Inheritance of sex in humans

Humans typically have two sex chromosomes. Females usually have two X chromosomes, written as $$\mathrm{XX}$$, while males usually have one X chromosome and one Y chromosome, written as $$\mathrm{XY}$$.

An egg contributes one X chromosome to the offspring. A sperm contributes either an X chromosome or a Y chromosome. When a sperm fertilises an egg, the two chromosomes form the offspring’s sex chromosome combination:

• An X-carrying sperm and an X-carrying egg produce $$\mathrm{XX}$$, typically female.
• A Y-carrying sperm and an X-carrying egg produce $$\mathrm{XY}$$, typically male.

Because the egg contributes an X chromosome in either case, which sperm fertilises the egg determines whether the offspring has an $$\mathrm{XX}$$ or an $$\mathrm{XY}$$ combination.

Probability in genetic crosses

A genetic cross predicts how likely different offspring outcomes are. It does not guarantee the outcome for an individual offspring or the exact numbers in a family.

When every cell in a Punnett square represents an equally likely combination, each cell counts equally towards the prediction. The probability of an outcome is:

For example, if three of the four cells show offspring with a particular characteristic, the predicted probability of that characteristic is $$\frac{3}{4}$$, or $$75%$$. The probability of an offspring without it is $$\frac{1}{4}$$, or $$25%$$.

Ratios and expected numbers

A ratio compares the predicted numbers of different outcomes. In the example above, the ratio with the characteristic to without it is $$3:1$$. For any two-category ratio $$a:b$$, the corresponding proportions are $$\frac{a}{a+b}$$ and $$\frac{b}{a+b}$$.

To find an expected number, multiply the predicted proportion by the total number of offspring:

For 12 offspring with a predicted ratio of $$3:1$$, the expected numbers are $$\frac{3}{4} \times 12 = 9$$ with the characteristic and $$\frac{1}{4} \times 12 = 3$$ without it.

These are predictions, not guaranteed counts: the actual numbers can differ by chance. The outcome for one offspring does not determine the outcome for another. For example, an offspring with the characteristic does not make the next offspring more or less likely to have it.

Monohybrid crosses using genetic diagrams

A monohybrid cross predicts the inheritance of one characteristic. It shows which allele each parent can pass on, then combines the parental alleles to find the possible offspring genotypes.

An allele is a version of a gene. An individual has two alleles for the gene, but each gamete carries only one. The combination of alleles is the genotype; the observable form of the characteristic is the phenotype.

For the crosses below, suppose flower colour is controlled by a dominant allele $$P$$ for purple and a recessive allele $$p$$ for white. A plant with $$PP$$ or $$Pp$$ has purple flowers because one dominant allele is enough to produce the purple phenotype. A plant must have $$pp$$ to have white flowers.

A genotype with two identical alleles, such as $$PP$$ or $$pp$$, is homozygous. A genotype with two different alleles, such as $$Pp$$, is heterozygous.

Punnett square: two heterozygous parents

In a Punnett square, the possible gamete alleles from one parent go across the top and those from the other parent go down the side. Each cell combines one allele from each parent to show a possible offspring genotype.

For a cross between two heterozygous parents, $$Pp \times Pp$$, each parent can pass on either $$P$$ or $$p$$:

The four cells give a predicted genotype ratio of 1 $$PP$$ : 2 $$Pp$$ : 1 $$pp$$. Three cells have at least one dominant allele and therefore predict purple flowers; one has two recessive alleles and predicts white flowers. The predicted phenotypic ratio is 3 purple : 1 white, or 3 dominant : 1 recessive.

Punnett square: heterozygous and homozygous recessive parents

For a cross between a heterozygous parent and a homozygous recessive parent, $$Pp \times pp$$, the first parent can pass on $$P$$ or $$p$$. The recessive parent can pass on only $$p$$.

Two cells show $$Pp$$ and two show $$pp$$. The predicted phenotypic ratio is therefore 1 purple : 1 white, or 1 dominant : 1 recessive.

These ratios are predictions of the relative likelihood of each phenotype. The actual numbers in a particular group of offspring may not match the predicted ratio exactly.