“ I’d be interested in what your serious objections to it are.”
Well, to me the very idea is ridiculous. How could that possibly be known? Even if you took what we imagine today’s population to be and did a lot of fancy math to end up with such an accurate number from that long ago is difficult to accept. There was no census. There were no records of anything except various layers of sediment. 1200 breeding pairs in the whole world? That is a stretch. I guess to me it just sounds farcical. I am not a scientist, so this could be an elementary fact. I doubt it though.
I am not a scientist either, but I share your skepticism.
All they can measure is how fast the population accelerated in modern times, when there is little to deter it. A bit of war, famine, plague, genocide, abortion, etc., in recent times.. other than that, mathematicians could measure the rate of population acceleration absent any extinction level event.
Then, divide 8 billion by that rate of acceleration, and calculate how long ago the number would be zero. That’s probably where they got the first near extinction ‘data’ point.
Beyond that, it would have to be pure conjecture.