Discrepancy in time for genetic differences between human and chimpanzee to accumulate

Question

Genetic differences between human and chimpanzee include ~50,000 amino acid changes, ~30,000,000 point mutations in non-coding sequences, and millions of insertions, deletions, inversions, genomic rearrangements, and transposable element movements [1]. The vast majority of these genetic changes are neutral [2] [3]. For neutral mutations, the expected number of generations required to reach fixation in the population is the reciprocal of the mutation rate per site per generation [4]. This holds irrespective of selection at other linked loci, changes in population size, or almost any other conceivable complication [4]. The human mutation rate, μ, is ~10^-8 per site per generation [5]. Although μ can be orders of magnitude greater at certain sites, the fact that, as cited above, millions of neutral mutations occurred in the human line since its divergence from the chimpanzee line indicates that at least thousands of mutations occurred at the average rate of 10^-8 per site per generation. Since the expected number of generations required for any one of these mutations to reach fixation in the population is the reciprocal of μ, this number equals ~10⁸ generations. Since a generation is ~20 years for humans [5], the time required for any one of these thousands of neutral mutations to reach fixation is ~10⁹ years.

According to the currently-known fossil record, the human line diverged from the chimpanzee line between 6 and 8 million years ago [7].

How is this major discrepancy between population genetics and the fossil record to be reconciled?

References

[1] Chimpanzee Sequencing and Analysis Consortium. Initial sequence of the chimpanzee genome and comparison with the human genome. Nature 437, 69–87 (2005)

[2] Harris, E. E. Non-adaptive processes in primate and human evolution. Am. J. Phys. Anthropol. 143 (Suppl. 51), 13–45 (2010)

[3] Vallender, E. J., Mekel-Bobrov, N. & Lahn, B. T. Genetic basis of human brain evolution. Trends Neurosci. 31, 637–644 (2008)

[4] Lanfear et al, Population size and the rate of evolution. Trends in Ecology & Evolution, January 2014, Vol. 29, No. 1, Pages 33-42

[5] Kong, A. et al. Rate of de novo mutations and the importance of father’s age to disease risk. Nature 488, 471–475 (2012)

[6] Walker, R. et al. Growth rates and life histories in twenty-two small-scale societies. Am. J. Hum. Biol. 18, 295–311 (2006)

[7] Levin, N. Annual Review of Earth and Planetary Sciences, 43: 405-429 (2015)

Answer 1

Good literature work here and good question +1! In short, your main mistake was that you based your calculations on a single site and not on the whole genome. More info below.

Genome-wide vs sites specific mutation rate

The statistic of $10^8$ generations that you computed is the average rate of fixation of new neutral mutations per site. As considered the genome-wide statistic between humans and chimpanzee, you have to scale your predictions up to the entire genome. There are about $3 \cdot 10^{9}$ nucleotides in either the human of the chimp genome. That would result in a genome-wide mutation rate of $U ≈ 2 * 10^9 \cdot 10^{-8} = 20$ (the two is because mammals are diploids). Hence, the rate of fixation of 0.05 generation.

So, the expected time it would take for $30 \cdot 10^6$ new mutations to fix would be $30 \cdot 10^6 \cdot 0.05 = 15 \cdot 10^5$ generations. Because, such mutation can happen in either lineage (humans or chimps), we have to divide this number of 2 leading to $7.5 \cdot 10^5$. With a generation time of 20 years, that would take $1.5 \cdot 10^7$ years or 15 million years.

15 million years? Why not 6-8 million years as expected from fossil records?

Most of the discrepancy is probably due to vague approximation made in the computation. For example, you assumed a mutation rate of $10^{-8}$ while in reality, the average mutation rate is rather twice as large (Nachman et al., 2000, Kong et al., 2012, Wang et al., 2012, Rahbari et al. 2016).

Doubling this mutation rate would divide by 2 our expectation of 15 million years leading to an expectation of 7.5 million years that perfectly match the fossil records!

There is however another source that may cause an overestimation of the time needed... You assumed the absence of incomplete lineage sorting or in similar words, you assumed that the standing genetic variance in the ancestral population negligibly affected divergence among the two lineages. However, these discussions are for another time!