A Punnett Square: A tool to help manage simple genetic traits

Written and prepared by Dr. Jackie Atkins, Director of Science and Education

A Punnett squares is a handy tool to predict expected progeny outcomes from a specific mating.  A Punnett square only works with simply inherited traits (where one or just a few genes control the phenotype i.e., coat color, horned/polled, or many genetic conditions).  To use a Punnett square, you should know the genes involved with the trait, the genotypes of the parents, and whether certain alleles (variations of the same gene) are dominant, recessive, or somewhere in between.

A few principles that will help you understand how to use a Punnett square:

  • All animals have two copies of each gene and pass along one copy to their offspring.

  • In a population, there can be several alleles for one gene; but, an individual can have at most two varieties per gene.

  • An individual with the same two alleles for a gene is homozygous.  An individual with two different alleles for a gene is heterozygous.

  • An animal has an equal chance of passing on each one of their alleles.

  • In traits with complete dominance (for example coat color), an animal needs only one of the dominant alleles to display the dominant phenotype.  An animal needs two recessive alleles to display the recessive phenotype.

  • To organize a Punnett square, assign the top of the square for one parent’s genotype and use the left side of the square for the other parent.  You will want one row or column per genotype option.  The genotype options depend on the potential alleles passed from the parents to the offspring.  For example, if a parent has a genotype of Aa, the parent will pass either an A or a to the next generation and these would be the genotype options.  If looking at two genes, then all combinations of the alleles for each gene need to be included (an individual that is Aa for gene  1 and Bb for gene 2 could pass AB, Ab, aB, or ab to the next generation).  Starting with the top parent, you can fill in the each column with the header genotype.  Similarly, each row can be filled in with the genotype option listed to the left for that row.  Each resulting cell will represent a potential genotype for the offspring (half from the sire and half from the dam) and has an equal chance of occurring.

  • If you mate two heterozygous parents for one trait and the trait is only controlled by one gene, you will have a Punnett square with four blocks (two options per parent).  If you have a trait controlled by two genes (or if you are looking at the frequency of offspring for two traits) and the parents are heterozygous, then you will have a Punnett square with 16 cells (two different genes and two alleles/gene = four options per parent).  See examples below.

  • Some of the cells in the Punnett square will have duplicate genotypes and these can be added together to find predicted frequency of the offspring.

  • Some of the cells within the Punnett square will have different genotypes but the same phenotype.  For instance, with a completely dominant trait, the heterozygotes will appear the same as the homozygote dominant animals.  

Given the above principles, here are examples of using Punnett squares to predict offspring from different matings.

Example 1: Coat Color, a simply inherited trait that exhibits complete dominance.

Alleles: E = black and dominant, e = red and recessive
Mating: A heterozygous black sire to a heterozygous black damPunnett_Sq_Ex1

Progeny outcome: In this example, 25% of the calves will be homozygous black (EE), 50% of the calves will be heterozygous (Ee), and 25% of the calves will be homozygous red (ee).  As the black allele is dominant and it only takes one black allele to display the black phenotype, 75% of the calves will have a black coat color (EE and Ee calves) and only the homozygous red calves will have red coat color (25%, ee).


Example 2: Two genes that affect the same phenotype: Dilution of Color.

This is an instance where a second gene affects the phenotype of the first gene (a phenomenon called epistasis, see the ASA Science forum post called “Coat Color Dilution in Simmental Cattle” at http://www.simmental.org/forum).  The dilution effect is a dominant trait where the dilution allele will cause genotypically black animals to have a grey coat color.  Red animals are typically unaffected by the dilutor gene (or possibly slightly lighter in color) but can pass the gene to their offspring.

Coat color: E = black and dominant, e = red and recessive

Dilution: D = coat color dilution (if black) and dominant, d = normal coat color and recessive

Mating:  The sire is heterozygous for coat color (Ee) and homozygous for the normal dilutor allele (dd).   The sire has two potential genotype combinations, Ed and ed.  The dam is homozygous red (ee) and carries the dilutor allele (Dd).  The dam also has two possible genotype pairings, eD or ed.


Progeny outcome: Each one of the resulting cells has an equal chance of occurring and each cell is genotypically unique; therefore, each genotype has a 25% chance of occurring (1/4). Phenotypically, we would expect 25% of the calves to be grey (and a carrier of the dilutor allele),

25% black, and 50% red (with half of these carriers of the dilution mutation).


Example 3:  Two separate genes with two independent traits, Coat Color and Horned/Polled.


In this example, we will use two heterozygous parents for each trait to display a more complicated Punnett square (16 cells). Neither gene affects the other so the traits are independent of one another.  Both traits are completely dominant (black coat color is dominant to red and polled is dominant to horned).  In reality, there are other genes that affect these traits (dilution, see above, or the scurred gene in polled cattle, but for this example, we will ignore these other genes).


Alleles: Coat color: E = black and dominant, e = red and recessive

Horned/polled: P = polled and dominant, p = horned and recessive


Mating: The sire and dam are both heterozygous parents for each trait.  As these are completely dominant traits, both parents will be black and polled, but carry the red and horned alleles.  Each parent will have 4 potential genotype pairings.


Progeny outcomes: Any calves with at least one E will be black (denoted as E_) and calves with at least one P will be polled (denoted as P_).  Out of 16 animals, there will be 9 black and polled offspring (E_/P_; only one homozygous for both traits), 3 black and horned (E_/pp), 3 red and polled (ee/P_), and 1 red and horned (ee/pp) for a ratio of 9:3:3:1.

These principles can be applied to understanding the frequency of passing along any simply inherited traits including most of the genetic conditions we screen.  Combine the information you gain from DNA test results with Punnett squares to help predict potential traits in calves from certain matings.  Punnett squares are a useful tool to help make mating decisions to optimize your herd.  If you have any questions or comments, please post on the ASA science forum post about Punnett squares (www.simmental.org/forum under Genetic Evaluation).