Genetic Inheritance: Mendel's Laws, Crosses, Ratios, and Probability

Mendel's Laws of Inheritance and Genetic Crosses

Mendel's Laws of Inheritance

1. Law of Segregation: Each parent contributes only one of their two alleles for a specific trait to their offspring.
2. Law of Independent Assortment: Alleles for different traits are passed down independently of one another during gamete formation.
3. Law of Dominance: When an organism inherits two different alleles for a trait, the dominant allele will be expressed in the phenotype, masking the effect of the recessive allele.

Analyzing Monohybrid Inheritance

Case Study: Earlobes (Monohybrid Cross)

The results of the cross show:

• Mr. Jones: aa (Attached earlobes, recessive)
• Mrs. Jones: Aa (Free earlobes, heterozygous dominant)

Their children exhibit the following genotypes and phenotypes:

• 3 offspring with attached earlobes (Genotype: aa)
• 3 offspring with free earlobes (Genotype: Aa)

Analyzing Widow's Peak Inheritance

Mr. and Mrs. Smith both display a widow's peak, a dominant trait (W). However, since they have a child without a widow's peak (ww), both parents must carry the recessive allele. Therefore, both parents are likely heterozygous (Ww).

Using a Punnett square for a Ww x Ww cross, the probabilities for their offspring are:

• 25% chance of WW (Widow's peak)
• 50% chance of Ww (Widow's peak)
• 25% chance of ww (No widow's peak)

It is entirely possible for them to have a child without a widow's peak, meaning Mr. Smith's accusation regarding paternity is not genetically justified.

Test Crosses and Dihybrid Ratios

The Purpose of a Test Cross

A test cross is used to determine the unknown genotype of an organism displaying a dominant phenotype (i.e., whether it is homozygous dominant or heterozygous). This is achieved by crossing the organism with one that is homozygous recessive for that trait.

Dihybrid Cross Phenotypic Ratio (9:3:3:1)

When considering two independently assorting traits (a dihybrid cross), the offspring ratio is 9:3:3:1. This ratio represents the phenotypic distribution out of 16 possible offspring:

• 9/16: Offspring showing both dominant traits (e.g., A_B_)
• 3/16: Offspring showing the first dominant trait and the second recessive trait (e.g., A_bb)
• 3/16: Offspring showing the first recessive trait and the second dominant trait (e.g., aaB_)
• 1/16: Offspring showing both recessive traits (e.g., aabb)

Dihybrid Cross Example: Eye and Hair Color

A dihybrid cross is a genetic cross that considers two different traits, each represented by two alleles. It demonstrates how these traits segregate and assort independently during gamete formation.

Allele Key:

• Black eye: B | Red eye: b
• Brown hair: A | Grey hair: a

The resulting phenotypic ratios are:

• Black eye, Brown hair (B_A_): 9
• Black eye, Grey hair (B_aa): 3
• Red eye, Brown hair (bbA_): 3
• Red eye, Grey hair (bbaa): 1

Specialized Genetic Structures

Polytene Chromosomes

Polytene chromosomes are exceptionally large chromosomes consisting of many identical DNA strands lying parallel to each other. They are formed through multiple rounds of DNA replication without subsequent cell division (endomitosis).

These structures are primarily found in the salivary glands of certain organisms, such as fruit flies (Drosophila). They are characterized by distinct banding patterns, which are invaluable for studying gene expression and detailed chromosomal structure.

Fundamental Rules of Genetic Probability

Genotype and Phenotype Notation

1. A-B-: This represents the phenotype where the organism expresses the dominant trait for both locus A and locus B. This requires at least one dominant A allele and at least one dominant B allele.
2. AAb-: This specific genotype notation implies the organism is homozygous dominant for locus A (AA). Although the notation is unusual, the context suggests it represents a genotype that expresses the dominant B trait (i.e., having at least one dominant B allele).

Therefore, any organism with the genotype represented by AAb- is included within the broader phenotypic class A-B-.

Key Probability Rules

1. Addition Rule (The "OR" Rule): If you want to find the probability of either one mutually exclusive event happening or another, you add their individual probabilities.

   Example: When rolling a standard six-sided die, the chance of rolling a 2 or a 3 is 1/6 + 1/6 = 1/3.

2. Multiplication Rule (The "AND" Rule): If you want to find the probability of two or more independent events happening together, you multiply their individual probabilities.

   Example: The chance of flipping heads on a coin and rolling a 4 on a die is 1/2 * 1/6 = 1/12.

Calculating Combinations (Coin Flips)

For four independent events (e.g., four coin flips), the number of ways specific outcomes can occur is calculated using combinations (C):

1. Three Heads and One Tail:

   Number of ways = C(4, 3) = 4! / (3! * (4 - 3)!) = 4

2. Two Heads and Two Tails:

   Number of ways = C(4, 2) = 4! / (2! * (4 - 2)!) = 6