There are 3 gene (alleles) in all pigeons and coupled with other factors will allow you to manipulate the necessary genetics to produce what you need or want. Brown, Blue-Black, and Ash Red.
Black is Blue Bar with the Spread Gene Factor. The black of the bars is spread over the entire body to produce blacks.
In Budapest, the white beak comes from one of two genes. The Smokey gene or the Eastern European Sooty Gene. Western Blues like homing pigeons have a different blue gene. The Buda Blue is a very dark blue sometimes showing a characteristic bronzing in some feathers.
Regardless of Sex
WHITE BEAKS
Blacks
Black x Black = Black, Brown hens, and reds and yellows if the blacks are carrying recessive red genes. Also, White Beak blues and white beak Brown Bars.
Black x White Beak Blues = Black, White Beak Blues, White Beak Brown Bars.
Black x Red or Yellow = Black, Red and Yellows with Dark Tails known as unimproved recessive reds.
Black x T – Pattern = Very beautiful blacks
Black x Yellow or Red = Black, Red, Yellow, and Brown sometimes Brown Bars.
Black x Brown = Black, Brown, Red, Yellow, Brown Bars, Blue Bar.
Browns
Brown x Brown = Brown
Brown x Brown = Brown and Brown Bars
Brown x Brown = Brown and Yellow—–NEVER RED
Brown x Red = Brown, Brown Bar, Red, Yellow—Sometimes Black but rare
Brown Bar x Brown Bar = Brown Bar
Brown Bar x Brown Bar = Brown Bar and Yellow—Never Red
Brown Bar x Blue Bar = Brown Bar, Blue Bar, Red and Yellow —never Black.
Ash Red
There are not many Ash reds in Budapest. In order to produce Ash Reds you need to get the gene released from the white birds.
Black x White = 100% Ash Red. They can have bars or be spread ash red.
Ash Red Spread x Ash Red Spread = 100% Ash Red Spread
Ash Red Spread x Ash Red Bar = Both Ash Red Spread and Ash Red Bars.
Ash Red Spread x Black = Ash Red Spread and Black
Ash Red Bars x Black = Ash Red Bars, Blacks, Blues, Browns, Brown Bars. The ticking in the tail of the cock might tell you what you will produce. Black ticks make blacks and blue, brown ticks make browns.
Ash Red Spread x White = Ash Red Spread, whites, and possibly Ash Red with Bars (Mealy) Very rarely Ash Yellow bars (Cream or Isabella)
Whites will rarely produce Ash Red Bars or Ash Yellow Bars. However, they will produce many whites with speckled necks which keep the eyes blue.
Two Forms of Epistasis Exist
(ONE)
Red and Yellow are not real colors. They ALWAYS mask a color underneath them. They can usually cover the other colors well but black and blue will produce reds and yellows with dark tails. If the color is uniform the color underneath is brown and the birds have beautiful color and beautiful blue eyes.
(TWO)
The complete blending of Ash Red with Stork will produce White. The Ash Red covers the black beak and ceres and the black markings of the Storks. The white of the Stork intensifies and produces the White pigeon. Sometimes it is not perfect and you get birds with flecks and dark beaks. Select what you need for your program. White to white is not necessarily a good repeated mating because you will get dark (bull) eyes in some of the birds. I recommend crossing storks and a Ash Reds back to Whites periodically.
Sex Linked Matings
This is dependent of the sexes! In pigeons, the female determines the sex of the offspring. It is the reverse in mammals. There is no X and Y gene!
This involves the dilution of some major intense colors.
The dilute of Blue is Silver, dilute of Red is Yellow, dilute of Ash Red Bar is Cream or Isabella, dilute of Brown is Khaki. (I have only seen one specimen my entire life. It was raised by Dr. Szecsenyi and he sent it to me in the 1980’s. It was a poor breeder and I could never reproduce the gene.) In order to produce dilute, you must introduce the dilution to the color you are working with known as intense. The dilution is ALWAYS carried by the cock! Released in breeding to produce hens.
Yellow Cock and Red Hen = Red Cocks (100%) and Yellow Hens (100%)
Cream Bar Cock and Red Bar Hen = Red Bar Cocks (100%) and Cream Hens (100%)
Silver Cock x Blue Hen = Blue Cocks (100%) and Silver Hens (100%)
Cream Cocks and Silver Hens = Silver Cocks and Cream Hens. The young can be weak!
Yellow Cock x Black, Blue, Ash Red is a sex linked mating.
Silver Cock x Black, Blue, Ash Red is a sex linked mating.
Cream Cock x Black, Blue, Ash Red is a sex linked mating.
True duns (short down in the nest) are not generally produced. They are weak.
It is, also, very difficult to produce true White Beak Silvers. The blending of the Black Beak Silvers and the White Beak Blues might work. Their color will be beautiful.
Regardless of Sex
Black Beaks
Buda Blue, Grizzles, Storks, and Blacks
Blue x Blue = Blue and Silver (Rarely unless breed for the trait.)
Blue x Grizzles = Blues and Grizzles
Grizzle x Grizzle = Blue, Grizzle and Stork
Stork x Grizzle = Stork and Grizzle
Stork x Stork = Stork and rarely White, Sometimes pure white with black ceres and beak with no markings. (We call these Snowballs)
Blacks, Blue x White Beak Black = Blacks, usually light cere or plum colored. Color is usually poor because this is Eastern European Blue and Black. These Blacks must be breed together to produce dark beak and dark cere Blacks. I have seen 4 good specimens in my entire life. Two in Europe and two in the USA.