Description:
The white eggshell gene in Coturnix quail causes the bird to lay a pale, white egg. While the wildtype eggshell is a pale salmon with light shades of brown spots as well as a pale blue inner shell color, the white eggshell gene leaves both the inside and the outside of the egg as a chalky white color (1). Some hens will lay eggs with the white shell and few brown spots, but the majority of hens will only lay a handful of spotted eggs at the beginning of their reproductive cycle, and then phase out to all-white eggs (1).
Very few studies have been done on the white eggshell gene, and it is unknown how it interacts with other eggshell genes like Celadon or Red Egg, though it is suggested to be epistatic (meaning the genes work together) with Celadon (2).
It also is unknown how the gene interacts with the overall reproductive tract, or if it causes and deficiencies or issues with the egg quality itself. There were a wide array of egg sizes from the initial mutation without any abnormalities to the birds themselves, so it is unlike that it causes any major issues (1).
It is not linked to any plumage gene, and any color can be bred to have white eggs. It is impossible to tell if a bird is carrying the white egg gene by looking at it. It is also impossible to tell if a bird is heterozygous for the gene without test breeding or tracking the lineage. It is unknown whether it is currently in public hands or not.
It was discovered in a Maryland, US lab in 1964 (1). The gene symbol is we, and the order of dominance is White Egg < Wildtype.
Breeding with White Eggshell:
Breeding with white eggshell is somewhat tricky, because it is not possible to tell if males carry the gene without test breeding.
White Egg x White Egg = 100% White Egg
(we/we x we/we = 100% we/we )
White Egg x Wildtype Egg = 100% White Egg Carriers
(we/we x we+/we+ = 100% we/we+)
White Egg x Carrier = 50% Carrier, 50% White Egg
(we/we x we/we+ = 50% we/we+, 50% we/we)
Carrier x Carrier = 25% White Egg, 50% Carrier, 25% Wildtype Egg
(we/we+ x we/we+ = 25% we/we, 50% we/we+, 25% we+/we+)
Carrier x Standard = 50% Carrier, 50% Standard
(we/we+ x we+/we+ = 50% we/we+, 50% we+/we+)
References & Further Reading
Poole, H. K. "Egg shell pigmentation in Japanese quail. Genetic control of the white egg trait." (1964): 136-138.
Tsudzuki, Masaoki. "Mutations of Japanese quail (Coturnix japonica) and recent advances of molecular genetics for this species." The journal of poultry science 45.3 (2008): 159-179.