 Punnett Squares - Maple Help

Punnett Squares

Main Concept

The genes of an organism are functional segments of DNA that are responsible for determining biological traits; they are packaged into thread-like structures called chromosomes. Diploid organisms, such as humans, have chromosomes that come in homologous pairs (except for the sex chromosomes), with each parent contributing one chromosome per homologous pair. Each chromosome in a given homologous pair represents the same genes, but with different expressions (called alleles) of those genes. The combinations of which two alleles are expressed for a given gene (or a set of genes) is called the genotype. An organism's genotype, with regard to a given gene, gives rise to a certain phenotypic trait (the physical expression of the gene, such as eye or hair color) according to the relative dominance of the alleles making up the genotype. For example, a genotype containing two of the same alleles has the phenotypic trait corresponding to that allele, whereas a genotype containing two different alleles takes on the phenotypic trait of the more dominant of the two alleles.

Punnett squares are a useful tool in helping to predict the likelihood of an organism inheriting a specific trait. A Punnett square is a table that graphically illustrates the genotypes produced when two parents are crossed. Given the genotypes of the parents for a given gene or a set of genes, the Punnett square determines the offspring's possible genotypes, and in particular the probability for each potential genotype to occur. The table is indexed on two sides by the possible maternal and paternal allele contributions for a given set of genes. Each possible combination of allele contributions from the parents combine to form a potential genotype for the offspring, which is then inserted into the appropriate square of the table. When all of the squares are filled, the probability of the offspring having a given genotype is proportional to the number of squares in which that genotype occurs.

The maximum number of allele combinations a parent can theoretically contribute to an offspring (number of columns/rows) can be calculated using:

$#{\mathrm{of allele combinations = 2}}^{n}$,

where n is the number of genes under consideration. This maximum number is achieved only if the parent is heterozygous with respect to each gene, which means the parent has two distinct alleles for each of the genes representing the traits in question. Under the assumption of heterozygosity, when considering two traits, one may expect each parent to contribute four allele combinations.

A common Punnett square is a monohybrid cross (Adjust the slider to 1 in the activity below). This type of cross tracks one gene. Both parents are heterozygous (that is, they both have one dominant, A, and one recessive, a, allele for the trait). From the Punnett square, the following conclusions can be made:

 • There is a 1/4 = 25% chance for the offspring being homozygous dominant (AA).
 • There is a 1/2 = 50% chance for the offspring being heterozygous like the parents (Aa).
 • There is a 1/4 = 25% chance for the offspring being homozygous recessive (aa).

The demonstration below is an example of a monohybrid cross (Slider Position = 1), dihybrid cross (Slider Position = 2), and a trihybrid cross (Slider Position = 3). Select the checkbox to show the probabilities of achieving each of the possible genotypes in the offspring.    More MathApps