Monday, January 8, 2018

Teaching Hardy-Weinberg & Population Genetics using playing cards


In-Class Population Genetics Exercise (note that this exercise will take more than one class to complete: at the end of 1st class, remind students to hold onto their cards).
To perform this exercise, you will need: i) a class of students; ii) sufficient playing cards so that each student can obtain 2 cards each (remove joker & instruction cards); iii) one distinct set of playing cards (that will be distributed among the sets); iv) everyone has a personal response system (PRS), i.e. an iClicker.

When cards are initially handed out to the students, DO NOT shuffle them, as we want initial population be in a state of non-H-W-equilibrium.

These cards represent (initially) a one gene, two-allele system. Hearts & Diamonds represent the red allele (r), while spades & clubs represent the black (B) allele. We initially treat B as dominant over r. (A real-life equivalent is the B & r alleles at the K-locus for coat colour in Cocker Spaniels). Each student represents a diploid individual, who is hermaphroditic (capable of mating with anyone else in the population).

Initial census of the class:
(For all calculations, I am assuming that the class is comprised of N=270 individuals –see accompanying excel file for other values).
Total starting population size of 270, most of which will be BB or rr.
Use clicker to 1st count phenotypes (Black or red) in population
Use clicker to then count genotypes.
Ask students to calculate p & q in starting population (should be p~0.5, q~0.5).

Simulation of Random Mating:
In this exercise, the point is to establish a population which is stable, and in which Hardy-Weinberg equilibrium becomes established

A new organism will replace each individual organism.
Ask students to turn to someone nearby, and to randomly exchange one of their two playing cards. This represents a reproductive event.

Using clicker, ask students what they think has happened to the frequencies of p & q (same as before, increase in p/decrease in q, increase in q/decrease in p, decrease in p/decrease in q, increase in p, increase in q).
Explain why p & q don’t change (no loss or gain of cards)

Ask students what they think will happen to phenotypes (same as before, increase in BLACK/decrease in RED, increase in RED/decrease in BLACK). Assuming that there will be more heterozygotes, we should see increase in Black phenotypes, and a decrease in Red phenotypes.
Poll students using iClicker to determine the distribution of RED & BLACK phenotypes in the population. Compare to initial distribution.

Ask students what they think will happen to genotypes (same as before, increase in BB & Br decrease in rr; decrease in BB increase in Br decrease in rr; decrease in BB, increase in Br decrease in rr, increase in BB decrease in Br increase in rr). Assuming that there will be more heterozygotes (due to random mating), we should see increase in Br phenotypes, and a decrease in BB & rr genotypes.

Poll students using iClicker to determine the distribution of BB, Br & rr phenotypes in the population.

At this point, discuss concept of H-W equilibrium: what is a model, why is it useful, what are its limitations (i.e. assumptions: sexually reproducing organism, reasonable large population, mating is random, no migration into or out of the population, no mutations, no selection

Use H-W formula to calculate predicted genotypes & phenotypes in the population. Compare these values to observations made in class.
Discuss why values may not match (mating was not fully random, finite population means no fractional individuals possible).

Get class to repeat random mating exercise as above. Use clicker to poll for phenotypes & genotypes. Discuss why or why not these frequencies have changed, and if they are getting closer to H-W equilibrium (hopefully they are).

Get class to repeat random mating exercise one additional time above. Use clicker to poll for phenotypes & genotypes. Discuss why or why not these frequencies have changed, and if they are getting closer to H-W equilibrium (hopefully they have). Use this data to indicate that as long as the assumptions are not violated, and that p and q remain constant, the genotype frequencies will hold constant at the Hardy-Weinberg equilibrium values, generation after generation.

Now, we want to see what happens if we start to violate the assumptions, starting with random mating.
Ask students to “mate” with others of the same phenotype (RED with RED; BLACK with BLACK). This is assortative mating.

Ask students what they think will happen to phenotypes/genotypes (same as before;
Increase in BLACK (more BB) decrease in RED; Increase in BLACK (more Br) decrease in RED, Decrease in BLACK (but more Br) increase in RED, Decrease in BLACK (but more BB) increase in RED.

Poll students using iClicker to determine the distribution of RED & BLACK phenotypes in the population. Were the results (hopefully Decrease in BLACK (but more BB) increase in RED) what people predicted?

Discuss how while mating in the whole population was non-random (assortative mating), that within the subset of BLACK phenotypes mating was random (because mating was based on phenotypes, not genotypes.
Assuming that there were (before the assortative mating) 135 Br individuals in the class & 67 BB individuals (H-W predicts 67.5), then for the 202 individuals (and 404 alleles in the population), there should be 269 B alleles (p=0.665) and 135r alleles (q=0.335). From these p & q values, we can predict how many BB, Br & rr individuals would be produced. BB: p2=0.44 (~89 individuals), Br: 2pq=0.44 (~89 individuals), rr: q2=0.11 (~23 individuals).

Ask students what would happen if we continued to have assortative mating? Changes in phenotypes/genotypes?

Now, get students to undergo dissortative mating (BLACK with RED, whenever possible).

Ask students what will happen to phenotypes/genotypes (same as before;
Increase in BLACK (more BB) decrease in RED; Increase in BLACK (more Br) decrease in RED, Decrease in BLACK (but more Br) increase in RED, Decrease in BLACK (but more BB) increase in RED. This should show how we get an increase in the amount of heterozygotes.

To show how random mating will restore population to H-W equilibrium, get students to undergo one round of random mating. Use iClicker to examine genotypes.

Next, we shall consider why a violation of the assumption of large population might affect our estimate of H-W equilibrium. Pick a row of ~10 students at random from the class, and get them to input (via iClicker, their genotypes). How close are their values to the p & q of the whole population and the predicted H-W values? Repeat with another row (this is to increase your odds of getting some atypical p & q values). This will show how small samples may not provide accurate representations.

Using a shuffled spare deck of cards, get 5-10 students to select 2 cards each at random from the deck. While p & q are=0.5, the observed frequencies of BB, Br & rr should (hopefully) not be in H-W equilibrium.

Next we shall consider effect of selection. Start by imagining that people don’t like RED Cocker Spaniels, and start only breeding BLACK dogs with BLACK dogs. This means that RED dogs don’t contribute to the next generation. Ask all students with 2 red cards to sit out the next mating round. Quickly survey the students on their genotypes before and after 2 rounds of mating (with any RED phenotypes) getting dropped from the population. Ask the students if they think that the r allele will be lost from the population selection against RED continues?

Demonstrate (using the rare (q=0.038) green-backed cards that have been mixed in with the regular black-backed cards q=0.962) how that even there is strong selection, that rate recessive deleterious genes will be retained in low frequencies (mostly as heterozygotic state). In a class of 270, there should be ~20 green cards in total, H-W predicts that there will be 0.38 individuals that are greenback/greenback (i.e.~0), 19.7 individuals that greenback/blackback are and 250 that are blackback/blackback. This means that >98% of green cards will be in heterozygous state (and hidden from selection).

Ask how the efficiency of selection would be affected if r or greenback alleles were dominant or co-dominant?

Next, let us consider selection acting on a quantitative trait (ask students to define quantitative vs. quantitative: perhaps asking them to write a list of 4 quantitative and 4 qualitative traits). Using the values on the face of the cards as allelic value (A=1, 2,3,4,5,6,7,8,9,10,J=11,Q=12, &K=13), get students to indicate phenotypic values (in clicker group into sets of 5: (2-6, 7-11, 12-16, 17-21, 22-26). Discuss the bell-shaped nature of the data: all value cards are in same proportions in the gene pool, but few outliers.

Perform directional selection (all those with values less than 7 must sit out) in two successive rounds of mating. Note how mean and distribution of population phenotypes changes.

Next, start stabilizing selection (all those with values less than 7 or more than 18 must sit out). Note how mean and distribution of population phenotypes changes.

If time permits, do several rounds of assortative mating and divergent selection: Selection for high values of BLACK, and low values of RED. Examine phenotypes over time.

No comments:

Post a Comment