How many ancestors' DNA do we have per generation?

DNA can be recombined and it's pretty random which ancestor will donate how much DNA other than your parents which is an almost perfect 50/50 split. For example, my family have had DNA tests done and I have significantly more DNA in common with my maternal grandfather than my maternal grandmother (something like a 60/40 split). When you go back a certain number of generations you will find that some ancestors no longer donate any DNA to you. For instance I have ancestors from Cornwall but no detectable Cornish DNA. I imagine that this number will asymptote to a particular value. Each generation going back will double the potential number of remaining donors, but probably half of them will be eliminated from consideration.

So, potentially, if you go back 10 generations you will have 1024 ancestors but maybe only have DNA from 100 of them. Maybe 11 generations gives 110 ancestors, 12 gives 113, etc. and 125 is the limit (on average).

Is there a calculation or some research for the number of ancestors per generation you have identifiable DNA in common with?

• Out of curiosity, since DNA is such a young science - what proportion of the Cornish were tested to give a baseline of what constitutes Cornishness? How far back in time/generations? We'd also need to qualify what the percentages mean in terms of base-pairs, or is it some sort of selective sample of key sequences that was being tested for rather than the whole genome being sequenced? Commented Jun 11, 2022 at 2:41
• @JiminyCricket not many are really needed. It's possible to identify Cornwall and Devon specific clusters using ~70 samples from each as long as their grandparents are local source. Commented Jun 11, 2022 at 8:42
• @CJ this should at least give you a clue about the answer gcbias.org/2017/12/19/1628 Commented Jun 11, 2022 at 8:48
• en.wikipedia.org/wiki/Coalescent_theory Commented Jun 12, 2022 at 18:47