Mendel and the Gene Idea: Principles of Inheritance

Chapter 14: Mendel and the Gene Idea

Learning Objectives

• Explain Mendel's two laws of inheritance: the Law of Segregation and the Law of Independent Assortment.

• Describe the laws of probability and explain how they can be used to solve complex genetics problems.

Mendel's Experimental, Quantitative Approach

Principles of Heredity

Gregor Mendel deduced the basic principles of heredity by breeding garden peas in carefully planned experiments. His scientific approach involved quantitative analysis and careful record-keeping.

• A character is a heritable feature that varies among individuals (e.g., flower color).

• A trait is each variant for a character (e.g., purple or white flowers).

Advantages of Pea Plants for Genetic Study

• Variety and Heritable Traits: Pea plants were available in many varieties with distinct heritable features or characters, each with different variant traits.

• Short Generation Time and Large Offspring Numbers: Pea plants have a short generation time, and each mating produces many offspring—ideal for studying inheritance.

• Controlled Mating: Mating could be easily controlled. Plants could self-pollinate or be cross-pollinated by hand.

• Male and Female Organs in Pea Plants: Each pea plant contains both male (stamens) and female (carpel) reproductive organs.

• Natural vs. Cross-Pollination: In nature, pea plants typically self-fertilize using their own pollen. However, Mendel could cross-pollinate by transferring pollen from one plant to another.

• Selection of Simple Traits: Mendel chose to track only characters that occurred in two distinct, alternative forms (e.g., purple vs. white flowers).

• Use of True-Breeding Varieties: Mendel started his experiments with varieties that were true-breeding. When true-breeding plants self-pollinate, all their offspring have the same traits as their parents.

Mendel's Use of Hybridization

Generational Terminology

• Hybridization: Mating two contrasting, true-breeding varieties.

• P Generation (Parental): The true-breeding parent plants used in the initial cross.

• F1 Generation (First Filial): The hybrid offspring resulting from the P generation cross.

• F2 Generation (Second Filial): Produced when F1 individuals self-pollinate or cross-pollinate with other F1 plants.

Mendel's Key Discoveries from the F2 Generation

• Mendel's quantitative analysis of traits in the F2 generation led to the formulation of two key principles of heredity:

  • The Law of Segregation

  • The Law of Independent Assortment

The Law of Segregation

The Blending Hypothesis of Heredity

• In the 1800s, heredity was explained by the blending hypothesis, which suggested that parental traits mix together in offspring, producing intermediate traits.

• Mendel's experiments contradicted this hypothesis.

Mendel's Challenge to the Blending Hypothesis

• If blending were correct, crossing purple- and white-flowered pea plants should produce pale purple flowers in the F1 generation.

• However, all F1 hybrids had purple flowers, just as vibrant as the purple parent.

The Reappearance of Traits in F2 Generation

• When F1 plants self-fertilized, the F2 generation showed both purple and white flowers.

• The white trait, missing in the F1, reappeared in the F2 generation.

• Mendel's careful experimental method involved large sample sizes and detailed records, resulting in a 3:1 ratio of purple to white flowers in the F2 generation.

Dominant and Recessive Traits

• Only the purple flower factor affected flower color in F1 hybrids.

• The white flower factor was present but masked—it did not affect the trait's appearance.

• Purple flower color is a dominant trait; white flower color is a recessive trait.

• The white trait was not lost or diluted; it reappeared in the F2 generation, disproving the blending idea.

Consistency Across Other Traits

• Mendel observed the same inheritance pattern in six other traits, each with two distinct forms.

• Similar 3:1 ratios were found in all F2 generations.

The Heritable Factor = Gene

• What Mendel called a heritable factor is what we now know as a gene.

Table: Results of Mendel's F2 Crosses for Seven Characters in Pea Plants

Character	Dominant Trait	Recessive Trait	F2 Generation Dominant:Recessive Ratio
Flower color	Purple	White	3.15:1
Seed color	Yellow	Green	3.01:1
Seed shape	Round	Wrinkled	2.96:1
Pod color	Green	Yellow	2.82:1
Pod shape	Inflated	Constricted	3.01:1
Flower position	Axial	Terminal	3.14:1
Stem length	Tall	Dwarf	2.84:1

Mendel's Model of Inheritance

Four Related Concepts

1. Alternative versions of genes account for variations in inherited characters. - The gene for flower color in pea plants exists in two versions, one for purple flowers and one for white flowers. - These alternative versions of the same gene are called alleles. - Each gene resides at a specific locus on a specific chromosome. - The DNA at that locus can vary in its sequence of nucleotides. - The purple-flower and white-flower alleles are two different DNA sequence variations at the flower-color locus.

2. For each character, an organism inherits two copies of a gene, one from each parent. - A diploid organism inherits one set of chromosomes from each parent. - Contains two copies of each gene (alleles). - The loci of these genes are identical on both chromosomes. - The two alleles may be identical or different. - In F1 hybrids, the alleles often differ.

3. If the two alleles at a locus differ, then one, the dominant allele, determines the organism's appearance. The other, the recessive allele, has no noticeable effect on the organism's appearance. - In the flower-color example, F1 plants inherited a purple-flower allele from one parent and a white-flower allele from the other. - The F1 plants had purple flowers because the purple-flower allele is dominant over the white-flower allele.

4. Mendel's law of segregation states that the two alleles for a heritable character segregate (separate) during gamete production and end up in different gametes. - An egg or a sperm gets only one of the two alleles that are present in the organism. - Segregation of alleles corresponds to the distribution of homologous chromosomes to different gametes in meiosis. - If two identical alleles are present for a particular character, then that allele is present as a single copy in all gametes. - If two different alleles are present, then 50% of the gametes will receive one allele and 50% will receive the other allele.

Gamete Types and Random Fertilization

• F1 hybrids produce two types of gametes: half carry the purple-flower allele, half carry the white-flower allele.

• During self-pollination, these gametes combine randomly, resulting in four possible combinations of sperm and egg.

Using a Punnett Square

• A Punnett square is a tool used to predict the outcomes of genetic crosses between individuals with known genotypes.

• For the flower-color example, use a capital letter (P) for the dominant allele and a lowercase letter (p) for the recessive allele.

Physical Appearance of the F2 Offspring

• White-Flowered Offspring: One in four (1/4) F2 offspring will inherit two white-flower alleles and produce white flowers.

• Heterozygous Purple-Flowered Offspring: Half (2/4 or 1/2) of the F2 offspring will inherit one white-flower allele and one purple-flower allele, producing purple flowers.

• Homozygous Purple-Flowered Offspring: One in four (1/4) F2 offspring will inherit two purple-flower alleles and produce purple flowers.

• Overall Phenotypic Ratio: The physical appearance (phenotype) in the F2 generation follows a 3:1 ratio: 3 purple-flowered plants to 1 white-flowered plant.

Useful Genetic Vocabulary

Homozygous Organisms

• An organism with two identical alleles for a gene is called a homozygote.

• The gene is described as homozygous.

• Homozygotes are true-breeding (they consistently pass down the same trait to offspring).

Heterozygous Organisms

• An organism with two different alleles for a gene is called a heterozygote.

• The gene is described as heterozygous.

• Heterozygotes are not true-breeding (offspring may show variation in traits).

Phenotype and Genotype

• Phenotype: An organism's observable traits, including physiological traits and traits related to appearance.

• Genotype: An organism's genetic makeup. Two organisms can have the same phenotype but different genotypes (e.g., PP and Pp both have purple flowers).

• Only individuals with white flowers have the homozygous recessive genotype (pp) for the flower-color gene.

The Law of Independent Assortment

Monohybrid and Dihybrid Crosses

• Monohybrid Cross: A cross between two heterozygotes for a single trait (e.g., F1 monohybrids).

• Dihybrid Cross: Crossing two true-breeding parents that differ in two characters produces dihybrids in the F1 generation (heterozygous for both characters).

• A dihybrid cross is used to determine whether two traits are inherited together as a linked unit or independently of each other.

Mendel's Dihybrid Cross: Seed Color and Seed Shape

• Seed Color: Yellow (Y) is dominant to green (y).

• Seed Shape: Round (R) is dominant to wrinkled (r).

• Parental cross: True-breeding yellow, round seeds (YYRR) × true-breeding green, wrinkled seeds (yyrr).

• Result: F1 generation = all dihybrids (YyRr).

Dependent vs. Independent Assortment

• Dependent Assortment (Linked Inheritance): Assumes alleles are transmitted as a package (Y with R, y with r). Prediction: F1 gametes only YR and yr; F2 offspring only yellow round and green wrinkled. Expected 3:1 ratio. This did not match Mendel's results.

• Independent Assortment: The two allele pairs segregate independently. F1 (YyRr) produce four types of gametes in equal amounts: YR, Yr, yR, yr. F2 generation: 16 equally probable combinations. Four distinct phenotypes appear in a 9:3:3:1 ratio:

  • 9 yellow round

  • 3 yellow wrinkled

  • 3 green round

  • 1 green wrinkled

  This matched Mendel's experimental data.

Law of Independent Assortment

• Definition: Each pair of alleles segregates independently of any other pair of alleles during gamete formation.

• Applies to: Genes located on different, nonhomologous chromosomes or genes that are far apart on the same chromosome.

• Exception: Genes that are close together on the same chromosome tend to be inherited together (linked genes).

Summary Table: Mendel's Laws and Genetic Vocabulary

Term	Definition	Example
Allele	Alternative version of a gene	P (purple), p (white)
Homozygous	Two identical alleles for a gene	PP or pp
Heterozygous	Two different alleles for a gene	Pp
Phenotype	Observable traits	Purple flowers
Genotype	Genetic makeup	PP, Pp, or pp

Key Equations and Ratios

• Monohybrid Cross Phenotypic Ratio: $3:1$ (dominant:recessive)

• Dihybrid Cross Phenotypic Ratio: $9:3:3:1$

• Probability of genotype in F2 (monohybrid): $1:2:1$ (homozygous dominant : heterozygous : homozygous recessive)

Example: Punnett Square for Monohybrid Cross

Cross: PP × pp

• F1 genotype: all Pp (purple)

• F2 genotypes (from Pp × Pp):

	P	p
P	PP	Pp
p	Pp	pp

• Genotypic ratio: 1 PP : 2 Pp : 1 pp

• Phenotypic ratio: 3 purple : 1 white

Example: Dihybrid Cross Punnett Square

Cross: YyRr × YyRr

• Possible gametes: YR, Yr, yR, yr

• F2 phenotypic ratio: 9 yellow round : 3 yellow wrinkled : 3 green round : 1 green wrinkled

Additional info:

• These notes cover the foundational principles of Mendelian genetics, which are essential for understanding inheritance patterns in all sexually reproducing organisms.

• Linked genes and exceptions to independent assortment are discussed in more advanced chapters.