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Mendelian genetics population genetics allele frequencies evolutionary biology

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This document covers Mendelian Genetics in Populations, Population Genetics, and Hardy-Weinberg Equilibrium, explaining concepts like allele and genotype frequencies and calculations.

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Mendelian Genetics in Populations: Rocky Mountain bighorn sheep (Ovis canadensis). A population of bighorn sheep at the National Bison Range suffered the loss of genetic variation owing to genetic drift; the introduction of sheep from other populations dramatically increased genetic variation and t...

Mendelian Genetics in Populations: Rocky Mountain bighorn sheep (Ovis canadensis). A population of bighorn sheep at the National Bison Range suffered the loss of genetic variation owing to genetic drift; the introduction of sheep from other populations dramatically increased genetic variation and the fitness of the sheep CCR5 Gene CCR5-∆32 mutation CCR5 mutation: CCR5-∆32 individuals homozygous for CCR5-∆32 are much less likely to contract HIV M global AIDS epidemic will cause an increase in the frequency of the ∆32 allele O in human populations. D E If so, how fast will it L happen? Population genetics It begins with a model of what happens to allele and genotype frequencies in an idealized population. Once we know how Mendelian genes behave in the idealized population, we will be able to explore how they behave in real populations. All organisms exhibit genetic variation: Frequencies of genotypes and alleles in a population more genetic variation exists in populations than is visible in the phenotype. Before we can explore the A frequency is simply a proportion or a evolutionary processes that percentage, usually expressed as a shape genetic variation, we decimal fraction must be able to describe the genetic structure of a For example, if 20% population. of the alleles at a particular locus in a population are A, The usual way of doing so is we would say that to enumerate the types and the frequency of the frequencies of genotypes and A allele in the alleles in a population. population is 0.20 Genotypic and Allelic Frequencies Are Used to Describe the Gene Pool of a Population Allele and Genotype Calculating Genotypic Frequencies To calculate a genotypic frequency, we simply add up the number of individuals possessing the genotype and divide by the total number of individuals in the sample (N). For a locus with three genotypes AA, Aa, and aa, the frequency (f ) of each genotype is The sum of all the genotypic frequencies always equals 1 Calculating Allelic Frequencies Allelic frequencies can be calculated from: (1) numbers of genotypes (2) the frequencies of the genotypes Calculating Allelic Frequencies Allelic frequencies can be calculated from: (1) numbers of genotypes 1 2 Calculating Allelic Frequencies Allelic frequencies can be calculated from: (2) the frequencies of the genotypes Calculating Allelic Frequencies Loci with multiple alleles To calculate the allelic frequencies from the numbers of genotypes, we count up the number of copies of an allele by adding twice the number of homozygotes to the number of heterozygotes that possess the allele and divide this sum by twice the number of individuals in the sample. For a locus with three alleles (A1, A2, and A3) and six genotypes (A1A1, A1A2, A2A2, A1A3, A2A3, and A3A3), the frequencies (p, q, and r) of the alleles are: Calculating Allelic Frequencies Loci with multiple alleles Alternatively, we can calculate the frequencies of multiple alleles from the genotypic frequencies by extending. Add the frequency of the homozygote to half the frequency of each heterozygous genotype that possesses the allele: The human MN blood-type antigens are determined by two codominant alleles, LM and LN. The MN blood types and corresponding genotypes of 398 Finns in Karjala are tabulated here. The genotypic frequencies for the population are calculated with the following formula: The human MN blood-type antigens are determined by two codominant alleles, LM and LN. The MN blood types and corresponding genotypes of 398 Finns in Karjala are tabulated here. To calculate allelic frequencies from numbers of genotypes, we add the number of copies of the allele and divide by the number of copies of all alleles at that locus. The human MN blood-type antigens are determined by two codominant alleles, LM and LN. The MN blood types and corresponding genotypes of 398 Finns in Karjala are tabulated here. To calculate the allelic frequencies from genotypic frequencies, we add the frequency of the homozygote for that genotype to half the frequency of each heterozygote that contains that allele: Evolutionary Forces Potentially Cause Changes in Allelic Frequencies Mutation Genetic Selection EVOLUTION Drift Migration Mendelian Genetics in Populations: Hardy–Weinberg Equilibrium The life cycle of an idealized population We want to track the fate of Mendelian genes in a population Imagine that the mice in the figure have in their genome a Mendelian locus, the A locus, with two alleles: A and a. We can begin tracking these alleles at any point in the life cycle. We then follow them through one complete turn of the cycle, from one generation to the next, to see if their frequencies change. Simulation: adults choose their mates at random Simulation: adults choose their mates at random Imagine that 60% of the eggs and sperm received a copy of allele A, and 40% received a copy of allele a. That is, the frequency of allele A in the gene pool is 0.6, and the frequency of allele a is 0.4 Simulation: adults choose their mates at random We can close our eyes and put a finger down on the previous figure to choose an egg. Perhaps it carries a copy of allele A. Now we close our eyes and put down a finger to choose a sperm. Perhaps it carries a copy of allele a. If we combine these gametes, we get a zygote with genotype Aa. 100 zygotes we made, 34 had genotype AA, 57 had Aa, and 9 had aa Simulation: adults choose their mates at random imagine that all Imagine, We can choose any these zygotes furthermore, that number of gametes develop into when the adults we like for the juveniles, and that reproduce, they all standard donation, all the juveniles donate the same so we will choose survive to number of gametes 10 to make the adulthood. to the gene pool. arithmetic easy Summing the gametes carrying copies of each allele, we get 625 carrying A and 375 carrying a, for a total of 1,000. The frequency of allele A in the new gene pool is 0.625; the frequency of allele a is 0.375. Simulation: adults choose their mates at random Allele and genotype frequencies throughout the life cycle in a numerical simulation Simulation: adults choose their mates at random The fact that blind luck can cause a population to evolve unpredictably is an important result of population genetics. This mechanism of evolution is called genetic drift. We want to know what would have happened in our simulations if chance had played no role. A Numerical Calculation: Punnett square When blind luck plays no role, random mating in the gene pool of our model mouse population produces zygotes with predictable genotype frequencies A Numerical Calculation: Punnett square imagine that all Imagine, We can choose any these zygotes furthermore, that number of gametes develop into when the adults we like for the juveniles, and that reproduce, they all standard donation, all the juveniles donate the same so we will choose survive to number of gametes 10 to make the adulthood. to the gene pool. arithmetic easy Summing the gametes carrying each allele, we get 600 carrying copies of A and 400 carrying copies of a, for a total of 1,000. The frequency of allele A in the new gene pool is 0.6; the frequency of allele a is 0.4. A Numerical Calculation: Punnett square When blind luck plays no role, the allele frequencies for A and a in our population are in equilibrium: They do not change from one generation to the next. The population does not evolve. The primary goal of population genetics is to understand the processes that shape a population’s gene pool. First, we must ask what effects reproduction and Mendelian principles have on the genotypic and allelic frequencies: How do the segregation of alleles in gamete formation and the combining of alleles in fertilization influence the gene pool? Hardy–Weinberg law The Hardy–Weinberg law was formulated independently by both Godfrey H. Hardy and Wilhelm Weinberg in 1908. The law is actually a mathematical model that evaluates the effect of reproduction on the genotypic and allelic frequencies of a population. The Hardy–Weinberg equilibrium principle yields two fundamental conclusions: Assumption: If a population is large, randomly mating, and not affected by mutation, migration, or natural selection, then: Conclusion 1: The allele frequencies in a population will not change, generation after generation. Conclusion 2: the genotypic frequencies stabilize (will not change) after one generation in the proportions p2 (the frequency of AA), 2pq (the frequency of Aa), and q2 (the frequency of aa), where p equals the frequency of allele A and q equals the frequency of allele a. Genotypic Frequencies at Hardy–Weinberg Equilibrium How do the conditions of the Hardy–Weinberg law lead to genotypic proportions of p2, 2pq, and q2? The Hardy–Weinberg equilibrium principle Random mating will produce genotypes of the next generation in proportions p2(AA), 2pq(Aa), and q2(aa) assumptions that it makes about a population it assumes that the population is large members of the population mate randomly, which means that each genotype mates relative to its frequency. the allelic frequencies of the population are not affected by natural selection, migration, and mutation. Hardy– Weinberg law apply to a single locus. What Use Is the Hardy–Weinberg Equilibrium Principle? There is no selection. There is no mutation There is no migration There are random matings Implications of the Hardy–Weinberg Law population cannot evolve if it meets the Hardy– Weinberg assumptions, because evolution consists of change in the allelic frequencies of a population. the genotypic frequencies are determined by the allelic frequencies. The heterozygote frequency never exceeds 0.5 when the population is in Hardy–Weinberg equilibrium. single generation of random mating produces the equilibrium frequencies of p2, 2pq, and q2. Summary of the mechanisms of evolution Hardy–Weinberg principle serves as a null model. Biologists can measure allele and genotype frequencies in nature, and determine whether the Hardy–Weinberg conclusions holds. If a population is not in Hardy–Weinberg equilibrium then one or more of the Hardy–Weinberg model’s assumptions are being violated. Such a discovery does not, by itself, tell us which assumptions are being violated, but it indicates that further research may be rewarded with interesting discoveries. Testing the Hardy-Weinberg Principle 1. Calculate the allele frequencies 2. Calculate the genotype frequencies expected under Hardy–Weinberg equilibrium (p2, 2pq, and q2) Testing the Hardy-Weinberg Principle 3. Calculate the expected number of infants/offsprings of each genotype under Hardy–Weinberg equilibrium. 4. Calculate chi square Testing the Hardy-Weinberg Principle 5. Determine whether the test statistic is significant Will the Frequency of the CCR5-∆32 Allele Change? As long as individuals of all CCR5 genotypes survive and reproduce at equal rates; as long as no mutations convert some CCR5 alleles into others, as long as no one moves from one population to another, as long as populations are infinitely large, and as long as people choose their mates at random….. then no, the frequency of the CCR5@∆32 allele will not change Incorporating Selection in the Hardy-Weinberg Equation Natural selection Natural selection takes place when individuals with adaptive traits produce a greater number of offspring than that produced by others in the population. If the adaptive traits have a genetic basis, they are inherited by the offspring and appear with greater frequency in the next generation. Natural selection produces adaptations, such as those seen in the polar bears that inhabit the extreme Arctic environment. Selection: Violation of the Hardy–Weinberg equilibrium principle Selection happens when individuals with particular phenotypes survive to sexual maturity at higher rates than those with other phenotypes, or when individuals with particular phenotypes produce more offspring during reproduction than those with other phenotypes Adding Selection to the Hardy–Weinberg Analysis: Changes in Allele Frequencies Selection can cause allele frequencies to change across generations Assume that the frequency of allele B1 in the gene pool is 0.6 and the frequency of allele B2 is 0.4. After random mating, we get genotype frequencies for We incorporate selection by stipulating that the genotypes differ in survival. All of the B1B1 individuals survive, 75% of the B1B2 individuals survive, and 50% of the B2B2 individuals survive If we assume that each survivor donates 10 gametes to the new gene pool, then Calculating the allele frequencies The frequency of allele B2 has dropped by the same amount. Violation of the no-selection assumption has resulted in violation of conclusion 1 of the Hardy– Weinberg analysis. The population has evolved. Research on Allele Frequency Change by Selection: ADH locus: AdhF and AdhS Fruit flies, like most other animals, make an enzyme that breaks down ethanol, the poisonous active ingredient in beer, wine, and rotting fruit. This enzyme is called alcohol dehydrogenase, or ADH. Cavener and Clegg worked with populations of flies that had two alleles at the ADH locus: AdhF and AdhS. Hardy–Weinberg conclusion 1 appears to hold true in the control populations, but is clearly not valid in the experimental populations. Frequencies of the allele in four populations of fruit flies over 50 generations Selection to the Hardy–Weinberg Analysis: The Calculation of Genotype Frequencies Selection can change genotype frequencies so that they cannot be calculated by multiplying the allele frequencies assume that the initial frequency of each allele in the gene pool is 0.5. After random mating, we get genotype frequencies for B1B1, B1B2, and B2B2 of 0.25, 0.5, and 0.25. we incorporate selection this time, 60% of the B1B1 individuals survive, all of the B1B2 individuals survive, and 60% of the B2B2 individuals survive If we assume that each surviving adult donates 10 gametes to the next generation’s gene pool, then: Summing the gametes carrying each allele, we get 400 carrying B1 and 400 carrying B2, for a total of 800. Both alleles are still at a frequency of 0.5. Let us calculate frequencies of the three genotypes These genotype frequencies reveal that violation of the no-selection assumption has resulted in violation of conclusion 2 of the Hardy–Weinberg analysis. Research on Selection and Genotype Frequencies: sVEGFR1 and Malaria Research on Selection and Genotype Frequencies: sVEGFR1 and Malaria When a pregnant woman contracts the disease, the parasites invade the placenta via the mother’s circulatory system This triggers placental inflammation and may also interfere with placental development. The potential complications include spontaneous abortion, premature delivery, low birth weight, and higher risk of infant death. VEGFR Research on Selection and Genotype Frequencies: sVEGFR1 and Malaria Fetal cells in the placenta release a soluble form of this protein, sVEGFR1, into the mother’s circulation. By interacting with vascular endothelial growth factor, VEGFR1 influences both placental development and inflammation VEGFR1 with alleles cluster into a short group (S alleles) and a long group (L alleles). Cultured cord blood cells with genotypes SS and SL produce more VEGFR1 than do LL cells Research on Selection and Genotype Frequencies: sVEGFR1 and Malaria The researchers first determined the allele frequencies among 163 infants born from October through April, when the rate of placental malaria was at its annual low. The frequencies were The true frequency of heterozygotes is slightly higher than predicted, and the frequencies of homozygotes are slightly lower, but the discrepancies are modest. The infants thus conform to conclusion 2 of the Hardy–Weinberg analysis. Research on Selection and Genotype Frequencies: sVEGFR1 and Malaria Researchers then determined the allele frequencies among 76 infants born from May through September, when the rate of placental malaria was at its annual high. The frequencies were nearly the same as among the off- season newborns: There are substantially more heterozygotes than expected, and substantially fewer homozygotes. The genotypes of the infants born during peak malaria season are in violation of Hardy–Weinberg conclusion 2 The researchers surveyed Tanzanian infants born to first-time mothers during malaria season. The genotype counts (provided by Atis Muehlenbachs and Patrick Duffy, personal communication) were: Calculate the allele frequencies S L Calculate the genotype frequencies expected. frequencies of two alleles are p and q, then the expected frequencies of the genotypes are p2, 2pq, and q2 Calculate the expected number of infants of each genotype under Hardy– Weinberg equilibrium. Calculate the statistics The x2 test tells us that among infants born during malaria season, the alleles of the gene for VEGFR1 are not in Hardy– Weinberg equilibrium. This indicates that one or more assumptions of the Hardy– Weinberg analysis has been violated. Fitness and Selection Coefficient Fitness is defined as the relative reproductive success of a genotype. Fitness (W) ranges from 0 to 1. Suppose the average number of viable offspring produced by three genotypes is To calculate fitness for each genotype Fitness and Selection Coefficient overdominance or heterozygote advantage. Here, the heterozygote has higher fitness than the fitnesses of the two homozygotes (W11 < W12 > W22) underdominance underdominance, in which the heterozygote has lower fitness than both homozygotes (W11 > W12 < W22). Underdominance leads to an unstable equilibrium; Allelic frequencies will not change as long as they are at equilibrium but, if they are disturbed from the equilibrium point by some other evolutionary force, they will move away from equilibrium until one allele eventually becomes fixed. Mutation Recurrent mutation changes allelic frequencies Mutation can influence the rate at which one genetic variant increases at the expense of another. Reaching Equilibrium of Allelic Frequencies The mutation rates for most genes are low; so change in allelic frequency due to mutation in one generation is very small, and long periods of time are required for a population to reach mutational equilibrium. Nevertheless, if mutation is the only force acting on a population for long periods of time, mutation rates will determine allelic frequencies. Adding Mutation to the Hardy–Weinberg Analysis: Mutation as an Evolutionary Mechanism mutation (in the example) converts 1 of every 10,000 copies of allele A into a new copy of allele a. The frequency of A after mutation is given by the frequency before mutation minus the fraction lost to mutation; the frequency of a after mutation is given by the frequency before mutation plus the fraction gained by mutation. That is, The new allele frequencies are almost identical to the old allele frequencies. As a mechanism of evolution, mutation has had almost no effect. Almost no effect is not the same as exactly no effect. Could mutation of A into a, occurring at the rate of 1 copy per 10,000 every generation for many generations, eventually result in an appreciable change in allele frequencies? Over very long periods of time, mutation can eventually produce appreciable changes in allele frequency Cystic Fibrosis Cystic fibrosis is among the most common serious genetic diseases among people of European ancestry, affecting approximately 1 newborn in 2,500. Cystic fibrosis is inherited as an autosomal recessive trait. Affected individuals suffer chronic infections with the bacterium Pseudomonas aeruginosa and ultimately sustain severe lung damage Cystic Fibrosis Although cystic fibrosis was lethal for most of human history, in some populations as many as 4% of individuals are carriers. How can alleles that cause a lethal genetic disease remain this common? heterozygote superiority new disease alleles are constantly introduced into populations by mutation Adding Mutation to the Hardy–Weinberg Analysis: Mutation as an Evolutionary Mechanism Return to our model population of mice. Imagine a locus with two alleles, A and a, with initial frequencies of 0.9 and 0.1. A is the wild-type allele, and a is a recessive loss-of-function mutation. Furthermore, imagine that copies of A are converted by mutation into new copies of a at the rate of 1 copy per 10,000 per generation Mutation is a weak mechanism of evolution Almost no effect is not the same as exactly no effect Are the Alleles That Cause Cystic Fibrosis Maintained by a Balance between Mutation and Selection? Are the Alleles That Cause Cystic Fibrosis Maintained by a Balance between Mutation and Selection? Are the Alleles That Cause Cystic Fibrosis Maintained by a Balance between Mutation and Selection? Are the Alleles That Cause Cystic Fibrosis Maintained by a Balance between Mutation and Selection? In individuals with cystic fibrosis, P. aeruginosa cause chronic lung infections that eventually lead to severe lung damage. Selection against the alleles that cause cystic fibrosis appears to be strong. Until recently, few affected individuals survived to reproductive age; those that do survive are often infertile. And yet the alleles that cause cystic fibrosis have a collective frequency of approximately 0.02 among people of European ancestry. Could cystic fibrosis alleles be maintained at a frequency of 0.02 by mutation– selection balance? Steady supply of new mutations cannot, by itself, explain the maintenance of cystic fibrosis alleles at a frequency of 0.02.

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