Unit 5 Heredity: Learning Mendelian Genetics from First Principles

Genes, Alleles, and What “Mendelian” Means

Mendelian genetics is the set of rules that predicts how traits are inherited when a trait is mainly controlled by a single gene and that gene’s alleles follow simple patterns during sexual reproduction. The power of Mendel’s work is that it links something you can observe (phenotypes like purple vs. white flowers) to something you can’t directly see (how versions of a gene are carried and separated into gametes).

To understand Mendelian problems, you need a clear picture of what’s being “tracked” from parents to offspring.

Genes, loci, alleles, and homologous chromosomes

A gene is a region of DNA that influences a trait (often by coding for a protein or functional RNA). A gene sits at a particular physical position on a chromosome called its locus.

In diploid organisms (like humans and pea plants), most cells have two copies of each chromosome—one from each parent. The matching pair are homologous chromosomes. Because homologous chromosomes carry the same genes at the same loci, you typically have two copies of each gene in your body cells.

An allele is a version of a gene. For a given gene, you might carry two identical alleles or two different alleles.

• If both alleles are the same, you are homozygous for that gene.
• If the alleles differ, you are heterozygous.

This matters because Mendelian genetics is mostly about what happens to those two alleles when an organism makes gametes and then when fertilization recombines alleles from two parents.

Genotype vs. phenotype (and why they can differ)

Your genotype is the allele combination you carry for a gene (for example, two “purple” alleles, or one purple and one white). Your phenotype is the physical/physiological expression of the trait (for example, purple flowers).

A key Mendelian idea is dominance:

• A dominant allele is one whose trait shows up in the phenotype of a heterozygote.
• A recessive allele is masked in a heterozygote and only shows in the phenotype if the organism has two recessive alleles.

Important: “Dominant” does not mean “more common,” “better,” or “stronger.” Dominance is purely about the heterozygote’s phenotype.

How Mendelian genetics connects to meiosis

Mendel didn’t know about chromosomes, but his ratios make sense because of meiosis, the cell division that produces haploid gametes.

• Body cells are typically diploid (two alleles per gene).
• Gametes (sperm/eggs) are haploid (one allele per gene).

The entire logic of Mendelian genetics rests on this: meiosis separates allele pairs into different gametes, and fertilization randomly brings two gametes together.

Example: translating biology into symbols

Suppose a gene has two alleles, A and a.

• Genotypes: AA, Aa, aa
• If A is dominant, then AA and Aa share the same phenotype, while aa shows the recessive phenotype.

A common mistake is thinking that a heterozygote is “half dominant and half recessive.” In complete dominance, heterozygotes show the dominant phenotype (even though they still carry the recessive allele).

Exam Focus

• Typical question patterns:
  • Interpret allele notation and infer possible genotypes from a phenotype.
  • Connect meiosis/fertilization to why offspring inherit two alleles per gene.
  • Identify whether a description is genotype-level or phenotype-level.
• Common mistakes:
  • Treating “dominant” as “most common” rather than “expressed in heterozygotes.”
  • Mixing up homozygous vs. heterozygous when reading allele pairs.
  • Forgetting that gametes carry only one allele per gene.

Mendel’s Laws: Segregation and Independent Assortment

Mendel’s big contribution was recognizing predictable patterns in inheritance and expressing them as general “laws.” These laws still matter because they are the baseline model: when data don’t match Mendelian predictions, you have a clue that something else is happening (linkage, sex-linkage, multiple genes, etc.).

Law of Segregation (why each gamete gets one allele)

The Law of Segregation states that an organism’s two alleles for a gene separate during gamete formation, so each gamete receives only one allele.

Mechanism (how it actually happens):

• During meiosis, homologous chromosomes separate (specifically in meiosis I).
• If the alleles of a gene are on homologous chromosomes, then when homologs separate, the two alleles are “segregated” into different gametes.

Why it matters: segregation explains why recessive traits can “disappear” in one generation and reappear in the next. A recessive allele can be hidden in heterozygotes and then show up when two carriers produce offspring.

Quick worked reasoning: why a heterozygote makes two gamete types

If an individual is Aa, segregation means:

• Half the gametes carry A
• Half the gametes carry a

It’s tempting to think meiosis “chooses” the dominant allele more often—Mendelian inheritance assumes segregation is equally likely.

Law of Independent Assortment (when two genes don’t affect each other)

The Law of Independent Assortment says that alleles of different genes assort independently into gametes—meaning the allele you get for gene 1 does not influence which allele you get for gene 2.

Mechanism: during meiosis I, homologous chromosome pairs line up independently of other homologous pairs. This random orientation can produce different combinations of maternal and paternal chromosomes in gametes.

Critical condition: independent assortment holds best when the genes are on different chromosomes (or far apart on the same chromosome such that crossing over makes them behave approximately independently). If genes are close together on the same chromosome, they tend to be inherited together (genetic linkage), which is a classic way Mendelian predictions can fail.

Showing independent assortment in a dihybrid

Consider genotype AaBb, where the gene with alleles A/a is independent of the gene with alleles B/b. Segregation and independent assortment together predict four equally likely gamete types:

• AB, Ab, aB, ab

Each type is expected at 25% if the genes assort independently.

A common misconception is that a dihybrid produces only two gamete types (like AB and ab). That would be true only if the genes were completely linked and no recombination occurred (not the Mendelian independent assortment assumption).

Exam Focus

• Typical question patterns:
  • Explain (in words) how meiosis I produces segregation and independent assortment.
  • Predict gamete types and frequencies from a genotype like AaBb.
  • Decide whether independent assortment should apply given information about gene location/linkage.
• Common mistakes:
  • Applying independent assortment to genes that are stated (or implied) to be linked.
  • Confusing “alleles segregate” (one gene) with “genes assort independently” (two genes).
  • Forgetting that independent assortment is about gamete formation, not fertilization.

Predicting Inheritance with Punnett Squares and Probability

Mendelian genetics problems are really probability problems wrapped in biology. Your job is to model two steps:
1) Which gametes each parent can produce (based on segregation and assortment)
2) Which zygotes form when gametes combine at fertilization

Punnett squares: what they do (and what they don’t)

A Punnett square is a grid that lists possible gamete types from each parent and shows all possible allele combinations in offspring.

Why it matters: it helps you move from parental genotypes to predicted offspring genotypes/phenotypes.

What can go wrong: Punnett squares do not “guarantee” outcomes for a small family. They predict expected proportions over many offspring (or many matings). If a couple has four children, you should not expect their children to come out in a perfect 3:1 ratio—even if the probability model is correct.

Monohybrid crosses (one gene)

A monohybrid cross tracks inheritance of one gene.

Classic heterozygote cross: Aa \times Aa

Step 1: gametes

• Each parent produces A and a gametes in a 1:1 ratio.

Step 2: offspring genotypes (Punnett reasoning)

• Possible zygotes: AA, Aa, Aa, aa
• Genotype ratio: 1 AA : 2 Aa : 1 aa

If A is dominant:

• Phenotype ratio: 3 dominant : 1 recessive

Common misconception: Students sometimes say “genotype ratio is 3:1.” That 3:1 is the phenotype ratio under complete dominance; genotype is 1:2:1.

Testcross (a powerful Mendelian tool)

A testcross determines whether an individual with a dominant phenotype is AA or Aa by crossing it with a homozygous recessive individual (aa).

Why it works: the recessive parent contributes only a alleles, so the offspring’s phenotypes reveal what allele(s) the unknown parent contributed.

• If unknown is AA: all offspring are Aa (all dominant phenotype).
• If unknown is Aa: offspring are 1 Aa : 1 aa (1:1 dominant:recessive phenotype).

Dihybrid crosses (two genes) and the 9:3:3:1 idea

A dihybrid cross tracks two genes at once, assuming they assort independently and show complete dominance.

For AaBb \times AaBb:

• Each parent produces four gamete types: AB, Ab, aB, ab (each 25%).
• Combining those yields 16 equally likely genotype combinations.

Phenotypic ratio (under complete dominance and independent assortment):

• 9 show both dominant traits
• 3 show first dominant, second recessive
• 3 show first recessive, second dominant
• 1 shows both recessive

You do not need to memorize 9:3:3:1 blindly—what you need is to understand it comes from multiplying two independent 3:1 monohybrid phenotype ratios.

Probability rules you’re expected to use

Punnett squares are one method, but AP Biology often expects you to use probability more flexibly.

Product rule (AND)

If two events are independent and both must occur, multiply probabilities.

For example, in Aa \times Aa, probability of aa offspring is:
P(aa) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}

Sum rule (OR)

If there are multiple different ways for an outcome to occur, add their probabilities.

For example, probability of heterozygote Aa from Aa \times Aa:

• Way 1: get A from one parent and a from the other
• Way 2: get a from first and A from the other

So:
P(Aa) = \frac{1}{2} \times \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} = \frac{1}{2}

Worked problem: dihybrid probability without a 16-box Punnett

Cross: AaBb \times AaBb. What is the probability of aabb?

Treat each gene independently (that’s what independent assortment allows):

• From Aa \times Aa, probability of aa is \frac{1}{4}.
• From Bb \times Bb, probability of bb is \frac{1}{4}.

Use the product rule:
P(aabb) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}

A common mistake is to add \frac{1}{4} + \frac{1}{4} because you see two genes. Two conditions that must both happen are “AND,” so you multiply.

Exam Focus

• Typical question patterns:
  • Predict offspring genotype/phenotype ratios from monohybrid or dihybrid crosses.
  • Use product and sum rules to compute probabilities (often faster than drawing large Punnett squares).
  • Identify the genotype of an unknown individual using a testcross result.
• Common mistakes:
  • Confusing genotype ratios (1:2:1) with phenotype ratios (3:1).
  • Using the sum rule when the product rule is needed (or vice versa).
  • Assuming predicted ratios must appear exactly in small numbers of offspring.

Using Data to Evaluate Mendelian Predictions: Ratios, Pedigrees, and Chi-Square

In real experiments, you don’t get perfect ratios. AP Biology often asks you to decide whether observed data are “close enough” to a Mendelian expectation or whether the difference is too large to blame on chance.

Expected ratios vs. observed results

A Mendelian model gives you an expected ratio (like 3:1). If you have N total offspring, you can convert that ratio to expected counts.

Example: If 160 offspring are expected in a 3:1 phenotype ratio:

• Expected dominant phenotype: \frac{3}{4} \times 160 = 120
• Expected recessive phenotype: \frac{1}{4} \times 160 = 40

The observed numbers will likely differ somewhat due to random fertilization and sampling.

Pedigrees: inferring inheritance patterns in families

A pedigree is a family tree that tracks a trait across generations. Pedigrees matter because you can’t do controlled crosses in humans, so you infer genotypes and inheritance patterns from family data.

Autosomal dominant patterns (typical clues)

For an autosomal dominant trait (dominant allele on a non-sex chromosome), you often see:

• Trait appears in every generation (no “skipping”) if the family is large enough.
• An affected individual usually has an affected parent.
• Two unaffected parents typically do not have affected children (ignoring new mutations).

Genotype logic: affected individuals could be heterozygous; homozygous dominant can occur but may be rare depending on allele frequency and trait impact.

Autosomal recessive patterns (typical clues)

For an autosomal recessive trait:

• Trait can skip generations.
• Two unaffected parents can have an affected child if both are carriers.
• Trait may appear more often in siblings than in parents/children.

Genotype logic: affected individuals are typically homozygous recessive; unaffected carriers are heterozygous.

A common mistake is assuming “recessive means rare” or “dominant means common.” A recessive allele can be common, and a dominant allele can be rare; pedigrees are about transmission patterns, not frequency.

Chi-square goodness-of-fit: deciding if deviations are due to chance

The chi-square goodness-of-fit test is used to evaluate whether observed data fit an expected Mendelian ratio closely enough that any differences can reasonably be attributed to random chance.

The chi-square statistic is:
\chi^2 = \sum \frac{(O-E)^2}{E}

Where:

• O is the observed count in a category
• E is the expected count in that category
• The sum is across all phenotype (or genotype) categories you’re comparing

Interpretation idea (conceptual):

• Small \chi^2 means observed is close to expected.
• Large \chi^2 means observed is far from expected.

To make a decision, you compare your calculated \chi^2 to a critical value from a chi-square table using a chosen significance level (often 0.05 in biology contexts) and the correct degrees of freedom.

Degrees of freedom for a simple goodness-of-fit is usually:
df = k - 1

Where k is the number of categories.

Worked chi-square example (structure you should copy on exams)

Suppose you expect a 3:1 phenotype ratio and observe 90 dominant, 30 recessive (total 120).

1) Compute expected counts:

• Expected dominant: \frac{3}{4} \times 120 = 90
• Expected recessive: \frac{1}{4} \times 120 = 30

2) Compute \chi^2:
\chi^2 = \frac{(90-90)^2}{90} + \frac{(30-30)^2}{30} = 0

That’s a perfect match (rare in real life, but great for illustrating the process).

What usually happens is you get nonzero deviations; you still follow the same steps and then use the provided chi-square table (or one on your formula sheet) to conclude whether the deviation is likely due to chance.

Common misconception: chi-square does not “prove” your hypothesis is true. It only tells you whether the data are inconsistent enough with your expectation that you should doubt the model.

Exam Focus

• Typical question patterns:
  • Convert expected ratios into expected counts for a given sample size.
  • Use pedigrees to determine whether a trait is more consistent with autosomal dominant or autosomal recessive inheritance.
  • Calculate \chi^2 and interpret it using degrees of freedom and a provided table.
• Common mistakes:
  • Using expected ratios directly in the chi-square formula instead of expected counts.
  • Using the wrong degrees of freedom (forgetting it’s categories minus 1).
  • Treating “fail to reject” as “proved Mendelian model is correct.”

When Mendelian Predictions Fail (and How to Recognize Why)

Mendelian genetics is a model with assumptions. AP Biology frequently tests whether you can recognize when a situation does not meet those assumptions—because then a 3:1 or 9:3:3:1 ratio is not expected.

This section is not about abandoning Mendel; it’s about using Mendel as the baseline and spotting what changed.

Dominance is not always complete

Mendel’s classic pea traits often showed complete dominance (heterozygote looks like one homozygote). But many genes do not behave that way.

• Incomplete dominance: the heterozygote phenotype is intermediate (for example, red x white flowers producing pink). This often yields a 1:2:1 phenotype ratio in a heterozygote cross.
• Codominance: both alleles are fully expressed in the heterozygote (a common example is the AB blood type expressing both A and B antigens).

Why this matters for Mendelian problems: students often force every problem into a 3:1 phenotype expectation. The correct ratio depends on the heterozygote’s phenotype.

More than two alleles can exist in a population

A gene can have multiple alleles in the population (even though any diploid individual still carries only two). ABO blood type is a common example of a multiple-allele system.

Why it matters: multiple alleles expand the number of possible genotypes and require careful mapping from genotype to phenotype.

Linked genes violate independent assortment

Independent assortment assumes genes are on different chromosomes (or far apart). If two genes are close together on the same chromosome, they are linked and tend to be inherited together.

Crossing over in meiosis can separate linked genes, producing recombinant gametes, but the closer two genes are, the less often recombination occurs.

How this shows up in data: instead of a 9:3:3:1 dihybrid ratio, you might see an excess of parental phenotype combinations and fewer recombinants.

Sex-linked inheritance changes expected patterns

Genes on sex chromosomes (especially the X chromosome in humans) do not follow the same inheritance patterns as autosomal genes.

For X-linked recessive traits, males (with one X chromosome) express the trait with just one recessive allele, so pedigrees often show:

• More affected males than females
• No father-to-son transmission for X-linked traits (fathers pass Y to sons)

This is a common place where students incorrectly apply autosomal recessive logic.

Many traits are polygenic or influenced by environment

Mendelian genetics works best for single-gene traits with clear categories. But many traits (like height or skin color) are polygenic (influenced by many genes) and/or strongly influenced by environment.

In those cases, you should not expect simple ratios, and you often see continuous variation.

Exam Focus

• Typical question patterns:
  • Given an offspring ratio that deviates from 3:1 or 9:3:3:1, identify which assumption (complete dominance, independent assortment, etc.) is likely violated.
  • Distinguish incomplete dominance vs. codominance from phenotype descriptions.
  • Use pedigree clues to suspect autosomal vs. sex-linked inheritance.
• Common mistakes:
  • Assuming “dominant” always means a 3:1 phenotype ratio in heterozygote crosses.
  • Applying independent assortment automatically without considering linkage.
  • Treating sex-linked traits as autosomal (especially missing the father-to-son clue).