Lecture: Mendelian Genetics
Lecture script · about 15–20 minutes spoken · Week 11
Opening
Picture a family photo. Both parents share one look for some trait, and one of their children has a look that neither parent shows. Relatives lean in and ask where it came from. By the end of this lecture, you'll be able to answer them, and you'll be able to predict the odds before the child is born.
These ideas reach well beyond this course. A nursing student reading how traits pass from parents to children is using them. So is a gardener deciding which two plants to cross, and so is a lab technician checking whether a count lands near the odds. Each one is turning inheritance into a prediction that can be tested.
Here's where we are. In Week 9 you watched mitosis copy a cell. In Week 10 you watched meiosis halve the chromosomes and deal one chromosome from each pair into every egg and sperm. In this lecture I'll show you that the deal has rules, and that the rules let you predict. We'll learn the vocabulary, meet Mendel, state his two laws, fill a Punnett square, work the odds, run a test cross, add a second gene, and finish with a pair of coins. Next week, in Week 12, we bend Mendel's rule.
1. The vocabulary: gene, allele, genotype, phenotype
Think of a family cookbook. One page holds the bread recipe. Two copies of that page might differ a little: one says add honey, and the other says leave it out. Same page, different versions. That's the whole idea of this section.
Here are the terms. A gene is a stretch of DNA that carries the instructions for a trait, such as seed shape in a pea plant. An allele is one version of a gene. A body cell carries two alleles of each gene, one on each chromosome of a homologous pair, and the two can match or differ.
Some alleles win the tie. A dominant allele is an allele whose trait shows whenever it is present, even with a different allele beside it. We write it as a capital letter, like a big T. A recessive allele is an allele whose trait shows only when it is the only version present. We write it in lowercase, a little t.
Now two words that students swap all the time. Your genotype is the pair of alleles you carry, such as big T big T, big T little t, or little t little t. Your phenotype is the trait you show. I want you to hold a kitchen picture here: the genotype is the recipe, and the phenotype is the cake.
Two more. Homozygous means two matching alleles, big T big T or little t little t. Heterozygous means two different alleles, big T little t.
Here's the trap. Big T big T and big T little t look exactly the same, because the dominant allele shows in both. They look alike, but they cross differently, and you'll see why soon.
Pause and try this. A plant carries one big T and one little t. Is it homozygous or heterozygous, and which trait does it show?
Say the two alleles out loud before you decide.
Here's the answer. It's heterozygous, because its two alleles differ, and it shows the dominant trait, because the big T is present.
2. Dominant does not mean common
Imagine a crowd at a concert. Suppose one allele in that crowd is dominant and another is recessive. Most people's first guess is that the dominant allele must be in most of the crowd. It feels right. The word "dominant" sounds like winning.
But dominance answers a question about one body, not a crowd. It says that when big T sits beside little t inside one organism, the big T trait is the one you see. It says nothing about how many people or plants carry big T. A recessive allele can be far more common in a population than the dominant one.
So keep two questions apart. Inside one organism, which trait shows? That's dominance. Across a whole population, which allele is more common? That's a counting question, and dominance can't answer it.
Pause and try this. Someone says an allele must be dominant because most people in town carry it. What's wrong with that reasoning?
Ask yourself which of the two questions it mixes up.
Here's the answer. It mixes up how common an allele is with whether it's dominant; dominant only means the allele shows when present.
3. Mendel and his peas
Picture a garden bed of pea plants, some with round seeds and some with wrinkled ones. Anyone can see that a trait passes down. What Gregor Mendel's work gives you is a count, and a count lets you see a pattern.
Mendel lived from 1822 to 1884. He crossed garden peas at an Augustinian monastery in Brno, and he published Experiments in Plant Hybridization in 1866. Hardly anyone noticed the paper until it was rediscovered in 1900.
Geneticists name the generations of a cross. The parents are the P generation, their offspring are the F1 generation, and the offspring of the F1 are the F2 generation. For seed shape, Mendel's F2 plants gave 5,474 round seeds and 1,850 wrinkled seeds. Divide the first by the second and you get about 2.96, which is close to 3. So about 3 round seeds for every 1 wrinkled.
I want to be honest about which number matters. The raw counts are history. The fact to keep is the 3 to 1 ratio, and a real count lands near a ratio, not on it.
Pause and try this. Mendel's count came out about 2.96 to 1, not exactly 3 to 1. Does that count against the rule?
Think about what a ratio describes.
Here's the answer. No, because a ratio describes odds, and a real count lands near the odds, so about 2.96 supports a 3 to 1 rule.
4. The law of segregation
Picture a deck of two cards, one marked big T and one marked little t. Hand someone one card. They get big T or little t, never both. For each gene, every parent is a deck like that.
That's Mendel's first law. The law of segregation is Mendel's rule that each parent passes exactly one allele of each gene to each offspring, because the two alleles separate into different gametes when homologous chromosomes part in meiosis I.
This is where Week 10 pays off. A big T little t parent carries big T on one chromosome of a pair and little t on the other. In meiosis I the pair separates. Half of the gametes get the big T chromosome, and half get the little t chromosome. So the chance that a gamete carries big T is a half, and the chance it carries little t is a half.
A child still ends up with two alleles. One came from the egg, and one came from the sperm. Each parent gave one.
Pause and try this. A parent is little t little t. What allele or alleles can its gametes carry?
Picture both chromosomes in the pair.
Here's the answer. Only little t, because both chromosomes in the pair carry little t, so every gamete gets a little t.
5. The Punnett square
A Punnett square is a grid that lists one parent's possible gametes across the top and the other parent's down the side, so each box shows one equally likely offspring genotype. Think of it as bookkeeping. It makes sure you count every combination once.
Let's run a monohybrid cross, a cross that follows one gene: two heterozygous parents, big T little t crossed with big T little t. Across the top, write big T and little t for the first parent. Down the side, write big T and little t for the second parent. Now fill all four boxes, one allele from the top and one from the side.
The top-left box is big T big T. The top-right is big T little t. The bottom-left is little t big T, which is the same genotype as big T little t. The bottom-right is little t little t.
Now count. One big T big T, two big T little t, and one little t little t. That's a genotype ratio of 1 to 2 to 1. Then count what you'd see. Big T big T and big T little t both show the dominant trait, so 3 boxes are dominant and 1 is recessive. That's a phenotype ratio of 3 to 1, and there's Mendel's pattern.
Pause and try this. Someone reports the phenotype ratio of this cross as 1 to 2 to 1. What did they mix up?
Ask what you can see in each box.
Here's the answer. They gave the genotype ratio; since big T big T and big T little t look the same, the phenotype ratio is 3 to 1.
6. The product rule, the sum rule, and a family of four
Flip one coin, and heads comes up half the time. Flip two coins, and both land heads only a quarter of the time. That everyday fact is the first of two rules.
The product rule is the probability rule for two independent events both happening: multiply their probabilities. A little t from each big T little t parent is a half times a half, which is one quarter. That matches the one little t little t box out of four.
The sum rule is the probability rule for either of two outcomes that cannot happen at the same time: add their probabilities. The chance of the dominant trait is the chance of big T big T, one quarter, plus the chance of big T little t, one half. That's three quarters, matching 3 dominant boxes out of four. Multiply for "and." Add for "or."
Now a warning I want you to carry. A ratio is odds over many offspring, not a promise in a family of four. Picture two big T little t parents with four children. People expect exactly 3 with the dominant trait and 1 with the recessive. But each child is a new flip. Multiply three quarters by itself four times, and you get 81 out of 256, about 32 percent. In roughly one such family in three, all four children show the dominant trait.
Pause and try this. Two big T little t parents have four children, and all four show the dominant trait. Does that break Mendel's rule?
Think about how many offspring a ratio needs.
Here's the answer. No, it doesn't, because the 3 to 1 ratio holds over many offspring, and in four children an all-dominant family happens about one time in three.
7. The test cross
Say a seed seller hands you a tall plant and swears it's big T big T. You can't check by looking, because big T big T and big T little t look the same. But you can check by breeding.
A test cross is a cross between an organism that shows the dominant trait and a homozygous recessive partner, little t little t, used to learn whether the unknown is big T big T or big T little t. The little t little t partner is the key. It can only give little t, so every offspring shows you which allele the unknown parent gave.
Run both possibilities. If the unknown is big T little t, the boxes are two big T little t and two little t little t. That's 1 to 1: half dominant, half recessive. If the unknown is big T big T, all 4 boxes are big T little t. Every offspring shows the dominant trait.
Here's the honest limitation. One recessive offspring settles it, because only a little t from the unknown parent can make it. A run of dominant offspring only supports big T big T, since a heterozygous parent could pass big T to a small litter by chance.
Pause and try this. In a test cross, one offspring out of several shows the recessive trait. What's the unknown parent's genotype?
Ask where that offspring's second little t came from.
Here's the answer. It's big T little t, because the recessive offspring needed a little t from each parent, and a big T big T parent has no little t to give.
8. Independent assortment and the dihybrid cross
Now follow two traits at once in the same plant: height, with big T and little t, and seed color, with big Y and little y. Does the height allele a gamete gets change the color allele it gets? For genes on different chromosome pairs, no.
That's Mendel's second law. The law of independent assortment is Mendel's rule that the alleles of different genes go into gametes independently of one another, because each chromosome pair lines up at random in meiosis I. You met that random line-up in Week 10.
So a parent heterozygous for both genes can make four gamete types: big T big Y, big T little y, little t big Y, and little t little y. A dihybrid cross follows two genes at once. Cross two of these double heterozygotes and you need a grid of 4 by 4, which is 16 boxes. Fill them and sort by what you'd see: 9 show both dominant traits, 3 and 3 show one dominant and one recessive, and 1 shows both recessive. That's 9 to 3 to 3 to 1, and 9 plus 3 plus 3 plus 1 is 16.
The product rule gets there faster. Treat each gene as its own one-gene cross. Both dominant is three quarters times three quarters, or 9 sixteenths. Both recessive is a quarter times a quarter, or 1 sixteenth. Each mixed class is three quarters times a quarter, or 3 sixteenths.
Pause and try this. In the 9 to 3 to 3 to 1 ratio, which class is the 1?
Think about which class is the least likely.
Here's the answer. It's the class that shows both recessive traits, because a quarter times a quarter is the smallest product, 1 sixteenth.
9. Testing the odds with coins
A coin is a fair stand-in for a big T little t parent. Heads stands for big T, tails for little t, and each comes up half the time. Flip two coins at once and you've made one offspring of a two-heterozygote cross.
This week's lab uses that model. The coin-toss example is illustrative, a run built for this course. In 100 two-coin flips, the odds predict 25 big T big T, 50 big T little t, and 25 little t little t. That's the expected count: the total times the probability, so 100 times a quarter is 25. The model run gave 23, 52, and 25.
Now read it like a biologist. The dominant count is 23 plus 52, which is 75. The recessive count is 25. Divide 75 by 25 and you get 3. So the run reduces to 3 to 1, right on the prediction, even though the genotype counts sit a couple of flips away from 25, 50, and 25.
That gap is not an error. It's chance. The law of large numbers is the pattern that results from chance events land closer to the predicted odds as the number of trials grows. So 100 flips sit nearer the odds than 4 flips do. Your own run in the lab will differ from this one, and that's expected.
Pause and try this. In the coin-toss example, the big T big T count was 23, not 25. Does that mean the coins were unfair?
Think about what a run of chance events does.
Here's the answer. No, because a real run lands near the expected count, not on it, and a gap of 2 in 100 flips is ordinary chance.
Closing
Let me pull it together in the order we built it. A gene is the instruction, and an allele is one version of it. Your genotype is the recipe, and your phenotype is the cake. Dominant means an allele shows when present, not that it's common. Mendel published in 1866, and his F2 peas landed near 3 to 1. Each parent passes one allele, because meiosis I splits each pair. The Punnett square for two heterozygotes gives genotypes 1 to 2 to 1 and phenotypes 3 to 1. Multiply for "and," and add for "or." A test cross with a little t little t partner tells big T big T from big T little t. Two genes on different pairs assort independently and give 9 to 3 to 3 to 1. And a ratio is odds over many offspring, never a promise in a family of four.
Next in this module come the slide deck, the Readings & Resources page, the lecture tutorial, the practice set, and the quiz, then the discussion, the assignment, and the Coin-Toss Genetics lab. Next week, in Week 12, we see what happens when Mendel's simple rule bends.
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