Mendelian Genetics

Introduction to Mendelian Genetics

Gregor Mendel's pioneering work in the mid-19th century established the foundational principles of genetics. By studying the inheritance of traits in the garden pea (Pisum sativum), Mendel formulated laws that describe how traits are transmitted from one generation to the next. His experimental approach and analysis of discrete traits led to the discovery of predictable inheritance patterns.

The Garden Pea as a Model Organism

• Multiple Traits: Peas exhibit many easily distinguishable traits (e.g., flower color, seed shape).

• Ease of Cultivation: Peas are inexpensive, easy to grow, and have a short generation time.

• Large Offspring Numbers: Each mating produces many seeds, allowing for statistical analysis.

• Controlled Mating: Peas can self-fertilize or be crossbred artificially.

• True-Breeding Varieties: Many varieties breed true for specific traits, simplifying genetic analysis.

Mendel's Experimental Approach

Mendel controlled pollination by removing stamens from one flower and transferring pollen from another, ensuring precise crosses between plants with known traits.

Monohybrid Crosses

A monohybrid cross involves parents differing in a single trait. Mendel's classic experiment crossed true-breeding purple-flowered plants with white-flowered plants:

• P Generation: True-breeding parents (e.g., purple × white flowers)

• F1 Generation: All offspring had purple flowers (dominant trait)

• F2 Generation: Self-fertilization of F1 plants produced a 3:1 ratio of purple to white flowers

This pattern revealed that traits are inherited as discrete units, not blended.

Mendel's Postulates (Laws of Inheritance)

• 1. Unit Factors Exist in Pairs: Each individual carries two alleles for each trait, one from each parent.

• 2. Dominance and Recessiveness: In heterozygotes, one allele (dominant) masks the other (recessive).

• 3. Segregation: The two alleles for a trait separate during gamete formation, so each gamete receives only one allele.

• 4. Independent Assortment: Alleles for different traits assort independently during gamete formation (applies to genes on different chromosomes).

Genotype and Phenotype

• Genotype: The genetic constitution of an organism (e.g., WW, Ww, or ww).

• Phenotype: The observable trait (e.g., purple or white flowers).

• Homozygous: Two identical alleles (WW or ww).

• Heterozygous: Two different alleles (Ww).

Punnett Squares and Ratios

Punnett squares are used to visualize the possible genotypes and phenotypes resulting from a cross. For a monohybrid cross (Ww × Ww):

• Genotypic Ratio: 1 WW : 2 Ww : 1 ww

• Phenotypic Ratio: 3 purple : 1 white

Examples of Mendel's Traits and Ratios

Mendel studied seven contrasting traits in peas. The F2 ratios for each trait consistently approximated 3:1 for dominant:recessive phenotypes.

Dihybrid and Trihybrid Crosses

A dihybrid cross examines the inheritance of two traits simultaneously. Mendel's results showed a 9:3:3:1 phenotypic ratio in the F2 generation, supporting the law of independent assortment. Trihybrid crosses (three traits) further confirmed Mendel's principles, with the forked-line method simplifying probability calculations.

Product and Sum Laws of Probability

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

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

These laws are essential for predicting genetic outcomes in complex crosses.

Testcrosses

A testcross determines whether an individual with a dominant phenotype is homozygous or heterozygous by crossing it with a homozygous recessive individual. The resulting offspring phenotypes reveal the unknown genotype.

Chi-Square Analysis

The chi-square (χ2) test evaluates whether observed genetic ratios deviate significantly from expected ratios due to chance. The formula is:

• o: observed value

• e: expected value

Degrees of freedom (df) = number of categories - 1. The resulting χ2 value is compared to a probability table to determine if deviations are significant.

Pedigree Analysis

Pedigrees are family trees that track the inheritance of specific traits across generations. They are valuable tools for studying human genetics and identifying inheritance patterns of dominant and recessive traits.

Chromosomal Theory of Inheritance

The chromosomal theory, proposed by Sutton and Boveri, linked Mendel's laws to the behavior of chromosomes during meiosis. Genes are located on chromosomes, and their segregation and independent assortment during gamete formation explain Mendelian inheritance patterns.

Genetic Variation and Evolution

Independent assortment and fertilization produce extensive genetic variation, which is essential for evolution. In humans, with 23 chromosome pairs, the number of possible gamete combinations is (~8 million), and fertilization further increases genetic diversity.

Summary Table: Representative Human Traits

Key Equations

• Number of possible gametes: (where n = haploid chromosome number)

• Chi-square test:

Conclusion

Mendel's principles of inheritance, supported by experimental evidence and later by the chromosomal theory, form the basis of classical genetics. Understanding these laws is essential for predicting genetic outcomes, analyzing inheritance patterns, and appreciating the genetic diversity that drives evolution.