# Tag Archives: allele frequency

## Natufian Villages, Wisdom Teeth, and Probability

Some of the earliest villages ever discovered were from the Fertile Crescent (modern day middle east).  The culture that inhabited these villages has been dubbed Natufian, and dates to around 12,500 BC.  Two of these villages, Hayonim and ‘Ain Mallaha were relatively close to one another.  At first it would have been reasonable to presume that these villagers bred with one another.  They were close and each one had relatively small populations.  But, it turns out they didn’t, and the reason has much to do with simple probability.

Well, that and wisdom teeth, or the third-molars. The Hayonim people had ‘agenesis’ of the third molar – that is, they never grew in.  But, the ‘Ain Mallaha group nearly all had their third molars.

If it had been true that the two groups interbred, then we’d get a mixing of types – those that had wisdom teeth, and those that didn’t – in about equal proportions.   Therefore, since we don’t have that, there must not have been significant interbreeding.

Sounds reasonable enough.  But, how can I be so sure that IF there was interbreeding THEN the proportion of third molars would in fact be about equal in both groups (or at least spread around a bit more)?

To answer that question we need to go over what an “allele” is.

## Alleles as Soda-Pop

Genes are complicated little buggers.  It isn’t so simple as “this gene codes for that trait”.  Any single gene comes in a number of variations. We call those variants ‘alleles’.

Think of 2 soda cans.  One of them is flavored cherry, the other is flavored grape.  What they have in common is that they are both soda.  The gene is the soda.  But, this gene comes in one of two flavors – or we can say it has two alleles – grape and cherry.

So, an allele is like a flavor.  Sometimes, as is the case with eye color, a change in alleles is no big deal.  It really is much like a flavor in that it causes you no harm to have blue vs. brown eyes.  But, there are times when having a different flavor (allele) does matter, like in the case of polio.

Humans are diploids.  That means that we all have two chromosomes.  We get one from our Father and one from our Mother.  Each of them gave us one allele of each gene, and our ‘genotype’ for that gene (that is, what type of that gene we got) is a pairing of the alleles.  But, here’s the rub.  Our parents each had two alleles of the gene, and we end up with two.  How many possible choices were there for what we could have ended up with?  That all depends.

Let’s say the two allele variants for gene X are A and B.  If Dad had an AA pairing and Mom had a BB pairing, then our only possibility was an AB pairing.   However, if our Dad was AB and our Mom was BB, then we’d have 2 possible choices:  AB or BB.  And it would be a 50-50 chance that we got either one.

Now, if both our parents were AB, then we’d have 3 choices (note that $AB=BA$) but they are not all equally likely.   There’s only 1 AA and only 1 BB, but there are 2 AB’s.  So there is a 25% chance of AA, a 25% chance of BB, and a 50% chance of AB.

If it turns out that the A allele is dominant, then from the outside we’d not be able to tell the difference between someone with AA vs. someone with AB.  Only the BB’s would show any signs.  Again, this is no biggy with something as silly as eye color or handedness, but when it comes to diseases or something life threatening, it certainly is.

## Times Have Changed

Back in ye-olden days, sometime after Darwin did the damage, it was thought that a dominant gene variant, or allele, would, given enough time, simply wipe out a recessive one.  It seemed reasonable at the time.  If there is a negative selection value for a particular trait, evolution should select it out.  That’s how Natural Selection works, right?

Well, no.  As the above calculations show, life ain’t that simple.  If two members of a population have that AB type, where B is a deleterious (or “bad for you”) allele.  Then, there is a 1/4 probability that they will have a child with the negative BB variation.

In other words, no matter how bad a trait can be, it can never be wiped out unless you killed off all of the AB’s along with the BB’s.   But, since the AB’s don’t exhibit the negative trait, nature won’t “know” to select them out.  They pass the test.

## Back to Wisdom Teeth

Given this new information, we can answer the question posed at the beginning with some confidence.  Even though it is totally true that having wisdom teeth grow in in a prehistoric village can spell death (via infection and impaction), it would not do so until after the person reached breeding age.  In fact, wisdom teeth often don’t show up until the early twenties or later.  By then, the person could have had multiple children.

So, if there was breeding going on between these populations (the one without wisdom teeth, and the one with them) then there would have been a lot of mixing.

Even if the first was all AA’s which coded for NO wisdom teeth, and the other was all BB’s which coded for them.  And we allowed the A to be dominant, then we’d still see a ton of variation in both villages.  AA x BB = AB at least half the time.  And then AB x AB = BB 25% of the time.  In just 2 generations you’d have signs of wisdom teeth.  In a few more it would grow since AB x BB = BB 50% of the time.

## Disclaimer

I want to just make one last point.  When I’ve been using the word gene, I mean that almost metaphorically.  It could be that there’s a single gene for eye color (there isn’t), but that isn’t the point.  The point is that there is a gene, or a collection of genes, that code for a trait.  And that there are variants of that gene, or collection of genes, called alleles.  These different alleles combine to give us an array of possibilities.  Whether the trait we’re looking at is coded for by a single gene or a collection is often glossed over because it doesn’t actually make much of a difference from that standpoint.  But, it can seem confusing sometimes to hear “gene” but really be thinking of a collection of genes that work together.