Okay, now to return to this thread finally. Thanks for everyone’s patience. First off, I need to emphasize that when I’ve made this argument in public, I am always pointing out that I am (1) simplifying the math to make it easy to understand, and (2) rounding numbers to make it easy to remember.
However, @Agauger deserves a more careful answer to her questions.
Into the Weeds
I’m going to, now, enumerate several of the details that I’ve usually left out. In my view, none of these details undermine my point, or misrepresent the data.
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The formula D = T * R is only approximately correct, because it does not take into account mutations that (1) revert a lineage to its ancestral state (decreasing D), (2) are convergent with the other lineage (increasing D), or (3) mutate an already mutated position to a non-ancestral state (leaving D the same). It turns out that as TR increases, these effects cannot be ignored. So a more complicated formula is required when the observed D deviates far from 0%, which we will just represent as D = f(T * R) which is less than TR, where f() is a non-linear function that we are not going to specify here.
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Moreover, I often leave out the fact that it is actually closer to D = 2TR (because chimps are mutation away from ancestral sequence too). I can see why that might be confusing to people, but it is because I’m imagining the phylogenetic tree in my head, and computing lengths along both legs. I’ll still use the convention that leaves out the 2 here, but keep that in mind if you try and do your own work on this.
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The T in the formula is to the time of coalescence of the DNA lineage, which also depends on the Ne before divergence. The larger the Ne, the larger T will be compared to the time the two species separate. For this reason, we expect D to be larger than a naive calculation based on separation (6 to 9 million years ago, in the case of humans/chimps) would indicate.
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Mutation R (per year) is dependent on generation time. This introduces some real uncertainty as we extend these values millions of years into the past. The shorter the generation time, the higher the mutation rate per year. Rates of nucleotide substitution in primates and rodents and the generation-time effect hypothesis - PubMed Interpreting the Dependence of Mutation Rates on Age and Time - PMC So, if generation times for our ancestors were shorter, say, 6 mya to 2 mya, than we would expect D to be higher than we expect using a R measured using measured rates from today.
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The often quoted 2% and 20% (alternatively 1.5% and 15%) are rounded numbers from the original chimpanzee genome paper. Initial sequence of the chimpanzee genome and comparison with the human genome | Nature This measures the percentage of synonymous codons that are different between Humans and Chimps. Here is below. Note that the Ka/ Ks ratio is exactly as predicted by neutral theory (<1), as is the Ki / Ka ratio (in the paper). From the table below, you can see the actual percentages are about 1.2% for human/chimp and 18.7% for mice/rat.
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It is true that taking the whole genome into account, the difference between human/chimp is about 4%, but the difference between mice/rats by that measure is about 30%. Keeping in mind #1 above, that fits the pattern of being about 10x more than T*R, keeping in mind that D = f(TR) not TR itself. The two key points here is that the exact same measure of distance/similarity has to be used between mice/rat and human/chimp to be comparable, and the farther D is from 0%, the less the precise ratio of 10x will hold up. Nonetheless, we will always see humans/chimps much less different than mice/rats. If you do not like the measure I’ve used #4, use another measure, but you have to be consistent or the comparison is invalid.
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This information alone is enough to qualitatively (and semi-quantitatively) explain the human/chimp vs. mice/rate observation. As has already been noted, mice/rats have lower generation times and therefore higher mutation rates, and they diverged from each other very farther back in the past. In contrast, humans/chimps diverged more recently and mutate slower. That is why mice/rat is more different than human/chimp. No other design principle (other than common descent) has been able to even qualitatively explain this fact.
What About Quantitation?
One might legitimately ask for a quantitative test of all of this. I would expect as much from @agauger, and can give some published answers here. however, we have to keep all the uncertainties in perspective as we do this. There are several unknowns, so anything within a multiple of the true rate is a real success.
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Careful analysis (taking into account #1, #2, #3, and #4) was done of human and chimpanzee sequences in 2000 to compute R from D and T in humans. The rate (R) computed from this analysis was 1e-9 bp / year (Estimate of the Mutation Rate per Nucleotide in Humans | Genetics | Oxford Academic), about 2x the mutation rate we’ve directly measured in humans since 2010, which is about 0.5e-9 bp / year (and faster in chimps, Redirecting). Given all the uncertainty here, that is a pretty good estimate, however it did not include the whole genome and our best analytical approaches. Nonetheless, given all possible reasons for the math to be a bit off, this is a remarkably good prediction.
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Subsequently, we have developed better methods (see Inference of Natural Selection from Interspersed Genomic Elements Based on Polymorphism and Divergence | Molecular Biology and Evolution | Oxford Academic) that can more accurately estimate mutation rate across the genome. Of not, this what was used by the ArgWeaver paper, Genome-Wide Inference of Ancestral Recombination Graphs. These common descent estimates put the mutation rate closer to 0.7e-9/year.
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Keep in mind, once again, this all assumes that that mutation rates are constant. We know this is not the case. For example, chimpanzees certainly have higher mutation rates than us, at 0.6e-9/year. Direct estimation of de novo mutation rates in a chimpanzee parent-offspring trio by ultra-deep whole genome sequencing | Scientific Reports. All the discrepancies we see are easily explained by lower generation times in the past, for example, or a high Ne before divergence.
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A very important point is that the Y-Chromosomes mutate quicker and are also more divergent between chimp/human. That is an indepedent verification of common descent. This is a much better controlled experiment than looking at chimp/human vs. mice/rat. I’m going to leave out the details here, but they are fairly easy to find. Y-Chromosome divergence is often explained as problem for common descent, but it is actually a very strong validation of the D = TR formula.
All together, mutation rates are stunning validation of evolutionary theory. It was a quantitative test of common descent, showing that evolutionary theory could predict decades before genomes were known, what the generation to generation mutation rate would be when we could finally measure it.
Common Descent is a Design Principle
Perhaps there is another principle can explain these patterns, but no one has produced one. It is not enough to say that “God could have created things this way.” I agree. I think He created us too, just this way. However, He chose to create us in a manner perfectly explained by common descent. In science, we need a better mathematical and quantitative explanation of all this data before we leave common descent.
Notice also why all the ID and anti-evolution arguments we have heard leave these facts untouched. This is a positive case for common descent. At absolute best, if they were not in mathematical error, ID and anti-evolution arguments are evidence that God inspired some proteins here and there. However, even if Doug Axe is correct (he is not), we cannot show new enzymes are needed in human evolution, so his argument has no bearing on human evolution.
Not Against God’s Action
To be 100% clear, maybe God did act in our origins, science has not ruled it out. I affirm alongside you all that God providentially governs all things, including evolution, but I know this from Scripture, not any ID argument. From a Scriptural point of view, we might even find it warranted to affirm the de novo creation of Adam. I’ve been making that argument, so my opposition to ID is not because I oppose affirming God’s action. I just see no need for a bad argument to support something we already know.
Seeing no conflict between common descent and theology, I see no problem with this finding. Common descent is just how God created us.
@Agauger thanks for the honest engagement here. I hope that this makes sense to you. Happy to answer any more questions. I appreciate you’ve heard me out, and welcome attempt to engage this data.