Difficulty: Intermediate | Prerequisites: Part 1 of these notes (Mendel's laws, Punnett squares, monohybrid and dihybrid crosses).
Sections 14.2 and 14.3 extend the basic Mendelian framework from Part 1. First, you learn the probability tools (multiplication and addition rules) that replace Punnett squares once crosses involve more than two genes. Then the chapter shows what happens when inheritance is more complex than Mendel's pea traits: alleles that are not fully dominant, genes with more than two alleles, single genes affecting multiple traits, and multiple genes shaping one trait. These extensions do not break Mendel's laws; they layer additional complexity on top of them.
The multiplication rule handles "AND" (probability of two independent events both happening = multiply them). The addition rule handles "OR" (probability of either of two mutually exclusive outcomes = add them). Beyond simple dominance, alleles can show incomplete dominance (heterozygote is intermediate), codominance (both alleles visible), or belong to a series of more than two alleles (e.g. ABO blood types). One gene can affect multiple traits (pleiotropy), one gene can mask another (epistasis), and many genes can contribute additively to a single trait (polygenic inheritance). Environment modifies phenotype on top of all of this.
Multiplication rule
The probability that two or more independent events will occur together equals the product of their individual probabilities. Use it when a problem says "AND."
Addition rule
The probability that any one of several mutually exclusive events will occur equals the sum of their individual probabilities. Use it when a problem says "OR."
Complete dominance
The heterozygote is indistinguishable from the homozygous dominant. This is the standard Mendelian pattern (e.g. Pp looks identical to PP).
Incomplete dominance
Neither allele is fully dominant; the heterozygote has an intermediate phenotype. In simple terms, think of red x white snapdragons producing pink F1 flowers. F2 ratio is 1:2:1 (phenotypic = genotypic).
Codominance
Both alleles are expressed simultaneously in the heterozygote, and both phenotypes are visible (not a blend). Think of it as "both show up, side by side." Example: MN blood group, where heterozygotes have both M and N molecules on their red blood cells.
Multiple alleles
More than two allelic forms of a gene exist in the population, though any one individual still carries only two. Example: ABO blood group has three alleles (I^A, I^B, i) producing four blood types.
Pleiotropy
One gene influences multiple phenotypic characters. In simple terms, a single gene has widespread effects. Examples: sickle-cell disease, cystic fibrosis, and the pea flower-colour gene (which also affects seed-coat colour).
Epistasis
A gene at one locus alters the phenotypic expression of a gene at a second locus. Think of it as one gene "overriding" another. Example: in Labrador retrievers, the E/e gene controls whether any pigment is deposited, masking the B/b gene that determines black vs. brown.
Polygenic inheritance
Two or more genes contribute additively to a single phenotypic character, producing a continuous range of variation. Opposite of pleiotropy. Examples: human height, skin pigmentation.
Quantitative characters
Traits that vary along a continuum in the population rather than falling into discrete categories. Usually the result of polygenic inheritance.
Multifactorial
A character influenced by both genetic and environmental factors. Most polygenic characters are multifactorial.
Probability ranges from 0 (impossible) to 1 (certain); all outcomes for an event sum to 1
Each gamete-formation event is independent, like a coin toss: previous outcomes do not affect the next
When a problem asks for the probability that event A AND event B both happen, multiply their individual probabilities
Example: the chance of two coins both landing heads = 1/2 x 1/2 = 1/4
Genetics application: for an Rr x Rr cross, the probability of an rr offspring = 1/2 (r from egg) x 1/2 (r from sperm) = 1/4
This is the same probability you get from a Punnett square, but without drawing the grid
When a problem asks for the probability that event A OR event B occurs, and the events are mutually exclusive, add their individual probabilities
Example: for an Rr x Rr cross, heterozygous offspring (Rr) can arise two ways: R from egg + r from sperm (probability 1/4), or r from egg + R from sperm (probability 1/4). Total = 1/4 + 1/4 = 1/2
For a dihybrid cross (YyRr x YyRr), treat each gene independently and use the multiplication rule to combine
Probability of YYRR = 1/4 (YY) x 1/4 (RR) = 1/16
Probability of YyRR = 1/2 (Yy) x 1/4 (RR) = 1/8
For crosses involving three or more genes, the approach scales the same way: solve each gene as a monohybrid cross, then multiply across genes
Example: PpYyRr x Ppyyrr. Work each gene separately: Pp x Pp gives 1/4 PP, 1/2 Pp, 1/4 pp. Yy x yy gives 1/2 Yy, 1/2 yy. Rr x rr gives 1/2 Rr, 1/2 rr. Then multiply the relevant probabilities for any genotype combination you need.
Complete dominance: the heterozygote looks identical to the homozygous dominant (the standard Mendelian case)
Incomplete dominance: the heterozygote shows an intermediate phenotype. Red (C^R C^R) x white (C^W C^W) snapdragons produce pink (C^R C^W) F1. The F2 ratio is 1 red : 2 pink : 1 white (1:2:1), and here the phenotypic ratio matches the genotypic ratio because each genotype is distinguishable.
Codominance: both alleles are fully expressed in the heterozygote. In the MN blood group, MM individuals have only M molecules on red blood cells, NN have only N, and MN heterozygotes display both M and N. This is distinct from incomplete dominance because the phenotype is not a blend; both products appear.
The same allele pair can show different dominance relationships depending on the level at which you observe the phenotype.
Tay-Sachs disease: at the organismal level, the Tay-Sachs allele is recessive (only homozygous individuals develop the disease). At the biochemical level, heterozygotes show intermediate enzyme activity, characteristic of incomplete dominance. At the molecular level, heterozygotes produce equal numbers of normal and dysfunctional enzyme molecules, which is codominance.
Sickle-cell disease follows the same pattern: recessive at the organismal level (two copies needed for full disease), incompletely dominant at the organismal level for mild symptoms, and codominant at the molecular level (both normal and sickle haemoglobin are made).
Dominant does not mean common. Polydactyly (extra digits) is caused by a dominant allele but occurs in only about 1 in 400 births.
Although any individual carries at most two alleles, a gene can have more than two alleles in the population
ABO blood types: three alleles (I^A, I^B, i) produce six genotypes and four phenotypes
I^A and I^B are codominant with each other (both carbohydrates appear on red blood cells in I^A I^B individuals, giving type AB)
Both I^A and I^B are dominant over i
Genotype ii = type O (neither carbohydrate present)
Most genes affect multiple phenotypic characters
Cystic fibrosis: a single defective chloride-channel gene produces thick mucus in the lungs, poor nutrient absorption in the intestines, chronic bronchitis, and other symptoms
In peas, the gene for flower colour also affects the colour of the seed coat
In epistasis, a gene at one locus alters the phenotypic expression of a gene at a different locus
Labrador retriever coat colour involves two genes:
B/b determines pigment colour: B (black) is dominant to b (brown/chocolate)
E/e determines whether pigment is deposited at all: E (deposit pigment) is dominant to e (no deposit, resulting in yellow coat)
If the dog is ee, its coat is yellow regardless of the B/b genotype
The E/e gene is said to be epistatic to the B/b gene
Cross BbEe x BbEe (two black Labs, heterozygous for both genes):
Expected ratio: 9 black : 3 chocolate : 4 yellow (a modified 9:3:3:1)
The 4 yellow category combines the 3 + 1 groups that would normally be separate in a standard dihybrid, because ee masks all pigment
Other epistatic interactions produce different modified ratios (e.g. 9:7, 12:3:1), but all are variations of 9:3:3:1
The additive effect of two or more genes on a single phenotypic character
This is the opposite of pleiotropy (one gene, many traits). Polygenic inheritance is many genes, one trait.
Human skin pigmentation: at least three genes (A, B, C) contribute additively. Each capital-letter allele adds one "unit" of darkness; lowercase alleles contribute less.
AABBCC = very dark; aabbcc = very light; AaBbCc = intermediate
Genotypes with the same total number of uppercase alleles (e.g. AaBbCc and AABbcc) produce similar phenotypes
A cross of two AaBbCc individuals yields seven phenotypic classes along a continuum
Human height: over 180 genes with nearly 700 associated genetic variants contribute
These continuous distributions are characteristic of quantitative characters
Phenotype depends on genotype and environment
For some characters (e.g. ABO blood type), the phenotypic range for a given genotype is essentially zero; environment has no effect
For polygenic characters (e.g. skin colour, height), the phenotypic range is broad: nutrition influences height, sun exposure darkens skin, exercise alters build
Characters shaped by both genetic and environmental factors are called multifactorial
Students often think incomplete dominance and codominance are the same thing. They are not. Incomplete dominance produces a blended intermediate (pink from red + white). Codominance produces both parental phenotypes simultaneously (both M and N molecules on the same red blood cell).
Students frequently confuse epistasis with dominance. Dominance is the relationship between two alleles of the same gene. Epistasis is an interaction between genes at different loci.
Students sometimes assume that polygenic inheritance means the alleles do not follow Mendel's laws. Each individual gene in a polygenic system still segregates and assorts independently; the continuous phenotype arises from the combined effects of many genes, each following standard rules.
Students often mix up pleiotropy and polygenic inheritance. Pleiotropy: one gene affects many traits. Polygenic inheritance: many genes affect one trait. They are conceptual opposites.
⚠️ Know when to use the multiplication rule vs. the addition rule, and look for the keywords "AND" and "OR" in problems.
⚠️ Be able to distinguish complete dominance, incomplete dominance, and codominance, and know the expected F2 ratios for each (3:1, 1:2:1, and 1:2:1 respectively).
⚠️ For ABO blood types, be able to determine all possible offspring genotypes and phenotypes given two parental genotypes. This is a common exam question.
⚠️ Recognise modified dihybrid ratios (e.g. 9:3:4 for Labrador coat colour) as evidence of epistasis, and be able to explain which gene is epistatic.
⚠️ Understand that Tay-Sachs can be classified as recessive, incompletely dominant, or codominant depending on whether you are looking at the organismal, biochemical, or molecular level. Exam questions often test this distinction.
True or false: The multiplication rule is used when you want the probability that one event OR another will occur. (False: that is the addition rule. The multiplication rule is for "AND.")
Fill in the blank: When red and white snapdragons showing incomplete dominance are crossed, the F1 are all ___. (Pink)
True or false: A person with blood type AB has the genotype I^A I^B. (True)
Fill in the blank: In Labrador retrievers, the phenotypic ratio from a BbEe x BbEe cross is ___. (9 black : 3 chocolate : 4 yellow)
True or false: Polygenic inheritance means one gene affects many traits. (False: that is pleiotropy. Polygenic inheritance means many genes affect one trait.)
Q: In a cross between two pink snapdragons (C^R C^W x C^R C^W), what phenotypic ratio do you expect in the offspring?
A: 1 red : 2 pink : 1 white (1:2:1). Because dominance is incomplete, each genotype has a distinct phenotype.
Q: A mother has blood type A (I^A i) and a father has blood type B (I^B i). What blood types are possible in their children?
A: Type AB (I^A I^B), type A (I^A i), type B (I^B i), and type O (ii), each with a probability of 1/4.
Q: Two black Labrador retrievers (both BbEe) are crossed. What fraction of offspring are expected to be yellow?
A: 4/16 or 1/4. Any dog that is ee will be yellow, regardless of the B locus genotype. The probability of ee from Ee x Ee is 1/4.
Q: In a cross PpYyRr x Ppyyrr, what is the probability of offspring that are ppyyRr?
A: Calculate each gene independently. Pp x Pp: probability of pp = 1/4. Yy x yy: probability of yy = 1/2. Rr x rr: probability of Rr = 1/2. Multiply: 1/4 x 1/2 x 1/2 = 1/16.
Q: Why does the phenotypic ratio equal the genotypic ratio in incomplete dominance but not in complete dominance?
A: In incomplete dominance, each genotype (homozygous dominant, heterozygous, homozygous recessive) produces a distinct phenotype, so there are three phenotypic classes matching the three genotypic classes (1:2:1). In complete dominance, the heterozygote looks the same as the homozygous dominant, collapsing two genotypic classes into one phenotypic class (3:1).
The probability rules here are the same tools you will use for pedigree analysis in Section 14.4 (covered in Part 3 of these notes) and for population genetics later in the course. Epistasis connects to gene regulation and metabolic pathways, where the product of one gene is the substrate for another. Polygenic inheritance and environmental effects on phenotype lay the groundwork for quantitative genetics and the nature-vs.-nurture discussions in evolution and ecology chapters.
Probability in genetics, multiplication rule, addition rule, product rule genetics, sum rule genetics, incomplete dominance, codominance, complete dominance, MN blood group, ABO blood type, multiple alleles, pleiotropy, pleiotropic, epistasis, epistatic gene, Labrador coat colour genetics, polygenic inheritance, quantitative characters, continuous variation, multifactorial traits, nature vs. nurture genetics, Tay-Sachs dominance levels, sickle-cell codominance, snapdragon flower colour, skin pigmentation genetics