Mendelian Traits in Humans - Biology

1. Fundamental Concepts

Definition: Mendelian traits are inherited characteristics that follow the principles of inheritance described by Gregor Mendel.
Dominant and Recessive Traits: Dominant traits are expressed when at least one allele is dominant, while recessive traits are only expressed when both alleles are recessive.
Pedigree Analysis: A pedigree chart is a diagram that shows the occurrence of a trait in several generations of a family.

2. Key Concepts

Basic Rule: $${\text{If an individual has genotype } AA \text{ or } Aa, \text{ they will express the dominant trait.}}$$

Degree Preservation: The probability of inheriting a specific trait can be calculated using Punnett squares.

Application: Used to predict the likelihood of genetic diseases being passed on from parents to offspring.

3. Examples

Example 1 (Basic)

Problem: If a child has two parents who are carriers of a recessive genetic disease (genotype Aa), what is the probability that the child will inherit the disease?

Step-by-Step Solution:

Create a Punnett square with the genotypes of the parents (Aa x Aa).
The possible genotypes for the offspring are AA, Aa, Aa, aa.
The probability of each genotype is 25% for AA, 50% for Aa, and 25% for aa.
Since the disease is recessive, the child will have the disease if their genotype is aa.

Validation: The probability of the child having the disease (aa) is 25%.

Example 2 (Intermediate)

Problem: In a family where both parents are heterozygous for a recessive trait (Aa), what is the probability that two out of three children will have the recessive trait?

Step-by-Step Solution:

Calculate the probability of one child having the recessive trait (aa): $$\frac{1}{4}$$.
Calculate the probability of one child not having the recessive trait (AA or Aa): $$\frac{3}{4}$$.
Use the binomial probability formula to find the probability of exactly two out of three children having the recessive trait: $$P(X=2) = \binom{3}{2} \left(\frac{1}{4}\right)^2 \left(\frac{3}{4}\right)^1$$.
Simplify the expression: $$P(X=2) = 3 \cdot \left(\frac{1}{16}\right) \cdot \left(\frac{3}{4}\right) = \frac{9}{64}$$.

Validation: The probability that exactly two out of three children will have the recessive trait is $$\frac{9}{64}$$.

4. Problem-Solving Techniques

Punnett Square Method: Use Punnett squares to visualize all possible combinations of alleles from parents to offspring.
Probability Calculations: Apply basic probability rules to calculate the likelihood of certain genotypes occurring.
Family Tree Analysis: Construct pedigrees to track the inheritance patterns of traits over multiple generations.