I’m not sure why you think the epidemiologist fallacy applies here: There is no inference of causation from correlation. The model we are discussing simply estimates minimum population size at some point in the past based on current DNA data + knowledge about rates of change in DNA. (@RichardBuggs @Swamidass @glipsnort please correct me as needed.)
Consider this analogy, Jon: If a comet passes near the earth with a certain velocity, astronomers might pull out their slide rules and determine that the comet was in the Van Oort cloud 200,000 years ago. (Or maybe, just maybe, they would use computers.) They would say, “we have data about the current state of the comet and about the rate of change; these allow us to build a model that projects backwards in time.”
I would be astonished, simply astonished, if some theologian would enter a discussion about comet trajectories and chastise the astronomers for their overconfidence about the location of the comet 200,000 years ago. And if the theologian would justify his skepticism on the basis of the fact that astronomers are learning more and more about astronomy every year, the astonishment would increase. And if theologian were to further argue that there is a confounding factor of a known God who, according to many following the traditional understanding of the Scriptures, created the earth less than 10,000 years ago, so maybe the comet didn’t even exist 200,000 years ago, what would I think?
I would think about the argument between Galileo and Cardinal Bellarmine. It was Bellarmine, after all, who so adamantly argued that Galileo could say what he wanted about celestial mechanics as long as Galileo declared that the scientific findings were hypothetical.
The analogy between celestial mechanics and population genetics is sufficiently clear, I think, so I will not belabor the point further.
Have a great day on the eastern side of the pond, Jon!