Evolution: A Complexity View
rjlipton.wordpress.com
rjlipton.wordpress.com
That said, this kind of formal, mathematical approach to evolution is becoming increasingly powerful, and it's worth speculating if there might not be a provable theorem connecting random DNA variation and the laws of probability at the molecular level with the fact of macroscopic evolutionary change, speciation, etc... something like Boltzmann's H-theorem in thermodynamics, which attempts to show how micro-physics (kinetic theory) can be used to prove the macroscopic 2nd Law of Thermodynamics.
This would make evolution not a theory but a theorem, which I call "Darwin's Theorem". I've played around with the math a bit (I'm a physicist, not a mathematician) without getting anywhere, and wrote a what-if novel about the possibility (it plays with even more speculative ideas as well), in part with the thought of popularizing the idea, because I think it's worth people thinking about: http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/...
well, that's the kind of thing the GP wants to put in numbers and a mathematical system, to provide substantial arguments.
However, I am still reluctant to accept your distinction between natural selection and sexual selection. The article you link to even calls sexual selection "a mode of natural selection". The giraffe neck does not have fitness value in the sense of making it a better food processor, quite the opposite. But it does have fitness value in the sense of prospering those very genes, indeed otherwise the giraffe would not exist. Such a definition of fitness does tend to be tautological, but the alternative is no better, because it is inevitably based on a measure of survivability that in the end is necessarily arbitrary.
In other words, natural selection is about fit, that is, how well an organism "fits" or is suited to and environment. (That it what Darwin meant by fitness: Environmental suitability.)
Sexual selection refers to overt preferences in mating: A female bower bird chooses the male that builds the "best" bower (a completely useless artifice neither ever use), a human male prefers women with larger breasts (pretty much ditto), a peahen prefers the peacock with the more extravagant tail (ditto for sure, in fact, more extravagant tails are liabilities).
Examples are many. The term "runaway sexual selection" is used to refer to exaggerated traits that become prevalent and possibly dominant in specific, local populations (think of human characteristics you associate with certain groups: Sometime, somewhere, someone preferred those slightly larger eyes or slightly curvier hips and over time those became prevalent). These traits are generally completely irrelevant, with zero fitness value.
They exist because we think they look/smell good. Why did we come to prefer one over another? The same random variation that causes changes to fitness causes changes to fitness indicators, but those indicators are not necessarily honest signals.
One of the central themes in Dawkins's The Extended Phenotype is the putting into question of the validity of traditional role of the organism in Darwinistic reasoning and why Darwin's original definition of fitness does not hold up. There is actually an entire segment on the many modern (back then) definitions of fitness and problems with each of them. I don't recall what the final conclusion is but it is certain it is not the clear-cut case you make it.
I suppose you have background in a field where your definition of fitness is more firmly established. For instance, I know biological mathematics has come a long way, and I'm not up to speed with what definitions they are using.
I wrote a lengthier answer to Peter Whittaker. Check it out.