To start off, let's begin by discussing the basic terms that go along with genetics talk:
Phenotype: This is the actual visual appearance of the animal (from now on we'll say Gouldian). So.. your bird being Red Headed, Purple Breasted and Normal (Green) backed is its "Phenotype."
Genotype: The genotype, on the other hand, is the actual genetic make up of the bird which produces its phenotype. This is where things can get tricky - because a Purple Breasted bird can be a few genotypes - it can be Purple/White, Purple/Purple, Purple/Lilac. The "/" once again denotes that the color is "split" for something else. This will make more sense once we define Double-Factor and Single-Factor (also known to biologists as either Homozygous or Heterozygous).
Double-Factor: Double-Factor (simplified DF) indicates that the bird is homozygous for a trait. This means it has two of the same genes corresponding to that particular trait.
Single-Factor: Single factor (simplified SF) means just the opposite - the bird has only one of the genes corresponding to a particular trait. For instance - with the Yellow mutation, a male bird can either be SF or DF for the Yellow gene.
Sex-Linked: When a trait is sex-linked, it means the genes appear only on the sex chromosomes. It is useful to point out that these refer to genes on the male sex chromosome since the W female chromosome does not carry any sex linked genes. In birds, these chromosomes are denoted as Z and W (whereas in humans they are X and Y) - and male birds are identified as ZZ, with females being ZW (as some may notice, this is the reverse of the situation with humans: males are XY and females are XX).
Autosomal Traits: Autosomal traits are those that are located on chromosomes other than the sex chromosomes. For example, all breast color genes are autosomal genes and are not found on the sex chromosomes.
Dominant Trait: A dominant trait is one that will appear phenotypically if one or more parents contributes that trait.
Recessive Trait: The opposite of a dominant trait, a recessive trait is one that will only be phenotypically expressed if both parents contribute the recessive trait.
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