On the proportion of Nucleotides in the Genome and what it can tell us about Evolutio

Everything I have seen suggests that differences in GC content result from biases in mutational processes. These include biased gene conversion and biased repair mechanisms. The GC levels for eukaryotes can vary a lot: GC is ~43% for humans and ~20% for P. falciparum (malaria).

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Consider the following two cases.

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Case #1 : We have a genome. We keep tossing a coin, and every time it comes up heads we add an AT base-pair, and every time it comes up tails we add a CG base-pair.

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Now, this is not what you're trying to model. But it's what you're modeling. When you appeal to the Law Of Large Numbers in the way that you do, that's what you're modeling.

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Case #2 : We have a genome of a fixed length. We keep tossing a coin, and every time it comes up heads we change a CG base-pair into an AT base-pair, and every time it comes up tails we change an AT base-pair into a CG base pair.

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You probably shouldn't be modeling that, either. But that would be a "random walk" and wouldn't tend to anything.

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You're correct: you shouldn't be modeling either case if you're interested in the mutation question. If the number of A/T pairs is currently Na and the number of G/C pairs is Ng, the probability that a new mutation will increase the AT content is 0.67 * Ng / (Na + Ng) and the probability that it will increase the GC content is 0.67 * Na / (Na + Ng). This process is indeed biased toward 50% GC.

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Well, that depends again on what exactly is going on. What you're modeling there is where the mechanism for mutation is "Pick a base at random, then change it with equal probability to any base it isn't". This is somewhat simplistic.

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Oh, absolutely -- it's very simplistic. For a more realistic model you would substitute a transition probability matrix, various of which are floating around the literature. But it is at least a simplistic model of mutational substitutions, which is not true of either of the other models listed.

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What ratio GC/AT should we expect from a mutating genome ?

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As the good doctor said, we can't formulate any expectations, really. Not without knowing more about mutation and repair than we currently know. Note, for example, that a highly active family of transposons in a particular species will introduce lots of new sequence into the genome, pushing the GC content toward whatever the transposon happens to have.

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sfs, are you the same person as sfs1 on Tweb ?

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The last time I checked, yes, I was.