The Population Genetics

Because learning changes everything. ® Chapter 27 Population Genetics Genetics: Analysis & Principles SEVENTH EDITION Robert J. Brooker © 2021 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw Hill. © McGraw Hill 2 Population Genetics ©Riccardo Vallini Pics/Getty Images © McGraw Hill 3 Introduction Population genetics is concerned with genetic variation • Its extent within populations • Why it exists • How it changes over the course of many generations Population genetics emerged as a branch of genetics in the 1920s and 1930s • Its foundations are largely attributed to 3 mathematicians • Sir Ronald Fisher, Sewall Wright, and J. B. S. Haldane © McGraw Hill 4 27.1 Genes in Populations and the Hardy -Weinberg Equation The focus is shifted away from the individual and toward the population of which the individual is a member Conceptually, all of the alleles of every gene in a population make up the gene pool • Only individuals that reproduce contribute to the gene pool of the next generation Population geneticists study the genetic variation within the gene pool and how it changes from one generation to the next © McGraw Hill 5 What is a Population? 1 A population is a group of individuals of the same species that occupy the same region and can interbreed with each other A large population is usually composed of smaller groups called local populations • Members of a local population are far likelier to breed with each other than with members of the general population • Local populations are often separated from each other by moderate geographic barriers © McGraw Hill 6 Figure 27.1 (a) Large ground finch (b) A view of Daphne Major (the small island in the distance) from Santa Cruz Island (a): ©LABETAA Andre/Shutterstock; (b): ©Deborah Freund © McGraw Hill 7 What is a Population? 2 Populations typically are dynamic units that change from one generation to the next A population may change in 1. Size 2. Geographic location 3. Genetic composition Population geneticists have developed mathematical theories that predict how the gene pool will change in response to fluctuations in the above © McGraw Hill 8 Some Genes Are Monomorphic, but Most Are Polymorphic 1 The term polymorphism refers to the observation that many traits display variation within a population Figure 27.2 illustrates a striking example of polymorphism in the Hawaiian happy -face spider • All individuals are from the same species, Theridion grallator • But they differ in alleles that affect color and pattern © McGraw Hill 9 Figure 27.2 ©Geoff Oxford © McGraw Hill 10 Some Genes Are Monomorphic, but Most Are Polymorphic 2 At the DNA level, polymorphism is due to two or more alleles that influence the phenotype • In other words, it is due to genetic variation Polymorphic is also used to describe a gene that commonly exists as 2 or more alleles in a population A monomorphic gene exists predominantly as a single allele • By convention, when a single allele is found in at least 99% of all cases, the gene is considered monomorphic © McGraw Hill 11 Some Genes Are Monomorphic, but Most Are Polymorphic 3 Variation is often a single -nucleotide polymorphism (SNP ), which is a change in a single base pair in the DNA • SNPs account for 90% of variation among people • In humans, a gene that is 2,000 to 3,000 bp contains 10 different polymorphic sites on average © McGraw Hill 12 Variation in the Human β -globin Gene Alleles may arise through different types of genetic changes Variations in the  -globin gene in humans are: • A single nucleotide polymorphism which causes a major change leading to sickle cell disease • A deletion which eliminates function © McGraw Hill 13 Population Genetics Is Concerned with Allele and Genotypic Frequencies Two fundamental calculations are central to population genetics: 1.   Number of copies of an allele in a popul ation Allele frequency Total number of alleles for that gene in a population  Number of individuals with a particular genotype in a populati on 2. Genotype frequency Total number of individuals in a populat ion  © McGraw Hill 14 Calculating Allele Frequency Consider a population of 100 frogs • 64 dark green frogs with the genotype GG • 32 medium green frogs with the genotype Gg • 4 light green frogs with the genotype gg Frequency of allele g: (Remember that homozygotes have two copies of an allele but heterozygotes have only one)                 2   4    32 2   64   2   32   2   4 40 200 0.2, 20% or      © McGraw Hill 15 Calculating Genotype Frequency Consider a population of 100 frogs • 64 dark green frogs with the genotype GG • 32 medium green frogs with the genotype Gg • 4 light green frogs with the genotype gg • TOTAL = 100 Genotype frequency of light green frogs: 4/100 = 0.04, or 4% © McGraw Hill 16 Allele and Genotype Frequencies For a given trait, the allele and genotype frequencies are always less than or equal to 1 • That is, less than or equal to 100% For monomorphic genes • The allele frequency for the single allele will be equal to or close to 1.0 For polymorphic genes • The frequencies of all alleles should add up to 1.0 • In our frog example • Frequency of G allele + frequency of g allele = 1 • Frequency of G allele = 1 – frequency of g allele © McGraw Hill 17 The Hardy -Weinberg Equilibrium The Hardy -Weinberg equation was formulated independently by Godfrey Harold Hardy and Wilhelm Weinberg in 1908 • It is a simple mathematical expression that relates allele and genotype frequencies in a population The HW equation is also called an equilibrium • Under a given set of conditions (described later) • The allele and genotype frequencies do not change over the course of many generations © McGraw Hill 18 The Hardy -Weinberg Equation in Action 1 Consider our frog example with a polymorphic gene that exists in two alleles, G and g • The frequency of allele G is denoted by the variable p • The frequency of allele g is denoted by the variable q • p + q = 1 • For this gene, the Hardy -Weinberg equation states that • (p + q )2 = 1 • p 2 + 2 pq + q 2 = 1 © McGraw Hill 19 The Hardy -Weinberg Equation in Action 2 If p = 0.8 and q = 0.2, and if the population is in Hardy - Weinberg equilibrium, then • Frequency of GG = p 2 = (0.8) 2 = 0.64, or 64% • Frequency of Gg = 2 pq = 2(0.8)(0.2) = 0.32, or 32% • Frequency of gg = q 2 = (0.2) 2 = 0.04, or 4% © McGraw Hill 20 Compare Hardy -Weinberg and Punnett Square Figure 27.4 compares the Hardy -Weinberg equation with the Punnett square approach The frequency of gametes carrying a particular allele is equal to the allele frequency for a population in Hardy -Weinberg equilibrium. • Multiplying the allele frequencies gives the proportion of each allele combination in the population. © McGraw Hill 21 Figure 27.4 Access the text alternative for slide images. genotype 0.64, or 64% GG  genotype 0.16 0.16 0.32, 32% Gg or    genotype 0.04, or 4% gg  © McGraw Hill 22 Conditions for Hardy -Weinberg Equilibrium 1 Conditions required to reach equilibrium - unchanging allele and genotype frequencies from generation to generation: 1. No new mutations 2. No genetic drift. The population is so large allele frequencies do not change due to random sampling effects 3. No migration 4. No natural selection 5. Random mating © McGraw Hill 23 Conditions for Hardy -Weinberg Equilibrium 2 In reality, no population satisfies these conditions completely Some large populations have little migration or natural selection • In these cases, the HW equilibrium is nearly approximated for certain genes © McGraw Hill 24 Relationship between Gene and Allele Frequencies The HW equation provides a quantitative relationship between the allele and genotype frequencies • GG dominates when g is low • Gg dominates when both allele frequencies are intermediate • gg dominates when g is high Access the text alternative for slide images. © McGraw Hill 25 Determine if a Population Exhibits HW Equilibrium 1 A chi square test can be used to see if a population really exhibits HW equilibrium for a particular gene • The strategy is to compare observed genotype frequencies with expected genotype frequencies based on the Hardy - Weinberg equation • See your textbook for an example of the calculation; regarding MN blood type • If the null hypothesis is not rejected, you can accept the hypothesis that the population is in equilibrium • If the null hypothesis is rejected, this suggests that the population is in disequilibrium • One or more evolutionary factors are causing deviation from the HW equilibrium © McGraw Hill 26 27.2 Overview of Microevolution Genetic variation in natural populations changes over many generations Microevolution describes changes in a population’s gene pool from generation to generation • Driven by: • Mutation • Random genetic drift • Migration • Natural Selection • Nonrandom mating © McGraw Hill 27 © McGraw Hill 28 27.3 Natural Selection In the 1850s, Charles Darwin and Alfred Russel Wallace independently proposed the theory of natural selection • According to this theory, phenotypes may vary with regard to their reproductive success • Natural selection acts on phenotypes, which are governed by individuals’ genotypes • Reproductive success can be affected by • The ability to survive to reproductive age in a particular environment • Factors that directly affect reproduction such as fertility, mating success, etc. © McGraw Hill 29 Principles of Natural Selection 1 A modern description of natural selection can relate molecular genetics to the phenotypes of individuals 1. Within a population there is allelic variation arising from various factors such as mutations causing differences in DNA sequences • Distinct alleles may encode proteins of differing functions 2. Some alleles may encode proteins that enhance an individual’s survival or reproductive capacity © McGraw Hill 30 Principles of Natural Selection 2 3. Individuals with beneficial alleles are more likely to survive and reproduce 4. Over the course of many generations, allele frequencies of many different genes may change through natural selection • This significantly alters the characteristics of a species • The net result of natural selection is a population that is better adapted to its environment and/or more successful at reproduction © McGraw Hill 31 Darwinian Fitness Is a Measure of Reproductive Success A quantitative discussion of natural selection requires a discussion of Darwinian fitness • The relative likelihood that a genotype will survive and contribute to the gene pool of the next generation Darwinian fitness is a measure of reproductive success • It should not be confused with physical fitness Consider a gene with two alleles, A and a • The three genotypic classes can be assigned relative fitness values (w) according to their reproductive successes © McGraw Hill 32 Fitness Values Suppose the average reproductive successes are • AA  5 offspring • Aa  4 offspring • aa  1 offspring By convention, the gene with the highest reproductive ability is given a fitness value of 1.0 • The fitness values of the other genotypes are assigned relative to 1.0 Fitness values are denoted by the variable w • Fitness of AA: w AA = 1 • Fitness of Aa: w Aa = 4/5 = 0.8 • Fitness of aa: w aa = 1/5 = 0.2 © McGraw Hill 33 Reasons for Differences in Reproductive Success Differences in reproductive achievement could be due to the 1. Fittest genotype is more likely to survive 2. Fittest genotype is more likely to mate 3. Fittest genotype is more fertile This is the simplified case of single gene • Most traits are affected by variation in multiple genes © McGraw Hill 34 Four Patterns of Natural Selection 1 Natural selection acts on phenotypes (which are derived from an individual’s genotype) There are four ways that natural selection commonly operates 1. Directional selection • Favors the survival of one extreme phenotype that is better adapted to an environmental condition 2. Balancing selection • Favors the maintenance of two or more alleles © McGraw Hill 35 Four Patterns of Natural Selection 2 3. Disruptive (or diversifying) selection • Favors the survival of two (or more) different phenotypes 4. Stabilizing selection • Favors the survival of individuals with intermediate phenotypes © McGraw Hill 36 Figure 27.6 (a) An example of directional selection (b) Graphical representation of directional selection © McGraw Hill 37 Directional Selection Suppose a gene exist in two alleles A and a The three fitness values are • w AA = 1.0 • w Aa = 0.8 • w aa = 0.2 In the next generation, the HW equilibrium will be modified in the following way by directional selection: • Frequency of AA : p 2w AA • Frequency of Aa : 2 pqw Aa • Frequency of aa : q 2w aa © McGraw Hill 38 Mean Fitness of the Population 1 These three terms may not add up to 1.0, as they would in the HW equilibrium Instead, they sum to a value known as the mean fitness of the population Divide both sides by mean fitness: 22 AA Aa aa p w + 2pqw + q w = w 2 2 Aa aa AA 2pqw q w pw + + = 1 w w w © McGraw Hill 39 Mean Fitness of the Population 2 Calculate mean fitness of the population, if A = 0.5 and a = 0.5 22 AA Aa aa p w + 2pqw + q w = w 22 w = (0.5) (1) + 2(0.5)(0.5)(0.8) + (0.5) ( 0.2) w = 0.25 + 0.4 + 0.05 = 0.7 © McGraw Hill 40 Mean Fitness of the Population 3 After one generation of directional selection: 2 2 AA pw (0.5) (1) Frequency of AA genotype: = = 0.36 w 0.7 Aa 2pqw 2(0.5)(0.5)(0.8) Frequency of Aa genotype: = = 0.57 w 0.7 2 2 aa qw (0.5) (0.2) Frequency of aa genotype: = = 0.07 w 0.7 © McGraw Hill 41 Mean Fitness of the Population 4 2 Aa AA A 2 pqw pw Allele frequency of A: p = + ww (0.5) (1) (0.5)(0.5)(0.8) = + = 0.64 0.7 0.7 2 aa Aa A 2 q w pqw Allele frequency of a: q = + ww (0.5) (2) (0.5)(0.5)(0.8) = + =0.36 0.7 0.7 © McGraw Hill 42 Mean Fitness of the Population 5 After one generation • Frequency of A has increased from 0.5 to 0.64 • Frequency of a has decreased from 0.5 to 0.36 • This is because the AA genotype has the highest fitness Another interesting feature of natural selection is that it raises the mean fitness of the population from one generation to the next Therefore, the general trend is to increase A , decrease a , and increase the mean fitness of the population © McGraw Hill 43 Fate of a Beneficial Allele due to Directional Selection Let’s suppose a mutation introduces the A allele into a population • The population was originally monomorphic for the a allele • Frequency of allele A slowly rises at first • Rises much more rapidly at intermediate values • May be eventually fixed! Figure 27.7 © McGraw Hill 44 Directional Selection for DDT Resistance Directional selection is shown with real data on resistance to DDT in a mosquito population Figure 27.8 © McGraw Hill 45 Balancing Selection 1 A polymorphism may reach an equilibrium where opposing selective forces balance each other • The population is not evolving toward allele fixation or elimination • Such a situation is known as balancing selection It occurs when the h eterozygote has a higher fitness than either homozygote, called heterozygote advantage © McGraw Hill 46 Balancing Selection 2 To study this, we will also have to look at the selection coefficient • Measures the degree to which a genotype is selected against • s = 1 - w © McGraw Hill 47 Heterozygote Advantage 1 The heterozygote is at a selective advantage • The higher fitness of the heterozygote is balanced by the lower fitness of both corresponding homozygotes • Calculate selection coefficient from fitness: AA AA w = 0.7 s = 1 0.7 = 0.3  Aa Aa w 1.0 s 1 1.0 0      aa aa w 0.4 s 1 0.4 0.6      © McGraw Hill 48 Heterozygote Advantage 2 Under these conditions, the population will reach an equilibrium when: AA aa s p s q    p Allele frequency of A 0.6 0.3 0.6 0.67 aa AA aa s s s         q Allele frequency of a 0.3 0.3 0.6 0.33 AA AA aa s s s       © McGraw Hill 49 Heterozygote Advantage 3 Can sometimes explain the high frequency of deleterious alleles The Hb S allele of the human  -globin gene • Hb S Hb S displays sickle−cell anemia • Hb A Hb A are phenotypically normal • Hb A Hb S has the highest fitness in areas where malaria is endemic Heterozygotes have a better chance of survival if infected by the malarial parasite Plasmodium falciparum © McGraw Hill 50 Figure 27.9 (a) Malaria prevalence (b) Hb s allele frequency Access the text alternative for slide images. © McGraw Hill 51 Negative Frequency -Dependent Selection 1 Negative frequency -dependent selection is another mechanism of balancing selection • Rare individuals have a higher fitness than more common individuals; more likely to reproduce • Common individuals are less likely to produce • Selection always favors less numerous genotype • Always drives towards balance © McGraw Hill 52 Negative Frequency -Dependent Selection 2 Example is a rewardless flower (no nectar) • Pollinators learn to avoid common flower color with no nectar • They visit the rare flower color more frequently (nectar) • The relative fitness of the less -common flower increases © McGraw Hill 53 Figure 27.10 ©Paul Harcourt Davies/SPL/Science Source © McGraw Hill 54 Disruptive Selection Disruptive selection favors the survival of two or more different genotypes with different phenotypes • Also known as diversifying selection • Caused by fitness values for a given genotype that vary in different environments • Typically acts on traits that are determined by multiple genes • Likely to occur in populations that occupy diverse environments © McGraw Hill 55 Disruptive Selection (Figure 27.12) 1 (a) Land snails Example is a snail that lives in woods and open fields • brown shell color favored in woods with open soil • pink shell color favored in woods with leaf litter • yellow shell cover favored in sunny, grassy areas ©R. Koenig/ agefotostock © McGraw Hill 56 Disruptive Selection (Figure 27.12) 2 Habitat Brown Pink Yellow Beechwoods 0.23 0.61 0.16 Deciduous woods 0.05 0.68 0.27 Hedgerows 0.05 0.31 0.64 Rough herbage 0.004 0.22 0.78 © McGraw Hill 57 Stabilizing Selection In stabilizing selection , the extreme phenotypes are selected against • Intermediate phenotypes have the highest fitness values • Tends to decrease genetic diversity • Eliminates alleles that cause variation in phenotypes • Laying eggs is an example • Too many eggs drains resources to care for young • Too few eggs does not contribute many individuals to the next generation © McGraw Hill 58 Figure 27.13 © McGraw Hill 59 Experiment 27A: Natural Selection in Galapagos Finches 1 Since 1973, Peter and Rosemary Grant have studied natural selection in finches found on the Galapagos Islands • Concentrated on moderately isolated island • Observed various traits such as beak size over many years • Depth of beak was transmitted from parents to offspring, regardless of environmental conditions (it is a heritable trait) • Differences are due to genetic differences in the population © McGraw Hill 60 Experiment 27A: Natural Selection in Galapagos Finches 2 The Hypothesis • Beak size will be influenced by natural selection. Environments that produce large seeds will select for birds with large beaks © McGraw Hill 61 Testing the Hypothesis 1. In 1976, measure beak depth in parents and offspring of the species G. fortis. 2. Repeat the procedure on offspring that were born in 1978 and had reached mature size. A drought had occurred in 1977 that caused plants on the island to produce mostly larger seeds and relatively few small seeds. © McGraw Hill 62 Figure 27.15 © McGraw Hill 63 The Data Access the text alternative for slide images. Source: B. Rosemary Grant and Peter R. Grant (2003), What Darwin’s finches can teach us about the evolutionary origin and regulation of biodiversity. Bioscience 53, 965 -975. © McGraw Hill 64 Interpreting the Data 1976 was a wet year and the plants produced small seeds that the finches could all eat 1977 was a drought and the seeds that were available were larger and drier • Birds with large beaks could eat these more efficiently 1978 offspring had a clear increase in beak depth • Provides evidence of natural selection altering the nature of a trait • Cannot rule out genetic drift, however © McGraw Hill 65 27.4 Genetic Drift Genetic drift refers to random changes in allele frequencies due to random fluctuations • Sewall Wright played a key role in developing this concept in the 1930s In other words, allele frequencies may drift from generation to generation as a matter of chance Over the long run, genetic drift favors either the loss or the fixation of an allele • The fixed allele is monomorphic and cannot fluctuate • The rate depends on the population size © McGraw Hill 66 Figure 27.16 Access the text alternative for slide images. © McGraw Hill 67 Genetic Drift 1 How many new mutations do we expect in natural populations? If each individual has two copies of the gene of interest, then • Expected number of new mutations = 2 N  •  is the mutation rate • N is the number of individuals in a population • So a new mutation is more likely to occur in a large population than in a small one © McGraw Hill 68 Genetic Drift 2 How likely is it that a new mutation will be fixed or eliminated due to random genetic drift? • Probability of fixation of a newly arising allele due to genetic drift = 1/2 N • Assuming equal numbers of males and females contribute to the next generation • In other words, the probability of fixation, is the same as the initial allele frequency in the population • For example, if N = 20 • Probability of fixation = 1 / (2 × 20), or 2.5% • Conversely, a new allele may be lost from the population • Probability of elimination = 1 - 1 / 2 N , or 97.5% © McGraw Hill 69 Genetic Drift 3 The value of N has opposing effects with regard to new mutations and their eventual fixation • When N is very large • New mutations are much more likely to occur • However, each new mutation has a greater chance of being eliminated from the population due to random genetic drift • When N is very small • New mutations are less likely to occur • However, each new mutation has a greater chance of being fixed in the population due to random genetic drift © McGraw Hill 70 Genetic Drift 4 If fixation does occur, how many generations is it likely to take? • Depends on the number of individuals in the population fixation N equals the number of individuals in the population, assuming that males and females contribute equally to each succeeding generation t = 4N Where t equals the average number of generation s to achieve © McGraw Hill 71 Genetic Drift 5 Allele fixation will take much longer in large populations • With 1 million breeding members in a population, it will take 4 million generations to reach fixation! • With 100 individuals, fixation will take only 400 generations © McGraw Hill 72 Genetic Drift 6 In nature, allele frequencies in small populations are more susceptible to genetic drift • Bottleneck Effect • Founder Effect © McGraw Hill 73 Bottleneck Effect In nature, a population can be reduced dramatically in size by a natural disaster for example • Such a disaster randomly eliminates individuals regardless of their genotype • The period of the bottleneck, when the population size is very small, may be influenced by genetic drift Example: African cheetah (a) Bottleneck Flask Figure 27.17 © McGraw Hill 74 Founder Effect 1 A small group of individuals separates from a larger population and establishes a colony in a new location • This has two important consequences 1. The founding population is expected to have less genetic variation than the original population 2. The founding population will have allelic frequencies that may differ markedly from those of the original population, as a matter of chance © McGraw Hill 75 Founder Effect 2 Example: The Old Order Amish of Lancaster County, PA • Population of 8,000 is descended from just three couples that immigrated to the US in 1770 • Frequency of Ellis -van Creveld syndrome (a recessive form of dwarfism) is 7% • This is much higher than in any other population © McGraw Hill 76 27.5 Migration Migration between two different established populations can alter allele frequencies Gene flow is the transfer of alleles from donor population to recipient population, changing its gene pool The new population (the recipient population) is called a conglomerate • To calculate the allele frequencies in the conglomerate we must know 1. The original allele frequencies in the donor and recipient populations 2. The proportion of the conglomerate population that is due to migrants © McGraw Hill 77 Calculating the Change in Allele Frequency in the Conglomerate Population 1 c D R p m(p - p )  c p the change in allele frequency in the c onglomerate population  D p the allele frequency in the donor popul ation  R p the allele frequency in the original re cipient population  m the proportion of migrants in the congl omerate population  Number of migrants in the conglomerate p opulation m Total number of individuals in the congl omerate population  © McGraw Hill 78 Calculating the Change in Allele Frequency in the Conglomerate Population 2 Example: • Allele frequency of A is 0.7 and 0.3 in the donor and recipient populations, respectively • 20 individuals migrate and join the recipient population which has 80 members • Thus, the frequency of the A allele has increased from 0.3 to 0.38   20 20 80 0.2 m        0.2 0.7 0.3 c D R p m p p      0.3 0.08 0.38 C R C p p p       © McGraw Hill 79 Bidirectional migration In this example, migration was unidirectional In nature, it is common for individuals to migrate between populations in both directions This bidirectional migration has two important consequences 1. It tends to reduce allele frequency differences between populations 2. It can enhance genetic diversity within a population New mutations in one population can be introduced to neighboring group © McGraw Hill 80 27.6 Nonrandom Mating One of the conditions required to establish the HW equilibrium is random mating • It means that individuals choose their mates regardless of their genotypes and phenotypes In many cases, particularly in human populations, this condition is violated frequently © McGraw Hill 81 Nonrandom Mating 1 Mating and phenotypes • Assortative mating occurs when individuals do not mate randomly • Positive assortative mating occurs when individuals are more likely to mate due to similar phenotypic characteristics • Negative assortative mating occurs when individuals with dissimilar phenotypes mate preferentially © McGraw Hill 82 Nonrandom Mating 2 Mating and genotypes • Inbreeding is the mating between genetically -related individuals • Outbreeding is the mating between genetically -unrelated individuals • In the absence of other evolutionary forces, allele frequencies are not affected by in - or out -breeding • However, these patterns of mating do disrupt the balance of genotypes predicted by the HW equation © McGraw Hill 83 Inbreeding During inbreeding the gene pool is smaller, because the parents are related genetically Gustave Malecot developed methods to quantify the degree of inbreeding • An inbreeding coefficient (F) can be computed by analyzing the degree of relatedness within a pedigree • Probability that two alleles for a given gene in a particular individual will be identical because both copies are due to descent from common ancestor © McGraw Hill 84 Inbreeding Coefficient 1 Determine the coefficient of inbreeding for individual IV -1: 1. Identify all the common ancestors of the individual • A common ancestor is anyone who is an ancestor to both of the individual’s parents • IV -1 has one common ancestor, I -2 2. Determine the inbreeding paths - the shortest path through the pedigree that includes both parents and the common ancestor Access the text alternative for slide images. © McGraw Hill 85 Inbreeding Coefficient 2 The length of each inbreeding path is calculated by adding all the individuals in the path except the individual of interest • There is only one path in our example • Do not count the inbred individual IV -1  III -2  II -2  I-2  II -3  III -3 Access the text alternative for slide images. © McGraw Hill 86 Inbreeding Coefficient 3 Path: IV -1  III -2  II -2  I-2  II -3  III - Use the formula: • F is the inbreeding coefficient of the individual of interest • n is the number of individuals in the inbreeding path • Excluding the inbred offspring • F A is the breeding coefficient of the common ancestor ∑ indicates the sum of 1 2 �� 1 + F A for each inbreeding path (1 / 2) (1 ) n A FF   © McGraw Hill 87 Inbreeding Coefficient 4 • In our example, there is only one common ancestor • Since we don’t know anything about its heritage, we assume that F A = 0 • This is the probability that a gene in the inbred individual (IV -1) is homozygous due to its inheritance from a common ancestor (I -2) 5 (1 / 2) (1 0) (1 / 2) 1 / 32 3.125% n F       © McGraw Hill 88 Inbreeding Coefficient 5 The coefficient of inbreeding is also called the fixation coefficient • That explains the symbol F • The fixation coefficient is the probability that an allele will be fixed in the homozygous condition • In natural populations, the value of f tends to increase as the population size decreases because the choice of mates becomes more limited In some pedigrees, an individual may have two or more common ancestors and the common ancestor(s) may be inbred • See question 4 of More Genetic TIPS at the end of the chapter © McGraw Hill 89 Effects of Inbreeding Within a Population 1 Example, a situation in which the frequencies of A and a are p and q , respectively • p 2 + fpq equals the frequency of AA • 2pq(1 – f) equals the frequency of Aa • q 2 + fpq equals the frequency of aa • f is a measure of how much the frequencies vary from HW equilibrium due to nonrandom mating. • f varies from -1 to +1 © McGraw Hill 90 Effects of Inbreeding Within a Population 2 Suppose p = 0.8, q = 0.2 and f = 0.25 • The frequencies of the three genotypes are: 22 (0.8) (0.25)(0.8)(0.2) 0.68 AA p fpq              2 1 2 0.8 0.2 1 0.25 0.24 Aa pq f      22 (0.2) (0.25)(0.8)(0.2) 0.08 aa q fpq      © McGraw Hill 91 Effects of Inbreeding Within a Population 3 In the presence of inbreeding there will be : • 68% AA homozygotes • 24% Aa heterozygotes • 8% aa homozygotes In the absence of inbreeding (that is, f = 0) there will be : Thus, inbreeding raises the proportion of homozygotes and decreases that of heterozygotes = p AA 2 64% homozygotes = 2p 32%heterozygotes q = q aa 2 4% homozygotes © McGraw Hill 92 Consequences of Inbreeding The positive side is seen in the field of agriculture • Inbreeding results in a higher proportion of homozygotes, which may exhibit a desirable trait On the negative side, many genetic diseases are inherited in a recessive manner • Inbreeding increases the likelihood that an individual will be homozygous and therefore afflicted with the disease • In natural populations inbreeding will lower overall fitness • This is called inbreeding depression • Inbreeding can result from habitat destruction by humans © McGraw Hill 93 27.7 Sources of New Genetic Variation New genetic variation occurs in many ways • In eukaryotes, sexual reproduction produces new combinations of alleles • Prokaryotes also possess mechanisms for gene transfer • Rare DNA mutations give rise to new variants • Changes in chromosome structure and number • There are many other sources listed in Table 27.2 © McGraw Hill 94 Table 27.2 Type Description Independent assortment The independent segregation of different chromosomes may give rise to new combinations of alleles in offspring (see Chapter 2). Crossing over Recombination (crossing over) between homologous chromosomes can also produce new combinations of alleles that are located on the same chromosome (see Chapter 6). Interspecies crosses On occasion, members of different species may breed with each other to produce hybrid offspring. This topic is discussed in Chapter 29. Prokaryotic gene transfer Prokaryotic species have mechanisms of genetic transfer such as conjugation, transduction, and transformation (see Chapter 7). New alleles Point mutations can occur within a gene to create single -nucleotide polymorphisms (SNPs). In addition, genes can be altered by small deletions and additions. Gene mutations are discussed in Chapter 19. Type Description Gene duplications Events, such as misaligned crossovers, can add additional copies of a gene into a genome and lead to the formation of gene families (see Chapter 8). Chromosome structure and number Chromosome structure may be changed by deletions, duplications, inversions, and translocations. Changes in chromosome number result in aneuploid, polyploid, and alloploid offspring. These mechanisms are discussed in Chapters 8 and 29. Exon shuffling New genes can be created when exons of a preexisting gene are rearranged to make a gene that encodes a protein with a new combination of domains. Horizontal gene transfer Genes from one species can be introduced into a different strain of the same species or into another species and become incorporated into that species’ genome. Changes in repetitive sequences Short repetitive sequences are common in genomes due to the occurrence of transposable elements and tandem arrays. The numbers and lengths of repetitive sequences tend to show considerable variation in natural populations. © McGraw Hill 95 Mutations Provide the Source of Genetic Variation 1 Mutations involve changes in sequences and chromosome structure or number Mutations are random events that occur spontaneously at low rates • Mutagens increase the mutation rate The Russian geneticist Sergei Chetverikov was the first to suggest the following • Mutational variability provides the raw material for evolution but does not constitute evolution itself • Mutation can provide new alleles, but does not act as the major force dictating the final balance © McGraw Hill 96 Mutations Provide the Source of Genetic Variation 2 In population genetics it is useful to consider new mutations as they affect the survival and reproductive potential of the individual that inherits them A new mutation may be • Beneficial • Neutral • Deleterious • Neutral and deleterious mutations are far likelier to occur than beneficial mutations © McGraw Hill 97 Mutation Rate 1 The mutation rate is the probability that a gene will be altered by a new mutation • Expressed as the number of new mutations in a given gene per generation • It is commonly in the range of 10 –5 to 10 –6 per generation How does the mutation rate affect the allele frequencies in a population over time? • Consider a gene that exists as a functional allele A • The allele frequency of A is denoted by p © McGraw Hill 98 Mutation Rate 2 • A mutation can convert allele A into a different allele, a • The allele frequency of a is denoted by q • The mutation A  a occurs at a rate symbolized by  • The reverse mutation (a  A) occurs at a negligible rate © McGraw Hill 99 Mutation Rate 3 The increase in the frequency of the a allele after one generation is  q =  p For example, let’s consider the following conditions • p = 0.8 (that is, frequency of A is 80%) • q = 0.2 (that is, frequency of a is 20%) •  = 10 –5 (that is, the mutation rate of converting A to a) •  q =  p = (10 – 5) (0.8) = 0.000008 © McGraw Hill 100 Mutation Rate 4 Therefore, in the next generation, the allele frequencies are not significantly altered: To calculate the change in allele frequency after any number of generations: •  is the mutation rate of the conversion of A to a • t is the number of generations • p 0 is the frequency of allele A in the starting generation • p t is the frequency of allele A after t generations 1 0.2 0.000008 0.200008 n q     1 0.8 0.000008 0.799992 n p       t t0 1 μ p p  © McGraw Hill 101 Mutation Rate 5 To calculate the allele frequency after 1000 generations: • The occurrence of new mutations changes allele frequencies very slowly t p 1000 0.8 t (1 0.00001) p 0.792   © McGraw Hill 102 New Genes Are Produced via Exon Shuffling Many proteins have a modular structure • Two or more discrete domains with different functions • Each domain tends to be encoded by one exon or a series of adjacent exons Exon shuffling occurs when an exon and flanking introns are inserted into a gene • May involve duplication and rearrangement of exons • Results in novel genes with diverse functional modules • May be promoted by transposable elements • Can also be caused by nonhomologous double crossovers © McGraw Hill 103 Figure 27.19 Access the text alternative for slide images. © McGraw Hill 104 New Genes Are Acquired via Horizontal Gene Transfer 1 Horizontal gene transfer is the incorporation of genetic material from another organism without being the offspring of that organism • Often between different species. • This is a common phenomenon in prokaryotes • May account for 20 to 30% of variation in the genetic composition of modern prokaryotic species © McGraw Hill 105 New Genes Are Acquired via Horizontal Gene Transfer 2 Occurs in many ways • Occurs from prokaryotes to eukaryotes and vice versa • Prokaryotic cell may be engulfed by a eukaryotic cell • Bacterial conjugation, transduction and transformation Figure 27.20 © McGraw Hill 106 Genetic Variation Is Produced via Changes in Repetitive Sequences 1 Repetitive sequences are short (a few bases to a few thousand bp ) sequences repeated many times in a genome. • Can originate via transposable elements • Can be microsatellites , also known as short tandem repeats (STR). • Repeat of 1 to 6 bp sequence • Whole tandem repeat is usually less than a couple hundred bp © McGraw Hill 107 Genetic Variation Is Produced via Changes in Repetitive Sequences 2 • Minisatellite repeats are 6 to 80 bp covering 1,00 to 20,000 bp • These repeats can undergo mutation which changes the number of repeat units • Mechanisms that change micro and minisatellite repeat numbers are not well understood, but may involve replication errors (strand slippage) or recombination © McGraw Hill 108 DNA Fingerprinting Is Used for Identification and Relationship Testing DNA Fingerprinting , or DNA profiling , analyzes DNA from individuals based on the occurrence of repetitive sequences at specific sites in their genome • Can be used to identify individuals • Used in forensics to identify crime suspects • Can identify bacterial types in infections • Can be used for relationship testing • Closely related individuals have more similar fingerprints than distantly related individuals • Used in paternity testing • Certain microsatellites and minisatellites vary in human populations © McGraw Hill 109 DNA Fingerprinting Lane 1, Suspect 1 (S1) Lane 2, Suspect 2 (S2) Lane 3, DNA Evidence from a crime scene E(vs) DNA from S2 matches the DNA found at the crime scene. DNA fingerprinting now automated using PCR on microsatellites and fluorescent labeling ©Leonard Lessin Figure 27.21 © McGraw Hill 110 Figure 27.22 Access the text alternative for slide images. Because learning changes everything. ® www.mheducation.com © 2021 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.