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Reproduction » Punnett Squares and Genetic Crosses

What you'll learn this session

Study time: 30 minutes

AQA spec: 4.6.1.6

How probability helps predict the results of a single gene cross
How to complete a Punnett square and write the outcome as a ratio
How to read information from genetic crosses and family trees
Higher tier: how to build a Punnett square and make predictions

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Predicting what offspring will look like

Each parent passes one allele for a gene to their offspring through a gamete. Which allele ends up in a particular gamete is down to chance. That means we cannot say for certain what one offspring will be like, but we can work out how likely each outcome is.

This is what probability is for. A genetic cross is a way of showing which alleles two parents could pass on, and what that means for their offspring. In this lesson we only look at crosses involving a single gene. Remember, most characteristics are controlled by many genes, so a single gene cross only works for the simpler cases.

Key terms:

Probability: how likely it is that something will happen, shown as a fraction, a decimal or a percentage.
Punnett square: a diagram that shows all the possible combinations of alleles from the gametes of two parents.
Genetic cross: a prediction of the offspring that two parents could have.
Offspring: the young produced by the parents.

Completing a Punnett square

At every tier you need to be able to complete a Punnett square. The steps below show how a square is filled in. Building one from scratch is a Higher tier skill, covered later in this lesson.

We will use guinea pig coat colour. The allele for black fur, B, is dominant. The allele for white fur, b, is recessive. Here is a cross between two heterozygous black guinea pigs, Bb and Bb.

① Step 1: the gametes

Each parent makes gametes carrying one allele. A Bb parent makes gametes with B or with b.

② Step 2: the grid

The square has four boxes. One parent's gametes go along the top and the other parent's down the side.

③ Step 3: fill the boxes

In each box, write the allele from the top and the allele from the side. This gives the genotype of a possible offspring.

④ Step 4: read the result

Count the genotypes, then use the dominant and recessive rules to work out each phenotype.

The four boxes of the finished square are: BB, Bb, Bb and bb.

BB and Bb both have at least one B, so they are black. That is 3 boxes.
bb has no dominant allele, so it is white. That is 1 box.

Always write the capital letter first in a heterozygous genotype (Bb, not bB). It keeps your answers neat and easy to mark.

Showing the outcome as a ratio, fraction or percentage

The Punnett square above gives 3 black to 1 white. We use simple ratios and direct proportion to say this in different ways.

Ratio: 3 black : 1 white.
Fraction (probability): 3 out of 4 boxes are black, so the probability of black is 3/4. The probability of white is 1/4.
Percentage: 75% black and 25% white.

Direct proportion lets you scale this up. If the same cross produced 20 offspring, you would expect about 20 ÷ 4 × 3 = 15 black and 5 white.

Worked example

A black guinea pig (Bb) is crossed with a white guinea pig (bb). The white parent can only make gametes with b. The square gives Bb, Bb, bb, bb. That is 2 black : 2 white, which simplifies to a ratio of 1 : 1. The probability of a white offspring is 2/4 = 1/2, or 50%.

Worked example

A black guinea pig (BB) is crossed with a white guinea pig (bb). Every box in the square is Bb. All the offspring are black, so the probability of black is 4/4 = 100%. The ratio is 4 : 0, or all black.

Probability is not a guarantee

A ratio of 3 : 1 is what we expect, not what we always get. Each fertilisation is a separate chance event. If two Bb parents have four offspring, you might get 3 black and 1 white, but you might get 4 black or 2 and 2.

The result of one offspring does not change the next. If a pair has just had a white offspring, the chance of the next one being white is still 1/4. Results get closer to the ratio when there are more offspring.

Reading genetic crosses and family trees

A family tree shows how a characteristic is passed down through the generations. Squares usually show males and circles show females. Lines join parents to their children. Shaded shapes show individuals with the characteristic being followed.

To interpret a family tree or cross, work backwards from the phenotypes:

A recessive phenotype must have two recessive alleles, so its genotype is always known (bb).
If two parents show the dominant phenotype and have a child with the recessive phenotype, both parents must be heterozygous. The child got one b from each parent.
If a dominant phenotype is shown, there is at least one dominant allele, but the other allele may be either.

Worked example: reading a family tree

A family tree for guinea pig coat colour has three generations. In generation 1, a black male and a black female (both unshaded) are the parents. In generation 2, they have three offspring: two black and one white female (shaded). In generation 3, the white female (bb) is crossed with a black male and has black offspring only.

The shaded white female is bb. Her parents are both black but must have passed a b to her, so both are Bb. Her black offspring must each have received a b from her, so each is Bb.

Worked example

Two black guinea pigs have a litter that includes a white guinea pig. The white one is bb, so it received a b from each parent. The parents are black, so each must also carry B. Both parents are therefore Bb.

Higher tier only: constructing a cross and making predictions

Higher tier only

At higher tier you must build the Punnett square yourself from the information given, then use probability to make a prediction. Follow these steps:

1. Choose letters and write which allele is dominant. 2. Work out the parents' genotypes from the clues. 3. Write the gametes. 4. Draw and fill in the square. 5. Give the ratio or probability that the question asks for.

For example, a heterozygous black guinea pig is crossed with a white one. The prediction is a 50% chance of a black offspring. If the pair has 8 offspring, you would expect about 4 black and 4 white.

Common mistakes

Counting Bb as white because it has a b in it (the dominant allele B is expressed). Saying a 3 : 1 ratio means exactly 3 of every 4 offspring will be black. Forgetting to say which letter stands for which allele. Mixing up genotype (the alleles) and phenotype (what you see). Putting the parents' alleles in the boxes instead of the gametes.

Exam-style question

In guinea pigs, the allele for black fur (B) is dominant to the allele for white fur (b). Two heterozygous black guinea pigs are crossed.

(a) Complete a Punnett square to show the cross. [2 marks]

(b) State the ratio of black to white offspring. [1 mark]

Model answer

(a) Gametes B and b from each parent (1). Square shows BB, Bb, Bb, bb (1).

(b) 3 black : 1 white (1).

Exam tip

For part (c), the answer is a prediction, so use the probability of 1/4 and show your working. You are not guaranteed exactly 3.

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