Here are a couple of old posts on this topic:
The gene for pea comb (P) and the gene for blue egg (O) are on the same chromosome pair, and quite close together (we call it tightly linked, in the trade) about 5 map units apart (more about units later). In a purebred Ameraucana (call him George), both chromosomes in that pair would each have a blue gene and a pea gene. I'll show that as OP/OP, one OP for each chromosome. George's offspring, mated to a white or brown egglayer with a single comb (she'd be op/op), would always be OP/op, where o is for non-blue eggs and p is for non-pea comb. Since both O and P are dominant genes, all George's daughters (and sons) will be OP/op and have a pea comb; all his daughters will lay blue (or green) eggs.
It's pretty much impossible to tell a OP/OP from an OP/op, although there are subtleties of comb shape and egg colour that give hints.
Now, this is where it gets complicated. Take one of those daughters (OP/op, right?); call her Suzie. Suzie's offspring , when mated to a roo from a breed with non-pea comb and non-blue eggs (op/op; call him Fred) will all get one egg colour gene (O or o) and one pea (or non-pea) gene (P or p) from Suzie, and one o gene and one p gene from Fred. 95% of the time, during Suzie's egg formation, the O and P or (o and p) will stay together. These offspring will be half OP/op (blue egg, pea comb) and half op/op (non-blue egg, non-pea comb). Thus, for this 95%, you can predict egg colour from the comb.
However, 5% of the time (that's the 5 map units mentioned above), during Suzie's egg formation, the chromosomes in that pair will cross over between the two genes before they separate to form the egg, so that half of this 5% (=2.5%) of her offspring will get Op from her, and another 2.5% oP. These offspring will be Op/op (blue egg, single comb), and oo/Pp (non-blue egg, pea comb), respectively.
So, to sum it up, usually a pea combed female that has an Amer in its ancestry will lay blue/green eggs, but not always. I suspect that most Amers sold by hatcheries are offspring of matings like Suzie and Fred, rather than pure Amers; some may be even further removed. I had a so-called Amer roo from a hatchery that had a lovely pea comb, but all his daughters laid brown eggs.
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Blue egg colour is governed by a single gene, while brown is influenced by at least 12 or 13 different genes, some of large effect, and some of small. Parents have approximately equal effect on eggshell colour of female progeny (I say approximately, as it is possible some genes are carried on the Z chromosome) - choosing a male that hatched from a good dark shell is (as Coopslave says) probably the quickest way to darken colour.
Blue egg colour is distributed evenly throughout the shell, while brown is partially within the shell and (especially in the darker eggs) partially a thin veneer that can be scraped off. This is why, when you cross a blue and a brown egg breed, you get eggs that are quite blue on the inside, but can be a dark olive green on the outside.
The chemical responsible for brown egg colour is protoporphyrin, an intermediate in heme synthesis. "Protoporphyrins strengthen the egg shell, and are deposited where the shell is too thin as a result of calcium shortage. Spotting therefore tend to be heavier where the local soil is calcium-deficient, and in the eggs laid last in a clutch."
The blue egg chemical is biliverdin, a breakdown product of hemoglobin. "biliverdin of egg shells is produced from the shell gland, rather than from the breakdown of erythrocytes in the blood stream." I don't think diet will influence blue intensity, but that's just my opinion, and may well be wrong.
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Linkage between the pea comb locus and the blue egg locus is 95.7%; what this means is that if you cross an Ameraucana with a non-blue-egg bird with a single comb, and mate the offspring to more non-blue-egg bird(s) with single comb(s), and then hatch out 200 pullets, you should get approximately 96 pea-combed blue-egg-layers, 96 non-pea-combed non-blue-egg-layers, 4 pea-combed non-blue-egg-layers and 4 non-pea-combed blue-egg layers. (Of course actual numbers will vary, but should be close to that).
To figure out if your bird is OO or Oo, just mate it to a known oo; and hatch out a bunch. If all the offspring pullets lay blue, you know the original bird was OO; if only 50%, then Oo. Hatching 7 pullets who all lay blue eggs leaves you >99% sure the mum (or dad) was OO.