What is the Hardy-Weinberg equation and how do you use it in population genetics?

The Hardy-Weinberg equation uses p and q to represent allele frequencies in a population, where p is the frequency of a dominant allele A and q is the frequency of a recessive allele B. The equation states that 1 – p = q. You input these frequencies into a spreadsheet to calculate expected genotype frequencies and compare them against observed population data to test whether populations remain in genetic equilibrium across generations.

How does genetic drift affect allele frequencies in small populations?

Genetic drift causes random changes in allele frequencies, with effects more pronounced in smaller populations. When you run simulations with 25 zygotes versus 100 zygotes, smaller populations show greater deviation from Hardy-Weinberg expected frequencies because chance events have larger proportional impacts. Over multiple generations, alleles may disappear entirely from small populations due to random sampling alone, independent of selection.

What happens to allele frequencies when you violate Hardy-Weinberg assumptions?

Violating Hardy-Weinberg assumptions—such as introducing mutation, non-random mating, gene flow, or selection—causes allele frequencies to change across generations. For example, mutation adds new alleles to the population, non-random mating changes genotype frequencies without altering allele frequencies, and gene flow introduces alleles from external populations. Each violation produces distinct patterns of change that deviate from equilibrium predictions.

How do you calculate allele frequencies from genotype counts in a spreadsheet model?

To calculate allele frequencies, multiply the number of homozygous genotypes by 2 and add the number of heterozygous genotypes for each allele. Then divide the total number of that allele by the total number of alleles in the population. For example, if you have 10 AA individuals, 15 AB individuals, and 5 BB individuals in a population of 30, allele A frequency equals (10×2 + 15)/(30×2) = 0.583.

What is the founder effect and how does it demonstrate genetic drift?

The founder effect occurs when a small subset of individuals establishes a new population, carrying only a fraction of the original population's genetic diversity. In the simulation, drawing just 5 pairs of beads for generation 1 and then expanding to 50 beads for generation 2 demonstrates this. The initial random sample creates allele frequencies that differ from the source population, illustrating how genetic drift acts most strongly when populations begin small.

How do you set up a bead-based simulation to test Hardy-Weinberg equilibrium?

Begin with a bag containing equal numbers of two colored beads representing alleles A and a. Draw pairs of beads 20 times to represent one generation's genotypes, recording tallies for each genotype. Calculate the new allele frequency, then adjust the bead population to match this frequency before the next generation. Repeat for 10 generations, comparing observed allele frequencies to Hardy-Weinberg predictions to determine if equilibrium is maintained.

What does it mean when alleles disappear from a population during a simulation?

When an allele frequency reaches zero, that allele is lost from the population permanently. This occurs through genetic drift, especially in small populations where random sampling can eliminate rare alleles by chance alone. Once lost, an allele cannot reappear unless mutation introduces it again. Tracking allele loss across multiple simulation runs reveals how population size and random events determine which genetic variants persist.

Hardy-Weinberg and Genetic Drift

Concepts Instructor Prep Student Protocol

0 views06:19 min

Scientists once wondered why dominant traits like tan-colored giraffe spots do not become more frequent with each generation and replace recessive traits like dark brown spots. In thinking about this conundrum, in 1908, independent from each other, Godfrey H. Hardy and Wilhelm Weinberg independently derived a theory, today known as the Hardy-Weinberg Principle and represented by this equation.

The principle states that in the absence of evolution, i.e. at equilibrium, the allele and genotype frequencies of a population will remain constant from one generation to the next. To understand this equation, let's go back to the giraffe example. Uppercase A represents the tan allele since it is dominant, and lowercase a is for the brown allele because it is recessive. The frequency of these two alleles in the population are designated as p and q respectively. So how do we know the allele frequency? Well, each individual has two alleles. In this example, 40% of the alleles in the gene pool are tan. Thus, the frequency of the tan allele, p, is 0.4, and the frequency of the brown allele, q, is 0.6. Note that p plus q is always equal to one.

Now let's go back to the Hardy-Weinberg equation. Each term in the equation represents one genotype frequency. The frequency of the homozygous dominant genotype is p squared, and the homozygous recessive is represented by q squared. The heterozygous genotype is two pq. The reason we multiply by two here is that there are two different ways of generating a heterozygous genotype. Combined, these all represent 100% of genotypes. Thus, a total frequency of one. Using the values for p and q from our giraffe example, we can determine the genotype distribution of the color gene alleles in our giraffe population. Therefore, as per the Hardy-Weinberg Principle, at equilibrium, 16% of the giraffe population will be homozygous dominant, 48% will be heterozygous, and 36% are homozygous recessive.

To maintain this balance, the Hardy-Weinberg Equilibrium Principle states that a population should meet five main assumptions. There should be random mating, large population size, no mutation, no selection on the gene in question, and no gene flow in or out of the population. Most natural populations violate at least one of these assumptions and so equilibrium is rare…but in spite of this, the principle is used as a null model for population genetics. By comparing these expected values to the actual genotype frequency in a population, it can be determined whether that population is in Hardy-Weinberg Equilibrium. If not, then this means that some form of evolution or change in allele frequency is taking place.

A general misconception about evolution is that it requires natural selection to occur. However, this is not always the case. Genetic drift is one mechanism by which evolution can occur without natural selection. It is defined as a change in the allele frequency of a population due to chance. To envision this, let's go back to the example of a giraffe population and imagine their alleles of tan and brown being represented by marbles of two different colors. We will assume here that each color starts out equally abundant. If we were to start a new generation out of this population, we would need to breed pairs of individuals and thus select from four alleles per pair. If we select a breeding pair at random, then we might end up with two marbles of each color. However, by chance alone, some pairings will have only one color marble, or three of one color and one of the other. These chance deviations from 50-50 over multiple pairings to create a new generation might mean that the next generation no longer has an equal mixture of each allele.

It's this variation of relative allele frequencies over time that defines genetic drift. Therefore, unlike adaptive evolution, where allele frequency changes to select for traits that are fit for the environment, like ladybugs with a greater amount of melanin surviving better in colder climates because of an improved ability to absorb heat, genetic drift represents a type of evolution that is purely due to stochastic change. For example, the random removal of a section of a population through a catastrophic event.

In this lab, you will perform computer and colored bead simulations of Hardy-Weinberg Equilibrium and genetic drift in a population, and then test what happens when assumptions of the equilibrium are violated.

Print Procedure Steps

$$\rightleftharpoonup{xx}$$ $$\longleftharp{xx}$$, $$\longrightharp{xx}$$,

Class Simulation
- Begin by opening a new spreadsheet file. Following the Hardy-Weinberg equation where p is the frequency of a dominant allele A in a population, and q is defined as the frequency of a recessive allele B, input frequency p of allele A into cell B2, and frequency q of allele B into cell B3.
- Assign the value 0.5 to cell C2.
- Following the 1 – p = q equation, enter the formula “= 1 – C2” into cell C3 to calculate the frequency q of allele B. NOTE: Cells C2 and C3 will represent the gene pool used in the next few steps.
- Label cells E2 and F2 “Allele 1” and “Allele 2” respectively, then enter the RAND code for random formula into cell E3. =IF (RAND()
- Select cell E3 and drag the bottom right corner of the cell down to E27 to duplicate the formula into 25 cells, creating an allele for the other offspring, and enter the same formula that was used in cell E3 into cell F3.
- Add a third column of data starting with the description “Genotype” in cell G2, and add the CONCATENATE function to cell G3 to combine the two randomly generated alleles and to create a genotype.
- Drag this formula down for 25 cells and label cells H2, I2, and J2 AA, AB, and BB respectively.
- Then, input one IF function as shown here into cells H3, I3, and J3. Drag the formulas down for 25 rows per column. The formulas will return a 1 if the genotype in this row matches the genotype in the header row, and a 0 if the genotype in this row is one of the other two genotypes. H3: = IF (G3=”AA”,1,0) I3: =IF(OR(G3=”AB,G3=”BA”),1,0) J3: =IF(G3=”BB”,1,0)
- Then, label cell D28 as “SUM”, add the formula to cell H28, and drag the formula to cells I28 and J28 to get the total number of each genotype.
- Next, label cells H30 and J30 “A” and “B” respectively and label cell D31 “Number of alleles”.
- Add code to cells H31 and J31 to obtain the total number of alleles in the simulated generation, which is two times the frequency of the respective homozygous genotype, plus the frequency of the heterozygous genotype.
- Then, label cell E32 “Next gen allele frequency” and add code to cells H32 and J32 to obtain the ratio of alleles in the next generation.
- Using the gene frequencies generated in the mathematical model you just built, adjust the gene pool values in cells C2 and C3 to those from H32 and J32, and run 10 more generations, updating the gene pool with the resulting allele frequency each time.
- Record the ratio of the two variables at each time point in the spreadsheet on the table, and create a line graph to see how a small population changes over time. Hypotheses: The experimental hypothesis in this study is that smaller populations will deviate more from the Hardy-Weinberg expected frequencies of the alleles than will larger populations, because smaller populations are more susceptible to genetic drift. The null hypothesis is that the allele frequencies within the populations will not differ from the Hardy-Weinberg equilibrium equation expected frequencies, meaning that the allele frequencies will be the same from generation to generation.
- Set the frequency of gene A to 0.3 and gene B to 0.7, and run the model 10 more times, recording the ratio of the genes in the next generation in the table after each run.
- Then, drag the formulas for the cells further down to alter the model to include 100 zygotes and run the model another 10 times.
- After the last run, save all of the working data to a personal storage device and exit the spreadsheet program.
Simulation for Hardy-Weinberg and Genetic Drift
- To begin, find a partner and then collect one bag from the instructor.
- Verify that the bag contains beads of two different colors and an even number of each color.
- Designate one color as allele capital A and the other as small a. Hypotheses: The experimental hypothesis for this simulation is that allele frequencies will not change over the 10 generations of the experiment, and Hardy-Weinberg equilibrium will be observed. The null hypothesis is that equilibrium will not be seen in the population.
- Note the initial frequency in Table 1 next to generation zero. Using the Hardy-Weinberg equation, calculate the initial genotype frequencies of the population and note this in Table 1. Click Here to download Table A
- Then, discuss with your partner about the expected final allele and genotype frequencies after 10 generations of Hardy-Weinberg equilibrium. Note this next to prediction in Table 1.
- Draw a pair of beads from the bag. This represents the genotype of one individual in the next generation.
- Place a tally mark in the appropriate column next to Generation 1.
- Now, keeping each pair of beads out of the bag every time, repeat the drawing 20 times to fill out the generation one row of Table 1.
- Using the tallies, calculate the allele frequency for that generation, remembering to count both alleles in each genotype. Make a note of the new allele frequency, and then adjust the 100 beads to reflect the population after Generation 1 by adding and removing beads as necessary.
- Repeat the drawing of pairs from this adjusted population for another generation of 20 picks, recording all of the observations in Table 1.
- After calculating the allele frequency for this generation, adjust the population again to set up a third generation draw.
- Keep drawing, calculating allele frequencies, and adjusting the starting population until 10 generations have been recorded in total.
Violations of Hardy-Weinberg
- To test the effect of different physical and ecological scenarios on the Hardy-Weinberg equilibrium, first draw a slip of paper to determine which Hardy-Weinberg assumption you will be testing.
- Make a prediction of what you think might happen in your selected scenario before beginning the experiment, and record this on the board.
- If you selected the mutation scenario, select 5 alleles at random from the set and replace them with 5 of a third color, allele capital B.
- As before, perform the simulation by pulling pairs of beads from the bag for a generation of 20 picks, recording the results. Click Here to download Table B
- After each generation, make adjustments to have the starting population match the new allele frequency as before.
- Then, replace 5 random alleles again with the new color, and simulate the new generation for 20 picks.
- If you picked the non-random mating test, draw 1 allele at a time instead of 2 and then pair it with another of the same color pulled from the bag.
- As with the previous simulation, adjust the population to match the new allele frequencies at the end of the previous generation, and carry out the simulation for 10 generations in total.
- For the gene flow condition, begin by removing 10 alleles from the population and replacing them with 10 randomly selected alleles from another set of 100 beads.
- Adjust the allele frequency and repeat the gene flow of removing 10 beads and adding 10 beads from another bag at the beginning of each generation.
- If you drew small population size, simply start each generation with 60 alleles instead of 100.
- As usual, adjust allele frequencies each generation and record 10 generations. In the selection condition, draw from the original bag of beads but do not count any homozygous recessive pairs that are drawn when calculating the allele frequency at the end of each generation.
Simulation of Genetic Drift
- Make your predictions before running the simulations and record them on the board.
- If you have the small population size test, run the standard Hardy-Weinberg simulation as before, but instead start each generation with 30 alleles and not 100.
- If you drew the founder effect with two alleles test, start generation 1 by drawing only 5 pairs of beads from the bag.
- Then, creating the gene pool for generation 2, include only 50 beads at the allele frequency determined in generation 1. When you create the gene pool for generation 3 and all subsequent generations, include 100 beads.
- For a founder effect with 10 alleles, you will need to collect a bag containing random amounts of 10 different colored beads.
- Designate an allele name for each of the new alleles, and then calculate their initial allele frequency.
- Now, run the experiment in the same way as the founder effect with two alleles, by drawing just 5 pairs randomly for generation 1 and then creating the second generation with 50 alleles, and third and subsequent generations with 100. Click Here to download Table C
- If you have the natural disaster with 2 alleles, you will need to collect a paper plate from your instructor.
- Draw a line down the middle of the plate. Before generation 1, pour out all of the beads from a standard 100 bead setup onto the plate, and mix them randomly, spreading them evenly.
- Choose one side of the plate and take all of the beads from that side. You should draw from these to create generation 1.
- For generation 2 and beyond, adjust the population and use a total of 100 beads.
- Finally, if you selected the natural disaster with 10 alleles test, you will need to collect a bag containing 10 different colored beads.
- Assign a name to each new allele, and then place them on the plate and select half. Draw from these 50 beads for generation 1, and then calculate the allele frequencies to make a population of 100 in each subsequent round.
Results
- Using the entered functions, calculate the number of each allele by multiplying the number of the homozygous genotypes by 2 and adding the number of the heterozygous genotypes.
- The frequency can then be calculated by dividing the number of the allele in question by the total number of alleles. Enter the results into the table.
- Next, use the Hardy-Weinberg equation to calculate the expected genotype frequency of the next generation, and compare the results of the simulation with the expected frequency, using the table as a guide.
- Plot the changes of the population gene frequencies over time that you recorded in the table. Note any changes in allele frequencies over time and if any alleles decrease in frequency to the point that they disappear from the population.
- Plot the changes in the populations of the 25 and 100 zygotes with initial gene frequencies of 0.5 for each allele. Compare the results of the smaller population and the larger populations. NOTE: The observed allele frequencies are expected to differ slightly from the Hardy-Weinberg expected values as a result of chance from the RAND function.
- Using separate lines for each allele, graph the allele frequencies found for the original Hardy-Weinberg experiment over 10 generations.
- Compare the results across the class, and see if your results agree.
- Next, again using one line per allele, graph the results of your second experiment testing violations of the Hardy-Weinberg equilibrium, and share your finding with the class. Compare your actual results with your prediction.
- Finally, graph the results of your genetic drift simulation scenario in the same manner.
- Again, present your results to the group and hypothesize why your results did or did not match your prediction. Compare your results to those of your classmates’.