Sometimes Conditions for Hardy-Weinberg Equilibrium Are Disrupted Temporarily

1

Thought Questions:

• The Hardy-Weinberg may seem over-simplistic or unrealistic. What are the pros and cons of a simple vs.a complex model? A realistic vs.an unrealistic model?

• If you know the genotype frequency in a population, can you predict the allele frequency? Do you need to make any assumptions to make this prediction?

• If you know the allele frequency in a population, can you predict the genotype frequency? Do you need to make any assumptions to make such a prediction?

• Sometimes conditions for Hardy-Weinberg equilibrium are disrupted temporarily:

• What trends in allele frequencies or genotype frequencies would indicate that such a disruption is happening?

• During such a disruption, what might happen to the relationship between allele and genotype frequencies?

• Once all of the conditions for Hardy-Weinberg equilibrium are restored, what will happen to allele frequencies? To genotype frequencies (and how fast)?

• In general, why might continuous traits be more difficult to study than Mendelian traits? Why might they be easier?

• When conservation biologists or wildlife managers are studying population genetics, what types of traits are they likely to examine, continuous traits or Mendelian traits? What types of Mendelian traits might they use? Is this a sensible choice?

Learning Objectives:
(1)Review the Hardy-Weinberg theorem and the conditions that must be met for the theorem to predict allele frequencies and genotype frequencies.
(2)Demonstrate important factors that influence population genetics in a simulated population of moths.
(3)Simulate the effects of changing conditions such as
genetic drift, and
modes of natural selection

• directional selection

• stabilizing selection

• disruptive selection

Readings: Read Ch. 23 in Cambell et al. Review Ch. 14 if you are not completely comfortable with basic principles of genetics such as probability, alleles, or mutation.

LAB OVERVIEW

The Big Picture:

Evolution occurs in populations of organisms, rather than in individual organisms, and it typically takes a long time, from decades to millions of years. It is difficult to study speciation or other major evolutionary changes in an introductory biology class. Such changes have been observed both in the laboratory and in the field, and several examples will be described in the recitation lecture. In lab, we will use the important technique of simulation modeling to study evolutionary change.

BEFORE LAB / take-home quiz due at the beginning of lab this week: Attending recitation and reading the lab and your text should help you to complete this week’s take-home quiz that is due at the very beginning of lab this week. Do the take-home quiz individually; do not work in groups!
FIRST HOUR
IN GROUPS / Work on the simulation models using the lab computers. Do Part One ‘Testing the Hardy-Weinberg Theorem’ and Part Two: ‘Genetic Drift’ in their entirety. If you finish, review and discuss Part Three: ‘Modes of Natural Selection.’
SECOND HOUR
IN GROUPS / Work on Part Three: ‘Modes of Natural Selection’ and plan an oral presentation with members of your group to present your approaches to the exercise and the results of your simulated experiment.
THIRD HOUR
IN GROUPS / Each group will have 10 minutes to present results from Part Three: ‘Modes of Natural Selection.’
TAKE HOME ASSIGNMENT
IN GROUPS
due at beginning of week 12 lab, 11/29-12/3 / For Part One (Testing the Hardy-Weinberg Theorem) summarize the results using the worksheets provided and written interpretation of your results. The lab manual includes bold-faced questions that you should address in your interpretations.
For Part Two (Genetic Drift), use a combination of the worksheets provided and a written summary of your results and their interpretation. Again, pay attention to the questions in bold-faced type.
For Part Three (Modes of Natural Selection)

• Your group will be assigned a specific “goal” – (Group 1) directional selection for black moths, (Group 2) directional selection for white moths, (Group 3) stabilizing selection, or (Group 4) disruptive selection. Be sure to put your group number and your assigned “goal” on the worksheet provided.

• Listen carefully to and take notes of the results of each group’s natural selection study. Everyone will be required to turn in a written assignment that covers all of the various modes of natural selection. This information may also be on your recitation final exam.

The worksheets and accompanying written interpretations (and answers to bold-faced questions) should be signed by you and your group partners to indicate that each of you has contributed equally.

Introduction

Genetic changes that occur in generations of populations over long periods of time are the basis for evolution of a species. In a population of any species, there are typically individuals that show differences in phenotype for a particular trait. These differences may represent genetic variation in the population.

For example, the peppered moths (Biston betularia) occur in two different colors or morphs. One morph has light, almost white-colored wings with small flecks of brown, while the other morph is predominantly black or very dark brown in color. This trait is controlled by a single gene and is an example of a discrete or Mendelian trait.

Another example of variation both among species and within populations is found in the genus of Galapagos finches, (Neospiza), studied by Darwin during the voyage of the Beagle and more recently by Peter and Rosemary Grant of Princeton. Galapagos finches show variation in beak size. This is a complex trait controlled by many genes. It is an example of a continuous or quantitative trait.

The underlying basis for inherited phenotypic differences is the genetic composition of an organism. Each organism has many genes, with each gene occurring at a locus, a physical location along a chromosome. The specific genetic material at a given locus is called an allele. The specific allele(s) occurring at one locus or at many loci is called the genotype of an individual organism. (In diploid organisms, there are two copies of each chromosome and so two alleles for each locus.)

The expression of the genotype is the phenotype. Among the many different organisms within a population, there may be just one type of allele occurring at a given locus, or there may be two or more alleles at that locus. The term gene pool refers to the population’s total range of allelic variation at one or more loci. Mutations, both random and induced, are the sources of new alleles that cause the inherited variation that is essential for evolution of populations and species.

Quantifying genetic variation in populations

Geneticists interested in population genetics study allele frequencies as a way to predict whether a population is evolving. When there are two or more alleles for a particular gene, it is sometimes possible to determine the relative proportion of each allele in a gene pool.

If one is studying two alleles called A and a for a particular gene at a known locus, p can be designated as the frequency of the A allele, and q as the frequency of the a allele. The sum of p and q represents 100% of the alleles for this gene in the population. In mathematical notation:

p + q = 1

Consider a population of 100 individuals, each of which has two alleles for this gene. Therefore, if 80 percent of the alleles are A, then p = 0.8. Twenty percent of the alleles would then be a; therefore q = 1 –p = 0.2. Also notice that p = 1 – q.

What is the relationship between the allele frequency and the genotype frequency in a population? In 1908, two geneticists, G. H. Hardy and W. Weinberg, independently proposed an equation to relate allele frequency to genotype frequency. The equation recognizes that if the organisms are diploid, then they may carry three possible combinations of these alleles: AA, Aa, or aa.

For each genotype, the frequency can be determined by remembering how alleles segregate from the two haploid parental gametes (each carrying just one allele) to make the new, diploid zygote that grows into an offspring (with each diploid cell carrying two alleles).

The probability of inheriting the A allele from any one parent is 0.8, the frequency of that allele in the overall population. The probability of inheriting the A allele from the other parent is also 0.8. These two probabilities multiply together (see Campbell et al. 6th edition pp. 254-255 for a review of probability).

So, the probability of a genotype being AA is p p = p2 = (0.8)2 = 0.64. Similarly, the probability of the offspring’s diploid genotype being aa is q2 = (0.2)2 = 0.04.

Finally, the probability of the offspring’s diploid genotype being Aa, with an A allele from one parent and an a allele from the other parent is 2pq = 2(0.8)(0.2) = 0.16. Multiplication by 2 is necessary because there are ‘two ways’ to have the Aa genotype (i.e., Aa, or inheriting A from one parent and a from the other parent; and aA, inheriting a from one parent and A from the other parent.)

The genotype frequencies of the three possible combinations of these alleles must add up to 100% and they do: p2 + q2 + 2pq = 0.64 + 0.04 + 2(0.16) = 1.00. We would predict 64 AA, 4 aa and 32 Aa genotypes in this population of 100 individuals.

This overall view of the population also makes sense if you recall that the frequency of all alleles was:

p + q = 1.0

And so the sum of all genotype frequencies can be determined from the following equation:

(p + q)2 = (p + q)(p + q) = p2 + 2pq + q2 = 1.0

Finally, it is important to point out that there may not be any variation within a population for a given allele. If all individuals in a population are homozygous for an allele being studied, that allele is known as a fixed allele. It is also possible for more than two alleles to exist for a given gene, a more complex situation that we will not address in today’s lab.

Applications of the Hardy-Weinberg theorem.

Rather than simply review the Hardy-Weinberg theorem, let’s think about a population geneticist who has the job of monitoring a population.

First, her boss is asking her for the allele frequency in a population, but she only has information about the genotype frequency. Can she predict the allele frequency? Yes, at least for the current generation. She can simply count up how many alleles there are in a population.

But, what if she needs to predict either the allele frequency or the genotype frequency in the next generation? This is trickier. To determine whether or not allele and genotype frequencies are changing from one generation to the next, she needs information about natural selection, genetic drift, mating patterns, migration,and mutation.

What if she is in the reverse situation: her boss wants to know genotype frequency in the current generation of a population, but she only has information about allele frequency. She doesn’t really need to worry about natural selection, because that only happens between one generation and the next. But it is actually not possible to make this prediction without making certain assumptions about the mating pattern in the population, migration, mutation, and the occurrence of genetic drift.

OK, what does the Hardy-Weinberg theorem have to do with this? The Hardy-Weinberg theorem states that allele frequencies and genotype frequencies will remain constant over several generations provided a number of conditions are met.

These conditions are as follows:

1. Large breeding population. The effect of random changes in allele frequencies (genetic drift) is greatly reduced in a population with large number of individuals.

1. Random mating. Individuals in a population show no preference for mating with other individuals of a particular phenotype.

1. The alleles under study do not mutate. Alleles are not being mutated to create new alleles, which would change the gene pool and alter genotype frequencies in a population.

1. There is no migration of individuals into or out of the population. Therefore, the gene pool will not change due to migration.

1. There is no selective advantage for any individual. If all individuals in a population have an equal chance of surviving and reproducing, then all of the genotypes represented in the population are equally viable and all alleles should be inherited equally.

These five conditions are required if a population is to maintain Hardy-Weinberg equilibrium. If all conditions are met in a population, then no change in allele or genotype frequency will occur in that population. Also, when these conditions are met, there is a one-to-one relationship between allele frequency and genotype frequency, such that genotype frequency can be predicted from allele frequency.

Such a model may seem overly simplistic and rather unrealistic, since few (if any) populations in nature meet all of these conditions. As you become more familiar with modeling in ecology and evolution, you may realize that models are actually quite helpful when they fail to match what happens in the real world and the data collected from the real world.

When the conditions for Hardy-Weinberg break down, it is an indication that there may be because changes in the gene pool occurring in a population — a process known as microevolution. It is important to understand how deviations from Hardy-Weinberg criteria can reflect microevolution. Such deviations will be further described in the assignments that accompany this lab as you design experiments that will help you learn how different mechanisms of microevolution can influence population genetics.

An example of an evolving population

A famous example of natural selection involves British moths called peppered moths (Biston betularia). These moths are found in two different colors or morphs. One morph has light, almost white-colored wings with small flecks of brown, while the other morph is predominantly black or very dark brown in color. This trait is controlled by a single gene, and you may recall that we used it as an example of a discrete or Mendelian trait.

Because birds are predators of peppered moths, wing color is an important camouflage for moths — natural selection can occur for wing color and for the alleles affecting wing color. White morphs can blend well into the light, peppered appearance of lichen-colored trees but black or brown moths cannot. Black or brown morphs can blend well into the dark bark of trees affected by pollution, but white moths cannot. Presumably, natural selection was occurring both before and after industrialization. But the details of that natural selection depend on the selective environment — in this case, whether lichen-covered tree bark is common or whether industrial pollution kills off the lichens and darkens the bark on most trees.

Modeling exercises

You will use PopGenLab to learn how changes in important parameters of population genetics can influence evolution in simulated populations of moths. These moths resemble peppered moths, but are not exactly the same as them. You are provided with moths living in tree stands. A single gene with two alleles controls wing color of these moths, and each genotype produces a different color pattern.

Moth survival depends on the insect’s ability to blend against the bark of the trees. Three different tree types have bark colors that match the colors of the moths in the simulation. The experiments that you set up and analyze in PopGenLab will provide you with an important understanding of the factors influencing Hardy-Weinberg equilibrium and natural selection.

By varying parameters such as allele frequencies and survival rates of each genotype, population numbers, population carrying capacity, mating patterns, and the frequency of population crashes due to natural disasters, you will design experiments to help you understand how each parameter can affect evolution within the population of moths.

Getting to Know PopGenLab

This assignment is designed to help you become familiar with the operation of PopGenLab by applying the Hardy-Weinberg theorem to learn about Hardy-Weinberg equilibrium parameters. The first screen that appears in PopGenLab shows you an input parameter page with a table listing the default parameters for the laboratory conditions that you can manipulate when setting up your experiments. You should enlarge this window before you begin working.

Before you can set up any experiment in PopGenLab, you must be familiar with the input parameters that you can manipulate for this population of moths. A brief description of each input parameter is provided below. Refer back to this section as needed when you are working on different assignments.

Click on the Change Inputs button to see all the parameters you can manipulate for this lab. A new page will open with buttons for each of the input parameters located at the left side of each page (genotype frequency will be open as the first input parameter). Click on each input parameter and read the descriptions below. Change each parameter so that you can become familiar with how each input parameter operates. You can set these to exact values by clicking on the scoll bars.

Genotype Frequency - allele frequency for wing color (controlled by a single gene) is shown for two alleles, A and a, as a pie chart of the phenotype resulting from each of the three possible genotypes: AA (black moths), Aa (brown moths), and aa (white moths). Notice that the default frequency is 50% for each allele.