population dynamics - What is the percentage of people living in England in 1500 AD whose lineage is still alive?

This sounds a bit random, but it stems from a lecture in statistical genetics which I attended a while ago. We were shown a population lineage graph from which it was clear that most lineages eventually go extinct. The further you go in to the past, the smaller the percentage of the individuals living at that time whose lineage is still alive today. This probably makes sense in the context of evolution.

So I am curious about the speed of that process in human populations. I am aware that this speed, quite possibly, varies over time and geographically. Are there any estimates about that speed in European populations? To be more specific, I would take England at 1500 AD as a starting point. What is the percentage of the people living in England at that time whose lineage still exists?

EDIT

I am very grateful to @Richard Erickson for the reference to the Galton-Watson process. It is really fascinating that +70% of all known Chinese family names have become extinct. It would be really interesting to know more about the speed of the process of extinction - in particular in European populations.