In the March, 1924, issue of the American Pigeon Keeper an interesting article appeared by mr. Frank E. Pollex, a pigeon fancier from Toledo, Ohio, entitled,"The Laced or Silky Pigeons."
He describes an unusual appearance of the feathers in pigeons and he stated that silkiness is inherited as a recessive sex-linked character.
Silkiness in fowls and pigeons are quite similar in general appearance. In both forms the individual barbs remain practically free from one another due to the lack of rigidity and to a degenerative process involving the barbules. In fowls this phenomenon was first described by S.Jones in 1921 and in pigeons it was already described in 1765.

In 1939 a paper was published in the Journal of Heredity by Leon J.Cole and Willard F.Hollander from the Department of Genetics, Agricultural Experiment Station of the University of Wisconsin. They purchased a pair of silky Fantails from mr.Pollex in 1927 and testmatings were undertaken. There findings were entirely at variance with the interpretation that silkiness is recessive and sex-linked. The birds produced 23 youngsters of which 18 were silky and 5 normal. The normal offspring consisted of typical white Fantails, and of both sexes. The majority of the silkies closely resembled the parents; two grades of silkiness appeared: moderate and extreme. Further crosses of female moderate silkies with normal males gave 72 silky- and 81 normal offspring. Similarly, male moderate silkies in crosses with normals produced 74 silky- and 78 normal offspring.
All the evidence indicated that a simple dominant factor is responsible for silkiness. The silkies of extreme type appeared only among the offspring of silky x silky matings and must have been homozygous for silky. When an extreme silky was mated with a normal bird only moderate silkies were born.

A shipment of Ringneck doves (Streptopelia risoria) was received from a Californian dealer in November 1951. It was noted that one male dove possessed abnormal plumage resembling "silky" of the domestic pigeon. The male dove with "silky" plumage was immediately placed in mating, and produced a total of 24 silkies, and 14 normal offspring, indicating that the trait is dominant and that the male was heterozygous.

In 1988 a fancier brought me three Budgerigars for research purposes. The birds were all cocks, and it was noticed they could not fly. They showed a "hairy" plumage around the neck and the flight feathers were abnormally thinnish. Also the primary and secondary tailfeathers were abnormal. Having read the articles described above, I recognized these birds as moderate silkies. On inquiry it appeared that they were bred from normal parents and had normal brothers and sisters. Since they were all three cocks from "normal" parents the mutants couldn't have been sex-linked. Also in this case it seemed we are dealing with a single dominant gene.
Unfortunately the birds were in bad condition suffering from "going light" and they all died before test matings could have been carried out. During microscopical examination of the feathers it appeared to me that some parts of the barbs didn't contain any barbridges at all. Scientificly this kind of mutation could be interesting, but for exhibitions, at least in Budgerigars, the variety is worthless.

Conclusion:
The mutation is very rare in Budgerigars. In other birds such as Silky Fantail pigeons and Silky Bantam fowls the mutation is quite normal and especially in demand for shows. Genetically it is a dominant trait and by discovering it in Budgerigars we can see how same mutations can occur in totally different bird species.

Consulted and cited literature:

Cole L.J. and Hollander W.F.
The inheritance of silky plumage in the domestic pigeon.
Journal of Heredity 30: 197-201 (1939)

Miller W.J.
Silky plumage in the ringneck dove.
Journal of Heredity 47: 37-40 (1956)

Steele D.G.
Studies of inheritance in pigeons: Lace or silky, a sex-linked character(?).
Journal of Heredity 16: 321-327 (1925).

Jones S.V.H.
Inheritance of silkiness in fowls
Journal of Heredity 12: 117-128 (1921)