Kimura 1968

Citation

Kimura, M. (1968). Evolutionary rate at the molecular level. Nature, 217(5129), 624-626.

Links

• https://www.nature.com/articles/217624a0
• https://scholar.google.com/scholar?cluster=10145631598213248063

Notes

Before the neutral theory it was generally thought that most variation and evolutionary change was due to selection. This sparked the neutralist-selectionist debate. Also at this time there was little to no DNA sequence information. Kimura was working from a handful of protein sequences that were available at the time.

Paragraph Four

Kimura constructs an estimate of the rate of genome-wide nucleotide substitutions based on observed amino acid differences between species.

• Average years between amino acid substitutions in 100 amino acids [math]=28\times10^6[/math] yr (today this would be "a", Latin annus, symbolizing year).
• Genome size estimate [math]=4\times10^9[/math] bp (base pairs).
• Gene size coreesponding to 100 amino acids [math]=300[/math] bp.
• Adjustment to also include an estimated additional 20% synonymous mutations that do not change the amino acid [math]1 + 0.2 = 1.2[/math]

[math]28\times10^6 \div \left( \frac{4\times10^9}{300} \right) \div 1{\cdot}2 \doteqdot 1{\cdot}8 \mbox{ yr}[/math]

The publication (I don't know if this comes from Kimura or the typesetter) uses an obscure symbol, [math]\doteqdot[/math], for approximately equal to, [math]\approx[/math]. (This might be, or have been, more common in French typography, ?) It also uses a British style interpunct for the decimal place, which looks like multiplication; this has faded from use today.

Kimura argues that a fixation event every 1.8 years is too high of a rate to only be explained by selection. Haldane (1957), referenced here, is a useful publication to understand this argument. Essentially, this requires many overlapping simultaneous selective sweeps across the genome (the time from the occurrence of a new mutation to its fixation in the population is many generations). The action of selection is limited by an organisms fecundity. If all of the offspring with the most fit genotype survive and reproduce (as the most extreme example) the action of selection is seen in the reduction of survival and/or reproduction of organisms with other genotypes. How much can the number of offspring be reduced before the species becomes extinct? If half of the offspring are removed to select for a single trait, and half of the remaining offspring removed to select for another independently inherited trait, ... simultaneous selection for ten traits results in only one out of 1,024 [math]\left(1/2^{10}\right)[/math] offspring remaining. For many species of mammals this is beyond the number of offspring possible and the species should rapidly decrease in number over time. Relaxing selection so that more offspring survive doesn't really help because the fixation of selected alleles takes longer and more genes under selection will simultaneously overlap in time---also reducing the number of offspring.

This appears to assume that the entire genome is protein coding DNA sequence.

Let's update this calculation using human parameter values.

• A haploid genome size of 3.2 Gbp (Morton 1991).
• The proportion of fixed single base pair differences between humans and chimpanzees 0.0106 and an additional [math]5.09\times10^{6}[/math] indels (The Chimpanzee Sequencing and Analysis Consortium 2005).
• An approximate lineage divergence between human and chimpanzee sequences of six million years. (There is a lot of uncertainty surrounding this value, Kumar et al. 2005).

[math]\frac{6\times10^9\mbox{ a}}{0.0106\times3.2\times10^{9}\mbox{ bp events}+5.09\times10^6 \mbox{ indel events}}\approx[/math]

[math]\approx\frac{6\times10^9\mbox{ a}}{33.9\times10^6\mbox{ events} + 5.09\times10^6 \mbox{ events}}\approx[/math]

[math]\approx\frac{6\times10^9\mbox{ a}}{3.9\times10^7\mbox{ events}}\approx 150 \mbox{ a/event}[/math]

So, approximately 150 years go by between fixed evolutionary differences in the lineage leading to humans. The rate per year is much lower than Kimura's original estimate but still corresponds to a lot of selective forces (if all of the changes were due to selection). If we assume an average generation time of 25 years this is a fixation event every six generations.

If we strike a rough first-level balance between neutrality and selection and assume only 5% of the genome is under functional constraint (Mouse Genome Sequencing Consortium 2002) then the rate of selective change is 20 times (1/0.05) lower predicting a species-wide fixation event every 150×20=3,000 years or approximately every 120 generations, which is beginning to sound more reasonable (≈95% of changes are neutral and not due to selection).