Introductory Biology Lab Exercises - Hanover College
Introductory Biology Lab Exercises
LAB 14.
SIMULATION BY MODELS:
MECHANISMS OF EVOLUTION.
GOALS:
By the end of this lab you will understand that scientists can learn from modeling the natural world. Many of these models are complex and require the use of powerful computers. You will use simple models to study the change in allele frequency of a population over many generations.
BACKGROUND:
1. Models simulate the natural world when experiments become impractical.
We have already learned that some experiments are simply too large, require too much time, or are too costly to be done at this time. Thus, to study the change in allele frequency over an evolutionary time scale (thousands of generations) would, except for that of the fastest dividing bacteria, be impractical. However, appropriate models might simulate reality and provide valuable information of what could be expected in reality. Sometimes we can simulate reality with very simple means as we will simulate population genetics with the colored beads; in other cases we will need the computational power of computers to simulate the natural process. It should be noted that much of the short-term and long-term weather and climate projections are largely based on computer simulation.
In science, models help us understand the way natural systems function. The evolution of a species results from many complicated interactions between individuals and their environment. An evolutionary model helps us understand how the changes may happen by simplifying the system while keeping the essential principles.
2. Population genetics and evolution.
Evolution can be defined as a change of the allele frequency of a population. The purpose of this exercise is to help you understand what processes can results in a change of allele frequencies and lead to evolution. Under certain conditions (large population, no mutation, no migration, random breeding, and no selection) the allele frequency does not change from generation-to-generation. These conditions define the Hardy-Weinberg equilibrium. However, when we change one or more of these conditions, the allele frequencies will change in response.
Darwin suggested that species evolve to emphasize alleles that confer reproductive advantages, and Mendel explained how such changes are passed through generations. Population geneticists describe why genetic changes do not occur in groups unless any of five conditions act to direct a shift in the allele frequencies of any trait. This means that genetic diversity will remain in any sexually reproducing population, and new variations will not become common unless they arrive from outside the population or they confer an advantage, whether behavioral or physiological, to an individual's ability to reproduce.
INVESTIGATIONS:
A. MODELING POPULATION GENETICS WITH PLASTIC BEADS.
We will use colored beads to demonstrate population genetics and the Hardy-Weinberg principle in this laboratory session. Specifically, we will be looking at how populations change (or not) in genetic make-up over time.
The idea behind this exercise is that population genetics can be mimicked by following the fates of two alleles of a single gene, one represented by white beads and the other by red beads. The experiment starts with equal numbers of both beads mixed together in a bag representing a collection of gametes with one or the other of the two alleles. To represent fertilization, beads are pulled out in random pairs and scored for whether the individual produced by this fertilization is homozygous white (two white), homozygous red (two red), or heterozygous (one of each). Once the matings are completed, the allele frequencies of this new generation are determined and used to fill the bag with white and red beads to reflect the allele distribution in the new generation. Allele frequencies can be followed over many generations by repeating the procedure with each new bead mix.
The procedure can be manipulated to test the assumptions of the Hardy-Weinberg Equilibrium principle. It states that, given five assumptions (there is no natural selection for or against alleles, alleles are randomly mated, the population has many individuals, and mutation and migration do not add or remove alleles from the population), allele frequencies will not change from generation to generation. This is described by two mathematical equations: for one gene represented by two alleles, then
p + q = 1
and, in the next generation, alleles will be distributed according to
p2 + 2pq + q2 = 1
where p2 = frequency of homozygotes for one allele, q2 = frequency of homozygotes for the other allele, and 2pq = the frequency of heterozygotes in that population.
The bead selection experiment shows what happens if Hardy-Weinberg assumptions are obeyed, but it can show the effect of violating them. It then demonstrates what happens to allele frequencies in more realistic situations and illustrates basic mechanisms behind frequency changes, i.e., evolution.
Experiment 1. Hardy-Weinberg and Genetic Equilibrium
This experiment tests a population that obeys the Hardy-Weinberg assumptions.
Procedure:
1. Add 250 red and 250 white plastic beads to a bag and shake it to mix all of these "alleles." This gives a randomly mixed population of alleles with a frequency p = 0.5 (250/500) for the red and q = 0.5 for the white beads.
2. Blindly (alleles must be selected randomly!) pull out 25 pairs of alleles (i.e., 25 pairs of beads) to simulate fertilization between gametes and the production of a new diploid organism and place each pair in rows for RR (red homozygotes), WW, or RW pairings.
3. Count the numbers of red and white homozygotes and the heterozygotes, and determine new allele frequencies for this F1 generation according to
p = [2(# RR pairs) + (# RW pairs)]/50 (the frequency of red beads)
q = [2(# WW pairs) + (# RW pairs)]/50 (the frequency of white beads)
and round these numbers such that p + q = 1.00
Example: If 10 RR, 20 RW and 20 WW pairs were removed, then
p = [(2x10 RRs) + 20 RWs]/100 = (20+20)/100 = 40/100 = 0.4
and
q = [(2x20 WWs) + 20 RWs]/100 = (40+20)/100 = (60/100) = 0.6.
These results can be checked by remembering that p + q = 1, and because 0.4 + 0.6 = 1, they are right.
4. Add enough of each color of bead back to the bag to give 500 beads total with allele frequencies identical to those calculated in Step (#3) above. This is most easily done by:
a. determining the number of white and red beads that must be in the bag to begin the next generation, numbers calculated by
# red = p * total # beads, # White = q * total # beads
Example (from above):
p * total # red = 0.4 * 500 = 200 red needed in the bag next time
q * total # white = 0.6 * 500 = 300 white needed in the bag next time
Check:
# red + # white = 500 = 200 + 300
b. determining the number of white and red beads still in the bag by
# red = # red before mating - # red removed = # red remaining
# White = # white before mating - # white removed = # white remaining
Example (from above):
for red: 250 red before - 40 removed = 210 red still in the bag
for white: 250 white before - 60 removed = 190 white still in the bag
Note: the “before” number you use is the number of that color in the bag at the beginning of the previous round of mating. While you had 250 red beads in the bag for the first generation, the next generation will start with 200 red beads, and this is the number you will use for the second round. Make sure you understand this before going on!
c. determining how many beads of each color must be added to or removed from the bag by
# Red = # red that must be in the bag - # red still in the bag
# White = # white that must be in the bag - # white still in the bag
Example (from above):
200 - 210 = -10, 10 red beads must be REMOVED (as indicated by “-“).
300 - 190 = 110, 110 white beads must be ADDED
Check:
-10 (reds removed) + 110 (whites added) = 100 beads put back in the bag
in other words, you need to put a net total of 100 beads back into the bag.
5. Repeat this procedure four more times using the mix you generate at the end of each generation to begin the next. Record the genotype numbers, p and q for each generation in the table at the end of the chapter.
It is very important that this procedure and the reason behind the removal of every bead and each calculation be clear. By the end of Step 5, the calculations should reveal the frequency of the red and white alleles in a population five generations removed from the original. If none of the five assumptions mentioned above are violated, what should be the values of p and q?
Table 1. Experiment 1: Hardy-Weinberg Population genetics
| |Genotype distributions |Allele Frequency |
|Generation | | |
| |# red homo. |# hetero |#white homo. |p |q |
|P | | | | | |
|F1 | | | | | |
|F2 | | | | | |
|F3 | | | | | |
|F4 | | | | | |
|F5 | | | | | |
p’s and q’s of other groups at F5 Generation
Gp 1: p = q = Gp 2: p = q = Gp 3: p = q =
Gp 4: p = q = Gp 5: p = q = Gp 6: p = q =
Gp 7: p = q = Gp 8: p = q = Gp 9: p = q =
Experiment 2. Hardy-Weinberg and Evolution
As mentioned previously, the Hardy-Weinberg equation is not as important to show that allele frequencies remain stable with time, rather what must be assumed to come to that conclusion. Violating any one of those assumptions should cause the allele frequencies to change, i.e., evolution should occur.
Each lab group will be assigned the task of violating ONE of the Hardy-Weinberg assumptions. The group's goal is to kill progeny, kill parents, import or export alleles, mutate, or illustrate a mating preference, etc. during reproduction using the bead bag to show what happens to allele frequencies if that assigned assumption is violated. In other words, use the beads to mimic evolution by means of the violation of a single specific Hardy-Weinberg assumption. Again, the conditions a population must meet NOT to evolve are that there is/are:
1. NO natural selection for or against the allele.
2. NO net mutations creating or destroying alleles.
3. NO net migrations of alleles into or out of the population.
4. NO mating behavior favoring or discriminating against alleles.
5. NO small populations leading to genetic drift.
Procedure:
1. Design an experiment using the bead bag containing 250 white and 250 red beads that violates ONE (and ONLY one) of the Hardy-Weinberg assumptions.
2. Explain the experiment to the instructor and describe how it mimics a plausible natural example with the beads.
3. Perform the experiment, keeping track of the results for each of five successive generations on the second table at the end of this lab.
4. Explain the final data to the instructor and/or the class. Be sure to describe how the data confirms or confounds any original hypothesis and how the experiment's design either successfully tested the assigned assumption or must be modified to better illustrate evolution.
If the data are presented to the entire class, everyone must pay attention to each group's explanations and data. More importantly, ask questions of the students making the presentations, as this is what scientists must do everyday to design and evaluate their experiments. This is certainly true when data do not support the hypothesis that violating one of these assumptions should lead to evolution of the population.
Table 2. Experiment 2: Violation of Hardy-Weinberg Assumptions
Assumption violated =
| |Genotype distributions |Allele Frequency |
|Generation | | |
| |# red homo. |# hetero |#white homo. |p |q |
|P | | | | | |
|F1 | | | | | |
|F2 | | | | | |
|F3 | | | | | |
|F4 | | | | | |
|F5 | | | | | |
Assumption Violation: Class Results
|Violated Assumption |Genotype distributions in F5 Generation |Allele Frequency |
| |# red homo. |# hetero |#white homo. |p |q |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
Answer the following questions to ensure comprehension of this material:
1.) Compare the results for the bead counting experiment between your group and the entire class. What does this suggest about repeating experiments?
2.) How do the results compare with expected values?
3.) Analyze the experiments where groups violated a Hardy-Weinberg assumption. Did the results agree with the hypothesis that violating this assumption would lead to a change in allele frequencies?
B. MODELING POPULATION GENETICS WITH THE COMPUTER.
To start the program, click on the icon MSDOS SIMUL 386. The program you started is not a Windows program but a DOS program. The computer screen will turn black and ask you what type of display you want. We will use the “graphics” display, so type 1 and enter. The main menu of the program opens and offers 9 items (labeled 1 to 9) that describe the conditions for the populations to grow in the simulated program.
Item 0 allows you to change the configuration of the display and deserves special attention. When you type 0 you will answer three questions one-by-one:
a) What is the number of populations that evolve simultaneously (default is 8)? Type in the number of populations you want to see evolving simultaneously. Choose a number ................
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