They will have frequencies p and q in a population. If we know the allele frequencies, we can predict the genotype frequencies. The expected genotype frequencies of the two alleles are calculated as shown. This ought to look familiar: it's our old friend the Punnet's Square. Allele A or A 1 has a frequency of p, and allele a or A 2 has a frequency of q.
Multiply the allele frequencies to the get the probability of each genotype. The expected frequencies of the genotypes are therefore:. Let's take a look at some graphs of this to make it a little easier to see.
For values of p from 0 to 1, in intervals of 0. All of the above has to do with the allele and genotype frequencies we would expect to see. Next, let's look at the real world situation so we can compare. In a real world population, we can only see phenotypes, not genotypes or alleles. However, in a population of genotypes AA, Aa and aa, the observed frequency of allele A equals the sum of all of the AA genotype plus half of Aa genotype the A half.
The observed frequency of allele a is therefore half of the Aa individuals the a half plus all of aa individuals. Tip : If the alleles are codominant, each phenotype is distinct you can distinguish between tall, medium and short and your job is easier.
If the alleles are dominant and recessive , we can't visually tell the homozygous AA from the heterozygous Aa genotypes both are tall , so it's best to start with the homozygous recessive short aa individuals. Lets consider a "fight" between forward and backward mutation.
Forward mutation changes the A allele to the a allele at a rate u ; backward mutation changes a to A at a rate v. The first part on the right is accounts for alleles not mutated 1-u , and the second part accounts for the increase in p due to mutation from a to A the frequency of a times the mutation rate to A.
This is useful because it lets us calculate a theoretical equilibrium frequency which is defined as the point at which there is no more change in allele frequencies, i. In the real world we will generally not find specific evolutionary forces acting alone; there will always be some other force that might counteract a specific force of interest.
Our ability to detect these opposing evolutionary forces depends, of course, on the relative strengths of the two or more forces. However, it is instructive to examine the conditions where evolutionary forces oppose one another to give us a feel for the complexity of evolutionary processes. Here we will consider a simple case where mutation introduces a deleterious allele into the population and selection tries to eliminate it.
As above we define the mutation rate u as the mutation rate to the "a" allele. This will tend to increase the frequency of a i. This mutation pressure will increase the number of alleles which selection can act against. To select against the a allele, we first will assume complete dominance, i. Related Concepts 8. You have authorized LearnCasting of your reading list in Scitable.
Do you want to LearnCast this session? This article has been posted to your Facebook page via Scitable LearnCast. Random mating means that the frequency of mating of an individual or of any pair of individuals does not depend on the genotype. Teachers who are not familiar with this instructional design may find this lesson difficult to implement until you have had practice using the technique with less complicated content.
Teacher questioning that focuses on helping biology students build their understanding step by step instead of lecturing can be challenging until you have mastered it, especially with activities in which biology students are building mathematical models. Like most inquiry-based instruction, the role of the teacher here is as a facilitator—the guide on the side, not the sage on the stage.
Species evolve as the frequencies of various alleles change over generations. Change in allele frequency is caused by natural selection and genetic drift, among other reasons. Population genetics is the study of these changes.
New species arise when these changes accumulate to the extent that breeding with earlier forms is no longer possible Big Idea 1. Alleles are different forms of a gene; some alleles confer increased reproductive success on the individual and will increase in frequency in response to natural selection Big Ideas 2 and 3.
Constancy of allele frequency requires that no factors such as mutation, natural selection, or migration are adding or deleting alleles Big Idea 4. The Hardy-Weinberg equilibrium principle explains how genotype and allele frequencies are maintained Big Idea 5 and can be used to identify populations in which equilibrium does not exist Big Idea 6 , which can signal to researchers that they should seek the causes of this state Big Idea 7.
Next, a set of manipulatives is introduced by which students can model the frequencies of HD alleles; then students generate models to predict HD allele frequency change from one generation to the next in the absence of natural selection Exploration. Students compare and improve their models, and compare these against the current scientifically accepted model the HWeq Explanation.
The target audience is high school biology or AP biology and introductory college biology students with some experience with modeling especially mathematical modeling and with the 5E instructional approach. Minimal understanding of DNA structure, Mendelian genetics, and basic evolution and natural selection is assumed. For high school classes, the activity should take three to five minute periods. Detailed solutions, explanations, and other teacher guide information are provided in Supplement 1: Teachers Guide, along with a copy master for the Student Worksheet.
B and adaptation LS4. College Board, Explain why dominant traits do not eliminate recessive traits in a population, even if the recessives are very damaging.
Explain what the Hardy-Weinberg equilibrium principle is, and apply it to individual populations. Explain why traits that are expressed only after reproductive age of the individual do not affect allele frequency. At HWeq: Given the allele frequencies in the current generation of a population, compute genotype frequencies in that or the subsequent generation. Given the distribution of the three genotypes in a population and data from which to determine the allele frequencies, determine whether or not the population approximates HWeq.
Time required: Two to three minute periods, depending on student expertise and familiarity with 5E instruction. Students typically find fascinating the story of Nancy Wexler, her mother who died early of Huntington's Disease, and the work to identify the determinants of the disease among the inhabitants of the village of Barranquitas on the shores of Lake Marakibo in Venezuela Figure 1. Begin this activity by asking: What human genetic diseases do you know much about?
Have you ever met someone with a genetic disease? Nancy Wexler with HD patients in Barranquitas. Have you ever heard of Huntington's Disease? If it is so bad, why doesn't it disappear? Objective 2. Do you think the frequency of people with HD in Barranquitas will change over time increase or decrease? How could we predict? In the Exploration Phase, students seek to find answers to their own questions and those you pose.
Ask the following questions:. So why doesn't the HD mutant allele disappear in the Barranquitas population? How could we predict how the number of people with HD might change over time—from one generation to the next? Objectives 2, 3. Activity: Ask students to use the paper clips provided to represent a random sample of people of Barranquitas in the generation aged 40 to 59 and their Huntington alleles homozygotes of each type and heterozygotes , using the data from Wexler's research in Table 3.
Paper clip models of the two possible homozygotes and the heterozygote. Ask: What is the frequency of each allele in the generation aged to year-old population? Objective 6. Remember from the Wexler video that HD is caused by a dominant autosomal mutation. Then ask students to come up with a way to model all possible matings in the population, in their proper relative frequencies by drawing random pairs of alleles from the entire population of alleles, with allele pairs separated , modeling the change in allele frequency from one generation to the next.
Ask: So, how did the allele frequencies in the current generation compare to that of the next generation? The number of H alleles doesn't decrease. Does this surprise you? It surprised some scientists in the early s when this question first came up! And did everyone get the same thing, even though you started with different proportions of HH and Hh individuals? What do you predict will happen to the allele frequencies in the next generation?
Ask: Do you think the frequencies of HD alleles stay the same from generation to generation in nature? What kinds of things could change allele frequencies over time?
Objective 4, 5. Ask: How could you predict what the genotype proportions should be if there are no external forces acting on the population and mating is completely at random? What mathematical model could you come up with to predict these proportions? When HD genotype testing was developed, it appears that 2 of the HD individuals of the 40—year-old generation in Barranquitas were likely homozygous for the mutant allele HH Table 4.
How do these observed genotype frequencies compare to your predicted frequencies?
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