Calculate inheritance patterns, Punnett squares, and allele frequencies. Analyze monohybrid and dihybrid crosses with genotype/phenotype ratios and Hardy-Weinberg equilibrium.
Problem: In pea plants, purple flowers (P) are dominant over white flowers (p). If two heterozygous (Pp) plants are crossed, what are the expected genotype and phenotype ratios of the offspring?
Solution: Using a Punnett square for a Pp × Pp monohybrid cross:
Parent 1 gametes: P, p | Parent 2 gametes: P, p
Punnett square: PP, Pp, Pp, pp
Genotype ratio: 1 PP : 2 Pp : 1 pp
Phenotype ratio: 3 Purple : 1 White
This 3:1 phenotypic ratio is characteristic of a monohybrid cross between two heterozygotes, as first described by Gregor Mendel.
Problem: In pea plants, round seeds (R) are dominant over wrinkled (r), and yellow seeds (Y) are dominant over green (y). If two plants heterozygous for both traits (RrYy) are crossed, what is the expected phenotypic ratio?
Solution: Using a 4×4 Punnett square for a RrYy × RrYy dihybrid cross:
Each parent produces 4 gamete types: RY, Ry, rY, ry
Phenotype ratio: 9 Round-Yellow : 3 Round-Green : 3 Wrinkled-Yellow : 1 Wrinkled-Green
The classic 9:3:3:1 ratio emerges when both parents are heterozygous for both traits, demonstrating Mendel's Law of Independent Assortment.
Problem: In a population of 10,000 people, 1 in 2,500 has cystic fibrosis (an autosomal recessive disorder). What are the allele frequencies and carrier frequency?
Solution: q² = 1/2500 = 0.0004
q = √0.0004 = 0.02 (2% recessive allele frequency)
p = 1 − q = 0.98 (98% dominant allele frequency)
Carrier frequency (2pq) = 2 × 0.98 × 0.02 = 0.0392 ≈ 3.9%
This means about 392 out of 10,000 people are carriers (heterozygous) for cystic fibrosis, even though only 4 have the disease.
Problem: In snapdragons, red flowers (R) and white flowers (r) show incomplete dominance, producing pink flowers in heterozygotes (Rr). If a red (RR) and a white (rr) snapdragon are crossed, what are the offspring?
Solution: Using a Punnett square for RR × rr:
All offspring are Rr (Pink)
Genotype ratio: 0 RR : 4 Rr : 0 rr
Phenotype ratio: 0 Red : 4 Pink : 0 White
In incomplete dominance, the heterozygous phenotype is intermediate between the two homozygous phenotypes, creating a 1:2:1 phenotypic ratio in F2 generations.
A monohybrid cross examines the inheritance of a single gene with two alleles. Each parent contributes one allele per gamete. The Punnett square has 4 cells (2×2). Under complete dominance, the phenotypic ratio is typically 3:1 (dominant:recessive).
A dihybrid cross examines the inheritance of two genes simultaneously. Each parent produces 4 gamete combinations (e.g., AB, Ab, aB, ab). The Punnett square has 16 cells (4×4). The classic 9:3:3:1 ratio demonstrates Mendel's Law of Independent Assortment.
Where p is the frequency of the dominant allele (A), q is the frequency of the recessive allele (a), p² is the frequency of homozygous dominant (AA), 2pq is the frequency of heterozygous (Aa), and q² is the frequency of homozygous recessive (aa).
A dominant allele (uppercase) masks the effect of the recessive allele (lowercase) when both are present. For a recessive trait to be expressed, the individual must inherit two recessive alleles (homozygous recessive).
Genotype is the genetic makeup (e.g., AA, Aa, aa). Phenotype is the observable trait (e.g., purple or white flowers). Individuals with AA and Aa genotypes have the same phenotype if A is dominant over a.
Homozygous means having two identical alleles (AA or aa). Heterozygous means having two different alleles (Aa). Heterozygotes are also called carriers if the recessive allele causes a genetic disorder.
Genes for different traits are inherited independently of each other during gamete formation, provided they are on different chromosomes or far apart on the same chromosome. This creates the 9:3:3:1 dihybrid ratio.
⚠️ Important Note: Punnett squares show probabilities of offspring genotypes and phenotypes, not guaranteed outcomes. Actual results may vary, especially in small sample sizes. Hardy-Weinberg equilibrium assumes ideal conditions (random mating, no mutation, no selection, large population size, no gene flow). Real populations rarely satisfy all conditions perfectly.