In the field of genetics, a dihybrid cross is a cross of two organisms, in which the genes for two traits are examined. Specifically, both organisms are heterozygous for both traits, meaning that they carry both the dominant and recessive genes for that trait. Due of this, the dominant gene is expressed in both the parents, but seven out of 16 of the offspring will exhibit at least one recessive trait.
An expressed gene is one that exhibits in the organism. The simplest example is a visible trait, such as eye or hair color. In the basic form of gene expression, an individual carries two genes for each trait, but only one gene is expressed, or appears.
For each trait, there are dominant and recessive genes. A dominant gene is one that is always expressed, while a recessive gene is expressed only if both genes that the organism carries for that trait are recessive. Thus, an individual with two dominant genes or a dominant and a recessive gene will express the dominant gene. In other words, the recessive gene will only be expressed if the organism carries two recessive genes.
Genetics is a very complex science, but many genetic predictions, including those for a dihybrid cross, can be simplified by the use of a tool called a Punnett square. This is a grid set up with the possible gene combinations from one parent listed across the top, and the possible gene combinations for the other parent listed down one side. The grid squares are used to compute all the possible gene combinations that could be produced by crossing the two parent organisms. This can enable a user to compute the probability of an offspring having any given trait or combination of traits.
The hair and eye color of dogs can be used as an example of a dihybrid cross. In this example, the dominant hair color is black and is represented by H, while the recessive hair color is white and is represented by h. The dominant eye color is brown, represented by E, and the recessive eye color is blue, represented by e. Since both parents are heterozygous in a dihybrid cross, they both have a set of genes represented by HhEe. This means that the possible gene combinations from each parent listed on the Punnett square are HE, He, hE, and he.
To continue, four possible combinations of hair color genes can be produced by crossing this set of parents — HH, Hh, hH, and hh. By the same logic, the possible combinations of eye color genes are EE, Ee, eE, and ee. Since there are four possible combinations for each type of gene, the total number of possible gene combinations is 16.
Out of the 16 possible combinations, nine of the theoretical offspring will possess the dominant gene for both traits and, therefore, will have black hair and brown eyes, like the parent dogs. Only one out of 16 dogs produced by this cross would have both recessive traits of white hair and blue eyes. The remaining six offspring will each exhibit one dominant trait and one recessive trait, so three of the dogs would have black hair and blue eyes, while three would have white hair and brown eyes.