A Punnett square is a predictive tool used in genetics to determine the probability of offspring inheriting certain combinations of alleles from their parents. This diagram allows for the visualization of all potential genotypic outcomes from a cross. When studying the inheritance of two separate traits simultaneously (a dihybrid cross), the square expands to a 4×4 grid. This larger matrix, containing 16 individual boxes, is necessary to account for the increased number of allele combinations when tracking two distinct genes. The goal of this process is to calculate the likelihood of an offspring expressing a specific combination of observable characteristics, or phenotypes.
Generating the Gamete Allele Pairs
The most involved step in performing a dihybrid cross is accurately determining the four unique haploid gametes that each parent can contribute. This process is governed by Mendel’s Law of Independent Assortment, which states that the alleles for one gene separate into gametes independently of the alleles for the other gene. For a parent heterozygous for both traits, such as \(AaBb\), the alleles must be separated into four groups of two, with each group receiving one allele for the ‘A’ gene and one allele for the ‘B’ gene.
A systematic method, often referred to as the “FOIL” method, helps ensure all four possible combinations are identified correctly. The letters in the parent’s genotype (\(AaBb\)) are grouped to form the gametes. The “First” step combines the first allele of the first pair with the first allele of the second pair, yielding \(AB\).
The “Outer” step links the first allele of the first pair with the second allele of the second pair, resulting in \(Ab\). The “Inner” combination pairs the second allele of the first gene with the first allele of the second gene, producing \(aB\). The “Last” combination pairs the second allele of the first gene with the second allele of the second gene, resulting in the final gamete, \(ab\).
These four unique combinations—\(AB\), \(Ab\), \(aB\), and \(ab\)—represent the only possible genetic contributions from a parent with the \(AaBb\) genotype. Gametes are haploid, meaning they carry only half of the genetic material, which is why each combination contains only one letter from each original gene pair. If both parents are \(AaBb\), they produce the same four gamete types, which are used to set up the 4×4 grid.
Constructing the 4×4 Grid
Once the four distinct gamete allele pairs for each parent have been identified, the next step is constructing the 4×4 matrix. This grid has four rows and four columns, creating 16 interior cells necessary to map all possible fertilization events. This structure visually represents every possible fusion between the sperm and egg cells.
The four gamete combinations are written along the top edge of the square, one combination above each column, representing the contribution from one parent. The same four combinations are then written vertically down the left side, one combination beside each row, representing the contribution from the second parent.
In the most common dihybrid cross (\(AaBb \times AaBb\)), the same four gametes (\(AB, Ab, aB, ab\)) are placed on both the top and the side axes. This setup creates the framework for predicting the genotypes of the next generation. The axes serve as placeholders for the individual alleles that will be combined inside the square.
Filling in the Genotype Combinations
Filling the 16 internal boxes involves systematically combining the alleles from the row and column headers for each intersection. Each cell represents a potential zygote and contains four alleles, two from each parent. To adhere to standard genetic notation, the alleles must be combined with the same gene letters grouped together.
When combining the gamete \(AB\) from the top axis with \(aB\) from the side axis, the resulting genotype is \(AaBB\), not \(ABaB\). The alleles for the first gene (\(A\) and \(a\)) are placed together, and the alleles for the second gene (\(B\) and \(B\)) are placed together. The dominant allele (capital letter) is always written before its recessive counterpart in the pair, such as \(Aa\) instead of \(aA\).
Combining the gamete \(Ab\) from the top with \(aB\) from the side results in the genotype \(AaBb\). The cell where \(aB\) meets \(ab\) results in \(aaBb\). This methodical combination is repeated for all 16 cells until the entire square is filled with the genotypes of the potential offspring.
Interpreting the Phenotypic Outcomes
The final step is to translate the 16 resulting genotypes into observable phenotypes (physical traits). This requires understanding the relationship between dominant and recessive alleles for both traits being tracked. A dominant allele (capital letter) will mask the expression of a recessive allele when both are present in the genotype.
For a trait to be expressed as the recessive phenotype, the offspring must inherit two recessive alleles (homozygous recessive) for that specific gene. After establishing which genotypes correspond to which phenotypes, the total number of boxes displaying each unique trait combination is counted. For a classic dihybrid cross (\(AaBb \times AaBb\)), four distinct phenotypes are possible.
The count reveals a predictable ratio of 9:3:3:1 among the 16 total outcomes.
Phenotype Ratios
- The largest group (9/16) expresses the dominant phenotype for both traits.
- The first group of three (3/16) expresses the dominant phenotype for the first trait and the recessive phenotype for the second.
- The second group of three (3/16) expresses the recessive phenotype for the first trait and the dominant phenotype for the second.
- The single outcome (1/16) is homozygous recessive for both traits, expressing both recessive phenotypes.
This ratio provides the probability of inheriting each phenotype in the next generation.