The neutral theory of evolution appears to have won out over its rival, neo-Darwinian selection theory (see here and here). However, the neutral theory makes a very specific prediction about the rate at which mutations are fixed in a population, which I think warrants more testing and scrutiny. The evidence for this prediction which I’ve seen to date is frankly underwhelming.
What is the neutral theory of evolution?
Let’s begin with a few definitions. What is the neutral theory of evolution? Here’s a short definition given by Professor Terry Speed, formerly of Berkeley University:
The Neutral Theory of Molecular Evolution (Kimura) states, in essence, that most of the variation seen at the molecular level is selectively neutral — that is, there are no important fitness advantages or disadvantages associated with particular alleles — and that genetic drift, rather than natural selection, dominates the dynamics. This does not mean that mutations, when they occur, are all neutral, or that the genes themselves are unimportant. On the contrary, it is thought that most mutations are deleterious to the organism, and thus are unlikely to remain in the population long enough to contribute measurably to the “standing” variation. Only those mutations that do not have a harmful effect have an appreciable chance of sticking around long enough for us to see them. The Neutral Theory hypothesizes that this class of “allowable” mutations is composed entirely of selectively neutral variants. The alternative viewpoint (much simplified) is that advantageous mutations, while perhaps exceedingly rare, do play a major role in evolution, and that polymorphism at the molecular level can best (or, at least, possibly) be explained by natural selection.
The triumph of the neutral theory over neo-Darwinism
Professor PZ Myers recently wrote a very revealing post, titled, The state of modern evolutionary theory may not be what you think it is (February 14, 2014), about how the modern theory of evolution has completely changed from the Darwinian version that most of us were taught at school:
…[M]aybe we should be honest from the very beginning about the complexity of modern evolutionary theory and how it has grown to be very different from what Darwin knew.
First thing you have to know: the revolution is over. Neutral and nearly neutral theory won. The neutral theory states that most of the variation found in evolutionary lineages is a product of random genetic drift. Nearly neutral theory is an expansion of that idea that basically says that even slightly advantageous or deleterious mutations will escape selection — they’ll be overwhelmed by effects dependent on population size. This does not in any way imply that selection is unimportant, but only that most molecular differences will not be a product of adaptive, selective changes.
Professor Larry Moran, in a follow-up post, broadly concurred with Professor PZ Myers’ assessment:
Random genetic drift is a mechanism of evolution that results in fixation or elimination of alleles independently of natural selection. If there was no such thing as neutral mutations then random genetic drift would still be an important mechanism…
Random genetic drift is a mechanism of evolution that was discovered and described over 30 years before Neutral Theory came on the scene.
What Neutral Theory tells us is that a huge number of mutations are neutral and there are far more neutral mutations fixed by random genetic drift that there are beneficial mutations fixed by natural selection. The conclusion is inescapable. Random genetic drift is, by far, the dominant mechanism of evolution.…
The revolution is over and strict Darwinism lost. We now know that random genetic drift is an important mechanism of evolution and there’s more to evolution than natural selection. Unfortunately, this blatantly obvious fact is not understood by the vast majority of people and teachers. There are even many scientists who don’t understand evolution.
The neutral theory’s predictions regarding rates of fixation
The neutral theory makes a very specific prediction about the rate at which mutations are fixed within a population. This prediction follows from the fact that the only mutations being considered in the model are neutral mutations, as Professor Terry Speed points out in his course notes. He continues:
Whatever we imagine these mutations look like, however, they are
assumed to occur with mean rate generation (on whatever scale we are assessing mutations– transitions, transversions, third-base mutations, etc·). We want to know the rate at which these mutations that are entering the population become established in the population– the fixation process described above. This is known as substitution (a new type is substituted for an old). Then we can … show that
This simple result, that the rate of substitution equals the rate of mutation, has been instrumental in the study of molecular evolution, for good reason. Population genetics is notorious for its reliance on difficult to measure (and often confounded) parameters such as effective population size, mutation rate, and selection coefficients. Here is a formula which tells us that the data we observe (substitutions) is dependent only on one of these, mutation rate.
The neutral theory’s predictions regarding the time it takes for mutations to get fixed
There’s more. The neutral theory also makes a very specific prediction regarding the time it takes for a neutral mutation to get fixed in a population – that is, assuming it gets fixed:
Most neutral alleles [alternative versions of a gene – VJT] are lost soon after they appear. The average time (in generations) until loss of a neutral allele is 2(Ne/N) ln(2N) where N is the effective population size (the number of individuals contributing to the next generation’s gene pool) and N is the total population size. Only a small percentage of alleles fix. Fixation is the process of an allele increasing to a frequency at or near one. The probability of a neutral allele fixing in a population is equal to its frequency. For a new mutant in a diploid population [where each organism’s cells contain two sets of chromosomes, one from each parent – VJT], this frequency is 1/2N.
If mutations are neutral with respect to fitness, the rate of substitution (k) is equal to the rate of mutation(v). This does not mean every new mutant eventually reaches fixation. Alleles are added to the gene pool by mutation at the same rate they are lost to drift. For neutral alleles that do fix, it takes an average of 4N generations to do so. However, at equilibrium there are multiple alleles segregating in the population. In small populations, few mutations appear each generation. The ones that fix do so quickly relative to large populations. In large populations, more mutants appear over the generations. But, the ones that fix take much longer to do so. Thus, the rate of neutral evolution (in substitutions per generation) is independent of population size.
(Chris Colby, Introduction to Evolutionary Biology, Version 2, January 7, 1996, Talk Origins Archive.)
Actually, the figure of 4N generations is not quite correct: according to Professor David H.A. Fitch, of the Department of Biology at New York University, “the time it takes a particular mutant to achieve fixation from the time it arises is dependent on population size (this time is 4*Ne generations, where Ne is the effective breeding population (N if everybody contributes progeny).” (1997 Course notes, Population Size and Genetic Drift)
The implications for human evolution
What does that mean for human beings? In a post titled, Why are the human and chimpanzee/bonobo genomes so similar? (February 28, 2014), Professor Moran helpfully explains:
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.
What Professor Moran is saying here is that 121 mutations are being fixed in the human population, in each successive generation. Since 185,200 generations have elapsed since the human and chimpanzee lines diverged, this means that 22.4 million mutations have become fixed in the human lineage since our ancestors diverged from the line leading to chimps. That’s a staggering number.
Professor Moran thinks we shouldn’t be surprised. The rate of fixation is supported by three converging lines of evidence, as he explains, in a post titled, stimating the Human Mutation Rate: Direct Method (February 22, 2013):
There are basically three ways to estimate the mutation rate in the human lineage. I refer to them as the Biochemical Method, the Phylogenetic Method, and the Direct Method.
The Biochemical Method is based on our knowledge of biochemistry and DNA replication as well as estimates of the number of cell divisions between zygote and egg. It gives a value of 130 mutations per generation. The Phylogenetic Method depends on the fact that most mutations are neutral and that the rate of fixation of alleles is equal to the mutation rate. It also relies on a correct phylogeny. The Phylogenetic Method gives values between 112-160 mutations per generation. These two methods are pretty much in agreement.
The Direct Method involves sequencing the entire genomes of related individuals (e.g. mother, father, child) and simply counting the new mutations in the offspring. [Moran then cites a paper by Xue et al. (2009) which estimates the mutation rate at 103 mutations per generation.]
That’s not an observation, Professor Moran!
With the greatest respect to Professor Moran, none of these methods counts as an observation of the rate at which mutations get fixed in the human population. Inferring how many mutations must have taken place from an assumed time at which the human and chimp lineages diverged, is not the same thing as observing the rate at which mutations get fixed in the human line. And observing how many mutations occur in the space of one generation, from parent to child, is not the same thing as observing the rate at which mutations occur in the human population as a whole.
Professor Moran might respond that according to the mathematical assumptions underlying the neutral theory of evolution, the rate at which mutations get passed on from parent to child is the same as the rate at which mutations get fixed in the population as a whole. That may be so; but it does not mean that an observation of the former automatically counts as an observation of the latter. The equation of the two rates only occurs within a particular theory of evolution: the neutral theory. If we are to test this theory properly, then, we need a population in which we can observe mutations getting fixed, and see if the rate accords with the mutation rate from parent to offspring.
Mathematical quibbles with the neutral theory: backwards reasoning
I might add that some of the mathematical arguments supporting the neutral theory seem a little questionable to me. Take this “backwards reasoning” argument from Professor Terry Speed’s course notes, in support of the claim that the probability that a new mutation eventually gets fixed is exactly (1/2N), where N is the population size:
…[A]t time 0, there will be 2N gametes in the population, any of which might or might not leave descendants in the next generation. If they do not, the lineage of that allele copy is extinct in the population. If we follow the population through time, eventually all but one of the 2N original lineages will be extinct, and the remaining one will be fixed in the population. Because all of the original gametes have equal probability of generating the surviving lineage, the fixation probability of any allelic type is simply the frequency of that type.
The argument seems to picture the alleles as if they’re all competing against each other, on an individual basis. But what we need to remember is that the new allele (call it A) may be competing against the entire population, all of whose members have another version (call it B) of that gene. In this situation, does it really sound reasonable to say that “all of the original gametes have equal probability of generating the surviving lineage”? No wonder that Professor Speed himself is a little wary of this argument: he acknowledges that it is “simply a verbal argument,” but one which (he thinks) generates powerful insights.
The implausible claims of the neutral theory, when applies to human evolution
Although I’m happy to be proved wrong, the claim that more than 100 mutations get fixed in the entire human population, in each passing generation, strikes me as implausible. I’m tempted to ask: where are all these mutations that are fixed in the human population in 2014, but were not fixed in the human population one generation ago, in 1987? Has anyone identified them?
The time taken for these mutations to get fixed also seems extraordinary. We are told that for a population of N organisms, it takes (4*Ne) generations for a mutation to get fixed in the population, where Ne is the effective size of the human population. For most of human history, the effective population size appears to have been around 10,000, even though the actual human population size is thought to have been considerably higher (350,000 from the Middle Pleistocene onwards, according to a 2008 article by Professor John Hawks). Four times 10,000 equals 40,000 generations, and if we use Professor Moran’s figure of 27.5 years per generation, that’s equivalent to 1,100,000 years ago.
Let me spell that out: if we take a typical mutation out of the 100-odd mutations which (according to the neutral theory of evolution) got fixed in the human population within the last generation (from 1987 to 2014), we will find that that mutation first appeared in the human lineage some 1,100,000 years ago.
Am I the only one who thinks this figure is absolutely extraordinary? And for that matter, doesn’t the notion of a mutation that takes one million years to fix sound a little suspicious?
Should we trust mathematical estimates of how long it takes mutations to get fixed in the human population, given the enormous environmental upheavals (e.g. Ice Ages, the Toba eruption, and so on) that we’ve faced in the past million years?
And what about this? Anthropologist John Hawks estimates that positive selection in the past 5,000 years has occurred at a rate roughly 100 times higher than any other period of human evolution. He adds: “We are more different genetically from people living 5,000 years ago than they were different from Neanderthals.” All this hyper-evolution has been occurring at a time when the human population has been higher than ever before – which means that it should take much, much longer for mutations to get fixed in the population! So how does that work? Go figure.
Testing the neutral theory
Of course, I realize that testing the predictions of the neutral theory of evolution regarding how many mutations get fixed in the population in each generation, and how long it takes for a new mutation to get fixed, might be rather impractical for a long-lived, slow-reproducing species like Homo sapiens.
So I’d be very interested to hear from any readers with a biology background. How do the predictions of the neutral theory check out when applied to bacteria? What about simple eukaryotes? Have any studies been done for animals? Which ones? Over to you.
Fortunately for Torley, there are a number of papers that answer his question. The one that I talk about in class is from Richard Lenski’s long-term evolution experiment. Recall that mutation rates are about 10^-10 per generation. If the fixation rates of neutral alleles was equal to the mutation rate then (as predicted by population genetics) then this should be observable in the experiment run by Lenski (now 60,000 generations).
The result is just what you expect. The total number of neutral allele fixations is 35 in the bacterial cultures and this correspond to a mutation rate of 0.9 × 10^-10 or only slightly lower than what is predicted. There are lots of references in the paper and lots of other papers in the literature.
Wielgoss, S., Barrick, J. E., Tenaillon, O., Cruveiller, S., Chane-Woon-Ming, B., Médigue, C., Lenski, R. E. and D. Schneider (2011) Mutation rate inferred from synonymous substitutions in a long-term evolution experiment with Escherichia coli. G3: Genes, Genomes, Genetics 1, 183-186. [doi: 10.1534/g3.111.000406]
I think it is fair to conclude that short-term studies, done with microbes, lend support to the neutral and near-neutral theories of evolution.
Professor Moran also points out in his post that “Neutral Theory, per se, does not predict the rate of fixation of neutral alleles. That was what population genetics told us 80 years ago. What Neutral Theory says is that this may be the dominant form of evolution.”
Finally, with regard to anthropologist John Hawks’ claim that evolution is accelerating in modern times, Professor Moran writes: “John Hawks is probably wrong but in any case his argument is irrelevant. He’s talking about the small number of alleles that might be fixed by natural selection and not the vast majority of neutral alleles that are fixed by random genetic drift.”