Biologia

Mendelian genetics: Mendel's laws with solved exercises

Mendel's three laws explained simply: genotype, phenotype and the Punnett square, with 5 solved, verified exercises and 3 FAQs for review.

Recommended for: Grade 9 · Grade 10

Mendelian genetics explains how traits pass from parents to offspring through alleles. In short: every trait depends on a pair of alleles (one from each parent); if one allele is dominant (A) it masks the recessive one (a), and the Punnett square lets you predict the probabilities for the offspring.

Mendel’s three laws

  • Law of dominance: when you cross two pure lines that differ in one trait, the whole first generation (F1) shows the dominant trait.
  • Law of segregation: the two alleles of a gene separate into the gametes; in the F2 the recessive trait reappears with a phenotypic ratio of 3 : 1.
  • Law of independent assortment: different traits are inherited independently of one another, which is why a dihybrid cross gives the 9 : 3 : 3 : 1 ratio.

Genotype, phenotype and alleles

An allele is one of the possible forms of a gene. The genotype is the pair of alleles (AA, Aa or aa); the phenotype is what you actually observe. An individual is homozygous with two identical alleles (AA or aa) and heterozygous when they differ (Aa).

How to use a Punnett square

Write one parent’s gametes along the rows and the other parent’s along the columns, then fill each box by combining them. Counting the boxes gives you both the genotypic and the phenotypic ratio. For a cross involving two traits it is easier to treat each gene separately and multiply the probabilities (the product rule).

The exercises below apply the same method at increasing difficulty: from simple monohybrid crosses with a single trait up to the dihybrid cross and the product rule. Every result is verified by recounting the boxes of the Punnett square.

Solved exercises

1. Cross two heterozygous tall pea plants (Tt × Tt), where T = tall (dominant) and t = short (recessive). What fraction of the offspring will be short? base

Show solution
  1. Each Tt parent produces two kinds of gametes: T and t.
  2. Fill in the Punnett square by combining the gametes: you get TT, Tt, Tt, tt.
  3. Genotypic ratio 1 TT : 2 Tt : 1 tt; phenotypic ratio 3 tall : 1 short.
  4. Only the tt genotype gives a short plant: 1 case out of 4.

Answer: 1/4 of the offspring (25%) will be short.

2. Cross a homozygous dominant purple-flowered plant (PP) with a homozygous recessive white-flowered plant (pp). What are the genotype and phenotype of the first generation (F1)? base

Show solution
  1. PP produces only P gametes; pp produces only p gametes.
  2. Every P × p combination gives the genotype Pp.
  3. The whole F1 is heterozygous Pp.
  4. Because P is dominant, all plants have purple flowers.

Answer: 100% Pp, all with purple flowers.

3. Perform a test cross: cross a heterozygous individual Aa with a homozygous recessive aa (A dominant, a recessive). What are the genotypic and phenotypic ratios of the offspring? intermedio

Show solution
  1. The Aa parent produces A and a gametes; the aa parent produces only a gametes.
  2. Punnett square: Aa, Aa, aa, aa.
  3. Genotypic ratio 1 Aa : 1 aa (50% and 50%).
  4. Phenotype: half show the dominant trait (Aa), half the recessive trait (aa).

Answer: 1 Aa : 1 aa → 50% dominant, 50% recessive.

4. In the cross Aa × Aa, what is the probability that an offspring is heterozygous (Aa)? intermedio

Show solution
  1. Each parent produces A and a gametes, each with probability 1/2.
  2. The Punnett square gives AA, Aa, Aa, aa: a 1 : 2 : 1 ratio.
  3. The heterozygotes Aa occupy 2 of the 4 boxes.
  4. Probability = 2/4 = 1/2.

Answer: 1/2 (50%).

5. Dihybrid cross RrGg × RrGg (R = round seed, dominant; r = wrinkled; G = yellow, dominant; g = green). The two genes assort independently. Find: (a) P(round and yellow); (b) the full phenotypic ratio; (c) P(wrinkled and green). avanzato

Show solution
  1. Analyse each gene separately. For Rr × Rr: P(round, R_) = 3/4 and P(wrinkled, rr) = 1/4. Likewise P(yellow) = 3/4 and P(green) = 1/4.
  2. (a) Product rule: P(round and yellow) = 3/4 × 3/4 = 9/16.
  3. (b) Combining the two independent traits gives the classic ratio 9 round-yellow : 3 round-green : 3 wrinkled-yellow : 1 wrinkled-green.
  4. (c) P(wrinkled and green) = 1/4 × 1/4 = 1/16.

Answer: (a) 9/16; (b) 9 : 3 : 3 : 1; (c) 1/16.

FAQ

What is the difference between genotype and phenotype?

The genotype is the combination of alleles an individual carries for a trait (for example Aa), while the phenotype is the observable characteristic that results from it (for example a purple flower). Different genotypes such as AA and Aa can give the same phenotype, because A is dominant and masks a.

What does the law of segregation (Mendel's second law) state?

It states that the two alleles of a gene separate during the formation of gametes, so each gamete receives only one allele. At fertilisation the alleles recombine at random: that is why the cross Aa × Aa gives the genotypic ratio 1 : 2 : 1.

How can two parents with the same trait have a child that looks different?

If both parents are heterozygous (for example Bb, brown eyes), each can pass on the recessive allele b. So there is a 1 in 4 chance the child is bb and shows the recessive trait, for example blue eyes.