Mendel’s Laws and Monohybrid Crosses

Mendel’s laws describe how traits are inherited: the law of segregation says the two alleles for a gene separate when gametes form, and a monohybrid cross follows one gene, using a Punnett square to predict the offspring. In brief: crossing two heterozygous (Tt × Tt) individuals gives a genotype ratio of 1 TT : 2 Tt : 1 tt and a phenotype ratio of 3 dominant : 1 recessive. A test cross with a homozygous recessive individual reveals whether an organism showing the dominant trait is homozygous or heterozygous.

Mendel’s results, obtained with pea plants in the nineteenth century, still form the basis of genetics. This guide explains Mendel’s experiments, states his laws, shows how to carry out a monohybrid cross with a Punnett square step by step, covers ratios and test crosses, works through two examples and corrects frequent mistakes.

What did Mendel’s experiments show?

Gregor Mendel (1822 to 1884) grew garden peas (Pisum sativum) in the monastery garden in Brno. Peas were a good choice: they grow quickly, produce many seeds, show clear contrasting traits, and he could control which plants were crossed. He studied seven traits, including seed shape (round or wrinkled), seed color (yellow or green), flower color (purple or white) and plant height (tall or dwarf).

He started with true-breeding (pure-line) plants, which always produce offspring like themselves. When he crossed a tall plant with a dwarf plant (the parental, or P, generation), all the offspring (the first filial, or F1, generation) were tall. When he allowed the F1 plants to self-pollinate, the dwarf trait reappeared in about one quarter of the next generation (F2), which had a ratio of about 3 tall to 1 dwarf. In one data set, 787 of the F2 plants were tall and 277 were dwarf, a ratio of 2.84 to 1.

Mendel concluded that traits are controlled by discrete “factors” (now called genes), that each plant has two factors for each trait, and that one can hide the other.

What are Mendel’s laws?

• Law of dominance: when two different alleles are present, the dominant one is expressed in the phenotype. (This is sometimes treated as a principle and not a separate law.)
• Law of segregation: each organism has two alleles for each gene. During the formation of gametes, the two alleles separate, so that each gamete receives only one. Fertilization restores the pair.
• Law of independent assortment: alleles of different genes are distributed independently into gametes (this applies to genes on different chromosomes, and is explained in the next article).

Segregation corresponds to the separation of homologous chromosomes during meiosis, which was discovered after Mendel’s work.

How do you do a monohybrid cross with a Punnett square?

A monohybrid cross involves one gene with two alleles. The Punnett square, devised by Reginald Punnett, is a grid that shows all possible combinations of gametes. Follow these steps.

1. Define the alleles: choose a capital letter for the dominant allele and a lowercase letter for the recessive allele. For example, T for tall and t for dwarf.
2. Write the parental genotypes: for example, Tt × Tt.
3. Find the gametes: each parent gives either T or t, so write each gamete once along the top and the side of the grid.
4. Fill in the grid: combine the allele from the row and the column in each box.
5. Count: list the genotypes and phenotypes and give the ratios.

Cross Tt × Tt

What are genotypic and phenotypic ratios?

From the square above, there are four equally likely outcomes.

• Genotypic ratio: 1 TT : 2 Tt : 1 tt (25 percent, 50 percent and 25 percent).
• Phenotypic ratio: 3 tall : 1 dwarf (75 percent tall, 25 percent dwarf), since both TT and Tt are tall.

These are probabilities, not guarantees. If a couple has four children, they will not necessarily have exactly three with the dominant trait and one with the recessive trait. Each child has the same probability, 25 percent, of being tt. The ratios appear reliably only when the number of offspring is large.

What is a test cross?

A plant with the dominant phenotype could be TT or Tt. A test cross reveals which, by crossing it with a homozygous recessive (tt) individual.

• If the unknown is TT: TT × tt gives all Tt, so all offspring show the dominant phenotype.
• If the unknown is Tt: Tt × tt gives 1 Tt : 1 tt, so about half of the offspring show the recessive phenotype.

Even one recessive offspring proves that the unknown parent is heterozygous. If many offspring all show the dominant phenotype, the parent is probably homozygous. Breeders use test crosses to find out if an animal carries a hidden recessive allele.

Common monohybrid crosses

Worked example: pea plants and a human disorder

Example 1: round and wrinkled peas

Round seeds (R) are dominant over wrinkled seeds (r). A heterozygous round plant is crossed with a wrinkled plant. What are the offspring?

1. Parents: Rr × rr.
2. Gametes: Rr gives R or r; rr gives only r.
3. Offspring: Rr, Rr (round), rr, rr (wrinkled) in a Punnett square. Genotypic ratio 1 Rr : 1 rr. Phenotypic ratio 1 round : 1 wrinkled.
4. If 200 seeds are produced, about 100 are expected to be round and 100 wrinkled.

Example 2: cystic fibrosis

Cystic fibrosis is caused by a recessive allele (f). Two healthy parents have a child with cystic fibrosis. What are the parents’ genotypes, and what is the chance that their next child will be affected?

1. The affected child is ff, so it received an f from each parent.
2. The parents are healthy, so each has at least one dominant allele (F). Each parent is therefore Ff, a carrier.
3. Cross: Ff × Ff gives 1 FF : 2 Ff : 1 ff.
4. The probability that the next child is affected is 1/4, or 25 percent. The probability that the child is a carrier is 2/4, or 50 percent, and that the child is homozygous normal is 25 percent. Each child is an independent event, so having one affected child does not change the chance for the next.

For unaffected siblings, the probability of being a carrier is 2/3, because the ff outcome has already been excluded and only FF (1) and Ff (2) remain. This is a common source of mistakes in genetic counseling problems.

Who was Gregor Mendel?

Mendel presented his results to the Natural History Society of Brno in 1865 and published them in 1866. The work was little noticed at the time. In 1900 Hugo de Vries, Carl Correns and Erich von Tschermak independently reached similar conclusions and found Mendel’s paper. Some historians have argued that Mendel’s published ratios are closer to the expected values than random chance would predict. This has been discussed by statisticians since Ronald Fisher in 1936, with no agreement on the cause, and it does not change the validity of his laws.

Which mistakes are common?

Mistake 1: Expecting exactly 3:1 in a small family

Ratios are probabilities. Small samples vary widely.

Mistake 2: Saying a 25 percent chance means that one in four children will be affected

Each child has a 25 percent chance independently. A family could have none, or all four, affected.

Mistake 3: Putting both alleles of one parent in the same gamete

Each gamete receives only one allele of each gene, according to the law of segregation.

Mistake 4: Confusing genotypic and phenotypic ratios

For Tt × Tt, the genotypic ratio is 1:2:1, and the phenotypic ratio is 3:1.