My understanding from long ago biology classes was that it wasn't actually as simple as dominant brown/recessive blue. There are apparently dilution genes that can turn a brown eye hazel, for instance. Green can be a variant of brown or blue as well I believe, but don't quote me on that!
White coat is a recessive gene
The green/hazel eyes in humans comes from what is called mixed dominance or co-dominance, seen usually with one brown-eyed parent and one blue-eyed parent. In other words, in some people, brown is not completely dominant, but can share dominance and create an intermediate color. This is also the principle behind Gregor Mendel's pink flowers obtained from red and white parent flowers.
Coat color in dogs is apparently very complicated, because of multiple genes and two different types of melanin.
Before starting our list, we need to know that mammals have two forms of melanin in their coats. One, eumelanin, is dark, though it can vary somewhat in color due to variations in the protein that forms the framework of the pigment granule. The base form of melanin is black. Melanin can also appear brown (often called liver in dogs) or blue-gray. The second pigment, which varies from pale cream through shades of yellow, tan and red to mahogany (as in the Irish Setter), is called phaeomelanin. There are at least two and possibly as many as four gene series that determine where, on the dog and along the length of the hair, eumelanin and phaeomelanin appear.
Is white recessive in dogs? I guess you'd have to know more about the characteristics of the four genes' expressions. Or have experience breeding dogs.
