Mendelian Inheritance

• Gene — a segment of DNA on a chromosome that codes for a trait (for example, seed shape). Its position on the chromosome is its locus.
• Allele — one version of a gene (round or wrinkled). A diploid organism has two alleles for each gene, one on each homologous chromosome.
• Dominant allele — shows its effect whenever it is present. Written with a capital letter: $R$.
• Recessive allele — shows its effect only when no dominant allele is present. Written with the same letter in lower case: $r$.
• Homozygous — two identical alleles ($RR$ or $rr$). A homozygous organism is also called true-breeding or purebred.
• Heterozygous — two different alleles ($Rr$), sometimes called a hybrid.
• Genotype — the allele combination an organism has ($RR$, $Rr$ or $rr$).
• Phenotype — the observable trait that results (round or wrinkled seeds). Phenotype depends on genotype and can also be influenced by the environment.

Peas were a good choice: they grow quickly, produce many offspring, have traits with two clear forms (round or wrinkled seeds, yellow or green seeds, purple or white flowers, tall or short stems), and can be self-pollinated or cross-pollinated by hand. Mendel started with true-breeding plants, the P generation (parental). When he crossed round-seeded plants with wrinkled-seeded plants, every plant in the F₁ generation (first filial) had round seeds. The wrinkled trait seemed to vanish. When he let the F₁ plants self-pollinate, wrinkled seeds reappeared in the F₂ generation, in about one quarter of the offspring. For seed shape he counted 5474 round and 1850 wrinkled seeds, a ratio of about 2.96 to 1, very close to 3 : 1. He found the same pattern for every trait he studied.

• Law of segregation — each organism has two alleles for a trait, and they separate (segregate) when gametes form, so each gamete carries only one allele. Offspring get one allele from each parent.
• Law of independent assortment — alleles for different genes are sorted into gametes independently of each other. (This holds for genes on different chromosomes; you will use it for dihybrid crosses in the next topic.)

A monohybrid cross follows one gene. A Punnett square is a grid that lists every combination of gametes from the two parents. Each box is equally likely, so the boxes give the probabilities directly. Use the same five steps every time:

1. Key: choose a letter; capital for the dominant allele, lower case for the recessive allele. Say what each means.
2. Parental genotypes: write each parent's genotype from the information given.
3. Gametes: list the alleles each parent can pass on (one allele per gamete).
4. Punnett square: put one parent's gametes across the top and the other's down the side, then fill each box.
5. Ratios: count boxes to get the genotypic ratio, then group them into the phenotypic ratio, and convert to a probability or percentage if asked.

A plant with round seeds could be $RR$ or $Rr$; you cannot tell by looking. A test cross solves this by crossing the unknown with a homozygous recessive individual ($rr$). The $rr$ parent can only give $r$, so the offspring's phenotypes reveal the unknown parent's alleles. If the unknown is $RR$, every offspring is $Rr$ and round. If it is $Rr$, about half the offspring are $rr$ and wrinkled, a 1 : 1 ratio. Even one recessive offspring proves the unknown parent is heterozygous. If all offspring show the dominant trait, the parent is probably homozygous, and the larger the sample, the more confident you can be.

A Punnett square predicts probabilities, not guaranteed counts. A 3 : 1 ratio means each offspring has a $\frac{3}{4}$ chance of the dominant phenotype. It does not mean that exactly three out of every four children will have it. Each fertilization is an independent event, like a new coin toss. The product rule (and) says the probability that independent events all happen is the product of their probabilities: the chance that two children of $Aa\times Aa$ parents are both $aa$ is $\frac{1}{4}\times \frac{1}{4}=\frac{1}{16}$. The sum rule (or) says the probability of either of two mutually exclusive outcomes is their sum: the chance a child is $AA$ or $Aa$ is $\frac{1}{4}+\frac{1}{2}=\frac{3}{4}$. Finally, observed ratios only approach expected ratios in large samples. Mendel counted thousands of seeds, which is why his results came so close to 3 : 1, while a family with four children can easily have zero, two or even four children with a recessive trait.