Mendel the Magician

It is the start of the term in Biology 102 (Genetics), and thoughts turn to Mendel and his peas. Yes, I saw it in the faces of the students, and I told them that I saw it: the look. I know it because I made that face sometime during my undergraduate days. I don't recall whether it was in molecular biology or genetics, but when the instructor mentioned "Lac operon" I almost lost it. Seriously? The third time in as many years you're going to spend a couple of class sessions on the Lac operon?
So, I watch the faces of students particularly carefully when I say certain phrases, like "Mendel's peas", to judge whether they've heard this all before. Of course, my version has more detail, but in a class of 80 students, when you have to make sure that everybody is up to speed (the chemistry majors, the lone English major, etc.), it is incumbent on the instructor to try to make it enjoyable for everybody.
I thought I'd try a dramatic twist on Mendel's first law: segregation (of alleles into gametes). Mendel's laws were all inferred by analysis of phenotypic ratios of different traits in the offspring of crosses. In one cross, Mendel analyzed how the pea color phenotype (green or yellow) was inherited. Crossing green and yellow parents, he found that the F1 generation offspring all had yellow peas. Amazingly, if he mated these F1 together, the green color reappeared (as if by magic) in the next (F2) generation.

This was the teaser: how did one of the parental phenotypes disappear, and how did it reappear later? The answer is dominance, and to understand how this works, we need Mendel's first law: segregation (of alleles into gametes). Mendel had inferred that each pea has two versions (alleles) of the pea color gene, and that 50% of a plant's gametes contain one version and the other 50% the other version. The yellow parent has two copies of the Y allele (YY) and the green parent has two y (yy). So, all of the gametes from the yellow parent contains a Y; all of the gametes from the green parent contain a y.
Each F1 offspring, comprising genetic material inherited from both parents, have one Y and one y (Yy). That the F1 plants are all yellow defines the Y allele as conferring a dominant phenotype: being YY or Yy makes you yellow; only when you have no "dominant" alleles (yy) is the green phenotype evident. Assuming that gametes fuse randomly (without regard to what alleles they carry) at fertilization, we can predict the ratio of F2 generation phenotypes (yellow:green) with some simple probability calculations.
Probability? This time I saw some eye rolls and some seat-slumping. But I had anticipated and was ready for this. I handed a sealed envelope to a student sitting in one of the front rows, and then instructed each student in the class to choose a letter between A and F and write that letter down in their notes. Then I asked them to do the same: choose a whole number between 1 and 3 and write that down. "Please raise your hand if you chose the letter 'A.'" In my class of ~80 students (I hadn't taken roll so didn't know exactly how many were in attendance that day, and certainly wasn't going to take the time to count), about 9 had picked 'A.'
If you already know where I'm going with this, you probably feel the same way I did. The idea is that in a class of 80 students, if you give them a choice of six options (A, B, C, D, E, or F), then one-sixth of the students (on average) should choose each letter. 13 students should have picked 'A,' but of course the result (9) is just one sample from a probability distribution. Someday soon, when we start statistics (say, chi-square analysis), I'll use this example! Meantime, though, the demonstration isn't over yet.
"Please raise your hand if you picked the letter F." About twenty hands go up. "Please keep your hand raised if you also picked the number 2." Most of the hands drop. Four students in the class have chosen F2. "Please look around at your classmates and see that there are four students who have chosen the letter F and the number 2." Then I say, "Please open the envelope I handed you earlier and read the message inside." She reads: "Four students in class have chosen 'F2.'" Bam! Not a dry eye in the place.
And then, this!

Of course, the calculation is straightforward, I tell the students. With about 80 students in the class, about 1/6 should pick F, and about 1/3 should pick 2. Since these choices are independent events, we multiply the probabilities together to find that about 1/18 students should pick F2. 80 students * 1/18 students ~= 4 students that should pick F2.
Mendel had done the same calculations, presumably, I say. In the F1 generation of peas, 50% of gametes have Y, and 50% have y. If we assume that the gametes fuse randomly and that the two gametes that form an F2 plant are independent draws from the pool of F1 gametes, then the number of YY plants should be (50%)*(50%) = 25% of F2 plants. The number of yy plants should be (50%)*(50%) = 25% of F2 plants. The other 50% of the F2 plants are the heterozygotes (Yy and yY). Since only the yy plants have green peas (25% of the F2 generation), the rest of the F2s (75%) are yellow. Hence, there is a 3:1 ratio, which Mendel observed, of yellow:green peas.
"This was the first time I've tried this demonstration," I told the class. "And likely the last. Because if I know anything about probability, this is the only time I'll ever do this demonstration when it actually works they way I intended!"