Genetic Equidistance: A Puzzle in Biology?

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Your position cannot be reconciled with particular observations from protein sequences, particularly one observation. A ClustalW alignment of the cytochrome-c sequences of homo sapiens, the alligator, and the frog, reveal that the frog and the alligator are equidistant to humans by 13 residues each. Of these 13 different residues, 7 of them are located in the same position in the alligator and the frog.
To calculate how many of these positions should be shared, based on chance and probability, the following may be done:

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The chance for a position to be different between human and frog is 13/105.
The chance for a position to be different between human and alligator is 13/105.
The number of positions that would overlap based on chance: 13/105 x 13/105 x 105 = 1.6

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Your calculation is obviously incorrect. It assumes that the locations of the changed residues are statistically independent, which is false. For instance any residue which changed in the human lineage since the most recent common ancestor but remained the same in both of the others would be a shared difference,Assuming (as you do) that all residues are equally likely to change (IMHO probably incorrectly), and trusting your numbers we can estimate the number of residues that fall into this category. Since roughly half the difference should appear in each lineage, the number of residues that have actually changed since the common ancestor will be about half the genetic distance, thus I shall estimate this number of changes as 7.So we have 7/105 changed in the human lineage and 98/105 unchanged in each of the others. My estimate is therefore 7/105 * 98/105 * 98/105 * 105 ~= 6While this would be a very rough estimate of the number of residues that are different from the human in both the frog and the alligator, it is still better than yours - and far closer to the value you report.

My Message 19 which refutes your estimate of the expected overlap in the locations in differences between human and alligator and human and frog cytochrome c (from your Message 11). Except that I now believe that I can do better.A mutation in the lineage from the most recent common ancestor with the alligator should be expected to show as a difference with both other lineages. The chance that it will be "masked" by one of the other lineages mutating to have the same residue at that location is relatively small, and offset by other ways in which an overlap could be found. Thus the size of the overlap should be close to the number of mutations in the human lineage since the last common ancestor wit the alligator.If genetic equidistance is explained by mutations accumulating at the same rate in each lineage we would therefore expect half of the 13 differences between human and alligator to be shared with the frog. Which is 6-7, in close agreement with the actual figure of 7. Obviously this data poses no problem for the mainstream view at all - it is completely unsurprising..We should also note that since the size of the overlap is dominated by the number of changes in the human lineage, and that number is on the high side of the expected value, any hypothesis that predicts that the human lineage should show fewer changes than the other two DOES have a problem with this data.Edited by PaulK, : Restoring the parts that mysteriously vanished

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I realize that PaulK has attempted to refute the overlap feature, but his refutation has failed to take into account the above two points I delineated above, and I hope to demonstrate the other errors in Paul's rebuttal (emphasis on the word "hope").

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I think that hope is in vain. Surely you accept the basic point that if a mutation in the human lineage produces a change at a position which is unchanged in the other two lineages (unchanged since the mutual common ancestor of all 3 lineages, that is) then there will automatically be an overlap. How can it possibly be otherwise ?

To consider your two points:1) You claim that Shi Huang's calculations work for different yeast strains. But since that is all that you say, there is nothing more to deal with. Personally I doubt that that is entirely true- I suspect "cherry picking" of data.2) You claim that the results match Shi Huang's calculations when a protein is not under selective constraint, citing the blind mole rat. However, if the blind mole-rat alpha-crystallin is not under selective constraint it will change much faster by genetic drift, and thus the mutations - which are what we should be looking at - will be far more frequent in the blind mole rat lineage. As I have stated the overlap is dominated by mutations in the human lineage, so the overlap should be well under half the number of differences with the blind mole rat, consistent with the results.
Interestingly this offers a chance for a real test. If we use the blind mole rat instead of the human as our "middle" group we should find a much greater overlap (i.e. positions where the blind mole rat is different from both human and chicken). Want to take that test ?