BICOLOURS AND EYE COLOURS
In cats, a white-colour coat can be caused either by a gene for white coloration or by a gene for 'white patching.' Sometimes the white patching is so extensive that the cat appears solid white. If the white cat exhibited a few coloured hairs or a smudge of colour on its body (usually on the head) as a kitten, then it should have normal hearing even if it has blue eyes because it has inherited a non-deafness causing gene for white coat! Blue-eyed bicolour cats occur and the more white they have in the region of their eyes and ears, the more likely they are to be deaf. This is fully discussed in White Cats, Eye Colours and Deafness
Aries, a blue-eyed silver-tabby-and-white Norwegian Forest Cat bred by Raquel Ortega Cormenzana of MONTEGANCEDO*ES (Madrid). Sometimes bicolour cats with white faces have blue eyes. Aries has has perfect hearing because the white does not extend to the ears.
WHITE SPOTTING GENE AND EYE COLOUR
In bicolours, caused by the white spotting gene, eye colour appears to be related to the degree of white on the face. More white, especially around the eyes (“high whites”), seems linked to blue eyes. However it may not be as simple as that because not all white-faced cats have blue eyes. Other genes may be at work.
David Karamatic, a breeder in Australia, has worked with a line where the incidence of blue eyes in high-white cats appears to be inherited recessively i.e. some high white cats have orange eyes, while some had blue eyes, and this was not in strict relationship to the amount of white on the facial area.
The original cat was a male (from a colony), mostly white, but with some tabby markings and a tabby “cap.” His mother and sister both had a similar pattern, but with odd-eyes. This male was bred with two bicolour females and they had a number of high white bicolours, but none of the offspring had blue or odd eyes. He was then bred to one of his daughters resulting in a blue-eyed tortie-and-white (calico) and and odd eyed van-pattern male. Therefore the degree of white on the face does may not be the only factor involved in inheritance of blue eyes.
RUSSIAN BLUE-EYE GENE AND WHITE SPOTTING
This is a different gene and the cats are selectively bred for eye colour rather than coat pattern. In this case, the gene causing the eye colour can also cause white markings, but the white pattern is different from that in ordinary bicolours. This is more fully discussed in Blue-Eyed Breeds
CONSIDERATIONS FOR ALL BLUE-EYED BREEDS
There are various known and unknown genes involved in white spotting and in blue-eyes. In solid white and high white cats there is a link to deafness because melanin is involved in the development of the inner ear (the part that detects sound vibrations). BAER testing (acoustically evoked brain stem responses) is used by many European breeders to ensure that they don't deliberately breed deaf cats. The prevalence of deafness and partial hearing in an experimental colony of white cats was 67% (deaf - 0.55 coefficient of heritability) and 29% (partial hearing - 0.75 coefficient of heritability) which suggests a pleiotropic major gene (a gene that has 2 seemingly unrelated traits) and the likelihood of polygenes.
Geigy CA, Heid S, Steffen F, Danielson K, Jaggy A, Gaillard C (2007). "Does a pleiotropic gene explain deafness and blue irises in white cats?". Veterinary Journal. 173 (3): 548–553. PMID 16956778.
This was commented upon by Strain GM, in "Deafness in blue-eyed white cats: the uphill road to solving polygenic disorders."Vet J. 2007 May;173(3):471-2. Epub 2007 Feb 21.