A probability table wearing a grid

The Punnett square, devised by the British geneticist Reginald Punnett, is a way of applying the rules of probability to a genetic cross. All possible combinations of one parent's alleles go along the top and the other parent's down the side, representing their meiotic segregation into haploid gametes. Each box then holds the diploid genotype of a zygote that could result from that mating. Its validity rests on Mendel's law of segregation: paired alleles separate equally into gametes, so each combination is equally likely. That equal likelihood is what lets you count boxes instead of doing probability arithmetic, and it is the only reason the method works.

A worked example

In pea plants, yellow seed color (Y) is dominant to green (y). Two heterozygous yellow plants (Yy) are crossed. Give the genotypic and phenotypic ratios of the offspring, and the probability that a given seed is green.

  1. Write out each parent's gametes. A Yy plant segregates its two alleles equally, so it makes Y gametes and y gametes in equal numbers. Both parents do the same.
  2. Draw a 2 by 2 grid, with Y and y along the top for one parent and Y and y down the side for the other. Two gamete types from each parent give four boxes.
  3. Fill in each box by combining the row allele with the column allele: YY, Yy, yY and yy. The two heterozygous boxes are the same genotype reached two different ways, from a Y egg with a y sperm or a y egg with a Y sperm, and both must be counted.
  4. Collect the genotypes: 1 YY, 2 Yy, 1 yy. That is the 1:2:1 genotypic ratio.
  5. Apply dominance to get phenotypes. YY and Yy both show yellow seeds because Y is dominant, and only yy shows green. So 3 of the 4 boxes are yellow and 1 is green, a 3:1 phenotypic ratio.
  6. Read the probability off the grid: 1 of 4 boxes is yy, so the probability that a given seed is green is 1/4, which is 25 percent.

= Genotypes 1 YY : 2 Yy : 1 yy, phenotypes 3 yellow : 1 green, and a 1/4 or 25 percent chance that a given seed is green.

Where students go wrong

The most consequential mistake is listing gametes wrongly. A parent contributes one allele per gene to each gamete, not its whole genotype, so a Yy parent offers Y and y rather than a single Yy entry. The second is forgetting that identical-looking boxes are separate outcomes: Yy appears twice in a monohybrid square because it can be reached two ways, and collapsing them into one box turns a 1:2:1 ratio into a wrong 1:1:1. The third is reporting a genotypic ratio when the question asked for phenotypes, or the reverse, which is a reading error rather than a genetics error but costs the same.

Where this leads next

The grid scales in two directions. Following two genes at once produces a 4 by 4 square and the 9:3:3:1 ratio of the dihybrid cross page, and beyond that the method becomes unwieldy fast: four genes would need a 16 by 16 grid of 256 boxes, which is why the forked-line and probability methods take over. In the other direction, the square behaves differently when dominance is not simple, and the incomplete dominance and codominance page shows the same 1:2:1 genotypic ratio producing three visible phenotype classes instead of two.

Common mistakes

  • Putting a whole genotype such as Yy in one cell along the edge. Each edge entry is a single gamete, carrying one allele per gene.
  • Counting the two heterozygous boxes as one outcome, which turns the 1:2:1 genotypic ratio into a wrong 1:1:1.
  • Reporting 3:1 as the genotypic ratio. It is the phenotypic ratio; the genotypes fall 1:2:1.
  • Treating the predicted ratio as a promise about a particular litter or seed pod rather than an expectation across a large sample.

Related concepts

  • Dihybrid cross: A dihybrid cross follows two characteristics at once, starting from true-breeding parents that differ in both.
  • Incomplete dominance vs codominance: In incomplete dominance the heterozygote shows an intermediate phenotype, as a red and a white snapdragon parent give pink offspring.
  • Genotype vs phenotype: A genotype is an organism's underlying genetic makeup, including alleles that are not expressed.

Sources