Transmission Genetics: Mendelian Inheritance, Probability, and Pedigree Analysis CH 2 NEW SEM

Transmission Genetics: Mendelian Inheritance

Monohybrid and Dihybrid Crosses

Mendelian genetics explores how traits are inherited from one generation to the next. The monohybrid cross involves a single gene, while the dihybrid cross examines two genes simultaneously, revealing the principle of independent assortment.

• Monohybrid Cross: Involves one gene with two alleles (e.g., Yy x yy).

• Dihybrid Cross: Involves two genes, each with two alleles (e.g., RrGg x RrGg).

• Test Cross: Used to determine the genotype of an individual by crossing it with a homozygous recessive.

• Gene vs. Allele: A gene is a DNA region coding for a product; an allele is a variant of that gene.

• Genotype Example: A dihybrid that is yellow and round: Yy; Rr.

Dihybrid Cross: Gamete Formation and Probability

In a dihybrid cross, gametes are formed by the independent segregation of alleles. The probability of each gamete type is calculated by multiplying the probabilities for each gene.

• Gamete Types: For RrGg, possible gametes are RG, Rg, rG, rg.

• Probability Calculation: Each gamete has a probability of 1/4.

• Forked-Line Method: Used to determine gamete genotype frequency by multiplying probabilities.

Punnett Square Analysis

Punnett squares are used to visualize the outcome of genetic crosses. For a dihybrid cross, a 4x4 Punnett square shows all possible combinations of alleles.

• F2 Generation: Results from self-crossing F1 heterozygotes (RrGg x RrGg).

• Phenotypic Ratios: Classic dihybrid ratio is 9:3:3:1.

• Genotypic and Phenotypic Frequencies: Calculated using product and sum rules.

Mendel's Law of Independent Assortment

Mendel's second law states that alleles of different genes assort independently during gamete formation. This is illustrated by the 9:3:3:1 ratio in dihybrid crosses and is related to the random assortment of chromosomes during metaphase I of meiosis.

• Product Rule: Probability of independent events occurring together is the product of their individual probabilities.

• Sum Rule: Probability of mutually exclusive events is the sum of their individual probabilities.

• Example: Probability of being yellow and round = $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

Trihybrid Crosses and Branch Diagrams

Trihybrid crosses involve three genes, each with two alleles. The branch diagram method is used to predict phenotypic frequencies by multiplying probabilities for each trait.

• Number of Phenotypes: For n gene pairs, number of phenotypes = $2^n$.

• Number of Genotypes: For n gene pairs, number of genotypes = (number of genotypes per gene pair)$^n$.

• Example: RrGgWw x RrGgWw yields 8 phenotypes and 27 genotypes.

Probability Theory in Genetics

Rules of Probability

Probability theory is essential for predicting genetic outcomes. Four main rules are used:

• Product Rule: Probability of independent events occurring together.

• Sum Rule: Probability of mutually exclusive events.

• Conditional Probability: Probability modified by additional information.

• Binomial Probability: Used for events with two possible outcomes.

Example: For a cross Gg x Gg, the probability that a yellow-seeded progeny is heterozygous is $\frac{2}{3}$.

Human Genetics and Pedigree Analysis

Pedigrees: Symbols and Interpretation

Pedigrees are diagrams used to trace the inheritance of traits in families. Standard symbols represent individuals, relationships, and trait expression.

• Male: Square

• Female: Circle

• Expresses trait: Filled symbol

• Does not express trait: Unfilled symbol

• Generations: Roman numerals

Autosomal Dominant and Recessive Inheritance

Autosomal inheritance patterns parallel Mendel's principles. Dominant and recessive traits have distinct pedigree patterns.

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

• Autosomal Recessive: Trait often skips generations; affected individuals may have unaffected parents.

Pedigree Problem: Calculating Carrier Probability

Pedigree analysis can be used to calculate the probability that a child will inherit a recessive condition, based on the genotypes of the parents and their family history.

• Assign Genotypes: Use D for dominant and d for recessive alleles.

• Carrier Probability: Calculate the chance that both parents are carriers and both pass the recessive allele to their child.

• Example: If both parents are carriers, the probability their child will have the condition is $\frac{1}{4}$.

Summary Table: Dihybrid Cross Genotypes and Phenotypes

Genotype	Phenotype	Frequency
RRGG, RRGg, RrGG, RrGg	Round, Yellow (R-G-)	9/16
RRgg, Rrgg	Round, Green (R-gg)	3/16
rrGG, rrGg	Wrinkled, Yellow (rrG-)	3/16
rrgg	Wrinkled, Green (rrgg)	1/16

Key Equations

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

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

• Number of Phenotypes: $2^n$ (where n = number of gene pairs)

• Number of Genotypes: (genotypes per gene pair)$^n$

Additional info: Probability theory and pedigree analysis are foundational for understanding inheritance patterns and predicting genetic outcomes in both plants and humans.