Welcome to Genes and Patterns of Inheritance

Have you ever wondered why you have your mother's eye colour but your father's nose? Or why some conditions seem to "skip" generations or affect males more frequently than females? Genetics provides the rulebook for how traits pass from parents to offspring. Don't worry if this chapter seems daunting with all its letters and ratios—by breaking each pattern down step-by-step, you will master genetic crosses in no time!

1. Essential Genetic Vocabulary: The Building Blocks

Before drawing genetic crosses, you need to be comfortable with the core language of genetics. Think of your genome as a massive instruction library:

Gene: A length of DNA on a chromosome that codes for a particular polypeptide or characteristic (e.g., the gene for eye colour).
Allele: An alternative or different form of a gene (e.g., the allele for brown eyes vs. the allele for blue eyes).
Locus: The specific physical position of a gene on a chromosome.
Homozygous: Having two identical alleles for a particular gene (e.g., \(BB\) or \(bb\)). Homozygous organisms are described as pure-breeding or true-breeding.
Heterozygous: Having two different alleles for a particular gene (e.g., \(Bb\)).
Genotype: The genetic makeup of an organism, represented by letters (e.g., \(Aa\)).
Phenotype: The observable physical and biochemical characteristics of an organism, resulting from its genotype interacting with the environment (e.g., brown eyes, tall stem).
Dominant: An allele that is always expressed in the phenotype when present in either the homozygous or heterozygous state (represented by a capital letter, e.g., \(B\)).
Recessive: An allele that is only expressed in the phenotype when homozygous (represented by a lower-case letter, e.g., \(b\)). In a heterozygote (\(Bb\)), its effect is masked by the dominant allele.

Everyday Analogy: Think of a gene as a recipe category (e.g., "Cake Flavour") and alleles as different options of that recipe (e.g., "Chocolate" or "Vanilla"). Your genotype is what recipes you carry in your book, and your phenotype is the cake that actually gets baked!

Key Takeaway: Phenotype is what you see; Genotype is the underlying genetic combination of alleles.

2. Monohybrid Inheritance

Monohybrid inheritance refers to the inheritance of a single gene controlling one characteristic.

Constructing a Standard Monohybrid Cross

Always use a systematic layout in your exams to avoid losing marks:

1. Parental Phenotypes: Pure-breeding Tall \(\times\) Pure-breeding Dwarf
2. Parental Genotypes: \(TT \times tt\)
3. Gametes: Circle your gametes: \((T)\) and \((t)\)
4. \(F_1\) Genotype: All \(Tt\)
5. \(F_1\) Phenotype: All Tall plants

When crossing two heterozygous \(F_1\) individuals (\(Tt \times Tt\)):
Gametes: \((T), (t)\) and \((T), (t)\)
Punnett Square:
Crossing \(T\) and \(t\) gives offspring genotypes: \(1\ TT : 2\ Tt : 1\ tt\)
\(F_2\) Phenotypic Ratio: \(3\text{ Tall} : 1\text{ Dwarf}\) (or a classic \(3:1\) ratio).

The Test Cross (Backcross)

How can you determine if an individual displaying a dominant phenotype is homozygous dominant (\(TT\)) or heterozygous (\(Tt\))?
You perform a test cross by crossing the individual with a homozygous recessive individual (\(tt\)).

Outcome 1: If all offspring show the dominant phenotype, the unknown parent was homozygous dominant (\(TT\)).
Outcome 2: If approximately \(50\%\) of offspring show the dominant phenotype and \(50\%\) show the recessive phenotype (a \(1:1\) ratio), the unknown parent was heterozygous (\(Tt\)).

Key Takeaway: A cross between two heterozygotes for a single monohybrid gene yields a \(3:1\) phenotypic ratio. A test cross of a heterozygote gives a \(1:1\) ratio.

3. Codominance and Multiple Alleles

Codominance

Codominance occurs when both alleles in a heterozygote are expressed equally and contribute to the phenotype; neither allele is dominant over the other.

Example: Coat colour in shorthorn cattle.
Let \(C^R\) = allele for red hair, and \(C^W\) = allele for white hair.
Genotype \(C^R C^R\) = Red coat
Genotype \(C^W C^W\) = White coat
Genotype \(C^R C^W\) = Roan coat (a mixture of individual red and white hairs).
Crossing two roan cattle (\(C^R C^W \times C^R C^W\)) produces a phenotypic ratio of \(1\text{ Red} : 2\text{ Roan} : 1\text{ White}\) (\(1:2:1\)).

Multiple Alleles: ABO Blood Groups

A gene has multiple alleles when more than two alternative forms of that gene exist at a single locus within a population (though an individual still inherits only two alleles).

Human ABO blood groups are determined by an immunoglobulin gene \(I\) with three alleles:
1. \(I^A\) (codes for antigen A, codominant with \(I^B\))
2. \(I^B\) (codes for antigen B, codominant with \(I^A\))
3. \(I^O\) (codes for no antigen, recessive to both \(I^A\) and \(I^B\))

Genotypes and Resulting Phenotypes:
- \(I^A I^A\) or \(I^A I^O\) \(\rightarrow\) Blood Group A
- \(I^B I^B\) or \(I^B I^O\) \(\rightarrow\) Blood Group B
- \(I^A I^B\) \(\rightarrow\) Blood Group AB (demonstrates codominance)
- \(I^O I^O\) \(\rightarrow\) Blood Group O (homozygous recessive)

Key Takeaway: In codominance, the heterozygous phenotype is distinct and shows features of both alleles, giving a \(1:2:1\) ratio in the \(F_2\) generation instead of \(3:1\).

4. Dihybrid Inheritance

Dihybrid inheritance involves the simultaneous inheritance of two distinct characteristics, controlled by two different genes located on different chromosomes.

Mendel's Law of Independent Assortment

"Each member of a pair of alleles may combine randomly with either of another pair on different chromosomes during gamete formation."

This random assortment occurs during Metaphase I and Anaphase I of meiosis, when homologous pairs align independently along the equator.

Standard Dihybrid Cross

Consider seed shape (Round \(R\) dominant to Wrinkled \(r\)) and seed colour (Yellow \(Y\) dominant to Green \(y\)):
Parental cross: Pure-breeding Round Yellow (\(RRYY\)) \(\times\) Pure-breeding Wrinkled Green (\(rryy\))
\(F_1\) Generation: All \(RrYy\) (Round Yellow seeds)

When crossing two heterozygous \(F_1\) plants (\(RrYy \times RrYy\)):
Each parent produces 4 types of gametes in equal proportions: \((RY), (Ry), (rY), (ry)\).
A \(4 \times 4\) Punnett square (16 boxes) gives the classic \(F_2\) dihybrid ratio:
- \(9\) Round Yellow (dominant for both traits, \(R\_Y\_\))
- \(3\) Round Green (dominant for shape, recessive for colour, \(R\_yy\))
- \(3\) Wrinkled Yellow (recessive for shape, dominant for colour, \(rrY\_\))
- \(1\) Wrinkled Green (recessive for both traits, \(rryy\))
Ratio = \(9:3:3:1\)

Dihybrid Test Cross

Crossing a double heterozygote (\(RrYy\)) with a double homozygous recessive (\(rryy\)) yields offspring in equal proportions:
Ratio = \(1\text{ Round Yellow} : 1\text{ Round Green} : 1\text{ Wrinkled Yellow} : 1\text{ Wrinkled Green}\) (\(1:1:1:1\)).

Key Takeaway: Unlinked genes assort independently, producing a \(9:3:3:1\) phenotypic ratio when crossing double heterozygotes.

5. Sex-Linkage

Humans possess 22 pairs of autosomes and 1 pair of sex chromosomes (\(XX\) in females, \(XY\) in males). The \(Y\) chromosome is much smaller than the \(X\) chromosome and lacks many of the gene loci found on the non-homologous region of the \(X\) chromosome.

A gene is sex-linked if it is carried on one of the sex chromosomes (usually the \(X\) chromosome).

Why are Males More Vulnerable to X-Linked Recessive Conditions?

Females possess two \(X\) chromosomes (\(XX\)). If a female inherits a faulty recessive allele on one \(X\) chromosome, she will typically have a normal dominant allele on the other \(X\) to mask it. She is a phenotypically normal carrier.
Males possess only one \(X\) chromosome (\(XY\)) and are hemizygous. If a male inherits a faulty recessive allele on his single \(X\) chromosome, there is no corresponding locus on the \(Y\) chromosome to mask it. Therefore, he will express the condition.

Examples: Haemophilia and Red-Green Colour Blindness

Let \(X^H\) = normal clotting allele (dominant), and \(X^h\) = haemophilia allele (recessive):
- Carrier female: \(X^H X^h\)
- Affected male: \(X^h Y\)
- Unaffected male: \(X^H Y\)

Sample Cross: Carrier Mother (\(X^H X^h\)) \(\times\) Normal Father (\(X^H Y\))
Gametes: \((X^H), (X^h)\) and \((X^H), (Y)\)
Offspring:
- \(X^H X^H\) (Normal female)
- \(X^H X^h\) (Carrier female)
- \(X^H Y\) (Normal male)
- \(X^h Y\) (Male with haemophilia)
Notice: Only males develop the condition in this cross (\(50\%\) of sons are affected), and males cannot pass an X-linked allele to their sons because they pass a \(Y\) chromosome to sons.

Key Takeaway: Sex-linked recessive conditions affect males disproportionately because males have only one \(X\) chromosome.

6. Autosomal Linkage and Crossing Over

What is Autosomal Linkage?

Autosomal linkage occurs when two or more gene loci are situated on the same autosome (non-sex chromosome). Linked genes do not assort independently during meiosis; they tend to be inherited together as a single unit because they travel together into the same gamete.

If two genes are completely linked, a cross between two heterozygotes produces a \(3:1\) ratio rather than a \(9:3:3:1\) ratio!

Crossing Over and Recombinants

During Prophase I of meiosis, homologous chromosomes pair up to form bivalents. Non-sister chromatids wrap around each other, break, and rejoin at points called chiasmata. This process is called crossing over.

Crossing over can break the linkage between two genes on the same chromosome, creating new combinations of alleles called recombinant genotypes.

Parental Phenotypes: Offspring showing the same combinations of characteristics as the original parents (present in large numbers).
Recombinant Phenotypes: Offspring showing new, mixed combinations of characteristics produced by crossing over (present in smaller numbers).

Calculating Recombination Frequency

The closer two genes are on a chromosome, the less likely crossing over will occur between them. The percentage of recombinants can be used to map distances between genes:

\(\text{Recombination Frequency (\%)} = \frac{\text{Total number of recombinant offspring}}{\text{Total number of all offspring}} \times 100\)

\(1\%\) recombination frequency is defined as \(1\text{ map unit}\) (or centimorgan) along the chromosome.

Key Takeaway: Linkage prevents independent assortment, leading to high proportions of parental phenotypes and low proportions of recombinant phenotypes.

7. Epistasis

Epistasis is the interaction between two different gene loci, where one gene alters, masks, or suppresses the phenotypic expression of a second, completely separate gene locus.

Recessive Epistasis (\(9:3:4\) Ratio)

Occurs when two copies of a recessive allele at the epistatic locus (\(ee\)) mask the expression of alleles at a hypostatic locus (e.g., \(B/b\)).

Example: Coat colour in Labrador retrievers.
- Gene 1: Pigment colour (\(B\) = black, \(b\) = brown/chocolate)
- Gene 2: Pigment deposition in fur (\(E\) = pigment deposited, \(e\) = no pigment deposited)

- \(B\_E\_\) \(\rightarrow\) Black Labrador (9/16)
- \(bbE\_\) \(\rightarrow\) Chocolate Labrador (3/16)
- \(B\_ee\) or \(bbee\) \(\rightarrow\) Yellow Labrador (4/16) (because \(ee\) prevents any pigment deposition regardless of the \(B/b\) alleles).

Dominant Epistasis (\(12:3:1\) or \(13:3\) Ratio)

Occurs when a single dominant allele at the epistatic locus (e.g., \(A\)) completely masks the expression of alleles at another locus (e.g., \(B/b\)).
- \(A\_B\_\) and \(A\_bb\) display the epistatic phenotype (\(12/16\))
- \(aaB\_\) displays the dominant hypostatic phenotype (\(3/16\))
- \(aabb\) displays the double recessive phenotype (\(1/16\))

Duplicate Recessive Epistasis / Complementary Epistasis (\(9:7\) Ratio)

Occurs when dominant alleles at both loci (\(A\) and \(B\)) are essential for the expression of a characteristic (e.g., purple flowers in sweet peas requiring two functional enzymes in a pathway).
- \(A\_B\_\) \(\rightarrow\) Functional pathway (Purple, 9/16)
- \(A\_bb\), \(aaB\_\), or \(aabb\) \(\rightarrow\) Non-functional pathway (White, 7/16)

Key Takeaway: Modified \(F_2\) dihybrid ratios (such as \(9:3:4\), \(12:3:1\), or \(9:7\)) are a telltale sign of epistasis.

8. The Chi-Squared (\(\chi^2\)) Test in Genetics

When carrying out genetic crosses, observed numbers rarely match predicted theoretical ratios exactly due to chance variation during fertilization. The chi-squared test is a statistical test used to determine whether the difference between observed (\(O\)) and expected (\(E\)) results is statistically significant or merely due to chance.

Step-by-Step Chi-Squared Calculation

Step 1: State the Null Hypothesis (\(H_0\)):
"There is no statistically significant difference between the observed and expected phenotypic ratios; any difference is due to chance alone."

Step 2: Calculate Expected Numbers:
Divide the total sample size across the expected theoretical ratio (e.g., \(3:1\) or \(9:3:3:1\)).

Step 3: Use the Chi-Squared Formula:

\(\chi^2 = \sum \frac{(O - E)^2}{E}\)

Where:
- \(\sum\) = "sum of"
- \(O\) = Observed number
- \(E\) = Expected number

Step 4: Determine the Degrees of Freedom (\(df\)):
\(df = n - 1\), where \(n\) is the number of phenotypic categories.

Step 5: Compare Calculated \(\chi^2\) with the Critical Value (at \(p = 0.05\)):
- If calculated \(\chi^2 < \text{critical value}\) (i.e., \(p \ge 0.05\)):
Accept the null hypothesis. The difference between observed and expected results is not statistically significant and is due to chance alone.
- If calculated \(\chi^2 \ge \text{critical value}\) (i.e., \(p < 0.05\)):
Reject the null hypothesis. The difference is statistically significant and not due to chance (linkage or epistasis might be occurring).

Key Takeaway: The critical significance level in biology is \(p = 0.05\) (\(5\%\) probability that results are due to chance). If \(\chi^2\) is below the critical value, our observed data fits the genetic model.

Summary of Common Genetic Ratios to Memorise

Monohybrid heterozygous cross (\(Aa \times Aa\)): \(3:1\)
Monohybrid test cross (\(Aa \times aa\)): \(1:1\)
Codominance heterozygous cross (\(C^R C^W \times C^R C^W\)): \(1:2:1\)
Dihybrid heterozygous cross (\(AaBb \times AaBb\)): \(9:3:3:1\)
Dihybrid test cross (\(AaBb \times aabb\)): \(1:1:1:1\)
Recessive epistasis (\(AaBb \times AaBb\)): \(9:3:4\)
Dominant epistasis (\(AaBb \times AaBb\)): \(12:3:1\)
Complementary gene action / Duplicate recessive epistasis: \(9:7\)

Common Pitfalls to Avoid in the Exam

- Forgetting to label crosses clearly: Always write Parental Phenotypes, Parental Genotypes, Gametes (circled), Offspring Genotypes, and Offspring Phenotypes.
- Missing sex chromosomes in sex-linkage: Remember to write alleles as superscripts on \(X\) chromosomes (e.g., \(X^H X^h\), not just \(Hh\)) and leave the \(Y\) blank (e.g., \(X^H Y\)).
- Confusing ratios: Make sure to state which number in a ratio corresponds to which phenotype (e.g., write "\(3\text{ Tall} : 1\text{ Dwarf}\)", not just "\(3:1\)").
- Degrees of freedom error: Remember that degrees of freedom is the number of phenotypic classes minus one (\(n - 1\)), not total sample size minus one.