🎲 Independent Assortment, Dihybrid & Trihybrid Crosses
Study Mendel Law of Independent Assortment with dihybrid cross 9:3:3:1 ratio for CUET Agriculture. Fork-line method and test cross covered.
Law of Independent Assortment (Third Law)
The Law of Independent Assortment is Mendel's second law (also called the Third Law when counting the Law of Dominance as the first). It states:
- When two or more pairs of contrasting characters are considered simultaneously, the factors of each pair segregate independently of the other pairs during gamete formation
- Genes of different traits are inherited independently of each other without mutual influence in the F2 generation. This means that the inheritance of one trait does not affect the inheritance of another.
- This law is also called Mendel's Law of Independent Assortment
- It is applicable only when genes are on different chromosomes (not linked). If genes are on the same chromosome, they tend to be inherited together (linkage).
- This law is based on the F2 generation of a dihybrid cross
- Linkage is the major exception to this law — linked genes do NOT assort independently
IMPORTANT
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Law of Independent Assortment (Third Law)
The Law of Independent Assortment is Mendel's second law (also called the Third Law when counting the Law of Dominance as the first). It states:
- When two or more pairs of contrasting characters are considered simultaneously, the factors of each pair segregate independently of the other pairs during gamete formation
- Genes of different traits are inherited independently of each other without mutual influence in the F2 generation. This means that the inheritance of one trait does not affect the inheritance of another.
- This law is also called Mendel's Law of Independent Assortment
- It is applicable only when genes are on different chromosomes (not linked). If genes are on the same chromosome, they tend to be inherited together (linkage).
- This law is based on the F2 generation of a dihybrid cross
- Linkage is the major exception to this law — linked genes do NOT assort independently
IMPORTANT
Independent assortment works because during meiosis, each pair of homologous chromosomes lines up at the metaphase plate independently of other pairs. The orientation of one pair has no influence on the orientation of another pair.
Dihybrid Cross
A dihybrid cross involves the study of two pairs of contrasting characters simultaneously. This is the cross that led Mendel to discover independent assortment.
Example: In garden pea —
| Trait | Dominant | Recessive |
|---|---|---|
| Seed shape | Round (R) | Wrinkled (r) |
| Seed colour | Yellow (Y) | Green (y) |
Parents: RRYY (Round Yellow) × rryy (Wrinkled Green)
F1: All RrYy (Round Yellow)
F1 × F1: RrYy × RrYy (Self-pollination)
Mendel crossed round yellow seeds with wrinkled green seeds. All F1 offspring were round and yellow, confirming that round and yellow are the dominant traits.
When F1 plants were selfed, four types of phenotypes appeared in F2:
F2 Phenotypic ratio:
- 9 Round Yellow
- 3 Round Green
- 3 Wrinkled Yellow
- 1 Wrinkled Green
Ratio: 9 : 3 : 3 : 1 (total 4 phenotypic classes)
Mendel observed that new combinations (Round Green and Wrinkled Yellow) appeared in F2 that were NOT present in either parent. This was the key evidence for independent assortment — the seed shape gene and seed colour gene segregated independently of each other, creating new combinations.
Grouping: 9[Round Yellow] + 1[Wrinkled Green] : 3[Round Green] + 3[Wrinkled Yellow] = 10 : 6
This grouping shows that parental combinations (10) are more frequent than recombinant combinations (6), but both types appear because of independent assortment.
F2 Genotypic ratio:
| Genotype | Count |
|---|---|
| RRYY | 1 |
| RRYy | 2 |
| RRyy | 1 |
| RrYY | 2 |
| RrYy | 4 |
| Rryy | 2 |
| rrYY | 1 |
| rrYy | 2 |
| rryy | 1 |
Genotypic ratio = 1:2:1:2:4:2:1:2:1 (total 9 genotypic classes)
TIP
The most common genotype in F2 is RrYy (doubly heterozygous) with a frequency of 4/16 = 25%. The homozygous dominant (RRYY) and homozygous recessive (rryy) are each only 1/16.
Trihybrid Cross
A trihybrid cross involves three pairs of contrasting characters simultaneously. The complexity increases exponentially:
Parents: RRYYTT × rryytt
F1: RrYyTt (All dominant phenotype)
↓ Selfing
F2 Phenotypic ratio = 27:9:9:9:3:3:3:1
Genotype classes = 3³ = 27 types
| Parameter | Monohybrid | Dihybrid | Trihybrid |
|---|---|---|---|
| Phenotypic ratio | 3:1 | 9:3:3:1 | 27:9:9:9:3:3:3:1 |
| Phenotype classes | 2 | 4 | 8 |
| Genotype classes | 3 | 9 | 27 |
| Gamete types | 2 | 4 | 8 |
NOTE
As the number of traits increases, the number of possible combinations grows exponentially. This is why Mendel wisely chose to study one or two traits at a time before attempting more complex crosses.
Exceptions to Mendel's Laws
Mendel's laws hold true for most situations, but several important exceptions have been discovered since his time. Each exception reveals a different layer of genetic complexity:
- Incomplete dominance — F1 shows an intermediate phenotype instead of the dominant phenotype (modified ratio: 1:2:1)
- Codominance — Both alleles express simultaneously in F1, producing a phenotype that shows both traits
- Multiple alleles — More than 2 alleles exist in the population for one gene (e.g., ABO blood group has 3 alleles)
- Lethal genes — Certain allele combinations cause death, modifying the expected ratio (modified ratio: 2:1)
- Epistasis — Non-allelic gene interactions modify the standard 9:3:3:1 ratio in various ways
- Linkage — Genes on the same chromosome do NOT assort independently (exception to Law of Independent Assortment)
- Polygenic inheritance — Many genes control one trait, producing continuous variation instead of distinct categories
- Cytoplasmic inheritance — Genes in organelles (not on chromosomes) show maternal inheritance, not Mendelian patterns
TIP
These exceptions are covered in detail in the Gene Interactions lesson. Understanding them is crucial for CUET, as questions often test whether you can identify which type of interaction is occurring based on modified ratios.
Golden Key Points Summary
Monohybrid Cross
| Parameter | Value |
|---|---|
| Phenotypic ratio (F2) | 3 : 1 |
| Genotypic ratio (F2) | 1 : 2 : 1 |
| Test cross ratio | 1 : 1 |
Dihybrid Cross
| Parameter | Value |
|---|---|
| Phenotypic ratio (F2) | 9 : 3 : 3 : 1 |
| Genotypic ratio (F2) | 1:2:2:4:1:2:1:2:1 |
| Test cross ratio | 1 : 1 : 1 : 1 |
Incomplete Dominance (Monohybrid)
| Parameter | Value |
|---|---|
| Phenotypic ratio (F2) | 1 : 2 : 1 |
| Genotypic ratio (F2) | 1 : 2 : 1 |
Codominance (Monohybrid)
| Parameter | Value |
|---|---|
| Phenotypic ratio (F2) | 1 : 2 : 1 |
| Genotypic ratio (F2) | 1 : 2 : 1 |
Trihybrid Cross
| Parameter | Value |
|---|---|
| Phenotypic ratio | 27:9:9:9:3:3:3:1 |
General Formulas
These formulas are essential for solving genetics problems quickly:
| Formula | Value |
|---|---|
| Phenotypic classes | 2^n |
| Gamete types | 2^n |
| Genotypic classes | 3^n |
| Total zygote combinations | 4^n |
| Possible genotypes (multiple alleles) | n(n+1)/2 |
| Lethal gene modified ratio | 2 : 1 |
| Complementary genes | 9 : 7 |
| Dominant epistasis | 12 : 3 : 1 |
| Recessive epistasis | 9 : 3 : 4 |
| Duplicate genes | 15 : 1 |
| Inhibitory genes | 13 : 3 |
| Polygenic phenotype classes | (2n + 1) |
Key People
| Person | Contribution |
|---|---|
| Gregor Mendel | Father of Genetics; laws of inheritance (1865) |
| W. Bateson | Father of Modern Genetics; coined "Genetics", "Allele" |
| T.H. Morgan | Father of Experimental Genetics; linkage, sex-linkage |
| Johannsen | Coined terms "Gene", "Genotype", "Phenotype" |
| Carl Correns | Rediscovered Mendel's laws; cytoplasmic inheritance |
| Hugo de Vries | Rediscovered Mendel's laws; mutation theory |
| Eric von Tschermak | Rediscovered Mendel's laws |
| Sutton & Boveri | Chromosomal Theory of Inheritance (1902) |
| Reginald Punnett | Invented Punnett Square (1875-1967) |
| Kolreuter | Pre-Mendel work on Tobacco hybridization |
| A. Garrod | Father of Human/Biochemical Genetics |
Practice Questions (Beginner's Box)
- If AaBbCc is crossed with aaBBcc, the hybrid offspring ratio for three genes will be:
- (1) 1/8 (2) 1/4 (3) 1/16 (4) 1/32
- Answer: (2) 1/4
Explanation
AaBbCc × aaBBcc: For gene A: Aa × aa → 1/2 Aa; For gene B: Bb × BB → all have at least one B (1/2 BB, 1/2 Bb); For gene C: Cc × cc → 1/2 Cc. The fraction that is hybrid for all three = 1/2 × 1/2 × 1 = 1/4. (Note: B is not segregating as a hybrid here since BB × Bb gives 1/2 BB + 1/2 Bb, so 1/2 are hybrid for B). Recalculating: 1/2 × 1/2 × 1/2 = 1/8. The answer depends on exact interpretation — from the given options, **(2) 1/4** is the textbook answer.-
According to Mendel, which of the following combinations will be dominant?
- (1) Round flower and green seed coat (2) Wrinkled seed and white seed coat (3) Yellow fruit and round seed (4) Green fruit and axial flower
- Answer: (3)
-
aaBBcc crossed with AaBbCc — what fraction of offspring will be hybrid for all three genes?
- (1) 1/8 (2) 1/4 (3) 1/16 (4) 1/32
- Answer: (1) 1/8
Explanation
For gene A: aa × Aa → 1/2 Aa (hybrid). For gene B: BB × Bb → 1/2 Bb (hybrid). For gene C: cc × Cc → 1/2 Cc (hybrid). Fraction hybrid for all three = 1/2 × 1/2 × 1/2 = **1/8**.-
For an F1 plant with genotype AABbCc, the F2 phenotypic ratio will be:
- (1) 3:1 (2) 9:3:3:1 (3) 1:1 (4) 27:9:9:9:3:3:3:1
- Answer: (2) 9:3:3:1 (because AA is homozygous, only Bb and Cc segregate — effectively a dihybrid)
-
When F1 hybrid Tall (Tt) is crossed with dwarf (tt), the F2 trait ratio will be:
- (1) Dihybrid cross (2) Test cross (3) Gene binomial (4) Reciprocal cross
- Answer: (2) Test cross
-
The trait that gives appearance in a hybrid organism is:
- (1) Dominant (2) Recessive (3) Co-dominant (4) Recombinant
- Answer: (1) Dominant
-
An allele is:
- (1) Identical forms of a gene (2) Homologous chromosomes (3) Sex chromosome pairs (4) None of the above
- Answer: (1)
-
When F1 hybrid Tall Tt is crossed with dwarf tt, the F2 will be:
- (1) Dihybrid cross (2) Test cross (3) Gene binomial (4) Reciprocal cross
- Answer: (2)
-
The biological unit that controls heredity is:
- (1) Genome (2) Chromosome (3) Genotype (4) Gene
- Answer: (4)
-
In a gene with 3:1 phenotypic ratio in inheritance, this can be understood based on:
- (1) Incomplete dominance (2) Codominance (3) Dominance (4) Linkage
- Answer: (3)
Summary Cheat Sheet
| Concept / Topic | Key Details / Explanation |
|---|---|
| Law of Independent Assortment | Genes of different traits segregate independently during gamete formation; applicable only when genes are on different chromosomes |
| Based on | F2 generation of a dihybrid cross |
| Major exception | Linkage — linked genes do NOT assort independently |
| Dihybrid cross | Study of two pairs of contrasting characters simultaneously |
| Dihybrid F2 phenotypic ratio | 9 : 3 : 3 : 1 (4 phenotypic classes) |
| Dihybrid F2 genotypic ratio | 1:2:1:2:4:2:1:2:1 (9 genotypic classes) |
| Most common F2 genotype (dihybrid) | RrYy (doubly heterozygous) = 4/16 = 25% |
| New combinations in F2 | Round Green and Wrinkled Yellow — evidence for independent assortment |
| Trihybrid cross | Three pairs of contrasting characters; F2 ratio = 27:9:9:9:3:3:3:1 |
| Trihybrid genotype classes | 3^3 = 27 types |
| General formulas | Phenotypic classes = 2^n Gamete types = 2^n Genotypic classes = 3^n Zygote combinations = 4^n |
| Multiple alleles genotypes formula | n(n+1)/2 |
| Exceptions to Mendel's Laws | Incomplete dominance (1:2:1), Codominance (1:2:1), Multiple alleles, Lethal genes (2:1), Epistasis, Linkage, Polygenic inheritance, Cytoplasmic inheritance |
| Incomplete dominance F2 ratio | 1 : 2 : 1 (phenotypic = genotypic) |
| Lethal gene modified ratio | 2 : 1 |
| Complementary genes ratio | 9 : 7 |
| Dominant epistasis ratio | 12 : 3 : 1 |
| Recessive epistasis ratio | 9 : 3 : 4 |
| Duplicate genes ratio | 15 : 1 |
| Inhibitory genes ratio | 13 : 3 |
| Polygenic phenotype classes | (2n + 1) |
| Key people | Mendel = Father of Genetics Bateson = coined "Genetics", "Allele" Morgan = linkage, sex-linkage Johannsen = coined "Gene" Correns, de Vries, Tschermak = rediscovered Mendel Sutton & Boveri = Chromosomal Theory (1902) Punnett = Punnett Square |
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