A model shows that adaptation can be difficult without natural selection. Here's why.

Yes, this is the same image as in Mikkel Rasmussen’s post in June. And it’s appropriate because I want to discuss the same paper in some more detail. The paper (as you can see) is this one: Hössjer O., G. Bechly and A. Gauger. 2021. On the waiting time until coordinated mutations get fixed in regulatory sequences. Journal of Theoretical Biology 524: 110657. doi:10.1016/j.jtbi.2021.110657 It is by three affiliates of the Discovery Institute, and was published in a respected journal (at least, one in which I myself have published twice, which is the definition of respectability that appeals most to me). The first author is Professor of Mathematical Statistics at the University of Stockholm, Sweden, and has published highly technical papers in theoretical population genetics.

This paper has quite a lot of serious technical theoretical population genetics, and covers many cases, but in the cases they are most interested in, the model it analyzes can be very simple. There are a set of m stretches of DNA, considered to be able to contain potential binding site sequences, each stretch is L bases long and each binding site is W bases long. Neutral mutations are occurring at these sites. The mutation model is a simple symmetrical 4-state Jukes-Cantor model. In the simplest case, we ask how long it will take until, among these stretches of DNA, all m of them have at least one binding site each.

When all m of them have led exactly to a particular target sequence, say the particular 7-base sequence CAGTTAG, the stretch of DNA will then function as a regulatory sequence. Until then, the sites are not under selection, as only that target sequence functions. The question addressed is how long it will take for neutral evolution to find the target sequence. There is no selection pushing the sequence towards the target. The answer is: so long as to be implausible, longer than the life of the universe.

Mikkel Rasmussen’s post of 12 June, 2021 here at PT went right to the point: why did anyone think that this situation was how regulatory sequences evolved? The key to the extreme slowness of evolution is that partial matches to the target sequence are not rewarded by natural selection. Mikkel’s piece, as is typical for him, is masterly, clear, and cites lots of relevant information, including real examples that of regulatory sequences evolving by having partial matches rewarded by natural selection. Don’t just take my word for that, read his post.

What I want to do here is to supplement Mikkel’s post by explaining the population genetics part in a bit more detail, and show why it is easy to see why finding a match is delayed for an astronomical length of time when partial matches are not rewarded. Let’s consider that …