The word dominance, in the context of genetics, has been used for long time applied to characters or to alleles. A dominant character masks the expression of an alternative form. This loose definition would even apply when these alternatives are not determined by alleles of the same locus. In turn, a dominant allele refers to an alternative version at the same locus. This dual usage has led, as expected, to some confusion and shows how statistics can complement verbal definitions. Mendel, the pioneer of genetics, did not know the bases of the phenomenon of dominance.
Nor was he completely certain to look at characters defined by alleles. But the ubiquity of the phenomenon caused him to elevate his observations to the category of laws, that went, unfortunately, unnoticed until they were rediscovered decades later. Today, dominance and recessivity are concepts commonly used and not only by geneticists. Yet a question remains: do we really understand which are the mechanisms of dominance?
Dominance can be considered as a property of either characters or alleles in the living organisms. This must have an explanation in terms of their intrinsic architecture, which has been shaped by natural selection. To what extent dominance is a product of physiology or of evolution has been subject to much debate that is still ongoing. Classical genetics has considered dominance mainly as a result of intra-locus interactions. Indeed, simple mathematical models of positive and negative auto-regulatory circuits provide support to this notion. However, other models show that dominance can also result from the interaction of several loci (epistasis). This points to an intimate connection with epistasis, to such an extent that one can talk about epistatic dominance effects. Stemming from this, the word dominance in some parts of the text is not used with its classical meaning.
Dominance, from a phenomenological point of view, seems to have a general source: the existence of non-linear relationships between the genotypic and phenotypic values. However, the mechanisms generating these non-linearities are diverse. Models of gene expression, deterministic or stochastic, show the existence of strong non-linearities in the relationship between transactivator concentration and the product of transcription. The beautiful patterns of pigmentation of the butterfly wings are considered here as generated by stochastic processes producing sharp (sigmoidal) boundaries. However, similar events are probably underlying the action of transcription factors involved in developmental processes whose mutations are responsible for many human diseases.