As you go back in time further and further, you reach a point where almost all humans alive then have left us ZERO living descendants.
I don't think that's true, or even possible, for genealogical descent, except briefly before a catastrophic event where all but one or a few subpopulations were eradicated without any descendants.
Here's why: given the concept of an
Identical ancestors point, the mirror image, what we might dub the "Identical descendants point" is also implied: a point in the future where everyone alive today who will still have living descendants is the ancestor of everyone alive then. After that point, your genealogical heritage has become immortal, barring the extinction of the human race. Even if only a single breeding pair remains, their descendants will be yours and those of everyone alive today whose line hasn't died out before. The same is true in the past: mostly everyone alive 40k BP who successfully bred and left any descendants whatsoever over the first few generations after their lifetime is likely the ancestor of mostly everybody 30k years ago and of literally everybody today.
In the same vein, even if the Toba eruption did kill off 98% of humanity 70,000 years ago, while this means that most people alive in 70,500 BP or 71,000 BP didn't leave living descendants, the effect is short lived. By, say, 85,000 BP (or later if the survivors were scattered over a larger area), mostly everyone who successfully bred and still had ancestors 71ky BP probably had somebody among the 2% who survived and is thus a universal ancestor of everyone alive today.
Although the number of pedigree SLOTS doubles with each generation, you reach a point where the number of DISTINCT ancestors starts decreasing.
That's certainly true eventually, if only because of you go back far enough in time, your pedigree already includes a majority of the people alive at the time (or rather, of those among them leaving *any* descendants), so the effect of the smaller total population starts to outweigh the effect of a better penetration of that population. For example, if 60% of the global breeding population were your ancestors 1500 years ago, 85% 5000 years ago, and 100% at the beginning of the Holocene, the absolute number of your ancestors may still be largest 1500 years ago.
Supposedly this happens MUCH sooner than you might guess:
Pedigree collapse
If one considers as a function of time t the number of a given individual's ancestors who were alive at time t, it is likely that for most individuals this function has a maximum at around 1200 AD.
Is that supposed to be globally or only looking at Europeans for example? It sounds plausible for the latter - for any living European, it is possibly true that the number of *European* ancestors drops off again before 1200 because their pedigree has reached such a good penetration of the continent's population that population growth becomes the dominant driver. However I suspect they would be adding a *lot* of ancestors on other continents with every generation further in the past from the few isolated transcontinental ancestors they had at the time.