3.14 - 3.16 - Genetic crosses and pedigrees

3.14 — Building a genetic cross

A genetic cross follows alleles from the parents, through their gametes, into possible zygotes. For one autosomal gene, a parent has two alleles in each body cell but a gamete carries only one. At fertilisation, one gamete from each parent combines, restoring a pair of alleles in the zygote.

Use one letter for the alleles of one gene. The dominant allele is usually written as the capital letter and the recessive allele as the same lowercase letter. This shows that they are versions of the same gene, not two different genes.

Suppose allele $P$ gives purple pea flowers and is dominant to allele $p$, which gives white flowers.

The dominant phenotype alone does not reveal the genotype: a purple-flowered plant could be $PP$ or $Pp$. The recessive phenotype does reveal the genotype in this simple model, because white flowers appear only when no dominant $P$ allele is present.

Consider a cross between two heterozygous plants:

Parent genotypes: $Pp \times Pp$

Possible gametes from each parent: $P$ or $p$

Read each cell by combining one allele from the row gamete and one from the column gamete. The square therefore predicts three possible offspring genotypes: $PP$, $Pp$ and $pp$. It does not represent four actual offspring, and it does not guarantee that a family of four will contain one of each cell shown.

3.16 — Probability, ratios and percentages

When the four Punnett-square cells are equally likely, count the cells to convert the outcome into different mathematical forms. For the cross $Pp \times Pp$:

The genotype ratio is therefore $PP:Pp:pp = 1:2:1$. The two genotypes $PP$ and $Pp$ have the same purple phenotype, so the phenotype ratio is purple:white $=3:1$. Genotype and phenotype ratios answer different questions; they must not be interchanged.

Worked example: predicting a number of offspring

A grower produces 160 offspring from the cross $Pp \times Pp$. Calculate the expected number with white flowers.

The requested quantity is a number of offspring. The Punnett square shows that the probability of the white phenotype $pp$ is $\frac{1}{4}$, or 25%.

The answer is 40 offspring. This is one quarter of 160, so it agrees with the 25% prediction. It is an expected number across many fertilisations, not a guaranteed count.

Worked example: comparing observed and expected ratios

A separate $Pp \times Pp$ cross produces 91 purple and 29 white offspring. To write the observed purple:white ratio as $n:1$, divide both counts by the white count:

To one decimal place the observed ratio is 3.1:1, close to the expected 3:1. Random fertilisation causes sampling variation, so an observed count need not match the prediction exactly. This result is consistent with the model, but closeness alone is not proof of the inheritance mechanism. Always keep the requested order: reversing the counts answers white:purple instead.

Each fertilisation is a new event. If one offspring is white, that does not make the next offspring more or less likely to be white while the parents' genotypes remain the same.