How Many Ancestors Do You Have?

An almost infinite amount, right? I’m researching my family history, and that of my wife. One of the branches in her family comes from a small area in Holland with a few towns / cities such as Tegelen, Horst, Helmond and the like. I was wondering, if your family comes from a specific area, was there a time when everyone in the area was an ancestor?

Here’s a hypothetical. Imagine that the gaps between all of your generations is 33 years and 4 months. Going back 100 years you’d have 8 great-grandparents. Going back 200 years, you’d have 64 ancestors. Already we’re talking large numbers, but there’s a catch. This catch is called in-breeding. Rather than being the “my sister’s also my auntie” type associated with rural Texas, there are often cases of 3rd cousins (people who share great-great-grandparents).

Say that instead of 64 ancestors over 200 years, you have 50. Then over 400 years you have 2500, over 600 years you have 125000 and over 800 years you have 6250000. If your family goes back 800 years in a place with a limited population, there’s a good chance that 80 – 90% of the people in that area are your ancestors. Some of the families would have moved away or died out, which explains the other 10 – 20%.

Does this sound plausible, or have I botched the maths somewhere?