Punnett square

The Punnett square is a diagram designed by Reginald Punnett and used by biologists to determine the probability of an offspring having a particular genotype. It is made by comparing all the possible combinations of alleles from the mother with those from the father.

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Typical monohybrid cross

The Punnett square shows every possible combination when combining one maternal allele with one paternal allele. In this example, both organisms have the genotype Bb. They can produce gametes that contain either the B or b alleles. (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 having the genotype BB is 25%, Bb is 50%, and bb is 25%.

It is important to note that Punnett squares only give probabilities 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.

Typical dihybrid cross

More complicated crosses can be made by looking at two or more genes. The Punnett square only works, however, if the genes are independent of each other, which means that having a particular allele of gene X does not imply having a particular allele of gene Y.

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). Y represents the dominant allele for color (yellow), while y represents the recessive allele (green). Each plant has the genotype Rr Yy, and since the alleles for shape and color genes are independent, they can produce four types of gametes with all possible combinations: RY, Ry, rY and ry.

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.

Situations where Punnett squares do not apply

The phenotypic ratios of 3:1 and 9:3:3:1 are theoretical predictions based on the assumptions of segregation and independent assortment of alleles (see Mendelian inheritance). Deviations from the expected ratios can occur if any of the following conditions exists:

• the alleles in question are physically linked on the same chromosome
• one parent lacks a copy of the gene, e.g. human males have only one X chromosome, from their mother, so only the maternal alleles have an effect on the organism (see sex linkage)
• the survival rate of different genotypes is not the same, e.g. one combination of alleles may be incompatible with life so that the affected offspring expires in utero
• alleles may show incomplete dominance or co-dominance (see dominance relationship)
• there are genetic interactions (epistasis) between alleles of different genes
• the trait is inherited on genetic material from only one parent, e.g. mitochondrial DNA is only inherited from the mother (see maternal effect)
• the alleles are imprinted

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