: Evolutionary Computation

Variation and Variability

To accommodate a discussion of genetic representations and variational properties of the phenotype in the language of evolutionary biology, it is essential to clearly distinguish between "variation" and "variability", even though these words are often used synonymously in the 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 the way it changes in response to environmental and genetic influences. In the field of evolutionary computation it became clear that the way mutation and/or recombination changes the behavior of a model is determined by the way the model is coded or represented in the program. The genetic representation of a character thus determines the variability of the phenotype and not directly the genetic variation within populations. In this context the concept of developmental constraints (sensu Maynard-Smith et al. 1985; Schwenk, 1995) can be understood as the limits of variability of traits caused by their representation or coding 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 (Falconer, 1981; Barton and Turelli, 1989). 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, (Clayton and Robertson, 1955; MacKay et al., 1992), or in the case of more than one trait, by the mutational covariance matrix, M (Lande, 1975). Each of these quantities requires elaborate experimental designs to be estimated. An indirect method to assess the variability inherent is a body design is to determine the number and range of independently varying morphogenetic parameters, also called biological versatility (Vermeij, 1971).

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 and Lande, 1994; 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 dis-equilibrium among them (Bulmer, 1980; Turelli, 1988). 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 (see below). However, variability is under genetic control and may thus evolve.



next up previous
Next: Genetic Control of Up: No Title Previous: Evolutionary Computation



Thu Oct 5 13:21:55 EDT 1995