Mendelian Inheritance

01 / UNDERSTAND & APPLY

1. Why a disappearing trait mattered

Imagine crossing two plant lines that reliably differ in one visible character. All the first-generation offspring resemble one parent for that character. If inheritance were simple blending, the other parental form might appear to have been lost. Yet that form can reappear when the first-generation plants reproduce. The crucial idea is that an inherited unit can be present without producing its corresponding visible phenotype in a particular genotype.

Mendel used pea plants with distinguishable contrasting traits, controlled pollination and true-breeding lines. A true-breeding line consistently produces offspring with the same relevant trait after self-pollination across generations. Peas allow self-pollination but can also be cross-pollinated experimentally, making parental combinations controllable. Repeated crosses and counts across generations made stable statistical patterns visible.

The parental generation is P. Their offspring form F₁, the first filial generation. Crossing or selfing appropriate F₁ plants produces F₂. Keep these labels separate from genotypes: F₁ does not always mean heterozygous, and F₂ does not inherently mean a 3:1 ratio. Those conclusions depend on the particular cross and inheritance model.

This lesson begins with a deliberately simple model: one autosomal locus, two alleles, equal segregation, random fertilization, complete dominance and equal survival of the genotypes. Later sections identify which conclusions change when those assumptions are relaxed. The original practice problems below are constructed examples, not claims about actual examination questions.

02 / UNDERSTAND & APPLY

2. Gene, allele, genotype and phenotype

A gene occupies a locus, a location on a chromosome. Alleles are alternative versions at that locus. In an ordinary diploid organism, the two homologous chromosomes carry two allele copies for an autosomal locus, one inherited from each parent. Use A and a for two alleles of the same gene, rather than treating them as two different genes.

Genotype describes the allele combination. AA and aa are homozygous; Aa is heterozygous. Phenotype is the observable or measurable expression of a character. Under complete dominance, AA and Aa share the dominant phenotype, whereas aa has the recessive phenotype. A visible dominant phenotype therefore does not uniquely identify the genotype.

Dominance describes the relationship between alleles in a heterozygote for a specified phenotype. It does not mean that an allele is more common, stronger, healthier, evolutionarily superior or guaranteed to spread. A dominant allele can be rare. A recessive allele can be common. The capital letter is a notation choice, not evidence about population frequency or biological value.

For simple pea-plant exercises, a tall allele T is often treated as completely dominant to a dwarf allele t. TT and Tt then look tall, while tt looks dwarf. This is a model for that character. Do not transfer it indiscriminately to human height, which is influenced by many genes and environmental factors.

• Locus: the genomic position being considered.
• Allele: one version at that locus.
• Genotype: the inherited allele combination.
• Phenotype: the expressed character under specified conditions.
• Homozygote: two matching alleles; heterozygote: two different alleles.

03 / UNDERSTAND & APPLY

3. Segregation: one allele per gamete

The law of segregation states that the two alleles at a locus separate during gamete formation, so a normal gamete receives one allele. In the simple Mendelian model, an Aa individual produces A-bearing and a-bearing gametes with probabilities 1/2 and 1/2. An AA individual produces only A-bearing gametes for this locus. The alleles remain distinct; they do not permanently blend inside the heterozygote.

The chromosome-level explanation connects this rule to meiosis: homologous chromosomes separate during meiosis I, and meiosis ultimately produces haploid gametes. A Punnett square places the possible gametes from one parent along one edge and those from the other along the second edge. Each cell combines one gamete from each parent. It represents a possible fertilization outcome, not a fixed order of births or seeds.

Crossing AA with aa produces only Aa offspring. Selfing or crossing these Aa offspring gives AA, Aa, Aa and aa as four equally likely combinations. The two heterozygous cells have the same genotype but arise from two different parental allele routes. Thus genotype probabilities are 1/4 AA, 1/2 Aa and 1/4 aa. Under complete dominance, grouping AA and Aa yields the familiar 3:1 phenotype expectation.

04 / UNDERSTAND & APPLY

4. A test cross reveals a hidden genotype

A dominant-looking individual could be AA or Aa. A test cross pairs it with a homozygous recessive individual, aa. The recessive tester always contributes a, so each offspring directly reveals which allele came from the unknown parent. AA × aa produces only Aa. Aa × aa produces Aa and aa with equal expected probabilities.

If even one genuine recessive offspring appears under the simple model, the dominant parent must carry a recessive allele and is therefore heterozygous. The reverse inference requires more care: seeing only dominant offspring in a finite sample does not prove AA. An Aa parent could, by chance, contribute A in every observed fertilization.

A backcross crosses an offspring to a parental genotype or line. A test cross is defined by the homozygous recessive tester. A cross can be both, but the terms are not identical. In a textbook AA × aa cross, crossing the Aa F₁ back to aa is both a backcross and a test cross; crossing it to AA is a backcross but not a test cross.

05 / UNDERSTAND & APPLY

5. Two loci and independent assortment

Segregation concerns the separation of the two alleles at one locus. Independent assortment concerns how allele separation at one locus relates to allele separation at another. For independently assorting A/a and B/b loci, an AaBb individual produces AB, Ab, aB and ab gametes, each with probability 1/4. The probability of AB is P(A) × P(B) = 1/2 × 1/2.

Different homologous chromosome pairs orient independently during meiosis I. Genes on different chromosomes therefore generally follow independent assortment. Genes on the same chromosome can be linked: parental allele combinations may occur more often than recombinant combinations. Widely separated loci on one chromosome can show an observed recombination fraction close to 50% and behave approximately as unlinked loci. Never assume four equal gamete types merely because the genotype is AaBb.

For AaBb × AaBb with independent assortment and complete dominance at both loci, solve each locus separately. At A, the phenotype probabilities are 3/4 A– and 1/4 aa; at B, they are 3/4 B– and 1/4 bb. Multiply the appropriate pairs to get 9/16 A–B–, 3/16 A–bb, 3/16 aaB– and 1/16 aabb. The dash means the second allele is unspecified, not absent.

The resulting 9:3:3:1 phenotype ratio also assumes the phenotypic categories remain distinguishable and there is no gene interaction that changes their grouping. Linkage, epistasis, incomplete dominance or unequal survival can alter observed phenotype ratios. A ratio is the consequence of a model, not a password to apply whenever two traits appear.

06 / UNDERSTAND & APPLY

6. Probability tools that replace giant grids

Use the product rule for independent requirements that must all occur. Use the sum rule for mutually exclusive alternatives: an offspring cannot be AA and Aa simultaneously, so their probabilities can be added to obtain a dominant phenotype. If alternatives overlap, adding them without subtracting the overlap double-counts outcomes.

Use the complement rule for “at least one” questions. It is usually easier to calculate the probability of no recessive offspring and subtract from one. For a specified sequence, multiply probabilities in that sequence. For a specified number in any order, also count the possible orders. Exactly two recessive offspring among four can occur in six positions, not just one.

Conditional probability changes the sample space. In Aa × Aa, the probability of Aa among all offspring is 1/2. Among only the dominant-phenotype offspring, aa has already been excluded. The remaining possibilities have weights AA:Aa = 1:2, so the conditional probability of Aa is 2/3. This distinction commonly separates a correct solution from a plausible-looking one.

07 / UNDERSTAND & APPLY

7. Expected ratios are not promises

An expected 3:1 ratio does not mean every group of four offspring contains exactly three dominant and one recessive individual. Each fertilization is a new random event under the model. Four dominant offspring in a row do not force the next offspring to be recessive. Its probability remains 1/4 when the parental genotypes and assumptions remain unchanged.

Expected counts are sample size multiplied by probability. For 200 offspring from Aa × Aa, the expected number of aa individuals is 200 × 1/4 = 50. The actual count may differ. Larger samples generally show smaller relative random deviations, although exact agreement is never guaranteed. Small deviations alone do not establish linkage, mutation or an incorrect cross.

When interpreting an unusual result, separate prediction from explanation. First verify the proposed genotypes and the assumptions about segregation, dominance, independence and survival. Then consider sample size and sampling variability. Formal goodness-of-fit testing can evaluate departures, but it does not replace a coherent biological model.

08 / UNDERSTAND & APPLY

8. What changes beyond complete dominance?

In incomplete dominance, the heterozygote has a distinguishable intermediate phenotype. A heterozygote self-cross still segregates genotypes in a 1:2:1 expectation, but now the three genotypes also correspond to three phenotype categories, so the phenotype expectation is 1:2:1. The alleles have not blended permanently: the two homozygous forms can reappear.

In codominance, both allele-associated products or features are expressed in the heterozygote. The human ABO system illustrates codominance of Iᴬ and Iᴮ and the existence of multiple alleles in a population. An ordinary diploid individual still carries only two ABO alleles, even though the population has more than two alternatives. Dominance relationships must be specified for the allele pair under consideration.

Linkage changes joint transmission probabilities at different loci; it does not erase the distinction between the two alleles at a single locus. Epistasis changes how different genes combine to produce a phenotype. Polygenic inheritance involves contributions from multiple loci, often alongside environmental effects. Sex-linked inheritance requires tracking the relevant sex chromosomes rather than automatically applying an autosomal square.

These extensions do not make the basic method useless. Continue to identify gametes and their probabilities, combine them and map genotypes to phenotypes. What changes is the probability model or the phenotype mapping. For the present lesson, master the autosomal two-allele model and recognize explicit signals that a richer model is needed.

09 / UNDERSTAND & APPLY

9. Original practice with explanatory solutions

Write the parental genotypes and gamete probabilities before answering. Unless a question says otherwise, assume autosomal loci, complete dominance, equal segregation, random fertilization, independent offspring and equal survival. For multilocus questions, independent assortment is stated explicitly.

Suggested practice: try these nine questions in 15 minutes before checking the solutions. This is a study recommendation, not official exam timing. For every error, rewrite the parental genotypes, gamete probabilities and assumptions, then retry the question without notes the next day.