Mendelian Genetics: Principles of Heredity and Transmission

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 generation to generation and the behavior of chromosomes and genes.

• Alleles: Different versions of a gene.

• Genotype: The exact allelic composition of an organism.

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

Historical Concepts 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, with genetic material blending irreversibly.

Gregor Mendel and His Experiments

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 plant with a short life cycle.

• Self-fertilizing, allowing for pure-breeding strains.

• Flowers can be manipulated for cross-fertilization.

Mendel’s Experimental Approach

Mendel studied only discontinuous traits (traits with two distinct phenotypes), counted all results, performed reciprocal crosses, and focused on monogenic traits without genetic linkage.

• Traits studied: seed color, seed shape, pod color, pod shape, flower color, flower position, plant height.

Monohybrid Crosses and F1 Generation

Mendel cross-fertilized two true-breeding parent strains for each trait. The F1 generation always showed the dominant phenotype, disproving blending inheritance.

• Dominant Trait: The phenotype that appears in the F1.

• Recessive Trait: The phenotype that disappears in the F1 but reappears in the F2.

F2 Generation and Phenotypic Ratios

Allowing F1 plants to self-fertilize, Mendel observed a 3:1 ratio of dominant to recessive phenotypes in the F2 generation for all traits.

• Recessive phenotype returns in F2.

• Factors (genes) do not blend or change between generations.

F3 Generation and Genotypic Ratios

Self-fertilizing F2 plants, Mendel found a 1:2:1 ratio of genotypes in the F3 generation, confirming that not all dominant phenotype plants are genetically identical.

• 1/4 true-breeding dominant

• 1/2 heterozygous dominant

• 1/4 true-breeding recessive

Mendel’s Model of Heredity

Mendel proposed that each organism has two alleles for each gene, one from each parent. Alleles can be identical (homozygous) or different (heterozygous). In heterozygotes, one allele is dominant.

• Diploid parents produce haploid gametes.

• Gametes combine randomly to restore diploidy.

• No blending of alleles occurs.

Mendel’s First Law: The Law of Segregation

Each organism has two copies of each gene, which segregate randomly into gametes. This explains the 3:1 phenotypic ratio and 1:2:1 genotypic ratio in monohybrid crosses.

• F1 progeny are heterozygous and show the dominant phenotype.

• F2 progeny display both phenotypes in predictable ratios.

Punnett Squares

Punnett squares are used to predict the genotypes and phenotypes of progeny from genetic crosses. They visually represent the possible combinations of parental gametes.

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

• Phenotypic ratio depends on dominance relationships.

The Testcross

A testcross determines whether an organism with a dominant phenotype is homozygous or heterozygous by crossing it with a homozygous recessive individual.

• SS x ss: All progeny show dominant phenotype.

• Ss x ss: Progeny show a 1:1 ratio of dominant to recessive phenotypes.

Mendel’s Second Law: The Law of Independent Assortment

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

• Each trait behaves independently in crosses.

• F1 dihybrid plants produce 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 probability and branching diagrams to predict outcomes. The expected results can be calculated by multiplying probabilities for each independent trait.

• Punnett square for trihybrid cross has 64 boxes.

• Branching diagram method simplifies calculations.

Statistical Analysis: Chi-Square Test

The chi-square test is used to compare observed and expected results in genetic crosses. It helps determine whether deviations 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 each trait, 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 round	1850 wrinkled	2.96:1
Yellow x green seed	All yellow	6022 yellow	2001 green	3.01:1
Gray x white seed coat	All gray	705 purple	224 white	3.15:1
Green x yellow pod	All green	453 green	152 yellow	2.98:1
Inflated x constricted pod	All inflated	882 inflated	299 constricted	2.95:1
Axial x terminal flower	All axial	858 axial	282 terminal	3.04:1
Tall x short plant	All tall	787 tall	277 short	2.84:1

Example: Monohybrid Cross

Crossing round (RR) and wrinkled (rr) pea seeds:

• F1: All round (Rr)

• F2: 3 round : 1 wrinkled

Example: Dihybrid Cross

Crossing smooth yellow (SS YY) and wrinkled green (ss yy) peas:

• F1: All smooth yellow (Ss Yy)

• F2: 9 smooth yellow, 3 smooth green, 3 wrinkled yellow, 1 wrinkled green

Continuous vs. Discontinuous Traits

Some traits, like human height, are continuously variable and influenced by multiple genes and the environment. These require statistical and population genetics approaches.

Key Equations

• Genotypic ratio for monohybrid cross: $1:2:1$

• Phenotypic ratio for monohybrid cross: $3:1$

• Phenotypic ratio for dihybrid cross: $9:3:3:1$

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

Conclusion

Mendel’s laws of segregation and independent assortment form the foundation of classical genetics, explaining how traits are inherited and how genetic variation arises in populations. These principles are essential for understanding heredity, predicting outcomes of genetic crosses, and analyzing genetic data.