How to resolve the contradiction between the time required for the fixation of neutral mutations and the time available according to the fossil record

Question

More than thirty thousand synonymous single-nucleotide-substitutions have occurred in protein-coding genes in the human genome since the human lineage diverged from the chimp lineage ~7 million years ago (Bakewell et al, 2007, p.7490). Since, by definition, synonymous substitutions don’t change the amino acid, these substitutions must be selectively neutral mutations. For neutral mutations, the rate of evolution is simply equal to the point mutation rate U, “irrespective of selection at other linked loci, changes in population size, or almost any other conceivable complication” (Lanfear et al, 2014, p.36). This is problematic because U is approximately 10 to the -8 power for humans, which means that it took about a hundred million generations for each of these substitutions to become fixed in the human genome. Since each generation is more than ten years, a hundred million generations is more than a billion years, which is much longer than the ~7 million years since the human lineage diverged from the chimp lineage. How is this to be reconciled?

Bakewell, M. et al, “More genes underwent positive selection in chimpanzee evolution than in human evolution.” Proceedings of the National Academy of Sciences USA, vol 104, pages 7489–7494, 2007

Lanfear, R. et al, “Population size and the rate of evolution.” Trends in Ecology and Evolution, vol 29, pages 33–40, 2014

Answer 1

The parameters cited by OP are not in conflict.

The misconception relates to a disconnect between what the theory predicts and the type of observation we have available. This leads to an unnecessary assumption that the observed substitutions have become fixed, as well as a failure to account for standing variation at the time of divergence.

Lanfear et al. correctly states that "the rate of evolution at a site is $KU × 1/K = U$". To find the amount of (this type of) evolution between two populations over time, one would calculate $UTG$, where $T$ is the time in number of generations, and $G$ is the genome size. However, this is a calculation of neutral substitutions that have become fixed across two diverged populations, and is really most appropriate when $T$ is much greater than the expected time to fixation ($T>2N$, where $N$ is the effective population size).

To perfectly test the theory, one would need to census all substitutions in both populations in order to differentiate between substitutions that have become fixed and those that are polymorphic.

The observation we have here, however, is essentially a single individual from each population.

When one compares two individual genomes that have been separated, the SNPs observed between them will include:

1. sites with a SNP that originated since divergence and has become fixed (what the theory is talking about).
2. sites that are polymorphic, with SNPs that originated since divergence.
3. sites polymorphic in the original population, where a SNP became fixed in one lineage and lost in the other.
4. sites polymorphic in the original population that are still polymorphic.

SNPs originating since divergence that have become fixed

Even just applying the above calculation, considering only fixed SNPs (or those that will become fixed) provides the same order of magnitude as the observation of 30,000 substitutions in humans since divergence with chimps.

Bakewell et al. surveyed 5,215,415 synonymous sites, so we'll use that as $G$. Assuming 20 years per generation and 7 million years of divergence $7×10^6/20= 3.5×10^5$ generations:

$UTG = 10^{-8} × (3.5×10^5) × 5,215,415 = 18,253$ substitutions (though we don't know which of the 30,000 observed substitutions these are).

Sites that are polymorphic with SNPs that originated since divergence.

New mutations are entering the population all the time, with every individual.

Imagine this measurement was taken one generation after divergence, and where the ancestral population was all exactly identical.

The human genome is $3×10^9$ nucleotides, so $10^{-8} × 1 × (3×10^9) = 30$ substitutions. Humans and chimps are diploid, so an individual would have ~$30$ mutations on each set of $3×10^9$ nucleotides, or ~$60$ mutations compared to our hypothetical source population.

As Lanfear pointed out, each one of these substitutions is unlikely to eventually become fixed (they have probability $1/K$), but we're taking the measurement now, so we observe them. Many of them are likely to spread in the population at least a little bit, even if they eventually disappear.

We also know from Bakewell that both the observed human and chimp genomes contain sites that are not only polymorphic in the population, but polymorphic in the sequenced individuals.

Sites polymorphic in the original population, where a SNP became fixed in one population and lost in the other

Overlooked by OP is the fact that the most recent common ancestor of humans and chimps (which was a population, not an individual) was not full of identical individuals, but contained the standing genetic variation one sees in any species. This allows for the fixation of alternative alleles between the daughter populations, even in the absence of new substitutions.

We know in fact this happened. The gorilla genome showed us that ~30% of the gorilla genome is more closely related to human or chimp than the later are to each other. This is due to a phenomenon called incomplete lineage sorting, which occurs when two speciation events occur over a short span of time (again $T<2N$; the gorilla/human/chimp split is thought to have occurred ~10 million years ago). It is caused by variation in the ancestral population that gets differentially sorted into the daughter populations.

Sites polymorphic in the original population that are still polymorphic

It's possible there are still sites that retain polymorphism within the daughter populations that was present in the ancestral population. A wide survey of human and chimp genomes could find these alleles.

(This may be rare between humans and chimps. Estimates of the human effective population size are generally $<10,000$, so $2N=20,000$. Our estimate of ~350,000 generations probably means few sites in the genome have failed coalesce in that time.)