9 Mendelian Genetics

9.1 Learning Objectives

By the end of this chapter, you should be able to:

State Mendel’s principles of inheritance and explain their significance
Solve genetic problems involving monohybrid and dihybrid crosses
Distinguish between dominant and recessive inheritance patterns
Use Punnett squares and probability rules to predict genetic outcomes
Explain deviations from Mendelian inheritance including incomplete dominance, codominance, multiple alleles, and epistasis
Apply pedigree analysis to determine inheritance patterns in human families
Describe chromosome theory of inheritance and its relationship to Mendel’s principles
Connect Mendelian genetics to molecular genetics concepts

9.2 Introduction

Mendelian genetics forms the foundation of our understanding of heredity. Gregor Mendel’s careful experiments with pea plants in the 1860s revealed fundamental principles of inheritance that remain central to genetics today. This chapter examines Mendel’s discoveries, their rediscovery in 1900, and their extensions to more complex inheritance patterns. We will explore how simple mathematical principles govern the transmission of traits from parents to offspring and how these principles apply to humans and other organisms.

9.3 Historical Background

9.3.1 Pre-Mendelian Concepts

Blending inheritance: The prevailing theory before Mendel

Concept: Parental traits blend in offspring like paints
Prediction: Variation decreases each generation
Problem: Cannot explain reappearance of traits after skipping generations

Particulate inheritance: Proposed by Mendel

Concept: Discrete factors (genes) maintain identity across generations
Prediction: Traits can reappear after skipping generations
Support: Mendel’s experimental results

9.3.2 Gregor Mendel (1822-1884)

Background: Augustinian monk in Brno (now Czech Republic)

Education: University of Vienna (physics, mathematics, natural sciences)

Experimental organism: Garden pea (Pisum sativum)

Experimental design: Careful controls, large sample sizes, quantitative analysis

Why peas were ideal:

Easy to grow and hybridize
Short generation time
Many distinct varieties with contrasting traits
Self-fertilizing but can be cross-fertilized
Produce many offspring

9.3.3 Mendel’s Experimental Approach

Develop true-breeding lines: Self-fertilize for multiple generations
Perform controlled crosses: Artificial pollination
Track specific traits: Focus on seven clear characteristics
Count offspring: Large numbers for statistical reliability
Analyze ratios: Mathematical patterns in offspring

Seven traits studied:

Seed shape (round vs. wrinkled)
Seed color (yellow vs. green)
Flower color (purple vs. white)
Pod shape (inflated vs. constricted)
Pod color (green vs. yellow)
Flower position (axial vs. terminal)
Stem length (tall vs. dwarf)

9.4 Mendel’s Principles

9.4.1 Principle 1: Unit Factors in Pairs

Genetic characters are controlled by unit factors (genes) that occur in pairs

Gene: Unit of inheritance
Alleles: Alternative forms of a gene
Homozygous: Two identical alleles (AA or aa)
Heterozygous: Two different alleles (Aa)

9.4.2 Principle 2: Dominance/Recessiveness

When two different alleles are present, one may be expressed while the other has no noticeable effect

Dominant allele: Expressed in heterozygote (A)
Recessive allele: Not expressed in heterozygote (a)
Phenotype: Observable characteristic
Genotype: Genetic constitution

9.4.3 Principle 3: Segregation

During gamete formation, paired factors segregate randomly so each gamete receives one factor from each pair

Gametes: Haploid reproductive cells (sperm, egg)
Segregation: Separation of allele pairs during meiosis
Equal probability: Each gamete has 50% chance of receiving either allele

Mendel’s First Law: Law of Segregation

9.4.4 Principle 4: Independent Assortment

During gamete formation, segregation of one pair of factors is independent of other pairs

Applies to: Genes on different chromosomes or far apart on same chromosome
Result: All possible combinations of alleles occur with equal probability

Mendel’s Second Law: Law of Independent Assortment

9.5 Monohybrid Crosses

9.5.1 Basic Cross Terminology

P generation: Parental generation (true-breeding)

F₁ generation: First filial generation (offspring of P cross)

F₂ generation: Second filial generation (offspring of F₁ self-cross)

9.5.2 Mendel’s Monohybrid Experiments

Example: Seed shape (round vs. wrinkled)

P generation: Round (RR) × Wrinkled (rr)
F₁ generation: All round (Rr)
F₂ generation: 3 round : 1 wrinkled (1 RR : 2 Rr : 1 rr)

Mathematical pattern: (3:1) phenotypic ratio in F₂

9.5.3 Punnett Square Method

Developed by: Reginald Punnett (1905)

Method: Grid showing all possible gamete combinations

Monohybrid cross: 2×2 square

Example: Heterozygote cross (Rr × Rr)

    R    r
R   RR   Rr
r   Rr   rr

Results: 1 RR : 2 Rr : 1 rr genotypically, 3 round : 1 wrinkled phenotypically

9.5.4 Test Cross

Purpose: Determine genotype of individual with dominant phenotype Method: Cross with homozygous recessive (rr) Interpretation: - If all offspring show dominant trait: Parent is homozygous dominant (RR) - If 1:1 ratio: Parent is heterozygous (Rr)

9.6 Dihybrid Crosses

9.6.1 Mendel’s Dihybrid Experiments

Example: Seed shape and color

P generation: Round yellow (RRYY) × wrinkled green (rryy)
F₁ generation: All round yellow (RrYy)
F₂ generation: 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green

Mathematical pattern: (9:3:3:1) phenotypic ratio in F₂

9.6.2 Independent Assortment

Gamete formation: Four equally likely gamete types from double heterozygote

RrYy: RY, Ry, rY, ry (each 25%)

Punnett square: 4×4 square for dihybrid cross

9.6.3 Forked-Line Method

Alternative to Punnett squares

Procedure: Multiply probabilities along branches

Example: RrYy × RrYy

Probability of R_ (round): 3/4
Probability of rr (wrinkled): 1/4
Probability of Y_ (yellow): 3/4
Probability of yy (green): 1/4

Round yellow: (3/4) × (3/4) = 9/16

9.7 Probability Rules in Genetics

9.7.1 Product Rule

Probability of independent events both occurring

P(A and B) = P(A) × P(B)

Example: Probability of heterozygous offspring from heterozygous parents

P(heterozygous) = P(male R) × P(female r) + P(male r) × P(female R) = (1/2 × 1/2) + (1/2 × 1/2) = 1/2

9.7.2 Sum Rule

Probability of either of mutually exclusive events occurring

P(A or B) = P(A) + P(B)

Example: Probability of homozygous offspring

P(homozygous) = P(RR) + P(rr) = 1/4 + 1/4 = 1/2

9.7.3 Binomial Expansion

Useful for: Multiple offspring with two possible outcomes

Formula: (p + q)ⁿ where p = probability of one outcome, q = probability of other, n = number of trials

Example: Probability of exactly 2 affected children in family of 3 for autosomal recessive trait (carrier parents)

p = 1/4 (affected), q = 3/4 (unaffected), n = 3

P(2 affected) = [3!/(2!1!)] × (1/4)² × (3/4)¹ = 3 × (1/16) × (3/4) = 9/64

9.8 Extensions of Mendelian Genetics

9.8.1 Incomplete Dominance

Definition: Heterozygote shows intermediate phenotype

Example: Snapdragon flower color

RR: Red flowers
Rr: Pink flowers
rr: White flowers

F₂ ratio: 1:2:1 phenotypic ratio (matches genotypic ratio)

9.8.2 Codominance

Definition: Both alleles expressed fully in heterozygote

Example: ABO blood groups (A and B alleles codominant)

IᴬIᴮ: Type AB blood (both antigens present)
Different from incomplete dominance: Both traits visible, not blended

9.8.3 Multiple Alleles

Definition: More than two alleles exist in population

Example: ABO blood groups (Iᴬ, Iᴮ, i)

Iᴬ and Iᴮ: Codominant
i: Recessive to both
Four phenotypes: A, B, AB, O

9.8.4 Pleiotropy

Definition: One gene affects multiple traits

Example: Marfan syndrome (FBN1 gene)

Effects: Skeletal, ocular, cardiovascular abnormalities
Single gene mutation → multiple phenotypic effects

9.8.5 Epistasis

Definition: Interaction between genes where one gene masks expression of another

Example: Coat color in Labrador retrievers

B gene: Black (B) vs. brown (b)
E gene: Pigment deposition (E allows, e prevents)
ee genotype: Yellow regardless of B genotype

Modified ratios: 9:3:3:1 becomes 9:3:4 or other ratios

9.8.6 Polygenic Inheritance

Definition: Multiple genes contribute to continuous trait

Example: Human height, skin color

Characteristics: Continuous variation, bell-shaped distribution
Many genes: Additive effects
Environmental influence: Significant

9.8.7 Sex-Linked Inheritance

Definition: Genes on sex chromosomes (X or Y)

X-linked recessive pattern:

More common in males (hemizygous)
Affected males pass to all daughters (carriers)
Carrier females: 50% chance affected sons, 50% chance carrier daughters

Example: Color blindness, hemophilia

9.9 Chromosome Theory of Inheritance

9.9.1 Historical Development

Walter Sutton and Theodor Boveri (1902-1903): Chromosome theory

Thomas Hunt Morgan (1910): Experimental evidence using Drosophila

9.9.2 Key Principles

Genes are located on chromosomes
Chromosomes segregate and assort independently during meiosis
Specific genes occupy specific loci on chromosomes
Chromosomes undergo crossing over, producing recombination

9.9.3 Linkage and Recombination

Linked genes: Genes on same chromosome tend to be inherited together

Recombination: Crossing over produces new combinations of alleles

Recombination frequency: Percentage of recombinant offspring

<50%: Genes are linked
50%: Genes assort independently (unlinked or far apart)

Genetic map: Map units (centimorgans) based on recombination frequency

9.10 Human Genetics and Pedigree Analysis

9.10.1 Pedigree Symbols

Standard symbols:

Square: Male
Circle: Female
Filled: Affected
Half-filled: Carrier (for recessive traits)
Line through: Deceased
Roman numerals: Generations
Arabic numerals: Individuals within generation

9.10.2 Common Inheritance Patterns

Autosomal dominant:

Appears in every generation
Both sexes equally affected
Affected individuals have at least one affected parent
Example: Huntington disease

Autosomal recessive:

Can skip generations
Both sexes equally affected
More common with consanguinity
Example: Cystic fibrosis

X-linked recessive:

More males affected
No male-to-male transmission
Carrier females usually unaffected
Example: Hemophilia, color blindness

X-linked dominant:

Affected males pass to all daughters, no sons
Affected females pass to half children regardless of sex
Example: Hypophosphatemic rickets

Mitochondrial inheritance:

Maternal inheritance only
Both sexes affected
Variable expression due to heteroplasmy
Example: Leber’s hereditary optic neuropathy

9.10.3 Genetic Counseling

Purpose: Help individuals/families understand genetic risks

Components: Pedigree analysis, risk calculation, information provision, support

9.11 Modern Applications

9.11.1 Medical Genetics

Genetic testing: Diagnostic, predictive, carrier screening

Newborn screening: PKU, sickle cell, others

Prenatal testing: Amniocentesis, chorionic villus sampling

9.11.2 Agricultural Genetics

Selective breeding: Based on Mendelian principles

Marker-assisted selection: Using genetic markers for desirable traits

9.11.3 Conservation Genetics

Genetic diversity assessment: For endangered species Breeding programs: Maximize genetic diversity

9.12 9.10 Chapter Summary

9.12.1 Key Concepts

Mendel’s principles: Unit factors, dominance, segregation, independent assortment
Genetic crosses: Monohybrid (3:1), dihybrid (9:3:3:1)
Probability: Product rule, sum rule, binomial expansion
Extensions: Incomplete/codominance, multiple alleles, epistasis, pleiotropy
Chromosome theory: Genes on chromosomes, linkage, recombination
Human genetics: Pedigree analysis, inheritance patterns
Applications: Medical, agricultural, conservation genetics

9.12.2 Mendelian Ratios Summary

Cross Type	Parental Genotypes	F₁ Phenotype	F₂ Phenotypic Ratio	F₂ Genotypic Ratio
Monohybrid	AA × aa	All A	3:1	1:2:1
Dihybrid	AABB × aabb	All AB	9:3:3:1	Various
Test cross	A_ × aa	-	1:1 or all A	-
Incomplete dominance	RR × rr	All Rr (intermediate)	1:2:1	1:2:1

9.12.3 Human Inheritance Patterns

Pattern	Affected Males:Females	Transmission	Examples
Autosomal dominant	1:1	Vertical	Huntington, Marfan
Autosomal recessive	1:1	Horizontal	CF, sickle cell
X-linked recessive	Many:few	Diagonal	Hemophilia, color blindness
X-linked dominant	Few:many	Vertical	Hypophosphatemia
Mitochondrial	1:1	Maternal only	LHON, MELAS

9.12.4 Problem-Solving Approach

Identify inheritance pattern
Assign symbols to alleles
Determine parental genotypes
Determine possible gametes
Use Punnett square or probability rules
Calculate genotypic and phenotypic ratios
Check against expected ratios

9.13 Review Questions

9.13.1 Level 1: Recall and Understanding

State Mendel’s four principles of inheritance.
What is the difference between genotype and phenotype?
Explain why Mendel used pea plants for his experiments.
What phenotypic ratio is expected in F₂ of a monohybrid cross?
Define: homozygous, heterozygous, allele, locus.

9.13.2 Level 2: Application and Analysis

In peas, tall (T) is dominant to dwarf (t). If a heterozygous tall plant is crossed with a dwarf plant, what percentage of offspring will be tall?
In humans, albinism (lack of pigment) is autosomal recessive. Two normally pigmented parents have an albino child. What is the probability their next child will be albino?
In cats, black coat color is dominant to gray. A black cat whose mother was gray is mated with a gray cat. What proportion of offspring will be black?
For an X-linked recessive trait, if a normal man marries a carrier woman, what is the probability their son will be affected?
In peas, round seeds (R) are dominant to wrinkled (r), and yellow seeds (Y) are dominant to green (y). A plant with round yellow seeds is crossed with a plant with wrinkled green seeds. The offspring are: 51 round yellow, 49 round green, 52 wrinkled yellow, 48 wrinkled green. What were the genotypes of the parents?

9.13.3 Level 3: Synthesis and Evaluation

Why was Mendel’s work not appreciated during his lifetime? What factors led to its rediscovery in 1900?
Design a series of experiments to determine whether a new trait in Drosophila is autosomal or sex-linked, dominant or recessive.
How does the chromosome theory of inheritance explain both Mendel’s principles and exceptions to them?
Evaluate the statement: “Mendelian genetics is too simplistic to explain most human traits.”

9.14 Key Terms

Gene: Unit of heredity; segment of DNA encoding functional product
Allele: Alternative form of a gene
Genotype: Genetic constitution of an organism
Phenotype: Observable characteristics of an organism
Homozygous: Having identical alleles at a locus
Heterozygous: Having different alleles at a locus
Dominant: Allele expressed in heterozygote
Recessive: Allele not expressed in heterozygote
Punnett square: Diagram showing possible offspring genotypes
Monohybrid cross: Cross involving one trait
Dihybrid cross: Cross involving two traits
Test cross: Cross with homozygous recessive to determine genotype
Incomplete dominance: Heterozygote shows intermediate phenotype
Codominance: Both alleles expressed in heterozygote
Multiple alleles: More than two alleles exist in population
Epistasis: Interaction where one gene masks another
Pleiotropy: One gene affects multiple traits
Pedigree: Family tree showing inheritance of traits
Linkage: Genes on same chromosome inherited together
Recombination: New combinations of alleles from crossing over

9.15 Further Reading

9.15.1 Books

Griffiths, A. J. F., et al. (2015). Introduction to Genetic Analysis (11th ed.). W. H. Freeman.
Hartl, D. L., & Jones, E. W. (2009). Genetics: Analysis of Genes and Genomes (7th ed.). Jones & Bartlett.
Mendel, G. (1866). Experiments on Plant Hybridization. (Original paper translated in various sources)

9.15.2 Scientific Articles

Corcos, A. F., & Monaghan, F. V. (1985). Mendel’s work and its rediscovery: A new perspective. Critical Reviews in Plant Sciences, 3(4), 345-366.
Stern, C., & Sherwood, E. R. (Eds.). (1966). The Origin of Genetics: A Mendel Source Book. W. H. Freeman.
Dunn, L. C. (1965). A Short History of Genetics. McGraw-Hill.

9.15.3 Online Resources

MendelWeb: http://www.mendelweb.org
Online Mendelian Inheritance in Man (OMIM): https://www.omim.org
Genetics Home Reference: https://ghr.nlm.nih.gov

9.16 Quantitative Problems

Probability Calculations:
1. For an autosomal recessive disorder where both parents are carriers, what is the probability that in a family of 4 children, exactly 2 are affected?
2. What is the probability that at least 1 is affected?
3. If the first child is affected, what is the probability the next 3 are unaffected?
Dihybrid Cross Analysis: In tomatoes, red fruit (R) is dominant to yellow (r), and tall plants (T) are dominant to dwarf (t). A plant heterozygous for both traits is self-fertilized.
1. What proportion of offspring will be tall with red fruit?
2. What proportion will be dwarf with yellow fruit?
3. If 160 seeds are planted, how many would you expect to be tall with yellow fruit?
Pedigree Analysis: Analyze the following pedigree for a rare genetic disorder:
```
Generation I: Normal male × Carrier female → 2 normal sons, 1 affected daughter
Generation II: Affected female × Normal male → 1 affected son, 2 carrier daughters
```
1. What is the most likely mode of inheritance?
2. What is the probability that a carrier daughter from Generation II will have an affected child if she marries a normal man?
3. What would be different if the trait were autosomal dominant?

9.17 Case Study: Sickle Cell Disease

Background: Sickle cell disease results from a mutation in the β-globin gene (HBB).

Questions:

What is the molecular basis of sickle cell disease?
Why is the sickle cell allele maintained at relatively high frequency in some populations?
How does sickle cell illustrate both Mendelian inheritance and natural selection?
If both parents are carriers, what are the chances their child will have sickle cell disease? Be a carrier? Be unaffected?

Data for analysis:

Mutation: GAG → GTG at codon 6 (Glu → Val)
Inheritance: Autosomal recessive
Heterozygote advantage: Resistance to malaria
Population genetics: Up to 40% carriers in some regions of Africa
Clinical features: Anemia, pain crises, organ damage

Next Chapter: Molecular Genetics