Genetic traits are passed from parents to their offspring in the form of genes. We can think of genes as a data lookup table read by the software of life to determine what traits to develop.

Each gene comes in pairs of alleles. It can have one of two possible chemical structures, which we geeks can think of as a bit of digital data. Its value can be either 0 or 1.

Now, the reason for the genes coming in pairs is to allow us to inherit a genetic bit of data for each gene from both the father and the mother. Naturally, the father and the mother have genes which come in pairs, just like ours do. For each gene, one allele comes from the father, one from the mother.

Furthermore, which of the two alleles is inherited for each gene is "decided" randomly. That is why siblings' genetic code is similar but not identical.

If we continue the 0/1 model of genes as a lookup table, then each gene can have the binary value of 00, 01, 10, or 11. How the "software" interprets these values varies from gene to gene (though it is always the same for the same gene).

Most commonly, genes are interpreted according to the recessive/dominant formula (the other common formula uses the "incomplete dominance" model). Mathematically, this uses Boolean or in which the recessive gene equals to Boolean 0, the dominant gene corresponds to Boolean 1. That results in the following truth table:

00 = 0
01 = 1
10 = 1
11 = 1

In other words, whenever the dominant gene is present, it "wins". The recessive trait only manifests if inherited from both parents.

That makes the recessive trait rarer than the dominant trait. Assuming both 0 and 1 are equally distributed, the recessive trait will manifest in only 25% of the population, even if it is present in the genes of 75% of the population.

Interestingly, there is a philosophical point hidden there somewhere suggesting that the gentle, the weak, the soft, the meek, and such, is better fit to survive than the strong, the powerful, the arrogant, the pushy, and the like.

Why?

Consider a madman keen on destroying a dominant trait, for example, some Hitler killing off all people with brown eyes (dominant trait). That would be the end of brown eyes. If, on the other hand, he killed off all blue-eyed people, the next generation of children would promptly restore blue eyes.

NOTE: As the mathematician said in Jurassic Park, nature finds a way. There is a genetic phenomenon called mutation that would eventually restore brown eyes to existence.

Recessiveness (and, to some extent, dominance) of genes was first noted by Gregor Mendel in his pea plant experiments. It's a gross oversimplification, but entirely understandable given the lack of knowledge about the inherent basis for genetic traits and biochemistry. In most cases, a recessive gene will encode the absence of a protein (well, more usually it'll be the reduction in functionality of the gene rather than its complete absence - imagine an enzyme with a malformed active site, for instance). If (and this is a fairly big if) the level of the activity of the enzyme is not critical (so only a relatively small amount of functional enzyme needs to be present compared to the amount usually present) then carrying one copy that fails to encode a functional enzyme will still leave you with 50% of the normal level and everything will still work. With two copies, the level will drop further, the pathway will no longer work properly and a new phenotype will be expressed. This is classical recessiveness.

On the other hand, what if the concentration of the enzyme is important? As above, assume that our "recessive" is completely non-functional. With no copies of the recessive, we will have 100% of the normal level of enzymatic activity. With two copies of the recessive, we will have 0% of the normal level of enzymatic activity. With one copy of the recessive, we will have 50% of the normal level. This may be sufficient to have a phenotypic effect, which may well be halfway between the other two phenotypes. This is usually called incomplete dominance, but depends more on the characteristics of the recessive than anything else.

For an even more convoluted (but still observable) example, imagine a locus at which we have three alleles. A is normal. a is a typical recessive, reducing activity of the enzyme encoded at the locus by 50%. a' is a completely non-functional mutation. AA will be "normal", Aa will be "normal" (the activity level is 75% of normal), aa will be the "recessive phenotype" (the activity level is 75% of normal). However, Aa' will also be the "recessive phenotype". a' is dominant to A which is in turn dominant to a, but a' and aa both give the same phenotype.

gene interaction confuses things even further. Tubulin, the protein which polymerises into microtubules, is made up of two subunits (alpha and beta) encoded for by different genes. We'll call them A and B. A recessive mutation forms malformed subunits that are capable of binding to the other subunit but not of polymerising. AABb will have 50% of normal tubulin levels - 50% of the beta subunit will be malformed and therefore 50% of the tubulin formed will be unable to polymerise. AaBB will be the same. AAbb will have no functional tubulin and the organism will die. aaBB is the same. So far, we appear to have two recessive lethal mutations. However, AaBb will only have 25% of the normal levels of functional tubulin (simple probability) and will also be lethal.

The idea of a recessive gene is only really useful when genes are treated like black boxes. Nowadays we have sufficient understanding of the processes involved that different alleles can be catagorised on the basis of their biochemical effects. Trying to map these onto "recessive" and "domainant" just confuses people when things start behaving in ways that they don't expect. Even something thought of as a classical recessive may turn out to be significantly more complicated. Can't we stop trying to oversimplify things?