5.3 mendelian genetics

Mendelian Genetics

Introduction to Mendelian Genetics

Mendelian genetics is the study of how traits are inherited from one generation to the next, based on the foundational work of Gregor Mendel. This field explains the basic principles of heredity and the behavior of genes during reproduction.

• Gene: A segment of DNA that encodes information for a specific trait.

• Allele: Different forms of a gene found at the same locus on homologous chromosomes.

• Genotype: The genetic makeup of an organism, often represented by letters (e.g., AA, Aa, aa).

• Phenotype: The observable physical or physiological traits of an organism, determined by its genotype.

Mendel's Laws of Inheritance

Mendel's experiments with pea plants led to the formulation of two key laws:

• Law of Segregation: Each individual has two alleles for each gene, which segregate during gamete formation so that each gamete receives only one allele. This explains why offspring inherit one allele from each parent.

• Law of Independent Assortment: Genes for different traits assort independently of one another during gamete formation, provided the genes are on different chromosomes or far apart on the same chromosome.

Example: Mendel's dihybrid crosses (e.g., seed shape and seed color) demonstrated that traits are inherited independently, resulting in a 9:3:3:1 phenotypic ratio in the F2 generation.

Genotype and Phenotype

• Homozygous: Having two identical alleles for a gene (e.g., AA or aa).

• Heterozygous: Having two different alleles for a gene (e.g., Aa).

• Dominant allele: Expressed in the phenotype even if only one copy is present.

• Recessive allele: Expressed only when two copies are present.

Probability in Genetics

Probability is used to predict the outcomes of genetic crosses. The rules of probability apply to the inheritance of alleles:

• Rule of Multiplication: The probability of two independent events both occurring is the product of their individual probabilities.

• Rule of Addition: The probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.

Example: If the probability of inheriting allele A from one parent is 1/2 and from the other parent is 1/2, the probability of being AA is $1/2 \times 1/2 = 1/4$.

Punnett Squares

Punnett squares are diagrams used to predict the genotypic and phenotypic ratios of offspring from a genetic cross.

• Monohybrid cross: Examines the inheritance of one trait.

• Dihybrid cross: Examines the inheritance of two traits simultaneously.

Example: A monohybrid cross between two heterozygotes (Aa x Aa) yields a 3:1 phenotypic ratio.

Pedigree Analysis

Pedigrees are family trees used to track the inheritance of traits across generations. They help determine whether a trait is dominant, recessive, autosomal, or sex-linked.

• Autosomal recessive pattern: Trait often skips generations; affected individuals can have unaffected parents.

• Autosomal dominant pattern: Trait appears in every generation; affected individuals have at least one affected parent.

Hypothesis Testing in Genetics: Chi-Square Test

The chi-square ($\chi^2$) test is used to compare observed and expected results to determine if deviations are due to chance.

• Formula: $\chi^2 = \sum \frac{(O - E)^2}{E}$, where O = observed value, E = expected value.

• Compare the calculated $\chi^2$ value to a critical value from the chi-square table (based on degrees of freedom and significance level, usually 0.05).

• If $\chi^2$ is less than the critical value, fail to reject the null hypothesis (no significant difference between observed and expected values).

• If $\chi^2$ is greater than the critical value, reject the null hypothesis (significant difference exists).

Example: In a dihybrid cross, if the observed ratio of phenotypes does not significantly differ from the expected 9:3:3:1 ratio, the traits assort independently.

Summary Table: Key Concepts in Mendelian Genetics

Concept	Definition	Example
Gene	Unit of heredity encoding a trait	Gene for flower color
Allele	Alternative form of a gene	Purple vs. white flower allele
Genotype	Genetic makeup	AA, Aa, aa
Phenotype	Physical expression	Purple flowers
Law of Segregation	Alleles separate during gamete formation	Each gamete gets one allele
Law of Independent Assortment	Genes for different traits assort independently	Seed shape and color inherited independently
Punnett Square	Predicts offspring ratios	Monohybrid or dihybrid cross
Chi-square test	Statistical test for observed vs. expected ratios	$\chi^2 = \sum \frac{(O - E)^2}{E}$

Additional info: These notes expand on the transcript by providing definitions, formulas, and structured examples for clarity and completeness.