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This is a continuation of an earlier post, A short post on fixation, to which Professor Moran replied here. He has asked Dr. Kozulic to contact him directly; Dr. Kozulic is now answering that request as co-author of the present post. We asked Professor Moran to answer three questions relating to the fixation of neutral mutations. But before dealing with his answers, let’s confirm that both sides agree that the key point at issue here is the fixation of neutral mutations in the human lineage, subsequent to its divergence from the lineage leading to chimpanzees. In Professor Moran’s words:
In an attempt to show them that evolution CAN account for the differences between humans and chimps/bonobos, I wrote up a description of how Neutral Theory and random genetic drift produce genomes that differ by 22 million positions if we take the fossil evidence at face value and assume that chimps and humans last shared a common ancestor about 5 million years ago [Why are the human and chimpanzee/bonobo genomes so similar?].
The questions that Professor Moran didn’t answer
In a previous reply to a post by Torley, Professor Moran elaborated on the mutation rate determined in long-term experiments with E. coli. But in our view there has never been any dispute on this point. Indeed, in our post (April 5, 2014), we treated the quoted figure from that study of 35 mutations as fixed mutations (see below), in order to show that the fixation rate Professor Moran stated for the human population was over five orders of magnitude greater than for E. coli, and that this striking fact was in need of explanation. Our hope was that Professor Moran would start discussing population sizes, but unfortunately, that did not happen.
Then we quoted from a well-known textbook on population genetics, John Gillespie’s Population Genetics: A Concise Guide (Johns Hopkins University Press, Baltimore, second edition, 2004):
If 1/μ << N, the time scale of mutation is much less than drift, leading to a population with many unique alleles. If N << 1/μ, the time scale of drift is shorter, leading to a population devoid of variation. (2004, p. 31)
In the passage above, μ [mu] refers to the mutation rate and N to the population size. We then added:
Professor Moran is kindly requested to state whether he agrees with this statement, and if not, to provide some references to support his views.
Professor Moran responded:
As for the question, I can’t really answer it because I don’t know what John Gillespie means by the mutation rate (μ). If it’s 10-10 per bp per generation then 1/μ equals 1010, or 10 billion. There are very few population sizes that are larger than 10 billion. If Gillespie means something like 10-4 mutations per generation (E. coli) or 100 mutations per generation (Homo sapiens) then I agree with him, although it seems a bit silly to be talking about a population size of 1/100 (1/μ) in the case of humans.
Obviously, it would be very silly to speak of any population having a size of 0.01, and not just a human one! Thus it appears that Professor Moran realized that something was wrong with the mutation figure he was using, of 100 mutations per generation, but he did not bother to check what it was.
(Actually, Gillespie states on page 30 that “mutation rates are often small (10-5 to 10-10 depending on the context)”, so the mutation rate μ can only refer to the mutation rate per nucleotide (bp) per generation. But if μ is 10-10 per bp per generation then 1/μ equals 1010, or 10 billion. Since the effective human population size N was 10,000 or less during most of the Paleolithic era, it would follow that N << 1/μ, "leading to a population devoid of variation," as Gillespie states. This runs completely contrary to the scenario Professor Moran is proposing: he maintains that there was sufficient variation to fix 100 mutations in each generation, from five million years ago to the present.)
Quoting again from John Gillespie’s text, Population Genetics: A Concise Guide (Johns Hopkins University Press, Baltimore, second edition, 2004, page 54), in the passage below, Ne refers to the effective population size, μ to the mutation rate and v to the variance in the change:
Figure 2.9 illustrates the beta density for three values of 4Neμ for a symmetrical model with μ=v. Notice that if 4Neμ<1, the probability mass is concentrated near the boundaries. In this case we expect – in a probabilistic sense – to find the allele frequency near either zero or one. If 4Neu>1, the allele frequency piles up near its deterministic equilibrium value of one-half. In the former case genetic drift dominates mutation; in the latter case mutation dominates drift. When 4Neu = 1, we have the peculiar case where neither force has the upper hand.
If the numerical value of the mutation rate (μ) is 100 (or 133), as used by Professor Moran, the product 4Neμ is for all population sizes larger than 1. If so, two important cases of population genetics models, when 4Neμ = 1 and when 4Neμ<1, have impossibly high values for μ. With the only possibility left, 4Neμ>1, “the allele frequency piles up near its deterministic equilibrium value of one-half”, and “mutation dominates drift” in all cases. It appears impossible to avoid the conclusion that the mutation rate used by Professor Moran is much larger than the values commonly used in population genetics models. (Alternatively, if μ should really be 10-10, then 4Neμ<1, which would mean that genetic drift would dominate mutation in an effective population of, say, 10,000, which was the effective human population size for most of the Paleolithic.)
It is possible to express the mutation rate per nucleotide, per locus or per individual genome, as we noted in our previous post. Regarding the time units: the mutation rates quoted in the literature are usually rates per generation, rather than per year. The experimentally determined numerical values vary somewhat from study to study, but we will use the above-mentioned value for E. coli of about 1×10-10 (Lenski) as the mutation rate per nucleotide. Since a locus is typically taken to contain 1000 nucleotides, the mutation rate expressed per locus is therefore 1000 times higher (for a locus containing 768 nucleotides, Gillespie gives the value of 7.83 x 10-7 per locus, and 1 x 10-9 per nucleotide, on page 32). Finally, we can express the mutation rate per individual genome, which corresponds to about 100 for the human genome.
The crux of our dispute with Professor Moran, as agreed by both sides (see above) is the feasibility of 22 million neutral mutations being fixed in the human population, over a period of five million years. These mutations are nucleotide mutations. Professor Moran is kindly asked to answer the following two questions.
First, since we are talking about nucleotide mutations here, why doesn’t he apply the value for the mutation rate per nucleotide in his calculation?
Our second, related question is: since the dispute between us is not about the fixation rate of individual genomes(?), then why does he use the value for the mutation rate per individual genome?
Can Professor Moran provide a credible model to support his claims regarding fixation?
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Spread of Homo sapiens (1, red), Neandertals (2, olive) and early hominids (3, green). During most of the Paleolithic, the effective human population size was approximately 10,000. Figures shown on the map refer to arrival dates, in years before the present – for example, humans arrived in Australia 50,000 years ago and in Alaska 15,000 years ago. Image courtesy of Wikipedia.
Next, we would kindly ask our readers to take a close look at Table 1 in the Wielgoss paper, which Professor Moran cited in his reply. Taking as an example population Ara-3, the reader will notice that the 10 individuals from that population have 10 different mutations. These mutations are all in a polymorphic state – that is, a single individual (others not sampled may also have the same mutation) possesses a particular mutation, whereas the other individuals in that population do not possess that mutation, but have different ones instead. None of the mutations is therefore fixed, because if it were, all of the sampled individuals would have that particular mutation – for example, 756,799 C-T would be present in all 10 individuals – in addition to their own mutations. Accordingly, every new mutation on its way to fixation has to pass through a polymorphic state. For any given mutation, the probability of fixation is 1/(2N) and the time it takes to achieve fixation is 4N generations.
Lest Professor Moran object that Gillespie’s textbook might be considered hostile to his views, we would now like to quote from another textbook on population genetics. The following quote is taken from Daniel L. Hartl and Andrew G. Clark, Principles of Population Genetics (Fourth Edition, Sinauer Associates, 2007), Chapter 3, Random Genetic Drift, under the heading, “Absorption Time and Time to Fixation”, pages 112-113:
Equations 3.8 and 3.9 are of particular interest when p = 1/(2N), that is, when a new neutral mutation has just occurred and there is one copy in the population. In this case, the probability of eventual fixation is 1/(2N), and, given that the allele is eventually fixed, the average time to fixation is approximately 4N generations. On the other hand, the probability that a new allele is eventually lost is 1 – 1/(2N), and, given that the allele is eventually lost, the average time to loss is approximately 2*ln(2N) generations. In other words, new neutral alleles that are eventually fixed usually take a long time to be fixed, whereas those that are lost are lost very quickly. For the specific example of N = 500, the average new mutation that is eventually fixed requires 2000 generations to be fixed, whereas the average new mutation that is destined to be lost requires fewer than 14 generations to be lost. (Emphases ours – BK & VJT.)
Professor Moran believes that 100 mutations were fixed in each human generation for 5 million years, because that is required in order to explain the differences between human and chimp genomes. Can population genetics supply a model that delivers what is asked of it?
Let us now consider two hypothetical models:
1. In every human generation there was just a single couple that left descendants (effective population size 2Ne = 2), while all others were infertile or killed, so all new 100 mutations that appeared (scattered across some 3,000,000,000 possible sites in the genome) were fixed in the descendants.
2. In all individuals of one generation (2Ne can have any value), all the new mutations were of the same type and happened at the same sites, so regardless of which individuals mated, all descendants acquired the same mutations. This same process continued for thousands of generations, with various mutations.
The first model would require continual inbreeding, and the second, continual miracles. Neither model appears credible to us; nor do we believe Professor Moran would espouse either of these models. It is important to note, however, that that both models have one thing in common, which is why they both work: all of the mutations fix without having to pass through the polymorphic state. We suspect that Professor Moran’s back-of-the-envelope-calculations which he referred to (see the footnote below), share this same feature. We would therefore kindly ask Professor Moran to provide a numerical value for Ne that does the job, for a model that’s capable of delivering what he needs, which is: 100 new mutations being fixed in each human generation over a period of 5,000,000 years.
The pattern of fixation also needs to be explained
In our previous post, we referred to an article by Rasmus Nielsen et al., titled, A Scan for Positively Selected Genes in the Genomes of Humans and Chimpanzees (PLoS Biology, 3(6): e170. doi:10.1371/journal.pbio.0030170, published May 3, 2005), in particular to Figure 1 that shows that multiple mutations (up to 21) have become fixed in thousands of different proteins, leading us to state:
In short: it is the pattern of fixation which neither the theory of neutral evolution nor the neo-Darwinian theory of natural selection, nor any combination of the two, can adequately explain.
Until now, Professor Moran has provided no evidence that would contradict our statement. At this point we would kindly ask him to take a close look at two relevant articles, in order to better understand the challenges that the pattern of fixation poses for population genetic modeling:
Behe MJ, Snoke DW (2004) Simulating evolution by gene duplication of protein features that require multiple amino acid residues. Protein Science 13:10, pp. 2651-2664, doi:10.1110/ps.04802904
and
Lynch M (2005) Simple evolutionary pathways to complex proteins. Protein Science 14:9, pp. 2217-2225, doi:10.1110/ps.041171805.
Behe and Snoke’s response to Lynch can be found here.
Hundreds of orphan genes that characterize each species: why doesn’t Professor Moran recognize their existence?
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Karyotype of a human male. (A karyotype is a complete set of the chromosomes of a cell, usually arranged in pairs and in descending order of size.) Image courtesy of the National Human Genome Research Institute and Wikipedia.
We would also like to remind Professor Moran that a major issue from the start of this discussion [on macroevolution] still remains open. In a previous post, titled, So, why are the human and chimpanzee/bonobo genomes so similar? A reply to Professor Larry Moran (March 21, 2014), Torley wrote:
In conclusion, I’d like to point out that Professor Moran nowhere addressed the problem of the origin of orphan genes in his reply, so he didn’t really answer the first argument in my previous post, which was that we cannot claim to understand macroevolution until we ascertain the origin of the hundreds of chemically unique proteins and orphan genes that characterize each species.
Moran then responded:
I didn’t discuss orphan genes because it’s irrelevant to either of the points I was making. It has nothing to do with the question of human/chimp sequence similarity and it has nothing to do with the abundant evidence in support of macroevolution. Besides, I don’t accept his premise that there are hundreds of unique genes that characterize each species.
This is astonishing. Leaving aside the fact that orphan genes obviously do have an impact on sequence similarity and on the view of macroevolution, a prominent biochemist like Moran would normally be expected to give reasons for his refusal to recognize the reality of hundreds of unique genes and proteins found in the sequenced genomes of all species (on this point, see this paper by Kozulic). The reasons for his refusal can only be based on a defect which he has discovered in the experimental data, or in the logic underlying the interpretation of the data, or both. We hope that Professor Moran will use this opportunity to provide us with his reasons.
Is Professor Moran a Darwinist, protestations to the contrary notwithstanding?
On many occasions, Professor Moran has publicly stated that he does not consider himself a Darwinist. We would be in perfect agreement with him, and we ourselves would be happy to be called evolutionists, based on the following simple definition of evolution (Gillespie, p. xi): “Evolution is the change in the frequencies of genotypes through time, perhaps due to their differences in fitness.” But there is one crucial issue that divides us: the fundamental claim of Darwinism that variations among individuals of one species are fundamentally no different in kind from the variations between individuals of different species. We disagree. As long as Professor Moran accepts and promotes the above claim, he remains (in this important respect) a Darwinist, notwithstanding his protestations to the contrary.
To avoid any misunderstandings, we would like to say that we regard population genetics as an exact science. One of us (BK) views the present relationship between Darwinism and population genetics as follows: Darwinism is torturing population genetics to deliver what it cannot deliver – models that do not contradict what we currently know about the differences between species, which have been identified in the sequenced genomes of several thousand species.
Given the vital importance of population genetics models, we hope Professor Moran will answer all of the above questions. Since he is a biochemist, he can hardly be expected to know all the intricacies of population genetics (and neither would we claim to possess such knowledge), so we would encourage him to consult the textbooks and ask for assistance from his colleagues.
Footnote
In his February 28 post, titled, Why are the human and chimpanzee/bonobo genomes so similar?, Professor Moran wrote:
The human and chimp genomes are 98.6% identical or 1.4% different. That difference amounts to 44.8 million base pairs distributed throughout the entire genome. If this difference is due to evolution then it means that 22.4 million mutations have become fixed in each lineage (humans and chimp) since they diverged about five million years ago.
The average generation time of chimps and humans is 27.5 years. Thus, there have been 185,200 generations since they last shared a common ancestor if the time of divergence is accurate. (It’s based on the fossil record.) This corresponds to a substitution rate (fixation) of 121 mutations per generation and that’s very close to the mutation rate as predicted by evolutionary theory.