Beyond Simple Dominance

In incomplete dominance, neither allele fully masks the other, so the heterozygote has an intermediate phenotype. In snapdragons (Antirrhinum majus), red-flowered plants crossed with white-flowered plants give all pink F₁ plants. Because neither allele is dominant, we do not use capital and lower-case letters. Instead we use one letter with superscripts: $C^R$ for red and $C^W$ for white. So $C^R{C}^R$ is red, $C^R{C}^W$ is pink and $C^W{C}^W$ is white. This is not blending: crossing two pink plants brings red and white back, because the alleles were never mixed. With incomplete dominance the phenotypic ratio equals the genotypic ratio, since every genotype looks different.

In codominance, both alleles are fully expressed in the heterozygote, side by side, rather than producing an in-between form. In roan cattle, a red parent and a white parent produce offspring whose coats have a mix of red hairs and white hairs. No single hair is pink. Human ABO blood types include a codominant case: a person with alleles $I^A$ and $I^B$ makes both the A and the B markers (antigens) on their red blood cells.

Multiple alleles. A gene can have more than two alleles in a population, even though each person still carries only two. The ABO gene has three: $I^A$ and $I^B$ are codominant with each other, and both are completely dominant to $i$. That gives six genotypes but only four phenotypes.

Humans have 22 pairs of autosomes plus one pair of sex chromosomes: females are usually XX and males XY. The X chromosome is large and carries many genes; the Y is small and carries few. A gene found on the X but not the Y is X-linked (sex-linked). A male has only one X, so whatever allele is on it shows up in his phenotype. There is no second copy to mask a recessive allele. A female needs two copies of a recessive X-linked allele to show the trait; with one copy she is a carrier. This is why X-linked recessive conditions such as red-green colour blindness and hemophilia A are much more common in males. Early evidence for sex linkage came from Thomas Hunt Morgan's experiments with a white-eyed mutant fruit fly.

• Write X-linked alleles as superscripts on the X: $X^B$ (typical colour vision, dominant) and $X^b$ (colour blind, recessive). The Y carries no allele: $Y$.
• Female genotypes: $X^B{X}^B$ (typical), $X^B{X}^b$ (carrier, typical vision), $X^b{X}^b$ (colour blind).
• Male genotypes: $X^{B}Y$ (typical) or $X^{b}Y$ (colour blind).
• A son always gets his X from his mother and his Y from his father, so a father cannot pass an X-linked allele to his sons.

A dihybrid cross follows two genes at once. If the genes are on different chromosomes, Mendel's law of independent assortment applies. For a parent that is $YyRr$, the $Y$ allele is equally likely to end up with $R$ or with $r$, so the parent makes four kinds of gamete in equal numbers: $YR$, $Yr$, $yR$ and $yr$. (A quick way to list them is to pair each allele of the first gene with each allele of the second.) Two such parents give a 4 × 4 Punnett square of 16 equally likely boxes, and the classic phenotypic ratio is 9 : 3 : 3 : 1. You do not always need all 16 boxes, though. Because the genes assort independently, you can solve each gene with its own small square and multiply. For $AaBb\times AaBb$, $P(\text{dominant for A})=\frac{3}{4}$ and $P(\text{recessive for B})=\frac{1}{4}$, so $P(A\_bb)=\frac{3}{4}\times \frac{1}{4}=\frac{3}{16}$. This product rule also works for three or more genes, where a full Punnett square would be huge.

Reading pedigrees. For humans we cannot set up crosses, so geneticists study family trees called pedigrees. Squares are males and circles are females. A shaded symbol means the person shows the trait; a half-shaded symbol (or a dot) can mark a known carrier. A horizontal line joining a male and a female is a mating, and a vertical line drops to their children, listed left to right from oldest. Roman numerals number the generations.