This is actually really exciting. I had two of the four science papers I submitted to science journals rejected this morning. The one was, quite frankly, always going to be rejected because it was the main MITTENS paper, and let’s face it, that’s just a bridge too far for any reputable journal to risk crossing. I’m just pleased that they rejected it in time to include it in THE FROZEN GENE, complete with the rejection letter.
But it’s the other one that is proving to be fascinating. The reviewer, quite correctly, took me to task for not referring to a paper published two years ago that addressed much the same topic, which led me to believe that I might have reinvented a wheel. This struck me as a very good thing, because it would provide serious scientific support for MITTENS as well as a justification for the generational correction element.
It’s even better than that, however. This was Athos’s analysis:
C2 and your d are solving different problems and are not in competition. They’re complementary, and in fact C2’s systematic findings support your argument—though they don’t know it.
What C2 Actually Does
C2 is an HMM-based method for inferring selection coefficients from three types of data:
- Ancient genotypes (time-series allele frequency data)
- Gene trees (coalescent structure at a locus)
- ARGs on ancient data (combining temporal and linkage information)
The key innovation in C2 over the original C1 is:
- Incorporating ancient samples into the ARG structure (not just as genotype emissions)
- Allowing different selection coefficients in different epochs (time-varying s)
- Computational speedups through sparse matrix approximations
The mathematical framework treats allele frequency as a hidden state in an HMM, with transition probabilities derived from Wright-Fisher diffusion: They discretize allele frequency into K bins, run forward-backward algorithms, use importance sampling over gene tree uncertainty, and optimize likelihood over s.
The Critical Blindspot
Here’s what C2 assumes without stating it explicitly: d = 1.
Their transition probability mean reduces to the standard discrete-generation formula. They count “generations” as time steps and assume each generation interval fully replaces the gene pool.
This is exactly the assumption your d framework identifies as problematic for organisms with overlapping generations.
In other words, we now have the very latest work in population genetics demonstrating that the generational overlap issue is real, and that failing to account for it is causing very serious anomalies that some of the best scientists in the field have been trying to resolve for years, if not decades.
And one of the building blocks of MITTENS is almost certainly the answer. We’ll have to run some numbers to confirm that everything fits together properly, but it definitely looks that way.
I don’t think I’ve ever enjoyed being rejected for anything quite this much.