Genetics: Mendelian Inheritance, Probability, and Genetic Crosses

Genetics: Mendelian Inheritance and Probability

Introduction to Genetics

Genetics is the study of heredity and the variation of inherited characteristics. Mendelian genetics focuses on how traits are passed from parents to offspring through discrete units called genes. Each individual inherits two alleles for each gene, one from each parent.

Key Terms in Genetics

• Genotype: The set of alleles present in an individual (e.g., RR, Rr, rr).

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

• Dominant allele: An allele that determines the phenotype even when only one copy is present (e.g., R for round seeds).

• Recessive allele: An allele whose effect is masked in the presence of a dominant allele (e.g., r for wrinkled seeds).

• Homozygote: An individual with two identical alleles for a gene (e.g., RR or rr).

• Heterozygote: An individual with two different alleles for a gene (e.g., Rr).

Monohybrid Crosses

Definition and Purpose

A monohybrid cross examines the inheritance of a single gene with two alleles. It is used to predict the genotypic and phenotypic ratios of offspring from parents with different allele combinations.

• Mono-: Refers to one gene.

• Hybrid: Refers to parents with two different types of alleles.

Example: Seed Shape in Peas

• The gene R codes for an enzyme that synthesizes amylopectin (a branched starch).

• R (dominant): Produces round seeds due to functional amylopectin synthesis.

• r (recessive): Results in wrinkled seeds due to a non-functional enzyme (mutation creates an early stop codon).

Molecular Basis of Dominance and Recessiveness

• Dominant alleles produce a functional enzyme, leading to the dominant phenotype.

• Recessive alleles often result from mutations that produce a non-functional protein.

• Heterozygotes (Rr) have one functional and one non-functional allele, but the presence of one functional enzyme is sufficient for the dominant phenotype.

Punnett Square for Monohybrid Cross (Rr × Rr)

	R	r
R	RR	Rr
r	Rr	rr

• Genotypic ratio: 1 RR : 2 Rr : 1 rr

• Phenotypic ratio: 3 round : 1 wrinkled

Probability Theory in Genetics

Product Rule

• The probability that two independent events will both occur is the product of their individual probabilities.

• Formula: $P(A \text{ AND } B) = P(A) \times P(B)$

Sum Rule

• The probability that either of two mutually exclusive events will occur is the sum of their individual probabilities.

• Formula: $P(A \text{ OR } B) = P(A) + P(B)$

Application to Mendel’s Crosses

• For Rr × Rr:

  • Probability of RR zygote: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

  • Probability of Rr zygote: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

  • Probability of rR zygote: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

  • Total probability of heterozygote (Rr or rR): $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$

  • Probability of rr zygote: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

• Phenotypic probabilities:

  • Round seeds (RR or Rr): $\frac{1}{4} + \frac{1}{2} = \frac{3}{4}$

  • Wrinkled seeds (rr): $\frac{1}{4}$

Testcross

Purpose and Method

A testcross is used to determine whether an individual with a dominant phenotype is homozygous dominant or heterozygous. This is done by crossing the individual with a homozygous recessive individual and analyzing the offspring phenotypes.

• If all offspring display the dominant phenotype, the tested individual is likely homozygous dominant.

• If offspring display both dominant and recessive phenotypes, the tested individual is heterozygous.

Dihybrid Crosses and Independent Assortment

Definition and Principle

A dihybrid cross examines the inheritance of two different genes, each with two alleles, located on different chromosomes. According to Mendel’s Law of Independent Assortment, alleles of different genes assort independently during gamete formation.

• Example: Pea shape (R = round, r = wrinkled) and pea color (Y = yellow, y = green).

Gamete Formation (FOIL Method)

• For a dihybrid RrYy, possible gametes are determined using FOIL:

  • First: RY

  • Outside: Ry

  • Inside: rY

  • Last: ry

Punnett Square for Dihybrid Cross (RrYy × RrYy)

	RY	Ry	rY	ry
RY	RRYY	RRYy	RrYY	RrYy
Ry	RRYy	RRyy	RrYy	Rryy
rY	RrYY	RrYy	rrYY	rrYy
ry	RrYy	Rryy	rrYy	rryy

• Genotypic ratio: 9:3:3:1 (9 double dominant : 3 dominant/recessive : 3 recessive/dominant : 1 double recessive)

• Phenotypic ratio: 9 round yellow : 3 round green : 3 wrinkled yellow : 1 wrinkled green

Principle of Independent Assortment

• Each gamete receives one allele for each gene, and the distribution of alleles for one gene is independent of the distribution for another gene.

• This principle applies only to genes located on different chromosomes or far apart on the same chromosome.

Using Probability to Predict Dihybrid Outcomes

• Calculate the probability for each gene separately, then apply the product rule to combine probabilities for the two traits.

• For example, probability of round yellow offspring: $\frac{3}{4}$ (round) × $\frac{3}{4}$ (yellow) = $\frac{9}{16}$

Summary Table: Key Genetic Terms

Term	Definition	Example
Genotype	Allele combination in an individual	Rr
Phenotype	Observable trait	Round seed
Homozygote	Two identical alleles	RR or rr
Heterozygote	Two different alleles	Rr
Dominant allele	Expressed if present	R
Recessive allele	Masked by dominant	r

Example Application

• If a pea plant with round seeds is crossed with a wrinkled-seed plant, and some offspring have wrinkled seeds, the round-seed parent must be heterozygous (Rr).

Additional info: The notes also reference the molecular basis of dominance and recessiveness, emphasizing that dominant alleles often produce functional proteins, while recessive alleles may result from mutations that disrupt protein function. The FOIL method is a mnemonic for determining gamete combinations in dihybrid crosses.