Wow....you all are trying to understand something which is actually rather simple once you understand the basic terms of the topic. But rather doing that, you're attempting to explain what happens without understanding those terms, and in effect you're making things WAY HARDER than they need to be. It's a bit like scratching your left ear by reaching your right hand over your head. I'll try explaining some things to make it easier.
OK, what determines which gene is dominant and which is recessive in a heterozygous bird (i.e. a bird with two different versions of a gene)? Well, this may not always be the case, but for the most part, it has to do with how the mutation affected the original "normal" version of the gene. Genes are instructions for assembling proteins, which are made up of individual amino acids. A mutation is a change in the sequence of instructions, resulting in a change in the resulting protein. If that protein is involved in the color or pattern (from a genetic standpoint, they really don't differ), then a change in that protein will result in a change in appearance -- IF there is no "normal" version of the protein being produced. Remember that in most cases, each chromosome in the pair will generate proteins. So if there's one chromosome with a mutated version, and the other with a "normal" version, then both versions of the protein will be produced.
Sooo.......what does that mean? Think of your standard India Blue as having "normal" versions of all the genes for appearance (color and patterns). Now let's take a color mutation -- Bronze, for example. This results from a mutation (i.e. change) in one of the "normal" genes which affect feather coloration. If a pea has one copy of the Bronze mutation of the gene and one copy of the "normal" version, it means that some of the "normal" version of that protein is still being produced, and will thus allow for the "normal" India Blue coloration to show. The Bronze version of the protein will still be produced, but for whatever reason, the "normal" version in just one copy is enough to fulfill the required amount of that protein to result in "normal" India Blue coloration. You can think of the recessive mutations as being somewhat "broken" versions of the protein which don't function as well as the "normal" version. Birds with no "normal" version will thus have the "broken" appearance of their color mutation (in this case, Bronze, which might be resulting from feathers lacking the structure to refract, or "bend", light from brownish-black to blue). Huh? Yes, peas don't have blue pigment. Their blue color results from melanin, which is brownish-black, getting "bent" from feather structure to appear "blue". If the pigment goes to the "wrong" part of the feather, or the feather structure is altered, they will appear "brownish-black". Think of it like following a recipe to make a cake, but altering one of the ingredients -- the result will probably be a bit different than if you used everything in the original recipe. That's what mutations are -- an ingredient change.
Now, let's look at a visual Bronze -- what do we have? It's a pea which lacks the "normal" version of the specific gene of which Bronze is a mutated version. So it doesn't make any of the "normal" version of that protein -- both copies of that chromosome generate the Bronze version of that protein. The result is that the "normal" India Blue coloration is unable to form, and the Bronze color we see is what happens when only the mutated version of that protein is available.
OK, so what about dominant or partially- or incompletely-dominant mutations? They are also mutated versions of the "normal" version of the respective genes, and they also produce proteins. We can think of the various white-spotting mutations (White, Pied, White-Eyed) as producing "interfering" proteins -- they make something that results in pigment being blocked from getting deposited in the feathers. How they specifically work is beyond this scope (and beyond what I know in these cases), but you can think of them as little erasers which get generated by the mutated genes. Peas with one copy of one of these "eraser genes" will show milder "erasing" than those with two copies. Why? Because more "erasers" are being generated, from each member of the affected pair. As breeders have discovered, the Pied and White "eraser genes" are alleles -- which means they are two different mutated versions of the same gene. One (Pied) seems to be symmetrical in its "erasing" pattern, while the other (White) seems more random -- and potentially "erases" more. Having two copies of Pied (and thus no "normal" versions of that specific gene, and also no "White" versions, since they are alleles) results in what breeders call "Dark Pied" peas (slightly erased, in symmetrical areas -- throat, primaries, etc.). Having two copies of White results in "completely erased of pigment" peas. Having one copy of Pied and one copy of White (and thus no copies of the "normal" version) results in what is called "Pied". What's tricky is figuring out if a pea with a couple white feathers is that way because it has one copy of Pied, or one copy of White, or some other reason -- and I think that's what causes the "surprise" offspring sometimes.
Getting to White-Eyed, it is also a type of "eraser", except that it is not an allele of Pied/White. This means it is a mutation of a different gene, and also has a different resulting appearance -- most of the "erasing" is confined to the train. It also increases its "erasing" when there are two copies of it (and thus no "normal" version of that gene). Having one copy of White-Eyed usually results in a pea with some white eyes and some "normal" eyes in the train, while those with two copies typically have all (or almost all) white eyes. It also means that, since it's not an allele of Pied/White, that a pea can carry both. Thus we can have birds with varying combinations of Normal/Pied/White (but with no more than two copies in total, since they are alleles) and Normal/White-Eye.
These mutations are not completely dominant because birds being split (or heterozygous) will show intermediate appearances -- birds with one copy of White will still show some India Blue coloration, and birds with one copy of White-Eyed will still have some "normal" ocelli. Mutations which are completely dominant (as of yet, I don't think they exist in peafowl, but they do in other birds) will need only one copy of the mutated version to override the "normal" appearance. An example would be the various dark-factors in other birds. One copy results in slightly darker coloration, two copies even darker. How do these work? Well, one possibility is that these genes affect the rate of production of other proteins, increasing their output. Or they produce a version of the protein which "works" by affecting feather structure, decreasing light refraction.
OK, then how does sex-linked work? Same basic premise -- except that the genes are on the Z chromosome. Female birds have one copy of the Z chromosome, and one copy of the W. Males have two Zs. Remember in the beginning about how even if a bird has one copy of a mutated gene, but still has one "normal" copy, that the "normal" expression can still be seen? Well, if a female has a mutated gene on the Z chromosome, she doesn't have a normal version elsewhere -- there is no other Z. Males, however, do, so they can still produce the "normal" version of the protein on the other chromosome. So males can be split, but females can't.
I'll have to get back to this later.....ta-ta for now.
