Are mutations the cause of alleles?

Are mutations the cause of alleles?

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For example, some leopards have a mutation which causes black fur. So Black fur and normal fur colour (orange-white) are both alternate forms of the same gene, right? So does that mean that mutations cause alleles?


That's correct. Alleles are alternate forms of a gene that occur at the same locus and arise by mutation. Another example might be sickle cell anemia where a SNP (a single base change) is the cause of the disease.

Section 4: What causes mutations?

Sunlight and skin damage – It’s not in the small print!

Use with care!

Imagine for a moment that you are not studying biology but lying in the sun relaxing, listening perhaps to the sound of people and the sea. It feels great, but behind the feeling lurks a danger and it’s not mentioned in the ‘small print’ of the holiday brochures.

As you lie in the sun you will be exposed to ultra violet light radiation from the sun. If you are pale skinned and have not applied plenty of sun screen, the radiation will be damaging your skin. If this happens often it may lead to skin cancer including the very aggressive melanoma type. The damage is caused by solar Ultra-Violet type B (UVB) radiation making some of the ‘letters’ or bases of the DNA molecule fuse together. This change, or mutation, in the DNA sequence prevents the code from being read and translated correctly. Some sun-tanning devices can also damage your DNA. Remember, the damage may not be evident until perhaps some years later. Enjoy your time in the sun, after all it does help you produce the vitamin D you need, but be wise before the event, not after it!

Smoking tobacco causes lung cancer, and it kills – It’s on the packet!

In a similar way to solar radiation, some of the approx. 7,000 compounds in tobacco smoke distort the shape of the DNA molecule and causes changes or mutations in the DNA code. Smoking can cause lung cancer and also contribute to other health problems as well, such as poor breathing and heart conditions.

Other factors also contribute to cancer.
Solar radiation and smoking tobacco are just two of many factors that can contribute to cancer formation.
In general, factors can be divided into three groups or sets as shown in the Venn diagram below.

Graphic 10. Venn diagram showing three sets of factors that can contribute to cancer formation.Most cancers will develop when factors from the three sets are present as a mix, (the red intersection). Credit: Courtesy Professor Mel Greaves, FRS. (ICR)

What are the specific factors in each circle (set) in the diagram?

Selective and Environmental Pressures

Natural selection only acts on the population’s heritable traits: selecting for beneficial alleles and thus increasing their frequency in the population, while selecting against deleterious alleles and thereby decreasing their frequency—a process known as adaptive evolution. Natural selection does not act on individual alleles, however, but on entire organisms. An individual may carry a very beneficial genotype with a resulting phenotype that, for example, increases the ability to reproduce (fecundity), but if that same individual also carries an allele that results in a fatal childhood disease, that fecundity phenotype will not be passed on to the next generation because the individual will not live to reach reproductive age. Natural selection acts at the level of the individual it selects for individuals with greater contributions to the gene pool of the next generation, known as an organism’s evolutionary (Darwinian) fitness.

Fitness is often quantifiable and is measured by scientists in the field. However, it is not the absolute fitness of an individual that counts, but rather how it compares to the other organisms in the population. This concept, called relative fitness, allows researchers to determine which individuals are contributing additional offspring to the next generation, and thus, how the population might evolve.

There are several ways selection can affect population variation: stabilizing selection, directional selection, diversifying selection, frequency-dependent selection, and sexual selection. As natural selection influences the allele frequencies in a population, individuals can either become more or less genetically similar and the phenotypes displayed can become more similar or more disparate.

Stabilizing Selection

If natural selection favors an average phenotype, selecting against extreme variation, the population will undergo stabilizing selection (Figure 1a). In a population of mice that live in the woods, for example, natural selection is likely to favor individuals that best blend in with the forest floor and are less likely to be spotted by predators. Assuming the ground is a fairly consistent shade of brown, those mice whose fur is most closely matched to that color will be most likely to survive and reproduce, passing on their genes for their brown coat. Mice that carry alleles that make them a bit lighter or a bit darker will stand out against the ground and be more likely to fall victim to predation. As a result of this selection, the population’s genetic variance will decrease.

Directional Selection

When the environment changes, populations will often undergo directional selection (Figure 1b), which selects for phenotypes at one end of the spectrum of existing variation. A classic example of this type of selection is the evolution of the peppered moth in eighteenth- and nineteenth-century England. Prior to the Industrial Revolution, the moths were predominately light in color, which allowed them to blend in with the light-colored trees and lichens in their environment. But as soot began spewing from factories, the trees became darkened, and the light-colored moths became easier for predatory birds to spot. Over time, the frequency of the melanic form of the moth increased because they had a higher survival rate in habitats affected by air pollution because their darker coloration blended with the sooty trees. Similarly, the hypothetical mouse population may evolve to take on a different coloration if something were to cause the forest floor where they live to change color. The result of this type of selection is a shift in the population’s genetic variance toward the new, fit phenotype.

Diversifying Selection

Sometimes two or more distinct phenotypes can each have their advantages and be selected for by natural selection, while the intermediate phenotypes are, on average, less fit. Known as diversifying selection (Figure 1c), this is seen in many populations of animals that have multiple male forms. Large, dominant alpha males obtain mates by brute force, while small males can sneak in for furtive copulations with the females in an alpha male’s territory. In this case, both the alpha males and the “sneaking” males will be selected for, but medium-sized males, which can’t overtake the alpha males and are too big to sneak copulations, are selected against. Diversifying selection can also occur when environmental changes favor individuals on either end of the phenotypic spectrum. Imagine a population of mice living at the beach where there is light-colored sand interspersed with patches of tall grass. In this scenario, light-colored mice that blend in with the sand would be favored, as well as dark-colored mice that can hide in the grass. Medium-colored mice, on the other hand, would not blend in with either the grass or the sand, and would thus be more likely to be eaten by predators. The result of this type of selection is increased genetic variance as the population becomes more diverse.

Practice Question

Figure 1. Different types of natural selection can impact the distribution of phenotypes within a population. In (a) stabilizing selection, an average phenotype is favored. In (b) directional selection, a change in the environment shifts the spectrum of phenotypes observed. In (c) diversifying selection, two or more extreme phenotypes are selected for, while the average phenotype is selected against.

In recent years, factories have become cleaner, and less soot is released into the environment. What impact do you think this has had on the distribution of moth color in the population?

Frequency-dependent Selection

Figure 2. A yellow-throated side-blotched lizard is smaller than either the blue-throated or orange-throated males and appears a bit like the females of the species, allowing it to sneak copulations. (credit: “tinyfroglet”/Flickr)

Another type of selection, called frequency-dependent selection, favors phenotypes that are either common (positive frequency-dependent selection) or rare (negative frequency-dependent selection). An interesting example of this type of selection is seen in a unique group of lizards of the Pacific Northwest. Male common side-blotched lizards come in three throat-color patterns: orange, blue, and yellow. Each of these forms has a different reproductive strategy: orange males are the strongest and can fight other males for access to their females blue males are medium-sized and form strong pair bonds with their mates and yellow males (Figure 2) are the smallest, and look a bit like females, which allows them to sneak copulations. Like a game of rock-paper-scissors, orange beats blue, blue beats yellow, and yellow beats orange in the competition for females. That is, the big, strong orange males can fight off the blue males to mate with the blue’s pair-bonded females, the blue males are successful at guarding their mates against yellow sneaker males, and the yellow males can sneak copulations from the potential mates of the large, polygynous orange males.

In this scenario, orange males will be favored by natural selection when the population is dominated by blue males, blue males will thrive when the population is mostly yellow males, and yellow males will be selected for when orange males are the most populous. As a result, populations of side-blotched lizards cycle in the distribution of these phenotypes—in one generation, orange might be predominant, and then yellow males will begin to rise in frequency. Once yellow males make up a majority of the population, blue males will be selected for. Finally, when blue males become common, orange males will once again be favored.

Negative frequency-dependent selection serves to increase the population’s genetic variance by selecting for rare phenotypes, whereas positive frequency-dependent selection usually decreases genetic variance by selecting for common phenotypes.

Sexual Selection

Males and females of certain species are often quite different from one another in ways beyond the reproductive organs. Males are often larger, for example, and display many elaborate colors and adornments, like the peacock’s tail, while females tend to be smaller and duller in decoration. Such differences are known as sexual dimorphisms (Figure 3), which arise from the fact that in many populations, particularly animal populations, there is more variance in the reproductive success of the males than there is of the females. That is, some males—often the bigger, stronger, or more decorated males—get the vast majority of the total matings, while others receive none. This can occur because the males are better at fighting off other males, or because females will choose to mate with the bigger or more decorated males. In either case, this variation in reproductive success generates a strong selection pressure among males to get those matings, resulting in the evolution of bigger body size and elaborate ornaments to get the females’ attention. Females, on the other hand, tend to get a handful of selected matings therefore, they are more likely to select more desirable males.

Sexual dimorphism varies widely among species, of course, and some species are even sex-role reversed. In such cases, females tend to have a greater variance in their reproductive success than males and are correspondingly selected for the bigger body size and elaborate traits usually characteristic of males.

Figure 3. Sexual dimorphism is observed in (a) peacocks and peahens, (b) Argiope appensa spiders (the female spider is the large one), and in (c) wood ducks. (credit “spiders”: modification of work by “Sanba38″/Wikimedia Commons credit “duck”: modification of work by Kevin Cole)

The selection pressures on males and females to obtain matings is known as sexual selection it can result in the development of secondary sexual characteristics that do not benefit the individual’s likelihood of survival but help to maximize its reproductive success. Sexual selection can be so strong that it selects for traits that are actually detrimental to the individual’s survival. Think, once again, about the peacock’s tail. While it is beautiful and the male with the largest, most colorful tail is more likely to win the female, it is not the most practical appendage. In addition to being more visible to predators, it makes the males slower in their attempted escapes. There is some evidence that this risk, in fact, is why females like the big tails in the first place. The speculation is that large tails carry risk, and only the best males survive that risk: the bigger the tail, the more fit the male. This idea is known as the handicap principle.

The good genes hypothesis states that males develop these impressive ornaments to show off their efficient metabolism or their ability to fight disease. Females then choose males with the most impressive traits because it signals their genetic superiority, which they will then pass on to their offspring. Though it might be argued that females should not be picky because it will likely reduce their number of offspring, if better males father more fit offspring, it may be beneficial. Fewer, healthier offspring may increase the chances of survival more than many, weaker offspring.

In both the handicap principle and the good genes hypothesis, the trait is said to be an honest signal of the males’ quality, thus giving females a way to find the fittest mates— males that will pass the best genes to their offspring.

No Perfect Organism

Natural selection is a driving force in evolution and can generate populations that are better adapted to survive and successfully reproduce in their environments. But natural selection cannot produce the perfect organism. Natural selection can only select on existing variation in the population it does not create anything from scratch. Thus, it is limited by a population’s existing genetic variance and whatever new alleles arise through mutation and gene flow.

Natural selection is also limited because it works at the level of individuals, not alleles, and some alleles are linked due to their physical proximity in the genome, making them more likely to be passed on together (linkage disequilibrium). Any given individual may carry some beneficial alleles and some unfavorable alleles. It is the net effect of these alleles, or the organism’s fitness, upon which natural selection can act. As a result, good alleles can be lost if they are carried by individuals that also have several overwhelmingly bad alleles likewise, bad alleles can be kept if they are carried by individuals that have enough good alleles to result in an overall fitness benefit.

Furthermore, natural selection can be constrained by the relationships between different polymorphisms. One morph may confer a higher fitness than another, but may not increase in frequency due to the fact that going from the less beneficial to the more beneficial trait would require going through a less beneficial phenotype. Think back to the mice that live at the beach. Some are light-colored and blend in with the sand, while others are dark and blend in with the patches of grass. The dark-colored mice may be, overall, more fit than the light-colored mice, and at first glance, one might expect the light-colored mice be selected for a darker coloration. But remember that the intermediate phenotype, a medium-colored coat, is very bad for the mice—they cannot blend in with either the sand or the grass and are more likely to be eaten by predators. As a result, the light-colored mice would not be selected for a dark coloration because those individuals that began moving in that direction (began being selected for a darker coat) would be less fit than those that stayed light.

Finally, it is important to understand that not all evolution is adaptive. While natural selection selects the fittest individuals and often results in a more fit population overall, other forces of evolution, including genetic drift and gene flow, often do the opposite: introducing deleterious alleles to the population’s gene pool. Evolution has no purpose—it is not changing a population into a preconceived ideal. It is simply the sum of the various forces described in this chapter and how they influence the genetic and phenotypic variance of a population.

In Summary: Selective and Environmental Pressures

Because natural selection acts to increase the frequency of beneficial alleles and traits while decreasing the frequency of deleterious qualities, it is adaptive evolution. Natural selection acts at the level of the individual, selecting for those that have a higher overall fitness compared to the rest of the population. If the fit phenotypes are those that are similar, natural selection will result in stabilizing selection, and an overall decrease in the population’s variation. Directional selection works to shift a population’s variance toward a new, fit phenotype, as environmental conditions change. In contrast, diversifying selection results in increased genetic variance by selecting for two or more distinct phenotypes.

Other types of selection include frequency-dependent selection, in which individuals with either common (positive frequency-dependent selection) or rare (negative frequency-dependent selection) phenotypes are selected for. Finally, sexual selection results from the fact that one sex has more variance in the reproductive success than the other. As a result, males and females experience different selective pressures, which can often lead to the evolution of phenotypic differences, or sexual dimorphisms, between the two.

INS-gene mutations: from genetics and beta cell biology to clinical disease

A growing list of insulin gene mutations causing a new form of monogenic diabetes has drawn increasing attention over the past seven years. The mutations have been identified in the untranslated regions of the insulin gene as well as the coding sequence of preproinsulin including within the signal peptide, insulin B-chain, C-peptide, insulin A-chain, and the proteolytic cleavage sites both for signal peptidase and the prohormone convertases. These mutations affect a variety of different steps of insulin biosynthesis in pancreatic beta cells. Importantly, although many of these mutations cause proinsulin misfolding with early onset autosomal dominant diabetes, some of the mutant alleles appear to engage different cellular and molecular mechanisms that underlie beta cell failure and diabetes. In this article, we review the most recent advances in the field and discuss challenges as well as potential strategies to prevent/delay the development and progression of autosomal dominant diabetes caused by INS-gene mutations. It is worth noting that although diabetes caused by INS gene mutations is rare, increasing evidence suggests that defects in the pathway of insulin biosynthesis may also be involved in the progression of more common types of diabetes. Collectively, the (pre)proinsulin mutants provide insightful molecular models to better understand the pathogenesis of all forms of diabetes in which preproinsulin processing defects, proinsulin misfolding, and ER stress are involved.

Keywords: Diabetes Endoplasmic reticulum stress Insulin biosynthesis Insulin gene mutation Pancreatic beta cell Proinsulin misfolding.

Copyright © 2014 Elsevier Ltd. All rights reserved.


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Stabilizing Selection

If natural selection favors an average phenotype, selecting against extreme variation, the population will undergo stabilizing selection (Figure 1a). In a population of mice that live in the woods, for example, natural selection is likely to favor individuals that best blend in with the forest floor and are less likely to be spotted by predators. Assuming the ground is a fairly consistent shade of brown, those mice whose fur is most closely matched to that color will be most likely to survive and reproduce, passing on their genes for their brown coat. Mice that carry alleles that make them a bit lighter or a bit darker will stand out against the ground and be more likely to fall victim to predation. As a result of this selection, the population&rsquos genetic variance will decrease.

Evolution (DNA Mutation) & Case Study

Evolution – slow modifications of traits overtime for improvement
– Modifications are done in various ways, though all are related to mutations in DNA
Occurs through various ways: DNA Polymerase, crossing over, independent assortment, sex

DNA Polymerase
– Mistakes can be done in 3 ways, Addition, Deletion, and Substitution during S-phase
Addition, DNA Polymerase base-pairs an extra nucleotide (A, T, C, or G), causing frame-shift mutation
Deletion, DNA Polymerase left out one nucleotide while base-pairing, causing frame-shift mutation
— Frame shift mutation: error that causes the whole reading scheme of DNA (3 nucleotides at a time) to change, by altering the letters either through adding extras or leaving out existing ones
Substitution, replaces one nucleotide while base-pairing (thus instead of A — T, it became A — G)
– Overall, Addition and Deletion causes the most threat (as it alters all instructions that comes afterwards) all three could cause changes to START and / or STOP codons, thus resulting either no proteins made or long chain of amino acids

Evolution -> contains four stages
– Overproduction, having many offspring -> increase chance of surviving offspring
– Inherited Variation, modifications that came from their parents -> create more variations
– Struggle to Survive, exposure to environment and compete -> leave the negatively-affected-mutants out of competition for better DNA
— Done in three ways: natural selection (exposure to natural environments), artificial selection (exposure to humane environment), sexual selection (species deciding their partners)
– Successful Reproduction, offspring that survived and thrived through the selections, and produces offspring -> pass on positive DNA

7.6 – Evaluate the effect of mutation, gene flow and genetic drift on the gene pool of populations

Gene pool: all the genes in a population.

Genetic drift: random change in allele frequency by chance (unlike natural selection which is not based on chance but on which alleles are most favourable).

Gene flow: passing on genetic material from one population to another e.g. pollen blown to a new area.

Mutation Gene flow Genetic drift
Effect on gene pool of population Introduces new alleles which enter the gene pool = increases gene pool. Recombines DNA between population = increases gene pool. As a particular allele increases in frequency, it decreases the frequency of other alleles = decreases gene pool.

Step 3a: Mutations & Alleles

This brief video introduces mutation at the DNA level as the source of variation in genes. The next two activities will explore the mechanism and result of mutation in further detail.

Project video to the whole class.

Mutate a DNA Sequence (online)

This activity offers a closer look at the types of DNA mutations that can happen and their consequences. Make a small change to a DNA sequence of a gene and see the effect on the resulting protein product.

Have students explore individually or in pairs.

  • The arrangement of DNA building blocks in a gene specifies the order of amino acids in the protein it codes for.
  • During DNA replication, occasional errors change DNA sequences. This process is called mutation.
  • Changing the order of DNA building blocks in a gene can change the order of amino acids in the protein that it codes for, thereby changing the structure and function of the protein.

Computers with internet access.

To ensure your students understand frame shift mutations, you can review the content that's below the interactive.

Mutate a DNA Sequence (paper)

Using a paper model, students make a mutation of their choice (substitution, insertion, or deletion) in a gene during DNA replication. Then they transcribe and translate the mutated sequence to reveal the resulting amino acid sequence.

After completing the activity, students learn about the example gene and protein—Human Leukocyte Antigen (HLA-B)—including known variants.

You may wish to review the following:

  • DNA replication follows base-paring rules: A-T, C-G
  • Sometimes during DNA replication, a base is inserted, deleted, or substituted with a different one, changing the DNA sequence of a gene.
  • Changes in the DNA sequence of a gene can lead to changes in the protein it codes for.
  • Only mutations in germ cells (eggs or sperm) can be passed to offspring.

As in reality, the mutations students make are random. There will be variation in the resulting amino acid sequence.

Students may be tempted to skip using the “molecular machinery” (ribosome) in this model. Encourage them to use it as a visual reminder of where proteins are assembled.

  • During DNA replication, occasional errors change DNA sequences. This process is called mutation.
  • Changes in DNA sequences can lead to changes in proteins.

Using a paper model, students make a mutation and determine the effect on the resulting protein.

Students see the effect on a protein's structure caused by a change in a DNA sequence.

Make one copy per student or pair (copies may be re-used), or have students view on tables or computers:

Page 1 has two identical sets of strips. Give each student or pair a half-page:

Make one copy per student or pair (copies may be re-used), or project to the class:

What is an Allele?

This short interactive uses blue vs. brown eye color to introduce alleles, showing how different versions of a gene lead to differences in protein function and traits.

Some Common Genetic Mutations in Humans

Hair Color

The color of human hair is a multifactorial trait that generally depends on the interaction between the eumelanin and pheomelanin pigments. These pigments are coded for by different forms of the MC1R gene. The expression of this gene, however, is controlled by various other genes. The melanocortin 1 receptor (MC1R) gene in its normal form produces pheomelanin and converts it into eumelanin. In the event of mutation, the amount of pheomelanin builds up, and is not converted into eumelanin.

Pheomelanin produces colors from orange to yellow, while eumelanin is responsible for the black and brown pigments, and also for determining the darkness of the hair color. Blonde hair has a very low percentage of eumelanin, whereas brown hair has brown eumelanin in a large percentage. Black eumelanin leads to the presence of black hair. Pheomelanin is comparatively more stable, and hence breaks down very slowly when oxidized. As it decomposes, the color changes from red to orange to yellow, and finally to white. The interactions between these pigments, and their presence in varying concentration lead to the occurrence of natural hair colors like black, brown, red, blonde, and white.

Example: Red Hair

In the case of red hair color, due to the malfunction of the MC1R gene, the pheomelanin in the hair follicles, builds up and is not converted into eumelanin. The stable and reddish nature of the pheomelanin molecules cause the resultant red hair color. The inheritance of red hair color depends on the hair color of the parents. If both parents are red-haired, then the progeny also has red hair. However, in cases where one parent has a different hair color, the non-mutated gene copy from that parent may correct or compensate for the mutated gene copy from the other parent, resulting in progeny that may or may not have red hair.

Eye Color

The color of the eyes is a physical trait of humans that is determined by more than one gene. All humans originally had brown eyes. Somewhere along the course of evolution, different eye colors emerged due to genetic mutations. Since then, these mutations have been passed down through generations. A research paper in the Journal of Human Genetics provides evidence that close to 16 genes may be responsible for eye color, and the way these interact with each other determine the specific shade of color. However, the two main genes involved in this process are the OCA2 and the HERC2 genes located on chromosome 15. The OCA2 gene is responsible for production of melanin, a molecule that imparts color. The absence of this molecule leads to albinism. The HERC2 gene regulates the expression of the OCA2 gene. A specific mutation in the HERC2 gene along with single nucleotide polymorphisms (SNPs) in the OCA2 gene causes the development of a spectrum of different eye colors in humans. The condition of heterochromia, where the two eyes have different coloration, is also due to the interaction of the OCA2 and HERC2 genes.

Example: Blue Eyes

The occurrence of blue eyes is a recessive trait. The brown or black eye color is usually dominant over it. It is caused due to specific interactions between the OCA2 and HERC2 gene. The progeny only has blue eyes if both parents also have a blue eye color. If one of the parents has a different eye color, that color is usually seen in the progeny. However, there have been rare cases reported where this recessive trait skipped generations in family lineages, often occurring in alternate generations, irrespective of the eye colors of the parents.


While the occurrence of freckles is not dependent on genetic factors, their abundance is due to genetic mutations in the MC1R gene. Melanocytes are specialized cells in our skin, which produce the pigment melanin. Melanin protects our DNA from the harmful ultraviolet (UV) radiations given off by the sun. Generally melanocytes are evenly spread throughout the skin, causing the skin to tan due to melanin production. In individuals with mutated MC1R gene, these melanocytes are present in clumps across the skin, and on exposure to sunlight lead to the occurrence of freckles. Since the gene is mutated, the melanin produced exhibits a shade of red.

Cleft Chin

It is yet another example of multifactorial traits. Additionally, it also exhibits variable penetrance, which in simple words implies that this trait does not follow a strict pattern of inheritance. If a parent has a cleft chin, the offspring may or may not exhibit the same. This is because this trait essentially occurs due to the incomplete fusion of the jawbone during the process of embryogenesis. Modifier genes may be activated during the process, leading to a correction of the error and causing the progeny to show the absence of the cleft. However, if those genes are not activated, the error remains uncorrected, and the fetus is born with a cleft chin.

Double Eyelash

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This particular phenotype is also termed distichiasis. It is the condition where eyelids show presence of a double row of eyelashes. Hair follicles replace the oil glands present on the waterline along the eyelids. This occurs due to a mutation in the FOXC2 gene, which is responsible for most of the tissue development during embryogenesis. Extensive mutations in this gene may cause lymphedema and failure of the lymphatic system.


This trait is exhibited when genetic defects lead to shortened facial muscles, and cause the formation of indentations when an individual smiles. The aberrant muscles are caused due to defects caused in the subcutaneous connective tissue during the course of development of the embryo. The exact genetic cause for this is as yet unidentified, but geneticists believe that it may be a dominant trait caused due to a single gene mutation. The inheritance of this trait is variable. If both parents have this quality, then it is inherited by the child. But in the case of only one parent exhibiting dimples, the child may or may not show its presence.

Are mutations the cause of alleles? - Biology

We have learned how selection can change the frequencies of alleles and genotypes in populations. Selection typically eliminates variation from within populations. (The general exception to this claim is with the class selection models we have called "balancing" selection where alleles are maintained in the population by overdominance, habitat-specific selection, or frequency dependent selection). If selection removes variation, soon there will be no more variation for selection to act on, and evolution will grind to a halt, right? This would be true if it were not for the reality of Mutation which will restore genetic variation eliminated by selection. Thus, mutations are the fundamental raw material of evolution.

We will be gin by considering what mutation will do as an evolutionary force acting by itself. Simply, mutation will change allele frequencies, and hence, genotype frequencies. 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). We can express the frequency (p) of the A allele in the next generation (p t+1 ) in terms of these opposing forward and reverse mutations, much like forward and reverse chemical equations: (p t+1 ) = p t (1-u) + q t (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). We can also describe the change in allele frequency between generations ( D p) as: D p = (p t+1 ) - (p t ) . 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.e. when D p = 0 which is when (p t+1 ) = (p t ) from above: p t (1-u) + (1-p) t (v) = p t [remember, q=(1-p)]. Now solve for p and convince yourself that the equilibrium frequency = p = v/(u+v) . Similarly the equilibrium frequency of q = u/(u+v).


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.e., q will increase). In fact, q increases at a rate of u(1-q) remember, (1-q) = p, or the frequency of the A allele. 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.e., that the deleterious effects of the a allele are only observed in the aa homozygote. Under these conditions, the frequency of "a" (q) decreases by selection at a rate of -sq 2 (1-q) , where s is the selection coefficient. We won't derive this for you, but note that the amount of change generated by this selection is a function of the frequency of the aa homozygote (q 2 ) and the frequency of the A allele (1-q). In other words, the amount of change is proportional to the amount of genetic variation in the population, as we showed last lecture.

If we put these terms for mutation and selection together, the amount of change in the a allele is :

Now, if the "fight" between selection and mutation is a "draw", we have a condition where there is no change in the frequency of the a allele since mutation is increasing q just as fast as selection is reducing it. Under these conditions, D q = 0, and we say that the equilibrium allele frequency, q-hat, has been reached (in formal notation q-hat is q with a circumflex over it). We simply rearrange the above formula so that is becomes : u(1-q) = sq 2 (1-q) . We solve this for q to give the equilibrium allele frequency , q-hat: q = sqrt(u/s) (sqrt stands for square root).

Most mutation rates are fairly small numbers (about 10 -6 ), so this equation suggests that deleterious alleles will be maintained in mutation selection balance at fairly low frequencies. However, this statement is exactly what this mode is intended to illustrate: we cannot say what that frequency is until we know BOTH mutation rate and selection coefficient. However, we will refer back to mutation selection balance several times during the course, so it is essential that you have a feel for dynamics of this evolutionary interaction.

In population genetics, the term "migration" is really meant to describe Gene flow , defined as the movement of alleles from one area (deme, population, region) to another. Gene flow assumes some form of dispersal or migration (wind pollination, seed dispersal, birds flying, etc.) but dispersal is not gene flow (genes must be transferred, not just their carriers)

We can describe gene flow (migration) in a manner similar to mutation. Consider two populations, x and y with frequencies of the A allele of p x and p y . Now consider that some individuals from population y migrate into population x. The proportion of these y individuals that become parents in population x in the next generation = m . After the migration event, population x can be considered to consist of migrant individuals (proportion m) and non-migrant individuals (proportion [1-m]). Thus the frequency of the A allele in population x in the next generation (p x t+1 ) is just the frequency in the non-migrant portion (= p x [1-m]) plus the frequency in the migrant portion (p y m). Thus: p x t+1 = p x t [1-m] + p y m .

The change in allele frequency due to gene flow is D p = (p x t+1 ) - p x t which is just

[p x t [1-m] + p y m] - p x t Multiplying through and canceling terms leaves us with:

D p = -m(p x t - p y t ) . This makes intuitive sense: the change in p depends on the migration rate and the difference in p between the two populations. If we considered a grid or array of populations and focus on one of those populations as the recipient population with all other populations contributing equally to it, then p y would be replaced by the average p for all the other populations. Many scenarios are possible.

To address the combined effects of gene flow and selection, we will invoke a "fight" similar to what we described for mutation selection balance above. Consider that some weak allele is wafting over to the other side of the tracks, so to speak, where they do not survive (e.g., fish swimming into New York harbor). There is an evolutionary pressure changing allele frequencies in one direction ( into the harbor), and an opposing evolutionary force eliminating those alleles (sewage killing off genetically intolerant fish). Depending on the relative strengths of these two opposing forces, an equilibrium condition can arise.

Lets consider the movement of the "a" allele, and assume that it is completely recessive in its phenotype of death-by-sewage. The change in allele frequency from the migration into the harbor can be defined as above: D q = -m(q x t - q y t ) . (Note that we have changed p to q since we are considering the a allele x and y refer to the two populations). The change in allele frequency due to selection against this allele is -sq 2 (1-q) (note that this is the same expression we used in the mutation selection balance above). Putting these two pieces together, we can write the expression for the change in allele frequency that is due to BOTH gene flow and selection: D q = -m(q x t - q y t ) - sq x 2 (1-q x ) . When the "fight" between gene flow and selection is a "draw", the system will be in equilibrium and there will be no change in q,

and -m(q x t - q y t ) = sq 2 (1-q) .

So, back to the fish. Lets say that aa homozygotes drop dead the minute they enter the East river (but that AA and Aa fish are fine). Outside New York Harbor, the frequencies of the two alleles are equal (p = q= 0.5). It is discovered that in the East river, q = 0.1 over many generations, and the Mayor wants to know what proportion of the fish in the East river come from the outside each generation. This information gives us all we need: it's in equilibrium, q x = 0.1 (East River), q y = 0.5 (outside), and s = 1.0 since the aa's are dead. Plug in the values and you get m = 0.023. This says that 2.3% of the fish in the East river must come from outside each generation to maintain the allele frequency at q = 0.1


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