evolution calculations

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but, if the mutation rate is determined by comparing chimpanzee DNA with human DNA, what does it give us?
How such a research promotes TOE?

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That work does assume evolution is true -- more specifically, common ancestry for humans and chimps is true. All large-scale study of genetics makes that assumption, since it's the only approach yet offered that makes sense of the data. You can also estimate the mutation rate without that assumption, however, by examing mutations that are occurring today and that are noticed because that cause disease: http://www.ncbi.nlm.nih.gov/entrez/...http://www.ncbi.nlm.nih.gov/entrez/...You get just about the same answer whichever method you use. Put another way, the rate we observing mutations occurring today predicts how genetically different humans and chimpanzees should be if they diverged from a common ancestor five or six million years ago, and predicts it correctly. This is one of the many, many parts of genetics that makes sense if evolution is true, and no sense if it isn't.

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On a side note, could a mathematical model, not based on evidence, but on the premises of the theory - random mutation and selective pressure - show us that, given those premises, evolution has to happen? In other words, if we could state the premises in a mathematical form, would it be possible to prove mathematically that evolution is the logical conclusion?

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Well, sure, but it's not clear why anyone would (or should) care. You can show that neutral evolution has to happen, and you can show for particular choices of fitness landscapes that adaptive evolution has to happen, but you can also show for other choices of fitness landscapes that, once adapted, organisms will never change.

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No. Hardy-Weinberg is a theoretical model (with lots of assumptions and limitations) that shows how alleles can become fixed in a population.

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No, Hardy-Weinberg says nothing about fixation of alleles. It just tells you (in a particular model), what the relationship is between allele frequencies and genotype frequencies (i.e. how many heterozygotes and homozygotes you'll find given an allele frequency). One of the assumptions of H-W is that of an infinite population size, so that genetic drift does not occur.

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IOW, speciation has to happen.

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In a particular model. Models are not reality, and are only valid to the extent to which they have been tested against reality.

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I think the contrary. With genetic drift and constant mutations occuring I think there must be a selective pressure there to mantain and organisms form. The pressue is, however, to stay where it is. This would be true if it at an adaptive peak in a reasonably constant environment.

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Right. Or you could specify a model in which any genetic change is fatal, in any environment. That leads either to stability or extinction (which is a sort of stability, I suppose), depending on whether the environment changes significantly.