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Your budgie may be a number of different colours, each of which is caused by different mutations.

But before you understand your budgie's colours, it's important to know a few things:
What is a mutation?

A mutation is initially caused by an error in the copying of DNA as it is transcribed into a new strand for a developing cell and organism. However, that error can be inherited in later generations as it becomes a part of the genetic code. Just one difference in the DNA sequence can affect anything shown as a visual trait, including budgie's colouring.

What is a gene?

A gene is any sequence of DNA that codes for a specific protein. Proteins in the body are what control its functions, and therefore regulate the visual expression of the cells as well. The gene for albino, for example, deactivates the usual pigment present in the feathers and eyes of a budgie.

What is "wild type"?

"Wild type" indicates the mutation that would naturally occur in the wild, that is, the "default" or "standard" mutation. In budgies, the "wild type" form is green, with normal wing patterning.

What is "dominant" and "recessive"?

Dominant means that a trait covers up another and is expressed visually. For example, the spangle mutation in budgies is dominant to the normal wing pattern, so even if there is only one copy of the spangle gene, the bird will appear spangle.

In the case of recessive mutations, such as greywing, the normal wing pattern is dominant over the greywing pattern. Thus, if a bird has one copy of the greywing gene and one copy of the normal wing pattern, the bird will appear normal.

What does "single factor" and "double factor" mean?

First, let's understand chromosomes. All living organisms have one or more sets of chromosomes, which are condensed groups of DNA. These DNA groups have many different genes encoded in their strands, which are located at different parts of a chromosome. Each budgie has two sets of chromosomes, meaning there are similar pairs of each. In each pair of chromosomes, both carry information on the same sorts of things--for example, wing pattern-- but each chromosome can carry a different allele for the trait. An allele is a variation of a trait, like spangle or normal for wing pattern. If a budgie has the allele for spangle on one chromosome, and normal on the other, it will be spangle because that trait is dominant. However, it still has the capability to pass on the normal copy of the trait from the other chromosome to offspring.

Single factor indicates that there is only one copy of a specific trait (i.e spangle) carried by the bird. In the previous example, if the budgie had one copy of the spangle gene and one copy of the normal one, it would be single factor spangle. If instead of the normal gene on the other chromosome it had another spangle gene, it would be called double factor spangle.

"Single Factor" and "Double Factor" can only be used with dominant mutations. In the case of recessive mutations, the only way you would be able to visually see if a bird has the trait is if it has two copies of the gene, so although technically "double factor", recessive mutations are not commonly referred to as such.

What are sex-linked traits?

Sex linked traits occur when the gene for a trait is carried on one of the sex-determining chromosomes. In birds, the two sex chromosomes are technically Z and W, but for simplicity, we can refer to them as X and Y, like in mammals. Unlike most mammals, however, budgies' chromosomes are switched--in humans, females are XX and males are XY. In budgies, females are XY and males are XX.

When a trait is carried on one of those chromosomes, the gene is expressed differently. The usual dominant/recessive rules aren't applicable.

A common sex linked trait in budgies is the Ino gene, which causes a bird to be albino (if it is blue and white) or lutino (if it is green and yellow). The genes are carried on the X chromosomes only, not on the Y. Thus, if a female has one copy of the Ino trait on her X chromosome, she will express it visually, because her other chromosome is a Y. Sex-linked traits act dominant when there is only one X chromosome and can act either dominant or recessive when there are two X chromosomes, such as in males. A male with one copy the Ino gene on one of his two X chromosomes would not show it visually. A male with two copies of the Ino gene would show it visually. A good rule of thumb is to remember that in most sex-linked traits, all X chromosomes have to be "full" to express the gene--in the case of female budgies, they only have one to fill, male budgies have two.

Because the genes are located on the X chromosomes, a visually Ino female couldn't pass on the trait visually if she was bred with a normal budgie. The only chicks who would inherit the Ino gene would be the males, since they get one of their two X chromosomes from their mother. However, their other X chromosome with no Ino gene from the father would make the males only carry the trait and not show it visually.

Females are unable to carry Ino traits to their offspring in hidden, or split, form. However, if a male has one copy of the Ino gene, he has a 50% chance of passing on the gene to any of his daughters, who get their X chromosomes from him (the mother provides the sex-determining Y chromosome). Thus, if when breeding two budgies who have a normal appearance, one of the chicks is expressing a sex-linked trait, the chick must be female because the only way she could have inherited the trait is from her father in split form.

What does it mean when budgies are "split" for a trait?

When a budgie is "split" for something, it is similar to the single factor form of a dominant mutation--they only have one copy of a gene. Budgies carrying recessive mutations, however, only show the trait when they have two copies of it. In the "single factor" form, they do not look any different than the normal mutation. However, they still have the gene, and can pass it on to offspring if the other parent has the gene as well. This is known as "split" form.

What is co-dominance and incomplete dominance?
Co-dominance is where both traits are expressed equally, and incomplete dominance is when both traits mix to make a new visual trait. Either of these only happen when there is a different copy of each trait. For example, Opaline and Spangle are co-dominant because when a bird has the trait for both spangle and opaline, the bird expresses both in the wings. Neither is dominant to the other, hence the name "co-dominant". An example of incomplete dominance is in grey-green budgies, the genes for green body colour and grey body colour mix to see a new grey-green colour.

What are "violet factors"?

A violet budgie, apart from being very pretty, is also not a true violet. If it were, it would have to be some variation of green, like blue is. The blue colour in budgies exists because the yellow bit of the pigment in the feathers is not present, leaving a white face and blue body feathers. However, violet is actually a colour adding factor that exists on either blue birds or green birds. it is inherited as a dominant factor, so can exist in single or double factor forms. It adds a violet tint to the already existing body colour.

Grey is technically also a colour adding factor but works differently than violet because it completely obscures blue and is incompletely dominant to green. Also, violet can exist on top of grey.

Following is a brief list of the most common visual mutations in budgies:

Texas Clearbody
Ino (Albino/Lutino)

Dominant pied
Green body colour (when compared to blue)
Yellowface or Goldenface
Grey body colour (grey is dominant to blue but incompletely dominant to green)
Violet factors

Recessive pied

Fullbody greywing (Greywing and Clearwing, although these traits are recessive to normal colouring they are co-dominant when both traits are present)
Lacewing (Ino and Cinnamon)
Spangle Opaline

Grey-green body colour (grey is dominant to blue but incompletely dominant to green)

For detailed photos and descriptions of different mutations, be sure to read through this sticky:
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