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The Punnett square is a diagram that is used to predict an outcome of a particular cross or breeding experiment. It is named after Reginald C. Punnett, who devised the approach, and is used by biologists to determine the probability of an offspring's having a particular genotype. The Punnett square is a tabular summary of every possible combination of one maternal allele with one paternal allele for each gene being studied in the cross. These tables give the correct probabilities for the genotype outcomes of independent crosses where the probability of inheriting copies of each parental allele is independent. The Punnett Square is a visual representation of Mendelian inheritance.
In this example, both organisms have the genotype Bb. They can produce gametes that contain either the B or the b allele. (It is conventional in genetics to use capital letters to indicate dominant alleles and lower-case letters to indicate recessive alleles.) The probability of an individual offspring's having the genotype BB is 25%, Bb is 50%, and bb is 25%.
(M = Maternal, P = Paternal)
It is important to note that Punnett squares give probabilities only for genotypes, not phenotypes. The way in which the B and b alleles interact with each other to affect the appearance of the offspring depends on how the gene products (proteins) interact (see Mendelian inheritance). For classical dominant/recessive genes, like that which determines whether a rat has black hair (B) or white hair (b), the dominant allele will mask the recessive one. Thus, in the example above, 75% of the offspring will be black (BB or Bb) while only 25% will be white (bb). The ratio of the phenotypes is 3:1, typical for a monohybrid cross.
More complicated crosses can be made by looking at two or more genes. The Punnett square works, however, only if the genes are independent of each other, which means that having a particular allele of gene A does not alter the probability of possessing an allele of gene B. This is equivalent to stating that the genes are not linked, so that the two genes do not tend to sort together during meiosis.
The following example illustrates a dihybrid cross between two heterozygous pea plants. R represents the dominant allele for shape (round), while r represents the recessive allele (wrinkled). A represents the dominant allele for color (yellow), while a represents the recessive allele (green). If each plant has the genotype RrAa, and since the alleles for shape and color genes are independent, then they can produce four types of gametes with all possible combinations: RA, Ra, rA, and ra.
Since dominant traits mask recessive traits, there are nine combinations that have the phenotype round yellow, three that are round green, three that are wrinkled yellow, and one that is wrinkled green. The ratio 9:3:3:1 is typical for a dihybrid cross.
The tree method (AKA forkline, branching system) can also solve dihybrid and multihybrid crosses. A problem is converted to a series of monohybrid crosses, and the results are combined in a tree. This method does not calculate the gamete genotypes. However, a tree produces the same result as a Punnett square in less time.
This method is particularly advantageous when crossing homozygous organisms.