21 May 2014

Evolutionary Rates - Kimura


In his paper, "Evolutionary rate at the molecular level", Kimura (1968) discusses the rate of evolution as found in comparing various contemporary, at the time, studies with respect to nucleotide substitutions. Kimura began with the assumption that most mutations are neutral or nearly neutral, whereas the thinking at time was that most mutations were usually either harmful or helpful. It was Kimura's work that led to Neutral Theory becoming the Null Hypothesis in modern Molecular Evolution.

Kimura, according to my H-Index Calculator, has been cited over 39169 times, has an h-index >10 and a g-index >10.


Kimura begins by looking at the paper by Zuckerkandl and Pauling (1965) who compared studies of hemoglobin molecules who found, among mammals, in a chain of about 140 amino-acids there was a change in one amino-acid in a 107 year period. Then Kimura compares Buettner-Janusch and Hill's (1965) study on primate hemoglobin who found a substitution rate of 45x106 years. The study by Kaplan (1965) between were also compared and found a rate of 2.7x106 years.

Here, Kimura makes the assumption that nuclear DNA is similar among most mammals and that the GC content in mammalian DNA is uniform withing a value of 40-44%. Then Kimura assumes that 4x109 of nucleotide pairs are haploid chromosome complements. From this Kimura estimates a substitution rate within the population of ~2 years.

Compared to the 300 generations rate predicted by Haldane's paper (1957), this is a huge contrast. Kimura concluded, Haldane's erroneous fitness factor aside, that this could be accounted for if most mutations were in fact neutral or at least nearly neutral.

Thus the very high rate of nucleotide substitution which I have calculated can only be reconciled with the limit set by the substitutional load by assuming that most mutations produced by nucleotide replacement are almost neutral in natural selection. (Kimura, 1968, p. 625)

The next paper Kimura looks at is the work by Lewontin and Hubby (1966) who studied genetic variation in the fruit fly species Drosophila psseudoobscura and estimated in each individual that 12% of each loci are heterozygous. Kimura assumes that the heterozygosity would be much higher in nucleotide sequences. Since it is evident that the mutation rate in Drosophila is ten times that of humans, Kimura calculates a mutation rate of 1.5x10-5 and checks his calculation by looking at Drosophila neutral mutations, neucleotide pair mutation per generation the fact that the Drosophila genome is 1/20 the size of the human genome to get the same result.

Finally, Kimura looks at Kimura and Crow (1964) who found that for neutural mutations the probability that an individual in a population is heterozygous and if the individual is homozygous differ.

Looking at Watson's work (1965) Kimura finds that in gamete production substitution in base pairs could be 200-2000 and is reduced to ~2 by natural selection.


Firstly, as in my last post, it must be said that Kimura was in no way finding fault in evolution. In fact, Kimura was proposing a new idea to explain why organisms appear to change so quickly with low cost when calculations such as the one by Haldane say it would take a long time and be costly. In fact, Kimura has been proven correct with Neutral Theory being the Null Hypothesis, with Nearly Neutral Theory taking up much of the slack.

Secondly, Kimura has shown that evolution occurs at a even a faster rate than had previously been supposed. Once again, this supports not defeats evolution. This paper in no way shows that genomes are decaying.

Kimura sums up by stating that each generation is producing neutral or nearly neutral mutations that have been largely ignored and are occurring at a very high rate making random drift an important factor of evolution.

Questions to My Opponent

  • Did you actually read the paper before posting it?
  • If yes to the previous question; did you think neutral or nearly neutral mutations indicated that genomes are decaying?
  • Do you think "random drift" indicated genomic decay?
  • What on earth made you think that this paper demonstrated that the evolution of one species to another is impossible when it is a keystone to the modern understanding of evolution?


20 May 2014

Genome Decay Claim


Recently, a Creationist on Google+ presented a list of papers that he felt demonstrated that genomes are decaying and, therby, evolution of species from one form into another is impossible. The thread where this discussion occurred was a post titled Evolution: How it Works and How to Teach it. The articles cited by the Creationist are listed as follows:
  • J.B.S. Haldane. 1957. The cost of natural selection. J. Genetics55: 511-524
  • Kimura, M. 1968. Evolutionary rate at the molecular level. Nature 217:624-626
  • Muller, H.J. 1950. Our load of mutations. Amer. J. Human Genetics 2:111-176
  • Muller, H.J. 1964. The relation of recombination to mutational advance. Mutation Research 1:2-9
  • J.V. Neel, et al. 1986. The rate with which spontaneous mutation alters the electrophoretic mobility of polypeptides. PNAS 83:389-393
  • A.S. Kondrashov. 1995. Contamination of the genome by very slightly deleterious mutations: Why have we not died 100 times over? J. Theor. Biol. 175:583-594
  • S. Kondrashov. 2002. Direct estimates of human per nucleotide mutation rates at 20 loci causing Mendelian diseases. Human Mutation 21:12-27
  • M.W. Nachman and S.L. Crowell. 2000. Estimate of the mutation rate per nucleotide in humans. Genetics 156: 297-304
  • A. Eyre-Walker and P. Keightley. 1999. High genomic deleterious mutation rates in Hominids. Nature 397:344-347
  • J.F. Crow. 1997. The high spontaneous mutation rate: is it a health risk? PNAS 94:8380-8386
  • J.F. Crow. 1958. Genetic effects of radiation. Bulletin of the Atomic Scientists 14:19-20
  • M. Lynch, J. Conery, and R. Burger. 1995. Mutation accumulation and the extinction of small populations. The American Naturalist 146:489-518
  • K. Higgins and M. Lynch. 2001. Metapopulation extinction caused by mutation accumulation. PNAS 98: 2928-2933
  • F. Hoyle. 1999. Mathematics of Evolution. Acorn Enterprises, LLC, Memphis, TN.
  • Howell et al. 1996. Evolution of human mtDNA. How rapid does the human mitochondrial genome evolve? A. J. Hum. Genet. 59: 501-509
  • Loewe, L. 2006. Quantifying the genomic decay paradox due to Muller’s ratchet in human mitochondrial DNA. Genet. Res., Camb 87:133-159
The conditions are that responses must be from credible, scientific journals. He cannot use apologist websites such as Answers in Genesis or Journal of Creations and the like. In turn I have agreed not to use sites like Talk Origins though I did correct him with his claim of Talk Origins being an "atheist apologist" website that rejects Creationist studies out-of-hand.

I don't see why you're arguing this point, I've agreed to only use scientific journals. To belabor the point; if you could show, scientifically, that Creationism is true, that the God of the Bible is the God of Creation and that the God of the Bible exists then most of the scientists on TO would be on the side of Creationist (though many would choose not to worship this God). AiG and the like, well they've stated on their webpage that they will not be swayed. Ken Ham said so quite bluntly in a recent debate that he wouldn't change his mind.

That's the difference.


I shall address each article as they appear in the list. The rate at which I post will be subject to numerous variables such as my ability to acquire an article, how busy I am in my family and work life and how motivated I am when I do have the time. Any claim by my Creationist opponent that suggests I am answering in a particular order, or rate, just to avoid dealing with challenging papers will be treated in the same vein as Godwin's Law. I shall try to determine several things.
  • If the author(s) is(are) actually challenging the validity of Evolutionary Theory, or disputing a detail of Evolutionary Theory.
  • If the conclusion of the article means what the Creationist thinks it says.
  • If the research is refuted, improved upon or verified by other research.

Haldane's Dilemma


The paper by Haldane (1957) discusses and attempts to quantify the rate at which otherwise harmful genetic mutations become fixed within an animal population due to natural selection by way of environmental change which favours individuals possessing the mutation. Based on his calculations, Haldane determined that an animal population can only fix this mutation in the population at a rate of 300 generations, at best, and avoid the collapse of the species. The implication being, by my opponent, that there would not be enough time for certain species (ie. humans from the other great apes) to have successfully diverged in the time frame mainstream science says that they have.

The Haldane (1957) paper, according to my H-Index Calculator, has been cited 5613 times and has an h-index >10 and a g-index >10.


Haldene first begins by looking at Haploid, Clonal or Self-Fertilizing organisms, or Maternally passed cytoplasmic traits. Stating that if A and a represent allalomorphic genes in these populations then for the representative nth population, prior to selection, we have the frequencies:

pnA, qna where pn + qn = 1.

The cost incurred to fix a gene in the population of such organisms is calculated to be:

The deaths over all generations for the species in question which Haldane calculated to be between 5-15 times the number of species members of a population each generation, 10 being typical.

Then Haldane looks at autosomal locus with pairs A and a in diploids giving their fitness as:

AA frequency: pn2 fitness: 1

Aa frequency: 2pnqn fitness: 1-k

aa frequency: qn2 fitness: 1-K

For the members of these species the total deaths over all generations was calculated to be between 10-100 times the number of members each generation with 30 being typical.

Haldane then examines autosomal locus in inbreeding diploids with the following frequency table:

AA frequency: pn2+fpnqn

Aa frequency: 2(1-k)(1-f)pnqn

aa frequency: (1-K)(fpnqn+qn2)

Here the deaths of heterozygotes can be ignored if the organisms employ full inbreeding and the cost is similar to that of in the first group of organisms. If there is partial inbreeding then the cost is slightly less than the first group and the breeding coefficient f is introduced where f>0. The cost is not significantly reduced unless A is recessive.

After this Haldane looks sex-linked characteristics in diploids. The frequency and fitness table produced is:

AA frequency: pn2 fitness: 1

Aa frequency: pnqn fitness: 1-k

aa frequency: qn2 fitness: 1-K

A frequency: pn fitness: 1

a frequency: qn fitness: 1-l

For this group Haldane calculates the death rate over all generations to carry a cost of 10-40 times the population of a generation where 20 is typical.

Lastly Haldane examines the cost to heterozygotes.According to Haldane's calculations the cost to heterozygotes is small and therefore little fixation can occur.


Haldane then concludes that the rate of change, for adapting a previously harmful gene to survive, over 300 generations is reasonable because if change occurred over too few generations this would render the gene unstable and the population would languish and collapse.

Interestingly, Haldane makes the assertion that multiple mutations would take the same amount to fix simultaneously as if they were fixed in sequence. Literally, Haldane claims that three mutations being selected for will take three times as long.

Can this slowness be avoided by selecting several genes at a time? I doubt it, for the following reason. Consider clonally reproducing bacteria, in which a number of disadvantageous genes are present, kept in being by mutation, each with frequencies of the order of 10-4. They become slightly advantageous through a change of environment or residual genotype. Among 1012 bacteria there might be one which possessed three such mutants. But since the cost of selection is proportional to the negative logarithm of the initial frequency the mean cost of selecting its descendants would be the same as that of selection for the three mutants in series, though the process might be quicker. The same argument applies to mutants linked by an inversion. Once several favourable mutants are so linked the inversion may be quickly selected. But the rarity of inversions containing several rare and favourable mutants will leave the cost unaltered. (Haldane, 1957, p. 522)

However, aside from mentioning the negative logarithm Haldane offers no good reason why multiple mutations could not be fixed any faster than one mutation. In his example, Haldane cites bacteria that reproduce clonally. Organisms that utilize sexual reproduction multiple mutations can be selected simultaneously, via sexual recombination, and likely have those traits fixed in the population sooner.

Furthermore, there is a problem in Haldane's calculations. In his paper, Haldane uses 1-k to represent the fitness of gene a. If k = 0.01 then the fitness j of gene a works out to be, by Haldane's calculations, j = 1 + 0.01 = 1.01. Using Haldan's equation with this fitness value, if population N = 100 000, the frequency that A is passed to next generations is p = 1/N = 1e-5 and the frequency that a is passed to the next generations q = 1 - p = 0.99999 we get the following value for deaths.

(q^2/j)*N = ((0.99999)^2)/1.01)*100 000 = 9.90e4

So a bit over 99 000 individuals need to die to pass a to the next generations and eventually cause fixation, 99 009 with better precision. To put that into perspective; 99 009/100 000 * 100 =~ 99%! Haldane perpetuates this error throughout his paper. The point is, there is no reasonable expectation that individuals carrying A have to die, particularly at such rates, but Haldane kept doing so because he normalized his fitness factor incorrectly by counting the previously killed off carriers of A in the calculation for the next generation.

Fixing a gene in a population is not restricted to adopting a previously harmful mutation either. Here, again, the fixation could possibly occur at a higher rate without destabilizing the population as noted by Valen (1963).

Dodson (1962) seized on this estimate of 300 generations, applied it to evolution within the genus Homo, and needless to say for this case, found a poor fit with observed and inferred facts. The most probable interpretation of this difference is that much of the evolution of this genus has been such to present no dilemma to the populations. The most commonly noted difference between successive species, and one that is probably responsible for some of the other differences, is the increase in brain size and presumably intelligence. There is no reason to believe that the part of this increase that occurred in the transition from H. erectus to H. sapiens was a direct adaptation to middle Pliestocene environmental changes (that is, would not have been valuable to the environments of Homo erectus), although it is conceivable that environmental changes (such as possible changes in predators and food) increased the selective advantage for greater intelligence or lowered a threshold of disadvantage for the cocomitant structural disturbance of the skull. The other functional complex known to have changed importantly is posture (and presumably locomotion); it is very possible that the only difficulties in the change of this complex also, were the reorganizations of the anatomy and the genome and not a greater than previous loss of individuals with the ancestral genotype. (Valen, 1963, p. 186-187)


It must first be said that Haldane was not presenting any fault with evolution, nor was he in any way defending Creationism or its poorly disguised brother Intelligent Design. Haldane, in his paper, was trying to come up with a means to calculate how quickly a population evolves if survival meant adopting a previously harmful gene. Nor is there any discussion or other indication about genomes decaying.

Secondly, Haldane's estimate of 300 generations was falsified by Dodson when he compared changes in genus Homo. There is no empirical grounds to accept 300 generations as sacrosanct and suggests that there is no dilemma.

Thirdly, Haldane's calculations are erroneous because he did not properly normalize his fitness factor correctly. Why should individual carrying gene A need to die in such large numbers to fix gene a? Clearly, the empirical evidence suggests that this does not happen on the norm and yet evolution proceeds unabated.

Lastly, although much more can probably yet be said, Haldane was a scientist and admitted that his work probably was not without error. His efforts, nonetheless, helped scientists better understand the evolutionary process. This is how science works!

To conclude, I am quite aware that my conclusions will probably need drastic revision. But I am convinced that quantitative arguments of the kind here put forward should play a part in all future discussions of evolution. (Haldane, 1957, p. 523)

Questions to my Opponent

How did you reach the conclusion that this paper supported a decaying genome?

What is it about the 300 generations estimate that you find significant seeing that it is evidently incorrect?

Did you actually spend time reading the paper?


  • Haldane's Dilemma, Evolutionary Rates, and Heterosis Valen, 1963