Geneticists commonly perform crosses of individuals exhibiting specific characteristics to determine how those traits are inherited. The results obtained from these crosses may or may not provide insight into the genetic control of the traits under study. Consider for example a monohybrid trait for which two phenotypes are known. A cross between two individuals with identical phenotypes that yields an F1 exhibiting the same phenotype as the parents can result from any one of the following three crosses:
| Cross 1 | Cross 2 | |||||
|---|---|---|---|---|---|---|
| Phenotype 1 | X | Phenotype 1 | Phenotype 1 | X | Phenotype 1 | |
| (AA) | |
(AA) | (AA) | |
(Aa) | |
| Phenotype 1 | Phenotype 1 |
| Cross 3 | ||
|---|---|---|
| Phenotype 2 | X | Phenotype 2 |
| (aa) | |
(aa) |
| Phenotype 2 |
The results of these crosses can be readily predicted through use of a Punnett Square:
| Cross 1 | Cross 2 | Cross 3 | ||
|---|---|---|---|---|
| AA X AA | AA X Aa | aa X aa | ||
|
|
|
||
 |
 |
 |
A cross between two individuals exhibiting different phenotypes that yields an F1 exhibiting two different phenotypes results from the following cross:
| Cross 4 | ||
|---|---|---|
| Phenotype 1 | X | Phenotype 2 |
| (Aa) | |
(aa) |
| Phenotype 1 and Phenotype 2 | ||
The results of this cross (a 1:1 ratio of Phenotype 1 to Phenotype 2) can readily be predicted through use of a Punnett Square:
| Cross 4 |
|---|
| Aa X aa |
|
 |
A cross between two individuals with the same phenotype that yields an F1 exhibiting two different phenotypes results from the following cross:
| Cross 5 | ||
|---|---|---|
| Phenotype 1 | X | Phenotype 1 |
| (Aa) | |
(Aa) |
| Phenotype 1 and Phenotype 2 | ||
The results of this cross (a 3:1 ratio of Phenotype 1 to Phenotype 2) can readily be predicted through use of a Punnett Square:
| Cross 5 |
|---|
| Aa X Aa |
|
 |
A cross between two individuals with different phenotypes that yields an F1 with all the same phenotype results from the following cross:
| Cross 6 | ||
|---|---|---|
| Phenotype 1 | X | Phenotype 2 |
| (AA) | |
(aa) |
| Phenotype 1 | ||
The results of this cross (all Phenotype 1) can readily be predicted through use of a Punnett Square:
| Cross 6 |
|---|
| AA X aa |
|
 |
The above examples form the basis for understanding the inheritance of traits that exhibit a simple dominance/recessive relationship. Analysis of the simultaneous inheritance of multiple traits can be derived from the above examples through use of some simple mathematics. For example, the expected phentoypic ratio from a double heterozygous dihybrid cross will yield a 9:3:3:1 [(3:1)2] ratio of all phenotypes. Of course, offspring ratios rarely exhibit the exact proportions that are predicted from the above analysis. Therefore, the results must be tested statistically through use of a goodness of fit test. Commonly, geneticsts employ the Chi squared test to determine if the observed results fit the predictions of one of the above models.