Basic Principles of Heredity: Mendelian Genetics and Human Inheritance

Chapter 3: Basic Principles of Heredity

Subtopic 3.1 – Gregor Mendel and the Monohybrid Cross

The foundation of modern genetics was established by Gregor Mendel through his experiments with garden peas. Mendel's systematic approach and quantitative analysis led to the discovery of fundamental principles governing heredity.

• Importance of Meiosis: Meiosis enables the transmission of hereditary characteristics and the generation of new genetic combinations, which has been utilized in selective breeding of plants and animals.

• Mendel's Experimental Design:

  • Used true-breeding strains (traits unchanged over generations).

  • Crossed two strains differing in a single characteristic (monohybrid cross).

  • Parental generation (P) → First filial generation (F1) → Second filial generation (F2).

• Dominant and Recessive Traits:

  • In F1, only one trait appears (dominant); the other is hidden (recessive).

  • In F2, the recessive trait reappears, typically in a 3:1 ratio (dominant:recessive).

  • Reciprocal crosses showed results were not sex-dependent.

• Alleles and Genotype:

  • Each characteristic is controlled by two discrete factors, now called alleles.

  • Genotype determines phenotype (observable traits).

  • Dominant alleles are represented by uppercase letters (e.g., P for purple), recessive by lowercase (e.g., p for white).

  • Homozygous dominant (PP), homozygous recessive (pp), heterozygous (Pp).

• Punnett Square: A tool to predict genotypes and phenotypes of offspring. Explains the 3:1 phenotypic ratio in F2 generation.

• Testcross: Used to determine the genotype of an individual with a dominant phenotype by crossing with a homozygous recessive individual.

  • If all offspring show the dominant trait, the tested individual is homozygous dominant.

  • If offspring show a 1:1 ratio of dominant to recessive, the tested individual is heterozygous.

• Example: In Labradors, black coat color (B) is dominant to chocolate (b). A testcross can reveal if a black Labrador is BB or Bb.

Subtopic 3.2 – Mendel’s Principle of Segregation

Mendel's first law, the Principle of Segregation, describes how alleles separate during gamete formation, ensuring each gamete receives only one allele for each gene.

• Law Statement: Each diploid organism possesses two alleles for a characteristic, which segregate during gamete formation.

• Mechanism: Homologous chromosomes (and their alleles) separate during meiosis I.

• Phenotypic Consequences:

  • Heterozygotes express the dominant phenotype, but their progeny can display both dominant and recessive phenotypes due to segregation.

  • In diploids, the effect of segregation is observed in the F2 generation (one-generation lag).

• Genetic Symbols:

  • Plants: Dominant allele (uppercase, e.g., P), recessive allele (lowercase, e.g., p).

  • Drosophila: Mutant phenotype names the allele; wild-type indicated by a “+” superscript (e.g., w for white eyes, w+ for wild-type).

  • Dominant mutations use uppercase (e.g., B for Bar eye, B+ for wild-type).

• Example: In Drosophila, w+/w is a heterozygote with wild-type eyes; w/w is white-eyed.

Subtopic 3.3 – Mendel’s Principle of Independent Assortment

The Principle of Independent Assortment (Mendel's second law) states that alleles of different genes assort independently during gamete formation, provided the genes are on different chromosomes or far apart on the same chromosome.

• Dihybrid Cross: Cross between strains differing in two characteristics (e.g., seed color and seed shape).

• F1 Generation: All individuals are heterozygous for both traits (e.g., YyRr).

• F2 Generation: Four phenotypes appear in a 9:3:3:1 ratio, explained by a 16-cell Punnett square.

• Law Statement: Alleles for one gene segregate independently of alleles for another gene during gamete formation.

• Chromosomal Basis:

  • Independent assortment occurs because homologous chromosome pairs align and separate independently during meiosis I.

  • Number of possible gamete types: $2^n$, where $n$ is the number of chromosome pairs.

  • Humans (23 pairs): $2^{23} \approx 8$ million possible gametes.

• Genes on Same Chromosome: Crossing over during meiosis can allow independent assortment even for genes on the same chromosome, unless they are closely linked (gene linkage).

• Example: Mendel’s dihybrid crosses (e.g., yellow-round × green-wrinkled peas) confirmed the 9:3:3:1 ratio, supporting independent assortment.

Subtopic 3.4 – Chi-square Analysis

The chi-square goodness-of-fit test is a statistical method used to determine whether observed genetic ratios deviate significantly from expected Mendelian ratios due to chance or other factors.

• Purpose: To test if deviations between observed and expected progeny numbers are due to random chance.

• Steps:

  1. Calculate chi-square value ($\chi^2$):

     • Formula: $\chi^2 = \sum \frac{(O - E)^2}{E}$

     • Where $O$ = observed value, $E$ = expected value.

  2. Determine degrees of freedom (df):

     • Formula: $df = n - 1$

     • Where $n$ = number of expected phenotypic classes.

  3. Find probability (P) value:

     • Compare calculated $\chi^2$ to a chi-square table using the appropriate df.

• Interpretation:

  • If $P \geq 0.05$, differences are likely due to chance (not significant).

  • If $P < 0.05$, differences are significant (not likely due to chance).

• Example Calculation:

  • Observed: 69 purple, 31 white (total 100); Expected (3:1): 75 purple, 25 white.

  • $\chi^2 = \frac{(69-75)^2}{75} + \frac{(31-25)^2}{25} = \frac{36}{75} + \frac{36}{25} = 0.48 + 1.44 = 1.92$

  • df = 2 - 1 = 1

  • P value between 0.5 and 0.1; thus, deviation is not significant.

df	P = 0.5	P = 0.1	P = 0.05
1	0.455	2.706	3.841

Additional info: Table values are inferred from standard chi-square tables for df = 1.

Subtopic 3.5 – Using Pedigrees to Study Human Inheritance

Pedigree analysis is a key tool for studying inheritance patterns in humans, where controlled crosses are not possible. Pedigrees help determine whether traits are dominant or recessive and can reveal carriers of genetic disorders.

• Challenges in Human Genetics:

  • No true-breeding lines, long generation times, small family sizes, and ethical constraints on experimental crosses.

• Pedigree Symbols:

  • Square: male; Circle: female.

  • Shaded: affected; Unshaded: unaffected (may be carrier).

  • Horizontal line: mating; Vertical line: offspring.

  • Roman numerals: generations; Arabic numbers: individuals.

• Dominant vs. Recessive Inheritance:

  • Dominant: Affected individuals in every generation; each affected person has an affected parent.

  • Recessive: Trait can skip generations; affected individuals may have unaffected (carrier) parents.

• Examples:

  • Dominant: Brachydactyly, achondroplasia, Huntington’s disease (late-onset lethal dominant).

  • Recessive: Albinism, cystic fibrosis (homozygosity for recessive allele).

• Carrier Detection: Pedigree analysis can reveal silent carriers (heterozygotes) in recessive inheritance.

• Genotype Deduction:

  • Affected child with unaffected parents indicates recessive inheritance; both parents are carriers.

  • Inferred genotypes can be deduced by analyzing affected and unaffected individuals across generations.

Trait Type	Pedigree Pattern	Examples
Dominant	Affected in every generation; affected parent to affected child	Brachydactyly, Achondroplasia, Huntington’s disease
Recessive	Trait can skip generations; affected child with unaffected parents	Albinism, Cystic fibrosis

Additional info: Table summarizes dominant vs. recessive pedigree patterns and examples.