Mendelian Genetics: Principles, Probability, and Exceptions

Topic 10: Mendelian Genetics

Introduction

Mendelian genetics is the study of how traits are inherited through the transmission of genes, based on the foundational work of Gregor Mendel. This topic covers the basic laws of inheritance, the use of probability in predicting genetic outcomes, and exceptions to Mendel's laws.

14.1 Exception: Linked Genes

Gene Linkage and Chromosomal Behavior

Genes located close together on the same chromosome are said to be linked. Linked genes tend to be inherited together because they are less likely to be separated by crossing over during meiosis.

• Linked Genes: Alleles of genes that are physically close on a chromosome are packaged together during meiosis.

• Gamete Formation: If genes Y and R are linked, only two types of gametes (YR and yr) are produced, each at 50% frequency.

• Independent Assortment: If genes are far apart, crossing over occurs frequently, resulting in four types of gametes (YR, Yr, yR, yr), each at 25% frequency.

Example: In a dihybrid cross with linked genes, the expected gamete ratios differ from those predicted by independent assortment.

14.2 Mendel's Laws Governed by Probability Rules

Probability in Genetic Crosses

Mendel's laws can be analyzed using probability rules similar to those used in coin tosses. These rules help predict the likelihood of specific genotypes and phenotypes in offspring.

• Multiplication Rule: Used to determine the probability of two or more independent events occurring together.

  • Probability of RR genotype from two R gametes: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

• Addition Rule: Used to determine the probability of two or more mutually exclusive events.

  • Probability of Rr genotype: $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$

• Punnett Squares: Useful for visualizing genetic crosses, but probability calculations are more efficient for complex crosses.

Example: In a trihybrid cross (PpYyRr x PpYyRr), the probability of offspring with at least two recessive traits is calculated by multiplying individual probabilities and summing relevant genotypes.

Sample Probability Table for Trihybrid Cross

Genotype	Probability
ppyyrr	1/16
ppyyRr	1/16
ppYyrr	1/16
Ppyyrr	2/16
Other relevant genotypes	Additional info: Probabilities calculated similarly

Result: The chance of progeny having at least two recessive traits from this cross is $\frac{6}{16}$ (or $\frac{3}{8}$).

Mendel's Laws Visualized

Chromosome Behavior During Meiosis

Homologous chromosomes assort independently during metaphase I of meiosis, leading to the Law of Independent Assortment. The alleles carried by these chromosomes also segregate independently, which is the Law of Segregation.

• Law of Segregation: Each individual has two alleles for each gene, which segregate during gamete formation.

• Law of Independent Assortment: Genes on different chromosomes assort independently during meiosis.

Example: The random orientation of chromosomes at metaphase I leads to different combinations of alleles in gametes.

14.3 Inheritance Patterns Don't Always Follow Mendel's Laws

Incomplete Dominance and Codominance

Not all alleles are completely dominant or recessive. Some inheritance patterns deviate from Mendel's laws.

• Incomplete Dominance: The heterozygote displays a phenotype intermediate between the two homozygotes.

  • Example: In snapdragons, red and white alleles produce pink flowers in heterozygotes.

• Codominance: Both alleles in a heterozygote are fully expressed.

  • Example: Human ABO blood group, where both IA and IB alleles are expressed.

Multiple Alleles and Dominance Hierarchies

Some genes have more than two alleles in a population, leading to a range of phenotypes.

• Rabbit Fur Colour: One gene with four alleles (C, cch, ch, c) produces various coat colours.

• Dominance Hierarchy: Some alleles are dominant over others, creating complex inheritance patterns.

Pleiotropy

Pleiotropy occurs when one gene affects multiple phenotypic traits.

• Example: Cystic fibrosis and sickle-cell disease cause multiple symptoms.

• Example: Albinism affects skin, hair, and eye colour, as well as vision.

Penetrance and Expressivity

Penetrance and expressivity describe how consistently a genotype produces its associated phenotype.

• Penetrance: The proportion of individuals with a genotype who display the expected phenotype.

  • Example: BRCA1 mutation has 65% penetrance for breast/ovarian cancer.

  • Example: MUTYH mutation is 100% penetrant for colon cancer.

• Expressivity: The degree to which a genotype is expressed in the phenotype.

  • Example: Beagle dogs with the same genotype for piebald gene show varying degrees of whiteness.

Table: Penetrance and Expressivity

Type	Description	Example
Complete Penetrance	All individuals show the phenotype	MUTYH mutation
Incomplete Penetrance	Some individuals show the phenotype	BRCA1 mutation
Constant Expressivity	Phenotype expressed to same degree	Additional info: Uniform trait expression
Variable Expressivity	Phenotype expressed to varying degrees	Piebald gene in beagles

Epistasis

Epistasis occurs when the expression of one gene is affected by another gene at a different locus.

• Example: In Labrador retrievers, one gene determines pigment deposition, another determines pigment colour.

• Phenotypic ratios differ from standard Mendelian ratios (e.g., not 9:3:3:1).

Multifactorial Inheritance

Phenotypes can be influenced by both genotype and environmental factors.

• Example: Hydrangea flower colour depends on soil pH and aluminum content.

• Nature vs Nurture: Identical twins can show phenotypic differences due to environmental influences.

Summary Table: Mendelian vs Non-Mendelian Inheritance

Pattern	Description	Example
Mendelian	Traits follow laws of segregation and independent assortment	Pea plant flower colour
Linked Genes	Genes inherited together due to proximity on chromosome	Fruit fly eye and wing traits
Incomplete Dominance	Heterozygote shows intermediate phenotype	Snapdragon flower colour
Codominance	Both alleles fully expressed	ABO blood group
Multiple Alleles	More than two alleles for a gene	Rabbit coat colour
Pleiotropy	One gene affects multiple traits	Cystic fibrosis
Epistasis	Gene interaction affects phenotype	Labrador coat colour
Penetrance/Expressivity	Variation in phenotype expression	BRCA1 mutation
Multifactorial	Genotype and environment influence phenotype	Hydrangea flower colour

Key Terms

• Allele: Alternative form of a gene.

• Genotype: Genetic makeup of an organism.

• Phenotype: Observable traits of an organism.

• Homozygous: Two identical alleles for a gene.

• Heterozygous: Two different alleles for a gene.

• Pleiotropy: One gene affects multiple traits.

• Epistasis: One gene affects the expression of another.

• Penetrance: Proportion of individuals showing phenotype.

• Expressivity: Degree to which phenotype is expressed.

• Multifactorial: Trait influenced by genes and environment.

Formulas and Equations

• Multiplication Rule: $P(A \text{ and } B) = P(A) \times P(B)$

• Addition Rule: $P(A \text{ or } B) = P(A) + P(B)$

Conclusion

Mendelian genetics provides the foundation for understanding inheritance, but real-world genetic patterns often involve exceptions such as linkage, incomplete dominance, codominance, multiple alleles, pleiotropy, epistasis, and environmental effects. Mastery of these concepts is essential for interpreting genetic outcomes and predicting phenotypes.