You are correct that the founder's Y chromosome should be the same as his father's - barring tiny mutations. The "founder" is defined like this: You notice th

You are correct that the founder's Y chromosome should be the same as his father's - barring tiny mutations. The "founder" is defined like this: You notice that a large portion of men in a population share a Y chromosome. The chromos are not exactly identical, due to the natural rate of mutations. You determine the amount of mutations, from the existing population, that would make all those Ys converge on the same chromosome back in time. Knowing the amount of mutations, and knowing the average natural rate of mutations, you can calculate the time - let's say 1000 years ago. It then follows that 1000 years ago there was a man who had lots of descendants - and this is the "founder". In the "career" of that chromosome, there's a natural bottleneck right until the "founder's" generation. After that there's a sudden expansion.