Difficulty: Introductory to Intermediate | Prerequisites: Cell cycle notes, basic understanding of DNA and chromosomes
Genetics is the study of how traits are inherited from one generation to the next. This topic builds directly on the cell cycle: meiosis is the mechanism that produces gametes, and the way chromosomes behave during meiosis determines how alleles are passed to offspring.
You will need to be comfortable with dominant and recessive alleles, how to set up Punnett squares, and the difference between genotype and phenotype. This unit also introduces statistical testing (the chi-squared test) as a way to determine whether observed data fit a predicted inheritance model.
If you are not yet solid on meiosis, homologous chromosomes, and independent assortment, review the cell cycle notes first.
Traits are inherited through alleles that follow predictable patterns: complete dominance, incomplete dominance, codominance, and X-linked inheritance. Punnett squares predict offspring ratios, and the chi-squared test tells you whether real data match those predictions. Pedigrees let you work backwards from a family's phenotypes to figure out the inheritance pattern.
Allele
One of two or more versions of a gene. Each parent contributes one allele for each gene. Think of alleles as different "flavours" of the same gene.
Genotype
The combination of alleles an organism carries for a particular gene (e.g. AA, Aa, aa). This is the genetic recipe.
Phenotype
The observable physical trait that results from the genotype (e.g. smooth seeds, wrinkled seeds). This is what you can see.
Homozygous
Having two identical alleles for a gene (AA or aa). In simple terms, both copies match.
Heterozygous
Having two different alleles for a gene (Aa). The organism carries one dominant and one recessive allele.
Complete dominance
An inheritance pattern where the dominant allele completely masks the recessive allele in heterozygotes. The heterozygote looks identical to the homozygous dominant.
Incomplete dominance
An inheritance pattern where the heterozygote shows a blended or intermediate phenotype. For example, a white-furred rabbit crossed with a black-furred rabbit produces grey offspring.
Codominance
An inheritance pattern where both alleles are fully expressed in the heterozygote. Neither masks the other. For example, a red and white flower producing red-and-white spotted offspring (not pink).
X-linked (sex-linked) trait
A trait whose gene is located on the X chromosome. Males (XY) have only one copy of X-linked genes, so a single recessive allele will produce the phenotype.
Punnett square
A grid used to predict the genotypes and phenotypes of offspring from a genetic cross.
Monohybrid cross
A cross examining the inheritance of a single gene.
Dihybrid cross
A cross examining two genes simultaneously. When the genes are on different chromosomes and assort independently, expected phenotypic ratios in F2 are 9:3:3:1.
Chi-squared (X²) test
A statistical test that compares observed data to expected data to determine whether any differences are due to chance or to a real biological effect. If X² is small (p > 0.05), the data fit the expected model.
Null hypothesis
The default assumption in a chi-squared test, typically that the genes are unlinked and assorting independently.
Degrees of freedom
The number of categories minus one. For a monohybrid cross with two phenotype classes, df = 1. For a dihybrid with four classes, df = 3.
Linked genes
Genes located close together on the same chromosome that tend to be inherited together, deviating from independent assortment.
Pedigree
A diagram showing the inheritance of a trait through multiple generations of a family. Squares represent males, circles represent females, and filled shapes indicate individuals expressing the trait.
Autosomal dominant
An inheritance pattern where the trait appears in every generation and an affected individual needs only one copy of the allele. Unaffected parents cannot have affected children (unless a new mutation occurs).
Monohybrid crosses and the 3:1 ratio
When two heterozygous parents (Aa x Aa) are crossed, the expected phenotypic ratio is 3 dominant : 1 recessive.
Example: in peas, smooth seeds (S) are dominant over wrinkled seeds (s). Cross Ss x Ss and you expect 3/4 smooth, 1/4 wrinkled.
When a cross yields all dominant offspring
If a single-trait cross produces offspring that all show the dominant phenotype, the parent with the dominant phenotype was homozygous (AA), not heterozygous.
A heterozygous parent crossed with a recessive parent (Aa x aa) would yield a 1:1 ratio, not all dominant.
Incomplete dominance
The heterozygote displays a phenotype intermediate between the two homozygotes.
Classic example: white-furred rabbit x black-furred rabbit produces grey offspring. Neither allele fully masks the other.
Codominance
Both alleles are fully and separately expressed in the heterozygote.
Distinct from incomplete dominance: codominance produces a "both visible" phenotype (spots, patches, both proteins), not a blend.
Dihybrid crosses and the 9:3:3:1 ratio
When two genes on different chromosomes are considered together and both parents are heterozygous for both (AaBb x AaBb), the expected phenotypic ratio is 9:3:3:1.
9/16 show both dominant traits
3/16 show dominant for gene A, recessive for gene B
3/16 show recessive for gene A, dominant for gene B
1/16 show both recessive traits
Calculating specific fractions from a dihybrid cross
To find the expected fraction for any one phenotype combination, multiply the individual probabilities. For example, the probability of normal wings (dominant, 3/4) and yellow body (recessive, 1/4) = 3/4 x 1/4 = 3/16.
X-linked recessive inheritance
The gene sits on the X chromosome. Males (XY) have only one X, so a single recessive allele is enough to express the trait.
If a female is homozygous recessive for an X-linked trait (XᵃXᵃ), all of her sons will have the trait. She passes one X to each child; sons get her X (carrying the recessive allele) and a Y from their father.
Carrier females (XᴬXᵃ) have a 50% chance of passing the recessive allele to each son.
Reading pedigrees
A pedigree uses standard symbols: squares for males, circles for females, filled shapes for affected individuals, horizontal lines for mating pairs, and vertical lines for offspring.
Identifying autosomal dominant inheritance from a pedigree
The trait appears in every generation (no skipping).
Affected individuals have at least one affected parent.
Unaffected individuals are homozygous recessive (aa).
Affected individuals who have unaffected children must be heterozygous (Aa), because they can pass on the recessive allele.
Worked example from the practice exam
In the pedigree provided, the trait appears in every generation and affected individuals always have at least one affected parent. This points to autosomal dominant inheritance.
Individual 1 (affected female): Aa
Individual 2 (unaffected male): aa
Individual 6 (unaffected female): aa
Individual 7 (affected male): Aa
Individual 7 must be Aa rather than AA, because some of his children (individuals 9 and 11) are unaffected.
What the chi-squared test does
It compares observed offspring counts to the counts you would expect under a particular genetic model (e.g. a 9:3:3:1 ratio). The result tells you whether any discrepancy is small enough to be due to random chance or large enough to suggest something else is going on (such as gene linkage).
How to run the test
State the null hypothesis (typically: the genes assort independently and follow the expected ratio).
Calculate expected values from the total number of offspring and the predicted ratio.
For each phenotype class, compute (observed - expected)² / expected.
Sum those values to get X².
Determine degrees of freedom: number of phenotype classes minus 1.
Compare X² to the critical value at p = 0.05.
Interpreting the result
If X² is less than the critical value (p > 0.05): fail to reject the null hypothesis. The data fit the expected ratio, and any difference is likely due to chance. The genes are unlinked.
If X² is greater than the critical value (p < 0.05): reject the null hypothesis. The data do not fit the expected ratio, suggesting something beyond chance (e.g. the genes are linked).
Worked example 1: dihybrid cross (insect wing size and body colour)
Two heterozygous insects (Wing+ WingS ; Body+ BodyY) are crossed. Expected 9:3:3:1 ratio from 100 offspring: 56.25, 18.75, 18.75, 6.25.
X² = 0.1878 + 0.1633 + 0.5633 + 0.49 = 1.40
Degrees of freedom = 3
Critical value at p = 0.05 with 3 df = 7.815
1.40 < 7.815, so we fail to reject the null hypothesis. The genes are unlinked.
Worked example 2: monohybrid cross (pea seed texture)
Smooth (dominant) x wrinkled (recessive), F2 data: 5474 smooth, 1850 wrinkled. Expected 3:1 ratio from 7324 total: 5493 smooth, 1831 wrinkled.
X² = 0.07 + 0.20 = 0.27
Degrees of freedom = 1
Critical value at p = 0.05 with 1 df = 3.841
0.27 < 3.841, so we fail to reject the null hypothesis. The observed ratio fits the expected 3:1, and the difference is due to random chance.
Students often confuse incomplete dominance with codominance. Incomplete dominance produces a blend (grey from black + white). Codominance produces a "both at once" phenotype (red spots and white spots on the same flower, not pink).
Students assume that if a cross yields all dominant offspring, the dominant parent must be heterozygous. The opposite is true: all-dominant offspring from a single-trait cross indicate the dominant parent was homozygous.
"Fail to reject the null hypothesis" does not mean the null is proven true. It means the data are consistent with it; the difference could be due to chance.
Students sometimes think X-linked recessive means only males can have the trait. Females can express it too, but they need two copies of the recessive allele (one on each X), which is less common.
⚠️ Know how to set up and interpret a chi-squared test from start to finish: null hypothesis, expected values, the formula, degrees of freedom, and what "fail to reject" means in plain language.
⚠️ Be able to distinguish incomplete dominance from codominance from a description of offspring phenotypes.
⚠️ Understand X-linked inheritance well enough to predict what fraction of sons or daughters will express a recessive trait, given the mother's genotype.
⚠️ Be able to read a pedigree, identify the inheritance pattern (autosomal dominant, autosomal recessive, X-linked), and assign genotypes to specific individuals.
⚠️ Know how to calculate expected fractions from a dihybrid cross by multiplying individual gene probabilities (e.g. 3/4 x 1/4 = 3/16).
True or false: In incomplete dominance, the heterozygote looks identical to the homozygous dominant. (False. The heterozygote shows an intermediate phenotype.)
Fill in the blank: If a female is homozygous recessive for an X-linked trait, ________% of her sons will express the trait. (100%)
True or false: A chi-squared value below the critical value means you reject the null hypothesis. (False. You fail to reject it; the data fit the expected model.)
Fill in the blank: In a dihybrid cross of two double heterozygotes, the expected phenotypic ratio is ________. (9:3:3:1)
True or false: In an autosomal dominant pedigree, two unaffected parents can produce affected offspring. (False. At least one parent must carry the dominant allele to pass it on.)
Q: A white-furred rabbit is crossed with a black-furred rabbit and all offspring are grey. What type of dominance is this?
A: Incomplete dominance. The heterozygote shows an intermediate phenotype (grey) rather than matching either parent.
Q: If a female has a recessive X-linked trait, what can you say about her sons?
A: All of her sons will have the trait. She can only pass an X chromosome carrying the recessive allele to her sons, and they have no second X to mask it.
Q: Two insects heterozygous for wing size and body colour (both on different chromosomes) are crossed. What fraction of offspring will have normal wings and a yellow body?
A: 3/16. Normal wings (dominant) = 3/4 probability. Yellow body (recessive) = 1/4 probability. Multiply: 3/4 x 1/4 = 3/16.
Q: You perform a chi-squared test on dihybrid cross data and get X² = 1.40 with 3 degrees of freedom. The critical value is 7.815. What do you conclude?
A: You fail to reject the null hypothesis. The observed data fit the expected 9:3:3:1 ratio, and the difference between observed and expected is small enough to be due to chance. The genes are unlinked.
Q: In a pedigree, the trait appears in every generation and affected individuals always have at least one affected parent. What is the inheritance pattern?
A: Autosomal dominant. The trait does not skip generations, and unaffected individuals are homozygous recessive.
Q: When a single-trait cross yields offspring that all have the dominant phenotype, was the dominant parent homozygous or heterozygous?
A: Homozygous dominant. If the dominant parent were heterozygous (Aa x aa), roughly half the offspring would show the recessive phenotype.
This material ties back to the cell cycle: meiosis (crossing over, independent assortment) is the engine that generates the genetic variation Mendel's laws describe. Understanding how chromosomes separate during meiosis I and II makes inheritance patterns far easier to predict.
Chi-squared analysis also connects to broader scientific reasoning and experimental design. The same statistical logic (null hypothesis, expected vs observed, p-values) appears across biology whenever you need to test whether data fit a model.
Mendelian genetics, inheritance patterns, alleles, genotype, phenotype, homozygous, heterozygous, dominant, recessive, Punnett square, monohybrid cross, dihybrid cross, 9:3:3:1 ratio, 3:1 ratio, complete dominance, incomplete dominance, codominance, blending inheritance, X-linked recessive, sex-linked traits, carrier female, pedigree analysis, autosomal dominant, autosomal recessive, chi-squared test, chi-square, goodness of fit, null hypothesis, degrees of freedom, p-value, linked genes, unlinked genes, independent assortment, F1 generation, F2 generation, P generation, test cross