Basic Principles of Inheritance

(a) Genotype and Phenotype

| Feature | Genotype | Phenotype |
|---|---|---|
| Definition | The genetic constitution (allelic combination) of an organism | The observable/expressed characteristics of an organism |
| Visibility | Cannot be seen directly; determined by molecular/breeding analysis | Can be observed directly (morphology, physiology, behaviour) |
| Example | $TT$, $Tt$, $tt$ | Tall, Tall, Dwarf |
| Stability | Remains constant throughout life | Can be influenced by environment |

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(b) Dominant and Recessive Characters

| Feature | Dominant Character | Recessive Character |
|---|---|---|
| Definition | The character that expresses itself in the $F_1$ hybrid (heterozygous condition) | The character that remains suppressed in the presence of the dominant allele |
| Expression | Expressed in both homozygous ($AA$) and heterozygous ($Aa$) state | Expressed only in homozygous state ($aa$) |
| Example | Tallness ($T$) in pea | Dwarfness ($t$) in pea |

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(c) Hybrid and Pure Individuals

| Feature | Hybrid Individual | Pure Individual |
|---|---|---|
| Definition | An individual produced by crossing two genetically different parents; carries two different alleles for a trait | An individual that breeds true for a trait; carries two identical alleles |
| Genotype | Heterozygous, e.g., $Tt$ | Homozygous, e.g., $TT$ or $tt$ |
| Offspring | Produces varied offspring on selfing | Produces identical offspring on selfing |

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(d) Heterozygous and Homozygous Progeny

| Feature | Heterozygous Progeny | Homozygous Progeny |
|---|---|---|
| Definition | Progeny carrying two different alleles for a gene locus | Progeny carrying two identical alleles for a gene locus |
| Genotype | e.g., $Tt$, $Aa$ | e.g., $TT$, $tt$, $AA$, $aa$ |
| Gametes produced | Two types of gametes | Only one type of gamete |
| Breeding behaviour | Does not breed true | Breeds true |

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(e) Monohybrid and Dihybrid Cross

| Feature | Monohybrid Cross | Dihybrid Cross |
|---|---|---|
| Definition | Cross between parents differing in only one pair of contrasting characters | Cross between parents differing in two pairs of contrasting characters |
| Example | $TT \times tt$ (tall $\times$ dwarf) | $TTRR \times ttrr$ (tall round $\times$ dwarf wrinkled) |
| $F_2$ Phenotypic ratio | $3:1$ | $9:3:3:1$ |
| $F_2$ Genotypic ratio | $1:2:1$ | $1:2:1:2:4:2:1:2:1$ |
| Law demonstrated | Law of Dominance and Law of Segregation | Law of Independent Assortment |

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(f) Gene and Allele

| Feature | Gene | Allele |
|---|---|---|
| Definition | A specific segment of DNA that codes for a particular protein/trait | Alternative forms of the same gene occupying the same locus on homologous chromosomes |
| Location | Occupies a specific locus on a chromosome | Present at the same locus but on homologous chromosomes |
| Example | Gene for seed colour in pea | $R$ (round) and $r$ (wrinkled) are alleles of the seed-shape gene |

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(g) Incomplete Dominance and Codominance

| Feature | Incomplete Dominance | Codominance |
|---|---|---|
| Definition | Neither allele is completely dominant; the heterozygote shows an intermediate phenotype | Both alleles are expressed simultaneously and independently in the heterozygote |
| $F_1$ Phenotype | Intermediate between two parents | Both parental phenotypes expressed together |
| $F_2$ Phenotypic ratio | $1:2:1$ (same as genotypic ratio) | $1:2:1$ (same as genotypic ratio) |
| Example | Flower colour in Antirrhinum (snapdragon): Red ($RR$) $\times$ White ($rr$) $\rightarrow$ Pink ($Rr$) | ABO blood groups: $I^A I^B$ genotype shows both A and B antigens (AB blood group) |

Given: Consider a monohybrid cross for seed shape in pea — Round ($R$, dominant) $\times$ Wrinkled ($r$, recessive).
- Pure dominant parent: $RR$
- Pure recessive parent: $rr$
- $F_1$ progeny: $Rr$ (heterozygous)

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(a) $F_1$ progeny ($Rr$) $\times$ Pure dominant parent ($RR$)

$$Rr \times RR$$

Using a Punnett square:

| | $R$ | $R$ |
|---|---|---|
| $R$ | $RR$ | $RR$ |
| $r$ | $Rr$ | $Rr$ |

Genotypic ratio: $RR : Rr = 1:1$ (i.e., $\frac{1}{2}$ homozygous dominant : $\frac{1}{2}$ heterozygous)

Phenotypic ratio: All offspring are Round = $1:0$ (100% Round)

$$\boxed{\text{Genotypic ratio} = 1:1 \quad \text{Phenotypic ratio} = \text{All Round (1:0)}}$$

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(b) $F_1$ progeny ($Rr$) $\times$ Pure recessive parent ($rr$) — This is a Test Cross

$$Rr \times rr$$

Using a Punnett square:

| | $R$ | $r$ |
|---|---|---|
| $r$ | $Rr$ | $rr$ |

Genotypic ratio: $Rr : rr = 1:1$

Phenotypic ratio: Round : Wrinkled $= 1:1$

$$\boxed{\text{Genotypic ratio} = 1:1 \quad \text{Phenotypic ratio} = 1 \text{ Round} : 1 \text{ Wrinkled}}$$

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(c) $F_1$ progeny ($Rr$) $\times$ $F_1$ progeny ($Rr$) — This gives the $F_2$ generation

$$Rr \times Rr$$

Using a Punnett square:

| | $R$ | $r$ |
|---|---|---|
| $R$ | $RR$ | $Rr$ |
| $r$ | $Rr$ | $rr$ |

Genotypic ratio: $RR : Rr : rr = 1:2:1$

Phenotypic ratio: Round ($RR + Rr$) : Wrinkled ($rr$) $= 3:1$

$$\boxed{\text{Genotypic ratio} = 1:2:1 \quad \text{Phenotypic ratio} = 3 \text{ Round} : 1 \text{ Wrinkled}}$$

Definition: A test cross is a cross between an individual showing a dominant phenotype (but of unknown genotype — either $TT$ or $Tt$) and a homozygous recessive individual ($tt$). It is used to determine whether the dominant phenotype individual is homozygous or heterozygous.

Concept: If the individual is homozygous dominant ($TT$), all offspring will show the dominant phenotype. If the individual is heterozygous ($Tt$), offspring will appear in a $1:1$ ratio of dominant to recessive phenotype.

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Case 1: Dominant parent is Homozygous ($TT$)

$$TT \times tt$$

$$\text{Gametes: } T, T \quad \times \quad t, t$$

| | $T$ | $T$ |
|---|---|---|
| $t$ | $Tt$ | $Tt$ |

- Genotypic ratio: All $Tt$ (100% heterozygous)
- Phenotypic ratio: All Tall — No recessive offspring appear
- Conclusion: Parent is homozygous dominant ($TT$)

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Case 2: Dominant parent is Heterozygous ($Tt$)

$$Tt \times tt$$

$$\text{Gametes: } T, t \quad \times \quad t, t$$

| | $T$ | $t$ |
|---|---|---|
| $t$ | $Tt$ | $tt$ |

- Genotypic ratio: $Tt : tt = 1:1$
- Phenotypic ratio: Tall : Dwarf $= 1:1$ — Recessive offspring appear
- Conclusion: Parent is heterozygous ($Tt$)

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Summary Table:

| Test Cross Result | Genotype of Dominant Parent |
|---|---|
| All offspring dominant | $TT$ (Homozygous dominant) |
| $1:1$ dominant : recessive | $Tt$ (Heterozygous) |

Significance: The test cross is a powerful tool used by geneticists to determine the genotype of an organism showing a dominant phenotype.

(a) Law of Dominance — Explained using Monohybrid Cross

Statement: When two homozygous parents differing in one pair of contrasting characters are crossed, only one character (dominant) expresses itself in the $F_1$ hybrid, while the other character (recessive) remains suppressed.

Monohybrid Cross (Seed shape in pea):

$$P: \quad RR \text{ (Round)} \times rr \text{ (Wrinkled)}$$

$$\text{Gametes: } R \quad \times \quad r$$

$$F_1: \quad Rr \text{ (Round)}$$

- In $F_1$, all plants are Round even though they carry the $r$ allele.
- $R$ (Round) is dominant over $r$ (Wrinkled).
- The recessive character (wrinkled) is suppressed in $F_1$.

Conclusion: The law of dominance states that in a heterozygote, one allele (dominant) masks the expression of the other allele (recessive).

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(b) Law of Segregation — Explained using Monohybrid Cross

Statement: The two alleles of a gene pair segregate (separate) from each other during gamete formation so that each gamete receives only one allele. The two alleles reunite at fertilisation.

Monohybrid Cross continued to $F_2$:

$$F_1 \times F_1: \quad Rr \times Rr$$

| | $R$ | $r$ |
|---|---|---|
| $R$ | $RR$ | $Rr$ |
| $r$ | $Rr$ | $rr$ |

- $F_2$ Genotypic ratio: $RR : Rr : rr = 1:2:1$
- $F_2$ Phenotypic ratio: Round : Wrinkled $= 3:1$

Explanation: In $F_1$ ($Rr$), the two alleles $R$ and $r$ segregate during meiosis. Each gamete receives either $R$ or $r$ (not both). On selfing, the recessive character (wrinkled) reappears in $F_2$ in $\frac{1}{4}$ of the offspring, proving that alleles had separated and remained intact.

Conclusion: Alleles segregate during gamete formation — this is also called the Law of Purity of Gametes.

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(c) Law of Independent Assortment — Explained using Dihybrid Cross

Statement: When two pairs of traits are combined in a hybrid, the segregation of one pair of characters is independent of the other pair of characters during gamete formation.

Dihybrid Cross (Seed shape and seed colour in pea):

- Round ($R$) dominant over Wrinkled ($r$)
- Yellow ($Y$) dominant over Green ($y$)

$$P: \quad RRYY \text{ (Round Yellow)} \times rryy \text{ (Wrinkled Green)}$$

$$F_1: \quad RrYy \text{ (Round Yellow — all dominant)}$$

$$F_1 \times F_1: \quad RrYy \times RrYy$$

$F_1$ produces 4 types of gametes: $RY$, $Ry$, $rY$, $ry$ (each with equal frequency $\frac{1}{4}$)

Punnett Square ($4 \times 4$):

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

$F_2$ Phenotypic ratio:

$$\text{Round Yellow} : \text{Round Green} : \text{Wrinkled Yellow} : \text{Wrinkled Green} = 9:3:3:1$$

- 9 Round Yellow ($R\_Y\_$)
- 3 Round Green ($R\_yy$)
- 3 Wrinkled Yellow ($rrY\_$)
- 1 Wrinkled Green ($rryy$)

Explanation: Two new combinations — Round Green and Wrinkled Yellow — appear in $F_2$ that were not present in the parents. This is possible only if the two gene pairs assort independently of each other during gamete formation.

Conclusion: The $9:3:3:1$ ratio in $F_2$ of a dihybrid cross confirms the Law of Independent Assortment.

Given:
- Let Red colour be controlled by allele $R$ (dominant) and non-red by $r$.
- Let Tall be controlled by allele $T$ (dominant) and dwarf by $t$.
- Parent 1: Red and Tall homozygous → Genotype: $RRTT$
- Parent 2: Red and Tall heterozygous → Genotype: $RrTt$

Cross:
$$RRTT \times RrTt$$

Gametes produced:
- $RRTT$ produces only one type of gamete: $RT$
- $RrTt$ produces four types of gametes: $RT$, $Rt$, $rT$, $rt$ (each with frequency $\frac{1}{4}$)

Punnett Square:

| Gametes of $RRTT$ | $RT$ (from $RrTt$) | $Rt$ (from $RrTt$) | $rT$ (from $RrTt$) | $rt$ (from $RrTt$) |
|---|---|---|---|---|
| $RT$ | $RRTT$ | $RRTt$ | $RrTT$ | $RrTt$ |

Offspring genotypes and their proportions:

| Genotype | Proportion | Phenotype |
|---|---|---|
| $RRTT$ | $\frac{1}{4}$ | Red, Tall |
| $RRTt$ | $\frac{1}{4}$ | Red, Tall |
| $RrTT$ | $\frac{1}{4}$ | Red, Tall |
| $RrTt$ | $\frac{1}{4}$ | Red, Tall |

Genotypic ratio:
$$RRTT : RRTt : RrTT : RrTt = 1:1:1:1$$

Phenotypic ratio:
All offspring are Red and Tall (since all carry at least one $R$ and one $T$ allele).

$$\boxed{\text{Genotypic ratio} = 1:1:1:1}$$
$$\boxed{\text{Phenotypic ratio} = \text{All Red and Tall} = 1 \text{ (only one phenotypic class)}}$$

Conclusion: Although four different genotypes are produced, all offspring express the same phenotype — Red and Tall — because $R$ is dominant over $r$ and $T$ is dominant over $t$.

Background:
In a normal dihybrid cross ($AaBb \times AaBb$), the expected $F_2$ phenotypic ratio is $9:3:3:1$ (when genes are on different chromosomes — independent assortment). However, when the observed ratio is $2:1:1:2$, it indicates linkage between the two genes.

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(a) How does the ratio 2:1:1:2 help in detecting linkage?

Expected ratio (no linkage): $9:3:3:1$ (total 16 combinations)

Observed ratio: $2:1:1:2$ (total 6 combinations)

Analysis:
- The ratio $2:1:1:2$ deviates significantly from the expected $9:3:3:1$ ratio.
- In the ratio $2:1:1:2$:
- The parental combinations ($AB$ and $ab$ phenotypes) appear in higher frequency (2 each).
- The recombinant combinations ($Ab$ and $aB$ phenotypes) appear in lower frequency (1 each).
- This deviation from the expected Mendelian ratio indicates that the two genes $A$ and $B$ are located on the same chromosome (linked) and do not assort independently.
- If genes were unlinked, parental and recombinant types would appear in equal frequency. The excess of parental types over recombinant types is the hallmark of linkage.
- The greater the deviation from the $9:3:3:1$ ratio (i.e., the greater the excess of parental combinations), the stronger the linkage between the two genes.

Conclusion: The appearance of parental phenotypic classes in higher proportion than recombinant classes, and the deviation from the $9:3:3:1$ ratio, is evidence of genetic linkage between the two loci.

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(b) How can the degree of linkage be determined?

The degree of linkage (or the distance between two linked genes) is measured by calculating the recombination frequency (also called crossover frequency or map distance).

Formula:
$$\text{Recombination Frequency (RF)} = \frac{\text{Number of recombinant offspring}}{\text{Total number of offspring}} \times 100\%$$

Steps:
1. Perform a test cross ($AaBb \times aabb$) to clearly identify parental and recombinant classes.
2. Count the number of offspring in each phenotypic class.
3. Identify parental types (same combination as parents) and recombinant types (new combinations).
4. Apply the formula above.

Interpretation:
- RF close to 0% → genes are very tightly linked (located very close together on the chromosome).
- RF close to 50% → genes are far apart on the chromosome (behave as if unlinked).
- 1% recombination frequency = 1 centimorgan (cM) = 1 map unit of distance on the genetic map.

In the given example:
- Ratio $2:1:1:2$ → parental types = $2+2 = 4$ parts; recombinant types = $1+1 = 2$ parts out of 6 total.
$$RF = \frac{2}{6} \times 100 = 33.3\%$$
- This indicates moderate linkage with a map distance of approximately $33.3$ cM between the two genes.

Conclusion: The degree of linkage is inversely proportional to the recombination frequency — lower recombination frequency means stronger (tighter) linkage.

Answer: No, the phenomenon of linkage is NOT absolute.

Explanation:

Linkage refers to the tendency of genes located on the same chromosome to be inherited together. However, linkage is rarely complete (absolute) in nature. This is because of the phenomenon of crossing over (recombination) that occurs during meiosis I (specifically during the pachytene stage of prophase I).

Reasons why linkage is not absolute:

1. Crossing Over: During meiosis, homologous chromosomes pair up and exchange segments at points called chiasmata. This physical exchange of chromosomal segments results in recombinant chromosomes carrying new combinations of alleles. Thus, even linked genes can be separated and appear in new combinations in the offspring.

2. Recombinant offspring: In any cross involving linked genes, a certain percentage of offspring always show recombinant phenotypes (new combinations not seen in parents). This proves that linkage is not absolute.

3. Distance-dependent: The frequency of crossing over (and hence recombination) depends on the physical distance between genes on the chromosome. Genes that are far apart on the same chromosome show higher recombination frequency (up to 50%) and may appear to assort almost independently.

4. Observations in nature: In Drosophila, Morgan and his colleagues observed that while some genes showed strong linkage, recombinant offspring were always produced in some proportion, confirming that crossing over breaks linkage.

Types of Linkage:
- Complete linkage: Genes are so close together that no crossing over occurs between them (very rare; e.g., genes in male Drosophila). Parental combinations only are produced.
- Incomplete linkage: Crossing over occurs between linked genes, producing both parental and recombinant combinations. This is the most common situation in nature.

Conclusion:
Linkage is generally incomplete in nature. The occurrence of crossing over during meiosis ensures that even genes on the same chromosome can be separated and recombined, generating genetic variation. Therefore, linkage is not an absolute phenomenon — it is a tendency, not a certainty, and is broken by recombination. This is why the recombination frequency between two linked genes is always between $0\%$ (complete linkage) and $50\%$ (independent assortment).