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Genes in Populations

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Introduction and Goals

So far, we have talked about the behavior of genes that are passed from one generation to the next, focusing on the genotypes and phenotypes of individuals. Now we'll take a broader look at genetics and see how the genetics of populations are studied. As you will learn, evolutionary change takes place through changes in the genetic composition of a population. The field of population genetics spans the disciplines of genetics and evolution. By the end of this tutorial you should be able to describe:

  • Population genetics
  • Species definitions
  • How genetic variation in a population is studied
  • The Hardy-Weinberg equation
  • The factors that influence changes in allele frequencies

Performance Objectives

  • You should be able to describe the assumptions of a population in Hardy-Weinberg equilibrium
  • You should be able to apply the appropriate Hardy-Weinberg equation (solving for either allele and/or genotype frequency) to solve population genetics problems

As you read through the tutorial, answer the questions on the lecture preparation homework (click here to access the homework).


Population Genetics

A population is a group of organisms that are members of the same species and that live in the same geographical area. While natural selection occurs at the level of the individual, through variations in fitness among individuals, evolution occurs at the population level. The reason for this is demonstrated in the following table:




Life Span

One generation

Many generations

Genetic Characterization


Allele frequencies

Genetic Variability





Can change over time

The genotype of an individual is, for the most part, determined at the moment of fertilization and cannot be changed during that individual's lifetime. However, because populations are comprised of many individuals from different generations, the allele frequencies in a population can change over time thus evolve. Population geneticists focus their studies in two areas. The first area is the measurement of genetic variation within a population. Morphological characters (e.g., variations in length, weight, coloration) and molecular characters (e.g., variations in nucleotide sequences of DNA or in amino acid sequences of proteins) are examined and quantified. The second area is the examination of the mechanisms by which genetic variation changes over space and time. 

The evolutionary forces that can influence allele frequencies will be examined in the next tutorial. In this tutorial we will examine how allele frequencies are used to make predictions about the genotypes of a population.

Table Reference: After Table 20-1 in Strickberger, M.W. 1996. Evolution. Second Edition. Jones and Barlett, Sudbury, Massachusetts.


What is a Species?

When we study genetically related populations, we are studying groups of individuals that are all members of the same species. What is a species? This is a difficult question to answer and Tutorial 39 will focus on this topic. The problem in defining a species is that no single definition works for all cases. A recent survey found more than 25 separate concepts of species.

In this class we will use the biological species concept as our working definition, although later we will discuss why this concept does not work for all species. This concept defines a species as a group of potentially interbreeding individuals that can produce fertile offspring. This potential to interbreed means that individuals can move between populations, therefore, there is gene flow (really allele flow, because all members of a species have the same genes) between populations. Reproductive isolation from other species results in a gene poo lthat is closed to alleles from other species.



A species occupies an area termed its range. The US Geological Survey database contains range maps for most tree species found in the United States ( However, it is important to note that a species is usually restricted to specific habitats within its geographic range. For example, the map in Figure 1 shows that the entire state of Pennsylvania is part of the range of the bullfrog (Rana catesbieana); however, bullfrogs are not found on the Penn State, University Park campus. This is because bullfrog populations are found in bodies of water (e.g., ponds or lakes), therefore, they occupy only some of the habitats within their range.

Figure 1. Geographical area where the bullfrog can be found over the course of a year. Map from the Northern Praries Wildlife Research Center ( (Click image to enlarge)

Genetic Variation

As previously mentioned, population geneticists measure the amount of genetic variation found within a species. Variations can be measured within a population and between populations. When there is no variation among the members of a population, the population is monomorphic for that particular character; monomorphic means that just one form exists. For example, the population of squirrels (Sciurus carolinensis) on the Penn State campus is monomorphic; all of the squirrels in this population have gray fur.

However, this is not true of all squirrel populations. At Kent State, the squirrel population is polymorphic for fur color (i.e., they have either gray or black fur, Figure 3).

Variations in some populations for a given character can be extreme (for example, the variation of shell colors in a species of Caribbean snail, Figure 4).

Other factors, besides genetics, can contribute to the variation of a character within a population. For example, phenotypes can be affected by the environment. When you spend a lot of time in the sun, your skin becomes darker than the color that is determined by your genotype. As you learned, the genetic disorder PKU  can be suppressed by diet. Other examples of environmental alterations are all around us. No two trees look exactly alike because branching patterns and leaf and limb numbers can be influenced by light, water, and nutrient availability. In humans, IQ and size have been linked to diet in babies and young children.. In short, the environment can influence how genetic information is expressed.

Figure 2. Gray Squirrel. (Click image to enlarge)

Figure 3. Black Squirrel. (Click image to enlarge)

Figure 4. Snail Shells. (Click image to enlarge)

The Genetic Composition of a Population

Previously we examined the genotypes of individuals and how they relate to the phenotypes expressed in subsequent generations. Keep in mind, the genotype of an individual becomes fixed the moment that two gametes unite to form the diploid zygote (barring mutation). However, a population consists of a group of individuals that  may differ genotypically from one another. How do we describe the genotype of a population?

The genetic makeup of a population can be described by the frequency of alleles that exist in that population. This is typically expressed as a fractional equivalent of one. In other words, a population that has only one allele for a particular gene has an allele frequency of one for that allele. If two or more alleles for a particular gene exist, then each has an allele frequency that is some fraction of one (however, all of the allele frequencies must add up to one). In the example of cystic fibrosis, the major CF allele is found at a frequency of 0.04 (4%) in Caucasian populations. This means that the wild-type allele is found at a frequency of 0.96 (96%). Note that 0.96 + 0.04 = 1. Although the number of alleles may be quite variable (some genes have dozens of alleles), the simple arithmetic relationship still applies; that is, the frequencies of alleles for a given gene must add up to one.

Obviously a population can have many genes for which alternative alleles exist. In the human  species, about 30% of all genes have two or more alleles. In other words, 70% of the genes are fixed (have an allele frequency of one), whereas 30% of the genes have allele frequencies less than one.


Probability and Populations

The behavior of alternative (and sometimes deleterious) alleles found in human populations was discussed in Tutorial 31. Let's take a closer look at these alleles and see how the genetic composition of a population is studied. Allele frequencies can be calculated if one knows phenotypic frequencies (and vice versa).

How are allele frequencies actually determined? The Hardy-Weinberg equation can be used to calculate allele frequencies. For example, let's apply the equation to PKU disease and designate the PKU allele "q," and the wild-type allele "p." What is the allele frequency for the PKU allele?

The frequency of individuals who  are homozygous for the PKU allele in a population is q X q = q2. You should recognize this as the Rule of Multiplication. You should also know that q2 represents the PKU-affected individuals in the population because they are homozygous for q. The frequency of individuals who are homozygous for the wild-type alleles (the p allele) in a population is p X p = p2. The frequency of individuals who are heterozygous in a population (PKU carriers) is p X q = pq. Note, there are two ways to get this last calculation (depending on which parent donates the q allele); therefore, the Rule of Addition is also used to compute the odds of being heterozygous (pq + pq or 2pq).

In a population, the frequency of PKU individuals who are homozygous for the allele + those who are heterozygous for the allele + those who are homozygous for the wild-type allele = 1. In other words, p2 + 2pq + q2 = 1. This is the Hardy-Weinberg equation for genotypes. (You may also recognize this as a binomial expansion.) Before going on, be sure you understand what these terms represent.Now, let's solve our original PKU problem. Restated, what is the allele frequency for the PKU allele (q)? We know that the phenotypic frequency of PKU disease is 1:10,000 or 0.0001. Remember that this is the phenotypic frequency, but we want to determine the allele frequency for the PKU allele (q). Recognize that q2 is the phenotypic frequency (affected individuals) in the Hardy-Weinberg equation. Therefore, the square root of the phenotypic frequency will equal the allele frequency of the PKU allele. The square root of 0.0001 is 0.01.

Because the wild-type allele (p) + the PKU allele (q) must equal one (p + q = 1), we can determine the wild-type allele frequency. 1.0 - 0.01 = 0.99 = wild-type allele frequency.


Applying the Hardy-Weinberg Equation

Now let's try a problem using the squirrels from Kent State, which were described earlier in this tutorial. Take out a piece of paper and work along with the following description. The key to understanding the equation is writing it out yourself.

Suppose that you have decided to visit Kent State for the weekend to see these squirrels for yourself. You want to determine the frequency of black (B) and gray (b) alleles in the squirrel population. Since it is not possible to see all of the squirrels on campus, you decide to count 100 squirrels and use this as your sample to determine the allele frequencies. By the end of the day you have scored 100 squirrels; 84 were black and 16 were gray. Next you need to use the Hardy-Weinberg equation to determine the frequency of these two alleles in this population. At first you decide that the allele frequencies are 0.84 for the B allele and 0.16 for the b allele. Is this correct? Are you overlooking something? When you see a black squirrel, what is its genotype? Black squirrels are either BB or Bb. So some black squirrels are carrying the b allele. Black is a complete dominant, therefore, there is no way to tell which squirrels are heterozygous for this allele.

Since you do not know if a black squirrel has a BB or Bb genotype, you cannot use the number of black squirrels to determine the frequency of the black allele. But what about gray squirrels? Since gray is recessive to black, all of the gray squirrels are genotype bb, or they represent the q2 value in the p2 + 2pq + q2 equation. Suddenly this is looking much easier. If q2 = 16/100 = 0.16, then q = the square root of 0.16 = 0.4. Since p + q = 1, then 1 - q = p, so 1 - 0.4 = 0.6 = p. So the frequency of the black allele (B) is 0.6 and the frequency of the gray allele (b) is 0.4. Now that you have this information, you can estimate the frequencies of the different genotypes in the population: BB, Bb and bb.

Figure 4. Black Squirrel. (Click image to enlarge)

Multiple Alleles

All of the cases that we have examined have had a single gene with two alleles. But what about genes that have three or more alleles? This is dealt with in the same way, but the determination of allele frequencies becomes a bit more involved.


Tutorial 30 described the human ABO blood group system (Figure 5). This was used as an example of a gene with multiple alleles (IA, IB, i) and codominance because both alleles are expressed in AB heterozygous individuals. The O allele (designated as i) is recessive to the IA and IB alleles. Now we’ll work a problem for a system with three alleles. In  a human population, the IA allele has a frequency of 0.3 and the IB allele has a frequency of 0.1. Pull out a piece of paper and a pencil and write down these numbers.

First, calculate the frequency of the O allele. Remember, the allele frequencies for a particular gene must add up to one.  Now that you have these three allele frequencies, determine the frequencies for all of the possible genotypes in the population.  When you are finished, these should also add up to one.  If it is helpful, the HW equation that you would use for three alleles is p+q+r=1, and the equation for the genotypes is p2 + 2pq + q2 +2pr +2qr  + r2 = 1.  There will be some questions using three alleles in the tutorial quiz.

Figure 5. Multiple alleles for the ABO blood groups. (Click image to enlarge)


Using the Hardy-Weinberg Equation in Evolutionary Studies

You should now appreciate how the Hardy-Weinberg equation can be used to study the genetic composition of a population. But how does this fit into evolution studies?

The answer is that changes in allele frequencies are the most fundamental indication that evolution is occurring in a population. If two populations of the same species have the same allele frequency for a given gene, it can be concluded  that evolutionary forces are not operating on that gene (at least at that time). On the other hand, if the allele frequencies are different for a given gene, thenthese evolutionary forces, which we will discuss in Tutorial 37,  could be operating on that population.

Importantly, natural selection is only one force that can influence changes in allele frequencies. At least four other evolutionary forces  can also affect a change in allele frequency.

  • First is a small population size. If the population is small, then random changes in the gene pool (genetic drift) can alter the allele frequency.
  • Second is migration/immigration. If individuals migrate into or immigrate out of a given population, they can affect the allele frequency.
  • Third are mutations. Spontaneous mutations create new alleles, and these can affect allele frequencies.
  • Fourth are nonrandom matings. If mate selection is not random (for a particular gene), then this can alter the genotype frequencies in the population.

If allele frequencies remain stable between generations, then the population is considered to be in Hardy-Weinberg equilibrium.



This tutorial covered the basic principles of population genetics. A population is a group of organisms that are members of the same biological species and that live in the same geographic area. There can be gene flow between different populations of a biological species, however, reproductive isolation creates a gene pool that excludes alleles entering from other species. Characters in a population can be monomorphic, showing no variation, or polymorphic, having at least two different variants. Variation can be caused by the organism's genotype or by environmental effects. The Hardy-Weinberg equation can be used to examine genetic variation within populations. In the case of two alleles for a gene, the sum of the frequency of the alleles equals 1 or 100%. This is represented by the equation p + q = 1. To determine the frequencies of the three possible genotypes, use the equation p2 + 2pq + q2 = 1. When the allele frequencies stay the same between generations, the population is in Hardy-Weinberg equilibrium. Hardy-Weinberg equilibrium requires that allele frequencies within a population remain the same from one generation to the next, as long as certain conditions (including no mutation, large population size, no migration, random mating, and no natural selection) are met. The next tutorial will explore the evolutionary forces that can cause changes in allele and/or genotype frequencies in a population; that is, changes that lead to microevolution.




After reading this tutorial, you should understand the following terms:

  • gene flow
  • gene pool
  • genetic drift
  • Hardy-Weinberg equation
  • monomorphic
  • polymorphic
  • population
  • range
  • species




Case Study for Genes in Populations

DNA fingerprinting is used in a variety of fields including agriculture, medicine, and historical investigations. It has become particularly useful in forensics, especially in criminal investigations.

A DNA fingerprint is created in a series of steps:

  1. DNA must be isolated - at a crime scene DNA can be isolated from blood, saliva, semen, hair or skin. 
  2. If the amount of DNA that is isolated is small, PCR is used to amplify the isolated DNA (remember, you used PCR to amplify antibiotic resistance genes in bacteria when investigating the Salmonella outbreak at a chicken farm). 
  3. The amplified DNA is then cut into pieces using special enzymes known as "restriction enzymes". Restriction enzymes cut DNA at precise sequences (for example, the restriction enzyme EcoR1 cuts DNA at the sequence GAATTC).
  4. The DNA pieces are then run through a gel (using electricity); the smaller pieces travel further than the larger pieces. This creates a banding pattern that can be seen by fluorescing the DNA bands. 
  5. The pieces of DNA can be treated as alleles. If the frequencies of these alleles in the population are known, it is possible to calculate the probability, using the Hardy-Weinberg equation, that 2 unrelated people have the same set of alleles.

The DNA fingerprints below come from 3 sources – the victim of a violent crime, DNA evidence collected at the crime scene, and the primary suspect in the crime. There are 4 different gene sequences shown. For each gene, if a single band is seen that indicates the individual is homozygous for that particular gene. If two bands are seen, that indicates the individual is heterozygous.

  • Using the allele frequency information provided in the table below, calculate the probability that the DNA from the crime scene belongs to the suspect.


Gene SequenceAllele Frequencies
1Allele 1 = .3, Allele 2 = .4, Allele 3 = .3
2Allele 1 = .4, Allele 2 = .6
3Allele 1 = .1, Allele 2 = .9
4Allele 1 = .5, Allele 2 = .5

Now that you have read this tutorial and worked through the case study, go to ANGEL and complete the tutorial practice problems  to test your understanding.  Questions?  Either send your instructor a message through ANGEL or attend ao online office hour (the times are posted on ANGEL).