Re: Fred Hoyle's "Mathematics of Evolution"

From: Stephen E. Jones (
Date: Sun Jan 23 2000 - 09:37:33 EST

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    I am very excited, having just read Fred Hoyle's "Mathematics of
    Evolution"! This was a handwritten facsimile manuscript written by Hoyle
    in 1987, and published in 1999 by Panspermia advocate Brig Klyce.

    In his preface Hoyle states his belief that the Neo-Darwinian theory is

            "The criticism of the Darwinian theory given in this book arises
            straightforwardly from my belief that the theory is wrong, and that
            continued adherence to it is an impediment to discovering the
            correct evolutionary theory." (Hoyle F., "Mathematics of
            Evolution", [1987], Acorn Enterprises: Memphis TN, 1999, p.xv).

    In fact Hoyle believes Darwinism is a form of mental illness (personally
    I would not go quite *that* far!)!:

            "Because the old believers said that God came out of the sky,
            thereby connecting the Earth with events outside it, the new
            believers were obliged to say the opposite and to do so, as always,
            with intense conviction. Although the new believers had not a
            particle of evidence to support their statements on the matter, they
            asserted that the rabbit producing sludge (called soup to make it
            sound more palatable) was terrestrially located and that all chemical
            and biochemical transmogrifications of the sludge were terrestrially
            inspired. Because there was not a particle of evidence to support
            this view, new believers had to swallow it as an article of faith,
            otherwise they could not pass their examinations or secure a job or
            avoid the ridicule of their colleagues. So it came about from 1860
            onward that new believers became in a sense mentally ill, or, more
            precisely, either you became mentally ill or you quitted the subject
            of biology, as I had done in my early teens. The trouble for young
            biologists was that, with everyone around them ill, it became
            impossible for them to think they were well unless they were ill,
            which again is a situation you can read all about in the columns of
            Nature." (Hoyle F., 1999, pp3-4).

    To get to the bottom of Neo-Darwinism, Hoyle went back to the
    mathematics behind the Neo-Darwinian theory, of Fisher, Haldane, Sewall
    Wright and Kimura. He found the maths easy (!) but their explanations
    difficult to follow. So he just re-worked the entire Neo-Darwinian
    mathematical theory from scratch!:

            "My experience proved unrewarding. After a session with "the
            books," I would retreat, baffled. The mathematics was never
            difficult in itself. It was the words in which the mathematics was
            shrouded...At first I took the fault to be mine, but as the frustrating
            sessions were repeated again and again over a period of years, I
            came to suspect that the confusion was in the heads of the writers
            themselves. Eventually therefore, I decided to tackle this
            mathematics myself working de novo...Although my results were all
            arrived at independently, some-perhaps most-have been obtained
            before. Their arrangement, however, is I believe original." (Hoyle
            F., 1999, p5)

    In doing so, he independently arrived at many of the same results but he
    also found it didn't work as advertised. In particular, Hoyle found that
    Neo-Darwinism worked only for small-scale changes, and even then only
    "weakly in the general situation":

            "Finding the neo-Darwinian theory to work only weakly in the
            general situation, my impression is that some evolutionists have
            sought to speed things up by wrongly considering cases where
            species are only coping with environmental conditions they have
            experienced before, so that memory is being misinterpreted as
            discovery. The peppered moth, Biston betularia, so called because
            it has speckled lack and white wings, is frequently misinterpreted in
            this sense." (Hoyle F., 1999, p98).

    Moreover, he found that it would not even work at all for organisms above
    the level of bacteria if it were not for an "exquisite" system of sexual
    recombination and crossover, used by organisms higher than single-celled

            "To have any hope of success the neo-Darwinian theory must
            therefore appeal to a reproductive model quite different from the
            model mostly adopted by single-celled organisms. This is already an
            immense climb down from what is usually claimed for the theory.
            Gone is its "obvious" status. Only if a model can be found that
            contrives to uncouple the selective properties of one gene from
            another, permitting the occasional good mutation to survive and
            prosper in a sea of bad mutations, can evolution be made to work at
            all. How exquisitely complex the model needs to be to achieve such
            a remarkable result will be discussed in the next chapter. Then the
            mathematical properties of the complex model will be investigated
            up to the end of Chapter 5." (Hoyle F., 1999, p10).

    That "exquisitely complex" model is sexual reproduction and crossover:

            "Two points of principle are worth emphasis. The first is that
            the usually supposed logical inevitability of the theory of
            evolution by natural selection is quite incorrect. There is no
            inevitability, just the reverse. It is only when the present asexual
            model is changed to the sophisticated model of sexual
            reproduction accompanied by crossover that the theory can be
            made to work, even in the limited degree to be discussed in
            Chapter 6." (Hoyle F., 1999, p20)

    But then Hoyle realises that the origin of this "exquisitely complex" system
    from an organic soup presents an "insuperable problem" and "beggars the

            "This presents an insuperable problem for the notion that life arose
            out of an abiological organic soup through the development of a
            primitive replicating system. A primitive replicating system could
            not have copied itself with anything like the fidelity of present-day
            systems (on which the estimate L [mutation rate] = 0.3 depends).
            With only poor copying fidelity, a primitive system could carry little
            genetic information without L becoming unbearably large, and how
            a primitive system could then improve its fidelity and also evolve
            into a sexual system with crossover beggars the imagination."
            (Hoyle F., 1999, p20)

    In effect, Hoyle has discovered another level of Irreducible Complexity. If
    single-celled organisms don't use sexual reproduction with crossover (and
    are reproductively highly successful without it), and everything above
    single-celled organisms does use it, then how and why did single-celled
    organisms ever invent such an "exquisitely complex" system, and why don't
    we find them still using it today?

    Hoyle claims that the Neo-Darwinists have concealed how crucial
    sexual reproduction with crossover is to their entire system:

            "This latter advantage of sexual reproduction seems to be the
            strongest argument claimed in the books for it over the asexual
            model... Fisher's The Genetical Theory of Natural Selection carries
            the point in the exquisite ellipticities that were so characteristic of
            Fisher. With quite some searching one can find it in Sewell Wright's
            treatise in four volumes Evolution and the Genetics of Populations
            (...1984) and more directly and clearly in J. Maynard Smith's The
            Evolution of Sex (...1978) What one does not find, however, is an
            appreciation of the really crucial aspect of the matter, that only with
            sexual reproduction accompanied by crossover can positive mutations
            make headway against the deleterious mutations which occur with
            far greater frequency, and which otherwise would swamp the
            advantageous mutations, not permitting them to make any headway
            at all." (Hoyle F., 1999, p39).

    Hoyle drives a few other nails in the Neo-Darwinism's coffin. First, he has
    another Irreducible Complexity type argument about Histone-4:

            "Even though natural selection may hold a protein to a unique chain
            of amino acids, shifts of base pairs can occur provided they do not
            go outside the redundancy permitted by the genetic code. Such
            selectively neutral variations in the DNA are found in the case of
            the protein histone-4, which has a chain of 102 amino acids. In
            humans about thirty distinct genes code for histone-4, apparently
            because there is need for a large amount of this particular protein to
            be produced. The genes have variations in their base pairs, but the
            variations are all of the kind permitted by the redundancy of the
            genetic code. They all code for the same amino acid chain. Other
            variations that did not code for the same amino acid chain must
            surely have occurred but were stamped out by natural selection.
            Essentially, the same amino acid chain being found also in other
            animals and even in plants, we have a case in histone-4 where more
            than 200 base pairs are conserved across the whole of biology. The
            problem for the neo-Darwinian theory is to explain how the one
            particular arrangement of base pairs came to be discovered in the
            first place. Evidently not by random processes, for with a chance
            1/4 of choosing each of the correct base pairs at random, the
            probability of discovering a segment of 200 specific base pairs is
            4^200, which is equal to 10^-120. Even if one were given a random
            choice for every atom in every galaxy in the whole visible universe
            the probability of discovering histone-4 would still only be a
            minuscule ~10^40." (Hoyle F., 1999, pp102-103).

    He notes that in response to this IC type arguments "the Darwinists retreat
    into an untestable position":

            "Faced with this situation, neo-Darwinians retreat into an untestable
            position. Histone-4 evolved step by step they characteristically
            argue, with each step requiring no more than a single base-pair
            change. To the objection that step-by step evolution was not
            possible because histone4 is an all-or-nothing case, they reply by
            admitting that, while in the present situation this may be true, the
            situation as it once was differed in this respect. In a more primitive
            situation, histone-4 evolved step by step it is claimed, thereby
            retreating neatly into the unknowable and untestable, a device
            which, however, is not logically tenable because primitive systems
            without sexuality and crossover cannot evolve." (Hoyle F., 1999,

    In a chapter title "Protein Phylogenies-More Illusions", Hoyle claims that:

            "Phylogenetic trees for proteins such as cytochrome-c are invalid
            unless ...most amino acids of enzymic chains do not matter, an
            exceedingly unlikely supposition in view of the mandatory character
            of the rest of the amino acids", and "Besides which, there are three
            further objections, one a reductio ad absurdum, another a flaw of
            logic, and the third a disproof by positive fact, that rule protein
            phylogenies so far out of court that one must wonder at the state of
            confusion which led to them ever being considered at all." (Hoyle
            F., 1999, pp130-131)!

    For larger-scale changes, Hoyle claims that regular "genetic storms" from
    outer space were needed to add "whole batteries of new genes":

            "External incidence appears to come in storms of rather short
            duration, the most recent very large storm being the one that
            occurred 65 million years ago, to which reference has already been
            made. Species seem to vary considerably in their sensitivities to
            genetic storms. Relatively insensitive species, those which largely
            exclude viruses, remain locked into a particular mode of
            existence....Other species, however, are highly sensitive to genetic
            invasion from outside. Such species face either extinction or
            immense change and fragmentation at a major genetic storm.
            Fragmentation comes from the imposition of a coarsely defined
            range of genetic possibilities, which after fragmentation are refined
            by the single base-pair adjustments discussed above. In effect, there
            is a genetic explosion, at first with the possibilities only broadly
            adapted to the environment, with the finescale adjustments
            subsequently taking place." (Hoyle F., 1999, p108).

    However in the preface written a decade later, Hoyle seems to have
    watered down his genetic storm idea (presumably because genes arriving
    on cue just when they were needed sounds too much like progressive
    creation!), and also because the event he thought was a genetic storm 65
    mya is now thought to be a comet and there was no great explosion of life
    after it:

            "A decade ago I thought new genes were acquired by an organism
            from the external environment, just as bacterium acquires a new
            gene by picking up a plasmid, except that, unlike the bacterial case,
            its external environment was taken to be external to the Earth. At
            acquisition, a new gene was supposed to go first into the store of
            redundant DNA, a process continuing until a considerable number
            had been added, when, in a genetic storm, cell programs become
            shuffled by a viral form of interference from outside. Most such
            shufflings would come to a bad end. But occasionally a situation
            both new and workable in a new niche in the terrestrial environment
            was considered to arise, setting evolution off on a new path" (Hoyle
            F., 1999, p.xvi).

    But now he opts for a type of front-loaded model with all the major genetic
    changes in place in the metazoa before the Cambrian Explosion.

            "Today, however, I would modify this picture somewhat to the
            view that 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 ecologic conditions permitted them to be so. For
            example, it would have been pointless call in a genetic system
            leading to the appearance of flowering plants before the means of
            successful pollination existed. The intricate interleaving of many
            organisms had to proceed in concert with each in a pattern that has
            grown every more complex with the passage of time. The first
            metazoans were relatively simple forms that could exist by
            themselves on an undeveloped Earth, but they already possessed
            the genes necessary for their subsequent development.." (Hoyle F.,
            1999, p.xvi).

    This however contradicts what is in his unrevised book because he
    mentions major changes, (e.g. gaps in the fossil record and the
    reptilemammal transition) whch happen long after the Cambrian Explosion:

            "So how did the chromosome structure of reptiles change into that
            of mammals? If we say by internal mutations, many small steps
            would be needed, since a large change of structure occurring in one
            step to one individual would be sterile, because it would be
            unmatched in individuals of the opposite sex. Indeed, any such large
            change would have small probability in the first place, and the
            further chance of a contemporary member of the opposite sex
            possessing just the same internally generated large change would be
            much smaller still. The consequent need to multiply minuscule
            probabilities rules out large spontaneous changes of chromosome
            structure, leaving only the alternative of very many small changes.
            Many changes should be traceable in the fossil record, which they
            have not been. The concept discussed in Chapter 6 of an externally
            incident genetic storm overcomes this difficulty, because both the
            chromosome sets P and M are exposed to the same external source
            of change." (Hoyle F., 1999, p138)

    And Hoyle still has to explain how the genetic components of this
    "exquisitely complex" system (including Histone-4) could arise in outer space
    in the first place, if they could not possibly arise on Earth:

            "This is a more efficient way of seeding a planet with life than a
            genetically random process of acquiring genes would be. If life
            exists in the universe on a very grand scale, we would be likely to
            have received it on the run only after a great deal of evolution had
            already taken place. In which case, the most efficient procedures
            would have become established already by 570 million years ago."
            (Hoyle F., 1999, pp.xvi).

    In his preface he writes of "entirely new genes, perhaps whole batteries of
    new genes...grafted onto the genetic complement of an already existing

            "The biggest physical storm occurring in ten years usually produces
            as much change as all the rest put together. And the biggest in a
            hundred years as much or more than all the rest. And, perhaps, even
            the biggest in a thousand years.... Something of the same sort seems
            to happen with evolution. The fine-tuning of genes produces small
            changes. The addition of entirely new genes, perhaps whole
            batteries of new genes, produces large changes, grafted onto the
            genetic complement of an already existing organism." (Hoyle F.,
            1999, pp.xv. Ellipses in original.)

    But at the end of the day, Hoyle cannot explain where these new snap-on
    components came from in the first place:

            "And the outcome of this essay? Well as common sense would
            suggest, the Darwinian theory is correct in the small but not in the
            large. Rabbits come from other slightly different rabbits, not from
            either soup or potatoes. Where they came from in the first place is a
            problem yet to be solved, like much else of a cosmic scale." (Hoyle
            F., 1999, p6)

    What I am excited about is that Hoyle's original "genetic storm" model,
    (which is what the evidence actually looks like), *is* in fact better explained
    by the progressive introduction of large blocks of new genetic code, by an
    Intelligent Designer. Indeed Phil Johnson on one of his tapes says that
    Panspermia is "the materialist version of supernatural creation"!

    BTW Hoyle above gives a possible explanation of the presence of `junk'
    DNA by suggesting that this may be the remnants of old discarded code:

            "It would explain why so much of DNA goes unused. Unexpressed
            DNA could be old eroded genetic material that has been discarded
            as new material has been acquired." (Hoyle F., 1999, p92)


            "Over long periods, a species must either acquire new undamaged
            genetic material or decline occurs. Redundant DNA may be an
            accumulation of genetic material that exceeded this limit at times in
            the past and which has now become discarded." (Hoyle F., 1999,

    My recommendation is to buy, beg, borrow, or steal, Hoyle's book! :-) The
    maths is incomprehensible to me, but some resident maths whizzes might
    actually *enjoy* that part! Anyway, Hoyle gives good verbal results of his
    calculations so even numerically challenged laymen like me can understand
    his points. I got mine secondhand, but it is listed on as

    'Mathematics of Evolution'
    by Fred Hoyle


    Our Price: $36.00

    Availability: Usually ships within 24 hours.


    Hardcover - 163 pages (October 1, 1999)
    Acorn Enterprises LLC; ISBN: 0966993403 Sales Rank: 89,020

    But if you can't get it, don't worry. I will be posting nice juicy quotes
    from it in my taglines! :-)


    "The criticism of the Darwinian theory given in this book arises
    straightforwardly from my belief that the theory is wrong, and that
    continued adherence to it is an impediment to discovering the correct
    evolutionary theory." (Hoyle F., "Mathematics of Evolution", [1987],
    Acorn Enterprises: Memphis TN, 1999, pp.xv)
    Stephen E. Jones | |

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