Mendelian Genetics: Monohybrid and Dihybrid Crosses

Monohybrid Crosses

A monohybrid cross is a genetic cross between two individuals involving one gene locus, where each parent is heterozygous or carries different alleles for a single gene.

• Alleles can be dominant (A) or recessive (a).

• Wild Type refers to the most common phenotype in a population (often denoted as WT), while mutant refers to a variant (often denoted as a).

• Genotypes are the genetic makeup (e.g., AA, Aa, aa), and phenotypes are the observable traits.

Punnett squares are used to predict the genotypic and phenotypic ratios of offspring from a cross.

• Example: Crossing two heterozygous purple plants (Pp x Pp) yields a 3:1 ratio of purple to white flowers.

Dihybrid Crosses

A dihybrid cross involves two genes, each with two alleles, and examines the inheritance of two traits simultaneously.

• Typically written as YyRr x YyRr (e.g., yellow/green and round/wrinkled seeds).

• Assumes independent assortment (Mendel's Second Law): alleles of different genes assort independently during gamete formation.

Two methods to solve dihybrid crosses:

1. Punnett Square: A 4x4 grid for two heterozygous parents.

2. Branch Diagram: Uses probability to calculate genotype/phenotype ratios.

Example Table: Dihybrid Cross Phenotypes

Expected phenotypic ratio for a dihybrid cross: 9:3:3:1 (Yellow Round : Yellow Wrinkled : Green Round : Green Wrinkled)

Genetic Probability and Laws

Product Law and Sum Law

• Product Law: The probability of two independent events both occurring is the product of their individual probabilities.

  • Example: Probability of heads on two coins:

• Sum Law: The probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.

  • Example: Probability of heads on one coin and tails on the other:

Binomial Theorem in Genetics

The binomial theorem is used to calculate the probability of a specific combination of outcomes in a series of independent events (e.g., the probability of having a certain number of male and female offspring).

• General formula:

• Where = total number of events, = number of times event 1 occurs, = number of times event 2 occurs, = probability of event 1, = probability of event 2.

• Example: Probability of 2 males and 2 females in 4 children:

Punnett Squares and Gamete Formation

Punnett Squares

• Visual tool to predict the outcome of genetic crosses.

• Each box represents a possible genotype of offspring.

• For a monohybrid cross (Aa x Aa):

  • Genotypic ratio: 1 AA : 2 Aa : 1 aa

  • Phenotypic ratio (if A is dominant): 3 dominant : 1 recessive

Gamete Formation

• Each parent produces gametes with one allele for each gene.

• For genotype AaBb, possible gametes: AB, Ab, aB, ab

• For genotype AaBbCc, possible gametes: ABC, ABc, AbC, Abc, aBC, aBc, abC, abc

Pedigree Analysis

Pedigree Symbols and Interpretation

• Pedigree: A diagram showing the occurrence of heritable traits across generations.

• Symbols:

  • Square: Male

  • Circle: Female

  • Filled symbol: Affected individual

  • Half-filled: Heterozygote (carrier for recessive trait)

  • Diagonal line: Deceased

  • Arrow: Propositus (first affected family member)

Modes of Inheritance

• Autosomal Recessive: Affected individuals have unaffected parents; both sexes affected equally; few affected offspring.

• Autosomal Dominant: Phenotype appears in every generation; affected parents pass trait to children; both sexes affected equally.

• Autosomal Polymorphism: Two or more common phenotypes exist in the population (e.g., widow's peak, earlobe attachment).

• X-linked Recessive: More males affected; affected males do not pass trait to sons, but all daughters are carriers.

• X-linked Dominant: Affected males pass trait to all daughters, not sons; affected females pass to half of offspring.

• Y-linked: Only males affected; very rare.

Pedigree Analysis Table

Practice Problems and Applications

• Use Punnett squares and probability laws to solve genetic cross problems.

• Apply the binomial theorem for multiple offspring scenarios.

• Analyze pedigrees to determine inheritance patterns.

Example Problem: Monohybrid Cross

• Cross two heterozygous (Aa x Aa):

  • Genotypes: 1 AA : 2 Aa : 1 aa

  • Phenotypes (if A is dominant): 3 dominant : 1 recessive

Example Problem: Dihybrid Cross

• Cross YyRr x YyRr:

  • Phenotypic ratio: 9:3:3:1 (Yellow Round : Yellow Wrinkled : Green Round : Green Wrinkled)

Example Problem: Probability with Binomial Theorem

• Probability of 3 males and 1 female in 4 children:

Key Terms

• Genotype: The genetic constitution of an organism.

• Phenotype: The observable characteristics of an organism.

• Allele: Different forms of a gene.

• Homozygous: Having two identical alleles for a gene.

• Heterozygous: Having two different alleles for a gene.

• Dominant: An allele that masks the effect of a recessive allele.

• Recessive: An allele whose effect is masked by a dominant allele.

• Wild Type: The most common allele or phenotype in a population.

• Mutant: An allele or phenotype that differs from the wild type.

• Independent Assortment: Mendel's Second Law; genes for different traits can segregate independently during gamete formation.

• Pedigree: A diagram showing family relationships and the transmission of inherited traits.

Additional info: This guide expands on the provided notes by including definitions, formulas, and structured tables for clarity and completeness, as expected in a college-level genetics course.