Why Two Tall Pea Plants Can Still Produce a Dwarf One

Children often resemble their parents, yet a feature can skip a generation and reappear. The reason is that features are controlled by pairs of genes, one from each parent, and some hide the effect of others.

This part covers the language of genetics, Mendel's three laws, and how to work out monohybrid and dihybrid crosses with ratios.

A gene is a unit of heredity, alleles are its alternative forms, the alleles an organism carries form its genotype, and the feature it shows is its phenotype.

- Gene — a segment of DNA on a chromosome that controls a character, such as plant height
- Allele — one of the alternative forms of a gene, such as $T$ for tall and $t$ for dwarf
- Homozygous — both alleles the same, $TT$ or $tt$; such plants breed true
- Heterozygous — two different alleles, $Tt$; a hybrid
- Dominant — the allele that shows its effect even when only one copy is present; written with a capital letter
- Recessive — the allele that shows only when two copies are present; written with a small letter
- Genotype — the genetic make-up, such as $TT$, $Tt$ or $tt$
- Phenotype — the visible character, such as tall or dwarf

Worked example. A pea plant has genotype $Tt$. Its phenotype is tall, because $T$ is dominant; it is heterozygous.

An everyday example. Farmers who grow hybrid seed buy fresh seed every season, because seeds saved from hybrid plants do not all breed true.

The misconception. Dominant does not mean better or more common; it only means the allele shows its effect in a heterozygote.

Dominance: one allele can mask another. Segregation: the two alleles of a pair separate into different gametes. Independent assortment: alleles of different characters are sorted into gametes independently.

1. Law of dominance

- In a heterozygote, only the dominant allele is expressed; the recessive allele is present but hidden
- Example: $Tt$ is tall

2. Law of segregation

- The two alleles of a pair separate during gamete formation, so each gamete carries only one
- The alleles do not blend; a hidden recessive allele comes out unchanged in a later generation
- Also called the law of purity of gametes

3. Law of independent assortment

- When two characters are considered together, the alleles of one pair separate independently of the other pair
- So new combinations of characters can appear

An everyday example. Red and white paint mixed into pink never separate again, yet a pure dwarf pea plant can reappear from tall parents — alleles do not blend like paint.

The boundary case. Independent assortment holds for genes on different chromosomes; genes lying close together on the same chromosome tend to be inherited together.

A monohybrid cross follows one character: pure tall crossed with pure dwarf gives all tall F1 plants, and two F1 plants give an F2 ratio of 3 tall to 1 dwarf, with genotypes 1 TT : 2 Tt : 1 tt.

Step 1 — parents. Pure tall $TT$ × pure dwarf $tt$. Gametes: $T$ and $t$. **F1: all $Tt$, all tall.

Step 2 — F1 × F1.** $Tt$ × $Tt$. Each parent makes gametes $T$ and $t$ in equal numbers.

Step 3 — Punnett square, combining each gamete of one parent with each of the other:

- $T$ with $T$ gives $TT$ — tall
- $T$ with $t$ gives $Tt$ — tall
- $t$ with $T$ gives $Tt$ — tall
- $t$ with $t$ gives $tt$ — dwarf

F2 ratios:

$$\text{phenotypic ratio}=3\text{ tall}:1\text{ dwarf}\text{genotypic ratio}=1TT:2Tt:1tt$$

Worked example. Out of $800$ F2 plants:

$$\text{tall}=800\times \frac{3}{4}=600\text{dwarf}=800\times \frac{1}{4}=200Tt=800\times \frac{2}{4}=400$$

An everyday example. A farmer who sows seeds from tall hybrid pea plants should expect roughly one dwarf plant in every four.

The substance. **A test cross with $tt$ reveals a tall plant's genotype**: all tall offspring means $TT$; about half dwarf means $Tt$.

A dihybrid cross follows two characters at once: crossing round yellow with wrinkled green pea seeds gives all round yellow F1 seeds, and the F2 generation shows 9 round yellow, 3 round green, 3 wrinkled yellow and 1 wrinkled green.

Step 1 — parents. Round yellow $RRYY$ × wrinkled green $rryy$. Gametes: $RY$ and $ry$. **F1: all $RrYy$, round yellow.

Step 2 — F1 gametes.** By independent assortment, $RrYy$ makes four kinds of gametes in equal numbers: $RY$, $Ry$, $rY$, $ry$.

Step 3 — Punnett square. Four gametes from each parent give $4\times 4=16$ combinations, which group as:

$$9\text{ round yellow}:3\text{ round green}:3\text{ wrinkled yellow}:1\text{ wrinkled green}$$

Why 9:3:3:1. Each character alone still gives $3:1$, and the two act independently:

$$\left(\frac{3}{4}+\frac{1}{4}\right)\left(\frac{3}{4}+\frac{1}{4}\right)=\frac{9}{16}+\frac{3}{16}+\frac{3}{16}+\frac{1}{16}$$

Worked example. Out of $1600$ F2 seeds: round yellow $=1600\times \frac{9}{16}=900$, round green $=300$, wrinkled yellow $=300$, wrinkled green $=100$. Round seeds alone: $900+300=1200$, and $1200:400=3:1$.

An everyday example. Crop breeders cross a large-grained variety with a disease-resistant one to find later plants with both features.

The substance. Round green and wrinkled yellow are new combinations not seen in either parent — direct evidence of independent assortment.