CH3: ndependent Assortment of Genes; Probability; Chi-square

How can you simplify a dihybrid cross?

1. they are essentially two monohybrid crosses, so seperate them into two events.

ex: if 120 offspring are produced, how many will be heterozygous for both genes? (AaxAa, BbxBb = AaBbxAaBb)

1. 50% Aa, 50% Bb, so 0.5 × 0.5 Bb = 0.25 × 120 = 30AaBb

tip to solve: AaBbCcDdEeFf is selfed; what is the probability of an offspring having the genotype AAbbCcDdeeFf?

1. for homo dom = ¼

2. hetero = ½

3. for homo recessive - 1/4

Product Rule

Multiply the probability outcomes of each independent event.
→ The probability of events occurring together = the product of their individual probabilities.
→ Multiply outcomes together.

Sum Rule

Add up the probabilities of mutually exclusive (“either/or”) events.
→ Used when the question says “either this or that.”
→ The probability of one or another event = the sum of their probabilities.

Polygenic Trait

A trait influenced by many genes.
→ Multiple gene products can contribute to one observable phenotype.
→ Produces continuously varying (quantitative) traits.
→ Caused by additive effects — each gene adds to the outcome.

ex: skin color, height, cancers, type 2 diabetes

Pleiotropic Gene

A single gene that influences many different traits.
→ One gene affects multiple phenotypic expressions.
Examples: schizophrenia, sickle cell anemia, Marfan syndrome.

Continuous Trait

A quantitative trait that varies gradually across a range.
→ Shows continuous variation (no clear categories).

Discrete Trait

A qualitative trait with clear “either/or” categories.
→ Shows distinct phenotypes, not blended.
Examples: Mendel’s peas — yellow or green, smooth or wrinkled.
→ In dominance/recessiveness, heterozygotes do not blend — they show the dominant phenotype.

What is incomplete dominance?

A type of inheritance where the heterozygote shows an intermediate phenotype between the two homozygotes.
→ Also called semi-dominance.
→ Caused by dose-dependent gene expression — one functional allele makes less product than two.

What is a null allele?

A mutant loss-of-function (LOF) allele that does not produce functional product.
→ In incomplete dominance, having one null allele reduces pigment (pink instead of red).

What’s the F₂ ratio in incomplete dominance?

1:2:1 — one red : two pink : one white
→ Typical for a monogenic cross with incomplete dominance.

Why is the heterozygote NOT a “blend”?

It only appears blended because of reduced gene dosage (less pigment produced).
The alleles themselves remain distinct — they don’t merge or mix, so it’s not true blending inheritance.

‘Overdominance’

’ is another heterozygous condition in which a heterozygote has an advantage over either homozygous condition

Linkage

occurs if genes are found close to one another on the same chromosome

Do all genes follow Mendelian inheritance?

No — not all genes assort independently.
→ Independent assortment can fail when genes are linked (found close together on the same chromosome).

Why does linkage reduce independent assortment?

→ The DNA between them is less likely to be broken during crossing over in Prophase I of Meiosis I.
→ (DNA breaks are caused by the enzyme SPO11.)

Why did Mendel’s peas follow independent assortment?

Mendel’s pea genes were on separate chromosomes or far apart on the same one,
→ So crossing over could easily occur, producing new combinations and novel phenotypes.

What is a centiMorgan (cM) or Map Unit (MU)?

A unit of genetic distance.
→ 1 cM = 1% recombination frequency
→ The recombinant offspring reveal the distance between genes.

How is a gene map made?

By using F₂ data from a test cross to calculate recombination frequencies.
→ Requires a dihybrid heterozygote test-crossed with a double recessive:
AaBb × aabb

What happens during a digenic cross when alleles segregate into gametes?

During meiosis, a heterozygote like AaBb forms haploid gametes that can carry different combinations of alleles depending on whether genes assort independently or are linked.

What gametes form if genes assort independently?

If genes are unlinked, the heterozygote AaBb produces four equal gametes:
→ AB, Ab, aB, ab
Each type = ¼ of gametes.
This happens when genes are on different chromosomes or far apart on the same one.

What is gene linkage?

Linkage occurs when two genes are located close together on the same chromosome.
→ This interferes with independent assortment because crossing over is less likely to occur between them. (less likely to get recombination bc of this)

What happens in a dihybrid test cross with complete linkage?

If genes are completely linked, the heterozygote AaBb produces only two gamete types:
→ AB and ab
Because there’s no space between a and b for SPO11 to cut the DNA, no crossing over occurs.
→ The alleles are inherited as a single unit.

What happens in partial linkage?

When genes are moderately close, some crossing over occurs.
→ Produces mostly parental (nonrecombinant) gametes (AB, ab)
→ Plus some recombinant gametes (Ab, aB)
Recombinant frequency reveals how far apart the genes are on the chromosome.