DNA and family trees - Yan Wong

Bang Goes The Theory ! BBC Dr Yan Wong

Dr Yan Wong is an evolutionary biologist specialising in computer and mathematical modelling of evolutionary genetics. He is a presenter of the BBC One science programme Bang Goes The Theory and a contributor to More or Less.

Following excerpts are quoted from a highly interesting article on evolutionary genetics by Yan Wong.



Statistics

Just like a surname, or the male lines of descent quoted in the Bible, these generate lineages that shrink or expand rather slowly. That's why we expect the proportion of Smiths in the phone-book to fluctuate only a little from decade to decade.

The surprise comes if we look at inheritance from both parents. Here, the numbers change drastically as the generations go by. For instance, we have two parents, four grandparents, eight great-grandparents, and so on.

Each generation back, we multiply the number by two. This leads to what is called an exponential increase: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and so on.

It's not long before we hit huge numbers. Take the specific case of Jesus and King David.

The number of generations between them is at least 35. Luke lists 42 generations down the male line, and Matthew gives an incomplete list of 27.

These numbers agree reasonably well with an average time between generations of 25 or 30 years - an estimate taken from documented historical records from Iceland and Canada.

So back in the time of David, Jesus would have had at least 2 x 2 x 2 x 2 (35 times); in other words 2^35 - or more than 34 billion potential ancestors. That's far more than the total population of the world, of course.

This is a good illustration of what's been called the "genealogical paradox".

Adam and Eve again!

How far do we have to go back to find the most recent common ancestor of all humans alive today? Again, estimates are remarkably short. Even taking account of distant isolation and local inbreeding, the quoted figures are 100 or so generations in the past: a mere 3,000 years ago.

And one can, of course, project this model into the future, too. The maths tells us that in 3,000 years someone alive today will be the common ancestor of all humanity.

A few thousand years after that, 80% of us (those who leave children who in turn leave children, and so on) will be ancestors of all humanity. What an inheritance!

Yan Wong
Read the entire article in the BBC magazine.