Basic chicken genetics: black and gold are a chicken's basic colours. Those colours can be modified or rearranged, but any colour on a chicken is a variant of black or gold.
E-locus genes are the pattern genes. They tell where the colours are going to be (like a paint-by-number). E-locus genes are always represented by an e-letter designation. E^R is birchen, e is duckwing, E is extended black. Those genes are usually listed first when a genetic description (genotype) is given.
Almost all other colour genes modify the black (eumelanin) or the gold (pheomelanin). Blue, for instance, dilutes black. So does Lavender. Dominant white colours all the black white instead. di is Dilute, and it makes gold paler. Recessive white is weird because is removes pigment from the entire chicken, covering any underlying pattern and colour. Barring is weirder because it removes pigment from the entire chicken but only in stripes.
Recessive white birds carry two copies of recessive white, and they are purely, entirely white. Sometimes, their chick down shows the original pattern (if you see white silkie chicks in TSC, they're striped. That's because they're recessive white, and the underlying pattern has striped down. White Leghorn chicks, however, are yellow. That's because they're really all black, but the black has been whited out.)
Ameraucanas are recessive white,
in most cases. Usually, (in almost all recessive white breeds) the underlying pattern is duckwing or partridge.
e-locus genes:
E = extended black. It is the most dominant of colour patterns and trumps all.
E^R = birchen.
e = duckwing
(There are more. I'm lazy).
All of these genes are alternatives of each other. The e-locus is a place on the chicken's chromosome. It can be filled by any one of these genes. Since a chicken has two of each chromosome (one from each parent) it has two e-locuses (loci?) So it can be E/E or E/e or E/E^R but not E/E^R/e.
Bl = blue, or, more precisely, the presence of a blue dilution gene. Its alternative is the dilution gene's
not being present, denoted by bl. So bl/bl (no dilution whatsoever black) is a possibility, as is Bl/Bl (super-dilution splash) and Bl/bl (blue).
Lav = black, or rather, that the lav dilution gene is not present. Lav/Lav = black, Lav/lav = black carrying a recessive lavender gene, lav/lav = lavender. Note that the chicken can be ONLY black or lavender (in this geneset anyway)
S = silver, s = gold. Like Lavender, this is an either/or.
c = recessive white. C = a lack of recessive white.
So:
White Ameraucana x Blue or Black Birchen Marans
Recessive white = e+/e+, bl/bl, c/c (probably)
Birchen (Black/gold) = E^R/E^R, bl/bl, C/C
Birchen (blue/gold) = E^R/E^R, Bl/bl, C/C
E^R/e,(They are black/gold birchen with shoulder leakage)
Bl/bl OR Bl/Bl (blue or black. All black hens will have black offspring, the blue hens will pass the blue gene to 50% of their offspring.)
C/c (They're split to recessive white, but do not look white themselves.)
Lavender Ameraucana x Blue or Black Birchen Marans
Lavender = E/E, lav/lav, bl/bl, C/C
Birchen (blue/gold) = E^R/E^R, Lav/Lav, Bl/bl, C/C
Birchen (Black/gold) = E^R/E^R, Lav/Lav, bl/bl, C/C
Chicks are E/E^R (black w/possible leakage on shoulders and throat)
Lav/lav (split to lavender, but black)
Bl/bl OR bl/bl (blue or black. Half of the offspring of the blues will be blue, all other chicks will be black.)
C/C (Not recessive white.)
I don't really want to mess with wheatens, so I'll refer you to
this site. Have fun.
A tip on sexing: Ameraucanas are usually slow-feathering. Due to the sexlinked nature of this gene, boys carry two copies and girls carry one. That means that the boys develop feathers more slowly than the girls do. Marans are the opposite.
I'd play with the Ameraucanas, personally. But I've never had a Marans, so enh.