Mathematics of Evolution. (Fred Hoyle).

Was
Darwin
Wrong?

A Knighted Astronomer's Fight Against Neo-Darwinism,
Using Mathematics As His Weapon.
a review by Gert Korthof
10 Oct 1999 (updated 3 Dec 2004)

"The Darwinian theory is wrong and the continued adherence to it is an impediment to discovering the correct evolutionary theory"
Fred Hoyle

There isn't any outsider who penetrated so deep in population genetics as astronomer- mathematician Sir Fred Hoyle, with such a mathematical knowledge, with such an integrity to find out the truth, and without distorting his subject of investigation.

Fred Hoyle was a lifelong Darwin, Darwinism and evolution critic. Every Darwin critic appears to know his famous Boeing-747 story to criticise the origin of life by pure chance. The story was much quoted, often without access to the original source. Mathematics of Evolution originally circulated as copies of a hand-written manuscript back in 1987, and has now for the first time been printed. This is fortunate because his Evolution from space (1981) and Why Neo-Darwinism Does Not Work (20) are out of print.
Mathematics of Evolution contains a number of surprises: Hoyle's personal confessions in the introduction; his histone-4 case; his thorough analysis of the infamous Haldane's Dilemma. The main part of Mathematics of Evolution consists of his calculations of the core assertions of Neo-Darwinian population genetics. Even if all mathematics is skipped, the book is still worth reading. His 'Life from space' (Panspermia) hypothesis is present at the background and comes to the surface at a few places. Mathematics of Evolution, doesn't have religious overtones. Hoyle's attitude can be described as: "how far does the neo-Darwinian theory work?" with the real possibility that it does not work or only partially works. This is in great contrast to the standard evolution textbooks. If one adds the fact that Fred Hoyle is recognised in his own area mathematics, theoretical physics and astronomy, then it's clear that this book is an exciting event for evolutionists and Darwin-critics alike.

Mathematics of Evolution
by Fred Hoyle
Acorn Enterprises LLC, Memphis, Tennessee
1999
142 pages
Contents:

	Foreword	ix
	Preface	xiii
	Introduction	1
1	Natural Selection and the Multigene Problem	7
2	Cell Division and Crossover	27
3	A Bisexual Model with Crossover	41
4	The Solution of the Single-Gene Problem by a Partial Differential Equation	59
5	Sociological Consequences of Deleterious Mutation Pressure	81
6	How Far Does the Neo-Darwinian Theory Work?	97
7	The Genetic Cost of Evolution	111
8	Protein Phylogenies - More Illusions	127
9	Summary and Conslusions	135
	(no index, no references)

Hoyle's Panspermia theory

Mathematics of Evolution does not contain an elaborated Panspermia theory. I found the following fragments:

the basic features of life, such as enzymes, tRNA, histones, the genetic code are extraterrestrial (p103).
"all genes in present day organisms were here already in the metazoans that invade the Earth 570 million years ago at the beginning of the Cambrian Era, making the subsequent story of terrestrial evolution into one in which genes have been called into operation as ecological conditions permitted them to be so." (xvi).
Particles from space less than 100 µm could contain micro-organisms, eggs, sperms of lower animals, viruses, viroids add genes to the gene pool of the Earth (p104).

the external incidence model (p108).

It is not clear to me what is precisely claimed in [2], because 570 millions years ago is not the origin of life. The first signs of life on Earth were 3.45 billion years ago and the oldest undoubted fossil algae (procaryotes) are found 2.9 billion years ago. Hoyle did not claim that all genes of the higher organisms, were present in the very first life forms. So his theory seems to depend on multiple extraterrestrial invasions of biological materials. Finally, hidden between the lines, a remark appears, that life was seeded on our Earth. Does this mean that life on Earth is the product of Extraterrestrial Intelligence?

Evaluation of the evidence

To believe in extraterrestrial life somewhere in the universe is one thing. To believe that extraterrestrial life contributed

in a substantial way to the origin and evolution of life on our own planet, is another thing. To believe that extraterrestrial life was the exclusive source of life on Earth, is an extraordinary claim. What kind of evidence could support such an extraordinary claim? Could there be direct or only circumstantial evidence? Circumstantial evidence could be some property or pattern of living organisms on Earth that could not be explained by neo-Darwinism. It could be only indirect evidence, because on its own it would not be enough. The properties should be linked with extraterrestrial origins. Direct evidence for example would be an organism recovered from a meteorite. However that would be mainly evidence for a possible transfer mechanism of life from space to Earth. The lifeform needs to be viable and able to multiply on Earth. All this has to be demonstrated. So far no analysable extraterrestrial lifeform has been found.

The strong points of this book are not rigorous testing of a hypothesis against the biological facts. It's not the goal of Mathematics of Evolution. However to evaluate the panspermia theory, one cannot escape a full confrontation of Hoyle's theory with all the relevant biological facts. Irrespective of the conclusion that neo-Darwinism is wrong, Hoyle's theory needs positive evidence.

Evaluation of the panspermia theory

Multiple extraterrestrial genetic injections can only be successful if they all have the same genetic code. In the end this boils down to the requirement that all extraterrestrial input must have the same origin. What's the probability of this? A single input of genetic information could explain the appearance of life on Earth.

And that means that our genetic code originated somewhere in space. The disadvantage of the single input hypothesis is that it leaves all further evolution of life to traditional Darwinian mechanisms of mutation and selection (18), which are insufficient according to Hoyle. Unless one claims that all genes were present in those first forms of life. Which is highly improbably because those first forms of life are too small to carry such a huge useless load (19). So both single and multiple invasions have their problems; the multiple invasions having the most serious problems.
Why is it a problem that the genetic code of the extraterrestrials and terrestrials should be the same? Is the code not necessarily derived from the laws of chemistry? No, it isn't! The genetic code is not a universal cosmic code. The problem with any theory that claims extraterrestrial genetic input, is that life on Earth is a closed genetic system. I strongly disagree with Hoyle's claim that

"terrestrial biology is not a closed system". (p3) Why? All Life on earth happens to have the same genetic code. That would be no problem, if it would be the only possible genetic code available to life. Our genetic code is one of billions and billions of possible codes (1). The current one looks like a 'frozen accident'. The probability that the genetic code of extraterrestrial DNA is the same as the genetic code on earth, equals the chance that a Boeing-747 arises from a junkyard! It doesn't make a difference if foreign DNA should have exactly the same 3D-structure and the same 4 bases as DNA on Earth, because the problem is not in the structure of DNA itself. The problem is in the meaning of the sequences of bases, which is determined by the genetic code. Hoyle knows that the genetic code is conserved and redundant but apparently not that it is a 'frozen accident'. Nothing more than a highly arbitrary assignment of 20 amino acids to 64 base triplets.

It does not help to send complete organisms with a built-in key to translate the DNA message either, because the only thing what will be achieved is a separate branch of life that will not mix with lifeforms on Earth. And it does not help to focus on the exceptions of the genetic code, if anybody would suggest that, because these are minor variations. And because they are minor, they are not too difficult to explain by evolution and so don't need extraterrestrial help. To circumvent the genetic code matching problem one could introduce extraterrestrial proteins directly into organisms. This will fail because there is no way to translate proteins back into the genome. It is forbidden by the so-called 'Central Dogma' (2). Hoyle's problem that extraterrestrial genes would at first not 'feel at home' on the Earth, is really an insignificant and small problem compared with the genetic code matching problem. If my analysis is correct, then there can be in principle no extraterrestrial input of genetic material into the Earth's genepool.

Diseases caused by extraterrestrial viruses is a highly improbable hypothesis for the same reason. Of course the genetic material of influenza viruses needs to have the same meaning as our own DNA to get the flu. Viruses depend on the machinery of the host cell. It's because the influenza virus and humans 'talk the same language', that we get sick (3). The point is: what is the probability that extraterrestrial viruses, if they exist, would have the same genetic code as humans? If extraterrestrial life is found, I would first have a look at its genetic code.
It is of not much help to go into historical questions of priority. Was Darwin the first to propose evolution by natural selection or had Blyth and Wallace priority? Blyth & Wallace were both evolutionists and had no idea of extraterrestrial origin of life as far as I know. Whatever the priority, it neither helps Hoyle's theory about extraterrestrial origin of life, nor does it help his criticism.

These are disappointing, unnecessary pages. Hoyle goes on pointing to discontinuities in the fossil record just like creationists. He really claims that multiple bombardments of lifeforms from space explain discontinuities of life. He calls it 'the external incidence model' (p108). Hoyle invokes 'genetic storms' to explain for example the sudden appearance of different orders of mammals. 'Genetic storms' are 100% speculation and extraterrestrial events or viruses triggering genetic storms are 200% speculation. Uptake of extraterrestrial DNA is 300% speculation. 'Genetic storm', 'genetic explosion' (p108) are concepts which do not occur in biology, Hoyle treats them as facts! At the most they are metaphors. "Other species are highly sensitive to genetic invasion from outside' (p108): show me the evidence. This is a description in a new language, not an explanation based on verified facts.

Panspermia: conclusion

When one combines (a) the perceived problems in the theory of evolution (Why Neo-Darwinism Does Not Work, 1982) and (b) observed signs of life in space (Life from Space,1981), then it is only logical to propose a Panspermia theory. I do not deny that there are unsolved problems in Evolution Theory. And it seems reasonable that raw organic material could come from space onto the Earth (4) and could have helped the origin of life. I also have no problem with the idea that the universe is 'biocentric', in the sense that the building blocks of life are widespread in the universe. However if Panspermia claims a substantial or even crucial contribution to the origin and/or evolution of life on earth, Hoyle needs criteria to discriminate between the extraterrestrial scenario and the spontaneous-origin-of-life-on-Earth scenario. What key observation would tell the difference?

How could Hoyle tell the difference if he assumes that the genetic code of terrestrial life is the same as that in the rest of the universe?

How far does the neo-Darwinian theory work?

The largest part of the book consists of calculations of the core claims of neo-Darwinism: evolution works by the selection of rare advantageous mutations. These are the questions traditionally answered by population genetics. Studying the textbooks (Fisher) he got mad and calculated it all from scratch! The questions he tries to answer:

Can rare advantageous mutations indeed become established in a population, in the face of a flood of disadvantageous mutations? If so, how fast? At what costs?

What is the effect of population size and generation time of organisms involved?
What is the effect of asexual opposed to sexual reproduction?
How severe must selection be to have effect?
How long will it take that a population accumulates so many small deleterious mutations, that it will go extinct?

My training in mathematics doesn't permit me to evaluate Hoyle's calculations. I hope professional population geneticists will check Hoyle's results. Nevertheless it's easy to notice if the outcomes contradict or confirm standard textbook knowledge. Hoyle builds up a tension: it is not easy to get rid of all the bad mutations, let alone to improve a species! His calculations culminate in the result that mutation and natural selection can only find advantageous protein variants

at most two base substitutions separated from the current status. That means that if 'only' 4 - 6 substitutions (9) are necessary to transform one enzyme into another, although a small number, this is still forbidden by neo-Darwinism according to Hoyle. These are the limits of the power of natural selection to change existing genes. In orthodox neo-Darwinism there are no such limits. "What the mathematics shows is that nineteenth- century biologists were correct as long as they remained within the range of practical experience. Where the situation went wrong was in making a huge extrapolation ..." (p108). So Hoyle arrives at rather pessimistic conclusions compared with the usual optimistic textbook view. Next it is a small step for Hoyle to claim that the protein histone-4 could never be produced in small steps. Why? Histone-4 has a chain of 102 amino acids and the structure is extremely conserved in all eukaryote species (16). Bovine histone-4 differs in only 2 positions

with peas! And that means extreme functional constraints must exist (17). Histones are necessary for chromosome condensation during cell division. The traditional neo-Darwinian step-by-step method must fail claims Hoyle, because it implies 100 non-functional steps. The alternative: a jump of 100 mutations of exactly the right kind would be highly improbable. The histone-4 case is in fact a case of Michael Behe's Irreducible Complexity long before Behe published his Darwin's Black Box, since the hand-written version of Mathematics of Evolution was 'published' in 1987. Hoyle is an Intelligent Design Theorist 'avant-la-lettre'. What makes Hoyle different is that he doesn't talk about 'the supernatural' and the 3-letter word. Hoyle indignantly rejects Neo-Darwinists' "retreat in the unknowable and untestable" (p103), when they claim that histone-4 historically had a different function and so could evolve stepwise. Hoyle would be right if evolutionists just claimed it

without doing research. But the question is open to further investigation. Evidence can and has been collected. Histone-precursors can be found in ancient bacteria Archaea (5). However the origin of histones is far from solved. This is not reported in the textbooks. It isn't even mentioned, let alone recognised as a difficult problem (7). On the other hand: does Hoyle seriously believe that histone-4 came hidden in a meteorite and incoporated itself into every eukaryotic cell? Is that itself not a "retreat in the unknowable and untestable"? More generally speaking: why does extraterrestrial evolution escape the problems that evolution encounters on Earth? More time? More space? Favourable conditions? Tell me!

Haldane's Dilemma

Hoyle's efforts to investigate the famous 'Haldane's Dilemma', also investigated by

Walter Remine, results in the surprising conclusion that "Haldane's so-called cost principle is an illusion." (p. 123). And since Remine uses Haldane's dilemma as an important argument against neo-Darwinian evolution, Remine's argument is an illusion. Furthermore Motoo Kimura 'bases' his Neutral theory of molecular evolution on a wrong result of Haldane's calculation of the cost of substitution. According to Hoyle Kimura's calculations of high costs only apply to a continuing declining environment. Maybe this is the most sensational chapter in the book. Hoyle's worries about deleterious mutations in the human species proved prophetic. In January this year (1999) the geneticist James Crow (6) stated: "3 new deleterious mutations per person per generation. Why aren't we extinct?"; "A way out is for mutations to be eliminated in bunches. This happens if selection operates such that individuals with the most mutations are preferentially eliminated".

Hoyle's claims about the evolutionary benefits of sex are also confirmed by remarks of Crow: "But such a process can only work in sexual species, where mutations are shuffled each generation by genetic recombination".

Protein evolution

Hoyle has several objections to constructing protein phylogenies. The original situation of a protein is irrecoverable. The facts show "direct and obvious disproof of the whole concept of protein phylogenies" (p134). Hoyle does not give references or quotes, so it's impossible to check which scientist draws which conclusions from which data. I suspect that current textbooks are more careful and aware of pitfalls. He points out that the situation with DNA phylogenies looks better, but also has its pitfalls.

Deleterious mutations

Hoyle devoted a chapter to the "Sociological Consequences of Deleterious Mutation Pressure" in which he describes how deleterious mutations accumulate in humans (he calls it 'genetic erosion'). Mutations accumulate if natural selection cannot eliminate them as fast as they are produced. But elimination of deleterious mutations means death or at least no reproduction. Hoyle is worried about the problem. In the last pages of his book he proposes what to do about it. However his proposal is impractical. Remarkably evolutionary biologists today are still wrestling with the problem of harmful mutations in humans. It's the theme of Mark Ridley's Mendel's Demon (10). Ridley also speculates about how to get rid of the excess of mutations. What Hoyle called 'genetic erosion' is now known as 'mutational meltdown'.

Mathematics of Evolution: Conclusion

Among the Darwin-critics Hoyle delivered a unique and mathematically underpinned criticism of neo-Darwinism. His own Panspermia theory is considerably weaker then neo-Darwinism, nevertheless functions as an alternative paradigm, which enables us to see old facts and problems from a new point of view. Strictly speaking his Panspermia and his criticism of neo-Darwinism are independent, but undoubtedly his belief in

Panspermia reinforces his belief that the neo-Darwinian theory is wrong. Even if not all of his calculations turn out to be correct, Hoyle's conclusions point to possible weak spots and unfinished parts in the neo-Darwinian theory of evolution. Although negative, it is a useful reminder for evolutionary biologists. If Hoyle would have finished his book, he could have made an important contribution to evolutionary biology just like mathematical biologist and population geneticist Motoo Kimura.

Population genetics revisited [18 Feb 2000]

    The science journal Nature published an important review of Mathematics of Evolution by John Maynard Smith (8). John Maynard Smith has been an authority in the field of evolutionary biology for decades. In the review he discusses "the cost of selection" (Haldane's dilemma) and the problem of non-functional intermediates.
    He agrees with Hoyle that the cost of selection is much lower than Haldane and Kimura concluded, however at the same time disagrees with Hoyle's conclusion that all costs are an illusion. He further suggests that others should verify Hoyle's results.
    The second problem JMS mentions is the problem if natural selection can achieve improvements if a couple of non-functional amino acid substitutions are necessary to reach a functional protein. JMS confirms that natural selection won't climb the mountain, if there is no stepwise path up the mountain and that all genetic change has an advantage on its own. JMS does not mention any evidence for the last claim. On the contrary: he shifts the burden of proof to Hoyle: Hoyle gives no reason why such intermediate steps could not have existed; it is merely an assertion. However, Hoyle unquestionably gives a reason: histone-H4. Where are all the functional intermediates of histone-H4? JMS doesn't give evidence. At least he could have mentioned an unusual diversity in Histone H4 proteins in Tetrahymena (a single-celled eukaryote) which was already known in 1992 (15) and later publications in 1996 and 1998 (5). The combination of asserting that natural selection cannot jump over non-functional intermediates and the fact that JMS completely ignores the histone-H4 case is puzzling. If there is a protein which lacks functional intermediates (in eukaryotes), then surely histone H4 or H3 are good candidates. According to Graur & Li(2000) Histone H3 is one of the slowest 'evolving' proteins known: 'evolving' more than 1,000 times more slowly than the apolipoproteins. And as recently as January 2003 histone specialists G. Felsenfeld and M. Groudine conclude that "Core histones are among the most highly conserved eukaryotic proteins known" (16). JMS knows about histone-H4: Hoyle discussed it in his Mathematics of evolution and JMS mentions histone-H4 in his own Evolutionary Genetics. JMS is silent about an important problem even when Hoyle points it out to him.
    Surprisingly the theory that natural selection cannot jump over non-funtional intermediates causes as much trouble for neo-Darwinism (histone-H4) as for Hoyle's panspermia theory. The second assertion is masterfully pointed out by JMS: "This is precisely the assumption he has rejected in order to conclude that intervention from outer space is needed." So there is a glaring inconsistency in Hoyle's panspermia theory. I think JMS is right here.
    What should we conclude? A reasonable conclusion must be that Hoyle's panspermia theory has an internal inconsistency because of the rejection of non-functional intermediates while claiming at the same time that all costs are an illusion. Additionally that neither JMS nor anybody else did give evidence that natural selection is in fact capable of producing all the necessary intermediates of functional proteins such as histone-H3/H4. It is not clear what the relevance is of histone variants in a group of primitive eukaryotes (15) for the evolution of the histones of the higher eukaryotes with conserved histones. JMS concluded his review with the remark that it might have been better for the reputation of Hoyle if his book had not been published. How can others 'verify Hoyle's results', if the book had not been published?

Fred Hoyle died on 20 August 2001 at the age of 86.

John Maddox: "Obituary: Fred Hoyle (1915-2001)", Nature 413, 270 (2001) 20 September.
An informative review of Hoyle's scientific career by an emeritus editor of Nature. Apart from Archaeopteryx, Maddox does not mention Hoyle's criticism of neo-Darwinism.

"Professor Sir Fred Hoyle [1915-2001]", Obituary by Chandra Wickramasinghe (Independent, 23 August 2001).

Massimo Pigliucci (2001) Impossible Evolution? Another Physicist challenges Darwin,
Skeptic, Vol.8. No.4, 2001, p54-57. (this is another review of Mathematics of Evolution)

    I found this review rather disappointing because Pigliucci doesn't seem to be really interested in population genetics and Hoyle asks really genuine and fundamental questions about population genetics and evolution. However, I like Pigliucci's "Denying Evolution. Creationism, Scientism, and the Nature of Science" and reviews of Hoyle's book are rare.
    Evolutionary biologist Pigliucci starts his review with a remarkable statement:
"Is evolution by natural selection possible? Most biologists would consider this a rather anachronistic question, satisfactorily settled during the first few decades after the publication of the Origin of Species in 1859."
I must disagree with this statement. Historically it is false. The criticism of natural selection was almost universal (11). "Indeed it is true that some of the leading Darwinists, like Huxley and Lyell, never believed in natural selection." (12). It was not until the occurrence of the evolutionary synthesis of the 1930s and 40s that natural selection was finally adopted by virtually all biologists. Pigliucci had better said: "The greatest triumph of Darwinism is that the theory of natural selection, for eighty years after 1859 a minority opinion, is now the prevailing explanation of evolutionary change" (13). What was settled during the first few decades after the publication of the Origin of Species was (a) that species are not fixed, (b) common descent of all life, and (c) species multiply (14). Sir Fred Hoyle completely ignored exactly these 3 theories of Darwin (and the evidence for them), and exclusively focuses on the mechanism of evolution.
    Pigliucci's attitude to population genetics is ambivalent. He thinks organisms are too complex for mathematical treatment and at the same time that a limited yet vast and sophisticated mathematical theory of evolution already exists. He seems to ignore that the theoretical (as opposed to empirical) demonstration of the power of natural selection to change organisms largely depends on theoretical population genetics. This was established in the 1930s and 40s and the product is called the neo-Darwinian synthesis. So if theoretical population genetics is the theoretical foundation of neo-Darwinism, Pigliucci is attacking the foundation of neo-Darwinism when he says that organisms are too complex for the mathematics we have devised thus far. If the mathematics is not good enough one can neither use it for a defence nor for criticism of neo-Darwinism. No proof, no disproof! [7 Dec 2002]

Gerda Horneck (2003) Could life travel across interplanetary space? Panspermia revisited in: "Evolution on Planet Earth. The Impact of the Physical Environment", edited by Lynn Rotschild and Adrian Lister, pp.109-127.

This is an overview of experimental data on the effects of extraterrestrial environment on the survival of micro-organisms.
She believes Panspermia is possible: "The transport of microbes inside rocks through the solar system might be a feasible process. If protected against solar UV and galactic cosmic radiation, spores may survive inside meteorites over extended periods of time."
Considering her positive attitude to Panspermia, and the fact that she gives an historical overview of Panspermia including Richter(1865), Arrhenius(1903), Pasteur, Darwin, Haldane, Oparin, etc, it is amazing that she ignored two of the pioneers of the modern version of panspermia Fred Hoyle and Chandra Wickramasinghe! She did not even mention F. Hoyle and N.C. Wickramasinghe(2002) "Astronomical Origins of Life: Steps Towards Panspermia", nor Wickramasinghe(2001) "Cosmic Dragons. Life and Death on our Planet". It looks as if Hoyle and Wickramasinghe contributed nothing to Panspermia theory. [27 July 2003]

Notes
I wish to thank the publisher, Brig Klyce, for all his efforts to get the manuscript published and so making it widely available for the first time and for sending me a review copy.
Brig Klyce also made a list of errata in the book.

See for an explanation of the details of the genetic code at Does life look life evolution?.
See for an explanation of the 'central dogma' review of Lamarck's Signature.
Comets, Contagion and Contingency, is a review of Diseases from Space by S.J. Senn, medical statistician. This is an example how an alternative paradigm stimulates scientific discussion. There is no mention of the possible human/influenza genetic code mismatch problem.
Max Bernstein, Scott Sandford, Louis Allamandola (1999): Life's Far-Flung Raw Materials, Scientific American, July 1999, pp26-33.
"The evolution of archaeal/eukaryotic histones thus illustrates that these proteins (...), were much less constrained and evolved at a much higher rate before their present role was fully established." p198, László Patthy(1999): Protein Evolution. Blackwell Science. Furthermore there are functional alternatives for histones: protamines (Nature, 403, 261-263(2000) ). Ouzounis and Kyrpides(1996) claim that "The H4 subfamily is most similar to archaean proteins and may be the progenitor of the other core histones", J Mol Evol 1996 Feb;42(2):234-9). Sandman, Pereira and Reeve(1998) "Diversity of prokaryotic chromosomal proteins and the origin of the nucleosome", Cellular and Molecular Life Sciences , Abstract Volume 54 Issue 12 (1998), pp 1350-1364 .
James Crow (1999): The odds of losing at genetic roulette, Nature 397, 293 - 294 (1999).
Histone is not in the index of Mark Ridley's Evolution and Douglas Futuyma's Evolutionary Biology. Although it is present in Peter Skelton's Evolution and in Monroe Strickberger's Evolution, we do not learn that the origin of histones is a problem. And although we learn from John Maynard Smith(1998) Evolutionary Genetics, p148, that Histone H4 evolves 100 times slower than haemoglobins and 830 times slower than fibrinopeptides, we do not learn that this is a problem for neo-Darwinism. The mean number of amino acid substitutions per site per billion (10⁹) years is 0.01. This number is also given by Page & Holmes(2000) Molecular Evolution. A Phylogenetic Approach, p235 and is based on data from Nei(1987). The frequency equals 1 in 100 billion years. Histone H3 is one of the slowest 'evolving' proteins known: 'evolving' more than 1,000 times more slowly than the apolipoproteins (Graur & Li(2000) Fundamentals of Molecular Evolution, p113). That would mean about 1-2 (non-synonymous) substitutions per nucleotide per trillion (=1,000,000,000,000 or 10¹² ) years! Graur & Li do not mention that this is a problem for neo-Darwinism. I conclude: the time for Histone H3 and H4 to substitute one amino acid is longer than the age of the Earth, our solar system and the universe. See also the letter from William Seager on the Feedback page about Histone-4.
John Maynard Smith, "Population genetics revisited", Nature 403, 594-595 (2000). (10 February)
Frances H. Arnold, "Combinatorial and computational challenges for biocatalyst design", Nature, 409, 253-257 (2001).
See review on this site of Mark Ridley's new book Mendel's Demon(2000).
Ernst Mayr(1982) The Growth of Biological Thought, p. 512
Ernst Mayr(1991) One Long Argument, p. 99.
ibid p. 163.
ibid p. 25. Pigliucci overlooked the fact that Darwin had five theories.
Lori A. Sadler and Clifford F. Brunk (1992) Phylogenetic Relationships and Unusual Diversity in Histone H4 Proteins within the Tetrahymena pyriformis Complex., Mol. Biol. Evol. 9(1):70-84. 1992. A rare publication about variations in eukaryotic histones. [notification by Nelson Alonso]
This is confirmed as recently as January 2003 by histone specialists G. Felsenfeld and M. Groudine in Nature: "Core histones are among the most highly conserved eukaryotic proteins known", Nature, 421, 448-453 (2003).
However, histone proteins can be modified in numerous ways. These modifications are catalysed by enzymes. So histone genes are conserved but histone proteins are modified. We should look at the evolution of enzymes that modify histone proteins. [09-10-2004]
A defence of panspermia without attacking neo-Darwinism is The Feathered Onion by Clive Trotman. [ 03-12-20004 ]
There are now 305,000 sequenced genes from 100,000 species. The number of species known to science is 1.7 million. Keith A. Crandall and Jennifer E. Buhay (2004) Genomic Databases and the Tree of Life, Science, Vol 306, issue 5699, 1144-1145, 12 Nov 2004.
Fred Hoyle, Chandra Wickramasinghe (1982) Why Neo-Darwinism Does Not Work, paperback: 34 pages, Univ College Cardiff Pr (June 1982).

Further Reading

Simon Mitton (2005) Conflict in the Cosmos: Fred Hoyle's Life in Science, NAP.
COSMIC ANCESTRY: The modern version of panspermia, by Brig Klyce, the publisher of Mathematics of Evolution. See also a list of errata in the book.
Cardiff University of Wales home page, with home page of Hoyle and Wickramasinghe, and Bibliography about Panspermia.
"Fred Hoyle's Boeing-story in the Evolution/Creation literature" has been moved to a separate file.
The Intelligent Universe, by Fred Hoyle is also reviewed on this site.
John Maddox (2002) Astronomy: The Hoyle story, Nature 417, 603-605. "The achievements of Fred Hoyle, one of the twentieth century's great innovators in astronomy, were celebrated at a recent meeting. In many respects, it emerged, Hoyle's thinking was ahead of his time." [7 Jun 2002]
comments by William Seager on this site about histone H4.
Francis Crick (1981) Life Itself. Its Origin and Nature (hardback, Simon and Schuster, 192 pages). In this book Nobel Prize winner Francis Crick proposes the theory of 'Directed Panspermia'. One of the rare books focussed on panspermia.
Clive Trotman (2004) The Feathered Onion. Creation of Life in the Universe. A defence of panspermia without attacking neo-Darwinism. [ 03-12-20004 ]
David H. DeVorkin (2005) wrote a review The Outsider of Conflict in the Cosmos: Fred Hoyle's Life in Science. Simon Mitton. xviii + 401 pp. Joseph Henry Press, 2005.
David Warmflash and Benjamin Weiss (2005) Did Life Come from Another World? New research indicates that microorganisms could have survived a journey from Mars to Earth. Scientific American Nov 2005 pp.40-47. Remarkably, Hoyle is not mentioned as a panspermia pioneer! 12 Nov 2005
Simon Mitton's recent excellent biography of Hoyle: Fred Hoyle: A Life in Science (Aurum Press, 2005)
Errors not corrected for three years point to incompetence, (21 Oct 07)
Fred Hoyle, Chandra Wickramasinghe (1993) Our Place in the Cosmos: The Unfinished Revolution Paperback, New edition, 208 pages. Contents listing available at amazon.
Simon Mitton (2011) Fred Hoyle. A Life in Science, Cambridge University Press, Cambridge, 2011. (Info). Forword by Paul Davies. See also google books.

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