Hoyle's Mathmatics of Evolution

Hello All,I will state right off that my knowledge of population genetics is pretty scant. But I've run across a review of Hoyle's book, "Mathmatics of Evolution", and part of it has caught my eye and interest:

quote:

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* 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.

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http://home.wxs.nl/~gkorthof/kortho46.htm

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Now I think I'll go out on a limb and state that I'm pessimistic right off the bat of Hoyle's calculations, though I'm a bit unsure. It also seems apparent that Hoyle, or rather the reviewer, is contesting the notion of natural selection positively selecting "beneficial" mutations when the likelihood of such mutations is so small compared to non-beneficial ones (neutral or deleterious). In reading about mutations here and elsewhere, this seems to be incorrect reasoning. But my question is, how can we decisively demonstrate that positive selection of beneficial mutations is occurring, in the midst of all these detrimental or neutral mutations? Is there any empirical, laboratory evidence of such?And feel free to rip and criticize this reviewer or Hoyle's arguments if necessary. Thanks for the help!

Thanks for these answers. In large part I agree with your statements about math attempting to prove (or I suppose in some cases like IDers - disprove) evolution, only to come up short.I think the crux of my problem, however, is a bit two-fold, and admittedly they both stem from either a misunderstanding or a lack of knowledge in the fields of math and evolutionary biology. So here is my central question that I'm trying to relate to in reading this Hoyle review -We have plenty of evidence of the so-called "microevolution", and creationists are going to continue to deny "macroevolution", at least on a larger scale of changes. They may agree that reproductive isolation creates species changes eventually, which ironically is macroevolution (or speciation) defined, but they do not accept such accumulation over longer periods of time. So when I start reading folks like Hoyle, whom many IDers will borrow concepts from (among others), they will demonstrate mathematically just how highly improbable it is to have so many phenotypical accumulations giving rise to such biological diversity. Now in my gut I feel they're doing two things wrong:1. Misunderstanding (sometimes deliberately) biological mutation and natural selection2. Failing to take into account other factors such as PE, and so on.I believe I can demonstrate #1 pretty well. But #2 is where I'm having a bit of difficulty - am I wrong about other factors playing a role in the so called "macroevolutionary" process? If so, how could I explain this a bit better? I've always been under the assumption that the primary role involved is slow-gradual steps. How about horizontal gene transfer, or cascade genes? Sorry if it sounds like I'm taking shots in the dark - as I mentioned my knowledge on this is a bit limited.Thanks again for any help.