For every gene with two alleles there are two homozygous genotypes and one heterozygous genotype. For each independently assorting gene associated with a phenotype, the number of completely homozygous genotypes increases geometrically. However, such homozygous genotypes, make up a smaller percentage of the total genotypes.

Completely homozygous genotypes are desirable since it is possible to set up a stock of organism that breeds true every generation.  These organism homozygous for multiple genotypes have to be "constructed" from a series of genetic crosses.   Such construction is often done using two genes at a time.

Example: Flag beetles have a box on their back which is divided into thirds (see below). The color in each box is normally beige (i.e., beige is wildtype).    Three recessive genes are known which color a different third of the box:  Kelly green (1), pure white (2) and orange (3).  These genes are independently assorting. 

Box on back of normal beetle:

Genetically:

In the lab, there are four strains of Flag beetles which breed true:

Strain 1:    Brown (all three sections).
Strain 2:    Green (section 1, other two sections are Brown).
Strain 3:    White (section 2, other two sections are Brown).
Strain 4:    Orange (section 3, other two sections are Brown).
 

  The Question: A certain Genetics professor decides to breed a special beetle which looks like the Irish Tricolor Flag (Green, White and Orange). How does he do this?

Desired Target Phenotype: Box on back of Irish Tricolor beetle:

Material at Hand:

There are four homozygous strains available in the lab.

The Desired Genotype of a Homozygous Irish Tricolor beetle

The target Irish Tricolor Flag beetle needs to have genotype wwggoo so that it will express the three different colors simultaneously.   This genotype  is approached through a number of steps.

Step one is to construct a double homozygote.  This double homozygote can be either white/green, white/orange, or green/orange (the other section of the box would be brown)

The professor decides to construct a green/orange beetle first (that is he works with genes 1 and 3 and ignores gene 2)

His target is a homozygous flag beetle with genotype ggWW00 and phenotype green brown and orange (seen below)  

In the F₁ generation, he gets all wildtype (entirely beige) beetles which must have the genotype GgWWOo.

 The F₁ beetles are intercrossed to make an F₂ generation.  In the F₂ generation he gets 9 different genotypes for gene 1 and 3.  These fall into four phenotypic classes  brown, green, orange, green & orange in a 9:3:3:1 ratio.  

Thus, 1/16 of the progeny will have the doubly recessive phenotype green & orange and have the corresponding genotype ggWWoo.  (Note: the professor might have to carry out this cross a number of times to get enough males and females to establish a viable, pure breeding green& orange population of Flag beetles.

F₂ Generation:

Step 2: Now that the professor has a homozygous green & orange strain established (section 2 is still brown)   he can cross individual beetles from that strain with individual beetles from the homozygous white strain (GGwwOO) that he has in the lab.

 This crosses produces a triple heterozygote in the F₁ generation (GgWwOo).  He then intercrosses the F₁ progeny to produce an F₂ .  He will then get the desired  homozygous IRISH TRICOLOR flag beetle in a very low frequency.

Genotypes and Phenotypes in the F₂ Generation:

The F₂ progeny have 8 phenotypes (Brown, white, green, orange, white&green, white&orange, green&orange and Irish Tricolor (white&green&orange) and 27 genotypes for genes 1, 2 and 3. The phenotypes are illustrated below.

 Tricolor should occur with a frequency of 1/64. The professor might have to repeat this cross a number of times to get enough Tricolor beetles to establish a new pure breeding lines (say 10 pairs of males and females).

Genotypes in the F₂ Generation