Turns out some animals like lobsters are immortal. They die off as individuals mostly through the statistical likelihood that they will get squashed, caught and/or eaten.
It also turns out that they remain fertile and some experts postulate that they even get more fertile as they get older. This being something to do with then getting bigger stronger safer and hornier.
How many lobsters can one 300 year old lobster beget, I wonder.
If there has ever been one immortal human (as a genetic anomaly) and he or she remains fertile, they could have hundreds of offspring.
If at least some of them have inherited the immortality then they could then have hundreds more. And so hundreds beget hundreds.
Which means if there has ever been an immortal of our species, that gene should quickly populate and replace all the inferior (finite) of the species. You can probably create an algorithm to determine how quick it would happen. My guess is only a few generations.
It’s unlikely it ever happened then – a proper immortal. Probably the process is so complex it would require many genetic anomalies all at once. It might be they are happening sequentially – the deviations- and all we have to do it wait. That there are some on the road to immortality that we don’t know about. And they don’t know because for now they buzz off like the rest of us.