Predicting Traits with Punnett Squares

Suppose a gardener crosses two pea plants that both have purple flowers, and both are Pp. The seeds are predicted to grow into mostly purple plants, with about one in four blooming white.

Neither parent had white flowers. So where was the white hiding? And could the gardener have predicted “one in four” before planting a single seed?

Explore: breed purple and white pea plants

In the simulation you choose the genotype of two parent pea plants: PP, Pp or pp. You see the filled Punnett square with its predictions, then grow 4, 40 or 1,000 offspring, each made by a random draw of one sex cell from each parent. A bar graph puts your real counts next to the predicted ones.

1. Parent 1’s genotype

PP Pp pp

2. Parent 2’s genotype

PP Pp pp

3. Number of offspring

4 40 1,000

Grow offspring Reset

Purple flowers

White flowers

White offspring in the last runs (up to 8)

none yet

Pick two parents and a number of offspring. Then press Grow offspring.

In this sketch: one gene with complete dominance (P purple, p white), no weather, soil or lost seeds, and every cross gives offspring. A Pp parent passes on P or p with a 50 percent chance, as the lesson says. A PP or pp parent makes only one kind of sex cell, so it is written twice to keep the 4-box square. The plants are labelled shapes, not to scale. Nothing here is measured; the computer makes the random draws.

A Punnett square gives the chance for each offspring, not an exact count. Real counts land near its ratio but rarely match it exactly.

Try this.

1. Cross two Pp plants. Predict how many of 4 offspring will be white. Grow them, then repeat three times.
2. Now grow 40, then 1,000. Predict first: will the share of white plants move closer to one in four, or stay just as scattered?
3. Cross a PP plant with a Pp plant. Both have purple flowers. Predict whether any offspring will be white, then test it.

Explain: alleles can hide but do not disappear

A pea flower shows one color, but each body cell of the plant carries two copies of the flower-color gene. An allele is one version of a gene. A pea plant gets one allele of each gene from each parent.

Pea plants have a purple allele and a white allele for flower color. Scientists write them as letters: P for purple and p for white.

• A dominant allele shows its trait even when there is only one copy. It gets a capital letter.
• A recessive allele shows its trait only when both copies are recessive. It gets a small letter.

When a dominant allele is there, it masks the recessive one. Masked means hidden from view, not destroyed. The p allele is still there, and it can still be passed on.

Your genotype is the pair of alleles you carry, such as Pp. Your phenotype is the trait that shows, such as purple flowers.

Genotype	Alleles	Phenotype
PP	two same alleles (homozygous)	purple
Pp	two different alleles (heterozygous)	purple
pp	two same alleles (homozygous)	white

A purple plant could be PP or Pp, so its looks do not tell you its genotype.

Sex cells carry only one allele of each pair, as you saw in that lesson. A PP plant can only pass on P. A pp plant can only pass on p. A Pp plant passes on P or p, with a 50 percent chance for each.

Explain: a Punnett square shows the chances

A Punnett square is a grid that shows every way the sex cells of two parents can join. It is a model that predicts offspring.

Here is how to build one for two Pp parents.

1. Write one parent’s sex cells, P and p, across the top.
2. Write the other parent’s sex cells, P and p, down the side.
3. In each box, put the letter from the top with the letter from the side.

	P	p
P	PP	Pp
p	Pp	pp

Probability is the chance that something will happen. Each box has the same chance, 1 in 4, because 1/2 × 1/2 = 1/4. A ratio compares two numbers, such as 3 purple to 1 white. You can write each prediction three ways.

What you predict	As fractions	As percents	As a ratio
Genotypes	1/4 PP, 2/4 Pp, 1/4 pp	25, 50, 25	1 PP : 2 Pp : 1 pp
Phenotypes	3/4 purple, 1/4 white	75, 25	3 purple : 1 white

Now the hidden white makes sense. Each parent is Pp. If both pass on p, the offspring is pp and blooms white. That has a 1 in 4 chance. This prediction needs both parents to be Pp. If one parent is PP, every offspring gets at least one P.

A Punnett square gives the chance for each offspring, not an exact count. Four seeds from two Pp parents might all bloom purple. The chance of that is about 32 percent. Mendel’s rules, and squares like this one, explain how many inherited traits are passed on. Later courses add other patterns.

Elaborate: Mendel’s pea counts

Mendel crossed pea plants that differed in one trait. Their first offspring all showed the dominant trait. He let those hybrid plants fertilize themselves and counted the next generation.

Trait (dominant vs recessive)	What was counted	Dominant (number)	Recessive (number)	Ratio (dominant ÷ recessive)
Seed shape: round vs wrinkled	seeds	5,474	1,850	2.96 : 1
Seed color: yellow vs green	seeds	6,022	2,001	?
Flower color: purple vs white	plants	705	224	?
Pod shape: full vs pinched	plants	882	299	2.95 : 1
Unripe pod color: green vs yellow	plants	428	152	2.82 : 1
Flower position: along the stem vs at the tip	plants	651	207	3.14 : 1
Stem length: tall vs short	plants	787	277	2.84 : 1

Source: Gregor Mendel’s pea paper, read at two meetings in Brno in 1865 and printed in 1866 (English translation by Abbott and Fairbanks, 2016). The plants grew in his garden beds and in some pots. The paper does not give a year for each row. For flower color, Mendel sorted plants by seed-coat color, which goes with flower color. The ratios were calculated here.

1. Find the two missing ratios. Divide the dominant count by the recessive count and round to two decimal places.
2. Which row is farthest from 3 : 1? Which row has the fewest offspring counted? What do you notice?
3. What percent of the flower-color plants were white? Divide 224 by the total, 929, and compare with 25 percent.

Design problem

Plan a model with beads that tests this question: does the number of offspring change how close a cross comes to 3 : 1?

One way to do it

Make two paper bags, one for each Pp parent. Put 20 purple beads (P) and 20 white beads (p) in each bag. All beads are the same size, about 1 centimetre across, so you cannot tell them apart by feel.

• Make one offspring: without looking, draw one bead from each bag. Record the pair, then put both beads back and shake the bags.
• Independent variable: the number of offspring you make: 4, 20 or 100.
• Dependent variable: the percent of offspring that are pp (white).
• Constants: the same bags, the same 20 and 20 beads, and putting beads back after every draw.
• Control: a PP bag (40 purple beads) paired with a Pp bag. It should never give a pp offspring, which checks that your method works.
• Repeated trials: make each group size 5 times and find the mean percent of white.
• Safety: pick up dropped beads so no one slips, and keep beads away from your mouth.

If the 100-offspring groups land closer to 25 percent than the 4-offspring groups, sample size matters. The bead model is not a real plant: it has one gene and no weather, soil or lost seeds.

Evaluate: check your thinking

The white was hiding in the parents’ genotypes. Both purple parents were Pp, so each carried a masked p allele. Each offspring had a 1 in 4 chance of getting p from both parents, and those pp plants bloomed white. A Punnett square predicts that chance, but not the exact count in a small group.

Science practices you used: making predictions and testing them, using a Punnett square as a model and naming its limits, calculating ratios and percents from real counts, and making a claim with evidence and reasoning.