On 05/07/2006, at 6:24 AM, David Hobby wrote:
So it sounds like we all agree on the broad outline. If you have a tribe of N people and one invader, then the "invader's genes" would start with a frequency of 1/N. Barring selection, the frequency would stay at about that level. Over generations, there is a roughly exponential increase in the number of the invader's descendants, and a matching exponential decrease in how many of his genes they each have.
In an infinitely expanding population with no inbreeding at all, then yes. But such a thing doesn't exist. Populations expand far less than exponentially once they're beyond the initial doubling period, in fact they tend to grow slowly in confined areas as they reach the carrying capacity of the environment.
On an island chain, all it would take would be a single incidence of interbreeding across each island over a few years to give most of the archipelago population a common ancestor 150 years later.
I know it's a bit counter-intuitive, but it's what happens. If I get some time later I'll try to do the model with numbers and a restriction of inbreeding to agents which are related at 3 or more steps (so no first-cousins).
Charlie _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
