Constructing a homozygote for more than one gene

For every gene with two alleles there are two homozygous genotypes and one heterozygous genotype. As one adds independently assorting genes, the number of completely homozygous genotypes increases geometrically. Such homozygous genotypes, make up a smaller percentage of the total genotypes.

Completely homozygous genotypes are desirable since they breed true every generation.  These homozygous genotypes have to be "constructed" from other homozygous genotypes.  Such construction is 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.  Three recessive genes are known which color a different third of the box: pure white, Kelly green and orange.  These genes are independently assorting. 

Box on back of normal beetle:

Genetically:

In the lab, we have four strains of Flag beetles which breed true for beige, orange, green and white.  A certain Genetics professor decides to breed a special beetle which looks like the Irish Tricolor (Green, White and Orange). How does he approach this?

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

Material at Hand:

There are four strains available in the lab.

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

Step one is to construct a double homozygote.  This double homozygote can be white/green, white/orange, or green, orange.

I decide to construct a green/orange beetle first (that is I work with genes 1 and 3 and ignore gene 2 which will be beige).

 My first target is the genotype  

In the F₂ generation I get 9 different genotypes. These fall into four phenotypic classes (for gene 1 and 2) beige, 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 genotype WWggoo.  (Note: I might have to carry out this cross a number of times to get enough males and females to establish a viable purebreeding green/orange population. 

F₂ Generation:

Step 2: Now that I have a homozygous green/orange strain  established, I can cross it with the homozygous white strain that I already have.

  This gives me a triple heterozygote in the F₁ generation.  If we intercross the F₁ progeny to produce an F₂ , we will get the desired triple homozygote IRISH TRICOLOR flag beetle.

F₂ Generation:

The F₂ generation has 27 genotypes and 8 phenotypes (Beige, white, green, orange, white/green, white/orange, green/orange and Irish Tricolor (white/green/orange).  Tricolor should occur with a frequency of 1/64.  I 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).

Mendelian Genetics Index