Lecture 2

Mendelian Genetics: Principles of Heredity and Transmission

Areas of Genetics

Genetics is the study of heredity and variation in organisms. Transmission genetics, also known as classical or Mendelian genetics, focuses on how traits are passed from one generation to the next, the behavior of chromosomes, and the arrangement of genes on chromosomes.

• Alleles: Different versions of a gene.

• Genotype: The exact allelic composition of an organism.

• Phenotype: The observable traits or behaviors of an organism.

Historical Notions of Heredity

Before Mendel, two main theories dominated:

• Inheritance of acquired characteristics: Traits acquired by parents could be passed to offspring (e.g., long neck in giraffes).

• Blending inheritance: Offspring are a mixture of parental traits, like mixing paint colors.

Mendel's experiments disproved blending inheritance and established the particulate nature of heredity.

Gregor Mendel and His Experimental Approach

Gregor Mendel, an Austrian monk, conducted experiments with garden peas to uncover the basic principles of heredity. His choice of pea plants was strategic:

• Annual lifecycle (12-18 weeks).

• Natural self-fertilization, allowing for pure-breeding strains.

• Ability to manually cross-fertilize by removing anthers and transferring pollen.

Mendel's Experimental Design

Mendel studied seven traits, each with two distinct phenotypes, and performed controlled crosses:

• Used true-breeding strains for each trait.

• Counted all offspring and performed reciprocal crosses.

• Focused on monogenic traits (controlled by a single gene).

Continuous vs. Discontinuous Traits

Mendel chose discontinuous traits (two distinct phenotypes), unlike traits such as human height, which are continuously variable and require statistical analysis.

Mendel's Monohybrid Crosses

In monohybrid crosses, Mendel observed:

• F1 generation: All offspring showed the dominant phenotype.

• F2 generation: Both dominant and recessive phenotypes appeared in a 3:1 ratio.

Mendel's F3 Generation and Ratios

Self-fertilizing F2 plants revealed a 1:2:1 ratio of genotypes:

• 1/4 true-breeding dominant

• 1/2 heterozygous

• 1/4 true-breeding recessive

Mendel's Model of Heredity

Mendel proposed that traits are controlled by factors (genes) with two alleles. Each organism receives one allele from each parent. Alleles can be:

• Homozygous: Both alleles identical (AA or aa).

• Heterozygous: Two different alleles (Aa).

In heterozygotes, one allele is dominant and the other is recessive.

Mendel's First Law: The Law of Segregation

Each organism has two copies of each gene, which segregate randomly into gametes. Gametes are haploid, and fertilization restores diploidy. No blending occurs; alleles remain distinct across generations.

• F1 progeny from true-breeding parents are heterozygous and show the dominant phenotype.

• F2 progeny exhibit a 1:2:1 genotype ratio and a 3:1 phenotype ratio.

Punnett Square: Predicting Genotypes and Phenotypes

The Punnett square is a tool to predict the genotypes and phenotypes of progeny from a genetic cross. It organizes possible gametes from each parent and shows the expected outcomes.

• Cross of Aa x Aa yields genotypes: AA, Aa, aa.

• Phenotype prediction depends on dominance relationships.

The Testcross

A testcross determines whether an organism with a dominant phenotype is homozygous or heterozygous. It involves crossing the organism with a homozygous recessive individual.

• If all progeny show the dominant phenotype, the tested organism is homozygous.

• If progeny show a 1:1 ratio of dominant to recessive, the tested organism is heterozygous.

Mendel's Second Law: The Law of Independent Assortment

During gamete formation, alleles for different genes segregate independently. This explains the inheritance of multiple traits and the 9:3:3:1 ratio observed in dihybrid crosses.

• Dihybrid cross: SS YY x ss yy yields F1 (Ss Yy), which produces four types of gametes.

• F2 generation shows four phenotypic classes in a 9:3:3:1 ratio.

Trihybrid Crosses and Probability

Mendel extended his experiments to three traits, using trihybrid crosses. The expected results can be calculated using probability laws rather than large Punnett squares.

• Each gene segregates independently.

• Expected frequencies are calculated by multiplying probabilities for each trait.

Chi-Square Test in Genetics

The chi-square test is used to compare observed and expected results in genetic crosses. It helps determine whether deviations from expected ratios are due to random chance or indicate a problem with the genetic model.

• If the difference is unlikely to occur by chance, the model may need revision.

Summary Table: Mendel's Observations for Seven Monohybrid Traits

This table summarizes Mendel's results for seven traits, showing the F1 and F2 phenotypes and the observed ratios.

Trait	F1 Phenotype	F2 Dominant	F2 Recessive	F2 Ratio
Round x wrinkled seed	All round	5474	1850	2.96:1
Yellow x green seed	All yellow	6022	2001	3.01:1
Gray x white seed coat	All gray	705	224	3.15:1
Purple x white flower	All purple	858	282	3.04:1
Axial x terminal flower	All axial	651	207	3.14:1
Inflated x constricted pod	All inflated	882	299	2.95:1
Tall x short plant	All tall	787	277	2.84:1

Key Equations

• Genotype ratio in F2: $1\ RR : 2\ Rr : 1\ rr$

• Phenotype ratio in F2: $3\ \text{dominant} : 1\ \text{recessive}$

• Dihybrid cross ratio: $9:3:3:1$

• Chi-square test: $\chi^2 = \sum \frac{(O - E)^2}{E}$

Conclusion

Mendel's principles of heredity—segregation and independent assortment—form the foundation of classical genetics. His careful experimental design, use of quantitative analysis, and application of probability and statistics revolutionized our understanding of how traits are inherited.