Numeric encoding in DNA

Stephen-
That is another question that is somewhat outside my area of knowledge, but I can tell you what I know. Number can be encoded in DNA in several ways. The most basic is that different individuals can have different numbers of copies of the same gene. Our chromosomes have lots of stretches of DNA that have been duplicated, sometimes many times. Something in the DNA replication process screws up, and you end up repeating a section of the chromosome, like a record skipping while you are making a copy of it. So if I have 2 copies of a gene, and you have 12, that is numeric information. Similar, but not necessarily to the point, are tandem repeats such as microsatellites. This is basically a stutter in (usually non-coding) DNA. A section of chromosome might have ATCATCATCATCATCATCATCATC so that is eight repeats. The other chromosome in the same person could have twelve repeats, and someone else could have 23. These things seem to combine a high mutation rate with very little selective pressure, meaning that they can evolve relatively randomly and very quickly, meaning they are very diverse within a population. For that reason they are often used for genealogical reconstructions and such.

Not exactly numeric, but not binary, is gene expression modulation. Genes are not necessarily just "on" or "off." A wide range of factors can turn up or down the expression a particular gene, including the particulars of the interactions of non-coding DNA in the promoter region at the beginning of that gene with the various promoter or repressers , which can themselves vary in concentration and structure. So the production from a gene is not 0 or 1 but rather can vary continuously from 0 to 1.

On the subject of telomeres, what their length determines is the number of times a cell can divide before its line dies out. This does not so much encode longevity, as take a part in determining the tradeoff between ability to heal and cancer risk. The body has many mechanisms that limit the ability of cells to divide rapidly, which reduces the risk of cancers (which are defined in part by their unchecked cell division)
but also limits healing (which requires cell division). Telomeres are one such mechanism. It is important to keep in mind though that there are enzymes that can extend telomeres, even in adult organisms, and most organisms have telomeres that are much longer than is needed for most of their cell lines to continue dividing throughout their lifetimes, and therefore telomeres are not in any meaningful sense coding for longevity.

I am sure there are other mechanisms of numeric encoding in genetic material, but I don't know what they are.

In response to your question about averaging of parental values, I would say this generally does not happen. For highly heritable traits, the mean value of the offspring should be similar to the mean value of the parents, but it is not the case that every individual offspring will be at or near that mean value. This is a point that is actually extremely important. During Darwin's time, there was a Scottish biologist whose name I can't remember now, who showed mathematically that if offspring get the mean value of their parents, Darwinian evolution does not work very well (effectively because variation is constantly being eliminated). Darwin was stumped for at least a while, until it was pointed out that each offspring does not get that mean value, but rather some value in a range centered on that mean. As an example, my brother is taller than either of my parents (even adjusting for sex) I am about the same height as my parents (again adjusting for sex) and my sister is (again adjusting) shorter than either of my parents.

So I am curious why you are asking all these questions about quantitative genetics. I assume you have had some idea for which genetics is a good analogy?

-Dan