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Hardy-Weinberg Principle • Mathematical description of Mendelian inheritance Godfrey Hardy (1877-1947) Wilhem Weinberg (1862 – 1937) Hardy-Weinberg Theorem In a non-evolving population, frequency of alleles and genotypes remain constant over generations You should be able to predict the genotype frequencies, given the allele frequencies DEVIATION from Hardy-Weinberg Equilibrium Indicates that EVOLUTION Is happening 3 Evolutionary Mechanisms (will put population out of HW Equilibrium): • • • • Genetic Drift Natural Selection Mutation Migration *Epigenetic modifications change expression of alleles but not the frequency of alleles themselves, so they won’t affect the actual inheritance of alleles However, if you count the phenotype frequencies, and not the genotype frequencies , you might see phenotypic frequencies out of HW Equilibrium due to epigenetic silencing of alleles. (epigenetic modifications can change phenotype, not genotype) Epigenetic modification could affect which alleles are exposed to natural selection (no effect of Genetic Drift) 4 Requirements of HW Violation Evolution Large population size Genetic drift Random Mating Inbreeding & other No Mutations Mutations No Natural Selection Natural Selection No Migration Migration An evolving population is one that violates Hardy-Weinberg Assumptions Examples of Deviation from Hardy-Weinberg Equilibrium Generation 1 Generation 2 Generation 3 Generation 4 AA 0.64 0.63 0.64 0.65 Aa 0.32 0.33 0.315 0.31 aa 0.04 0.04 0.045 0.04 Is this population in HW equilibrium? If not, how does it deviate? What could be the reason? 6 Evolutionary Mechanisms Genetic Drift (and Inbreeding) 7 Sources of Genetic Variation Mutation generates genetic variation Natural Selection Natural Selection acts on genetic or epigenetic variation in a population Without genetic or epigenetic variation, Natural Selection cannot occur Epigenetic modification changes expression of genes Genetic Drift causes fluctuations in allele frequencies and can reduce genetic variation 8 Sources of Genetic Variation Mutation generates genetic variation Natural Selection Natural Selection acts on genetic or epigenetic variation in a population Without genetic or epigenetic variation, Natural Selection cannot occur Epigenetic modification changes expression of genes Genetic Drift causes fluctuations in allele frequencies and can reduce genetic variation 9 Today’s OUTLINE: (1) Migration (2) Genetic Drift (3) Effective Population Size (4) Model of Genetic Drift (5) Heterozygosity (6) A Consequence of Genetic Drift: Inbreeding 10 Migration (fairly obvious) Can act as a Homogenizing force (If two populations are different, migration between them can reduce the differences) A population could go out of HW equilibrium with a lot of migration 11 Impact of Migration Immigration: could introduce genetic variation into a population Emigration: could reduce genetic variation in a population 12 Random Genetic Drift 13 Sewall Wright (1889-1988) • Sewall Wright worked on agricultural stocks (e.g. cows), and was consequently interested in small, inbred populations • Thus, he regarded Inbreeding and Genetic Drift as particularly important genetic mechanisms • Genetic Drift and Inbreeding could generate new gene interactions • These new gene interactions (epistasis caused by new recombinations) are the main substrate for selection 14 “Null Model” No Evolution: Null Model to test if no evolution is happening should simply be a population in Hardy-Weinberg Equilibrium No Selection: Null Model to test whether Natural Selection is occurring should have no selection, but should include Genetic Drift This is because Genetic Drift is operating even when there is no Natural Selection 15 “Null Model” No Selection: A model that tests for the presence of Natural Selection should include Genetic Drift This is because Genetic Drift is operating even when there is no Natural Selection So the null model that tests for natural selection should include demography, population growth and decline, as population size directly affects the level of genetic drift acting on a population 16 Even after the synthesis the relative importance of Natural Selection and Genetic Drift were debated • During the Evolutionary Synthesis, Sewall Wright focused more on importance of Genetic Drift, whereas Fisher focused on Natural Selection • Shortly after the Evolutionary Synthesis many focused on selection to the point of assuming that most phenotypes were the result of Natural Selection • Emphasis on Genetic Drift resurged in the 1970s, 80s with Kimura’s “Neutral Theory” • Then in the 2000s and 2010s interest in Selection increased with the ability to detect signatures of Natural Selection in genome sequence data 17 Motoo Kimura (1924-1994) The Neutral Theory of Molecular Evolution Classic Paper: Kimura, Motoo. 1968. Evolutionary rate at the molecular level. Nature. 217: 624–626. Classic Book: Kimura, Motoo (1983). The neutral theory of molecular evolution. Cambridge University Press. 18 Molecular Clock Observations of amino acid changes that occurred during the divergence between species, show that molecular evolution (mutations) takes place at a roughly constant rate. This suggests that molecular evolution is constant enough to provide a “molecular clock” of evolution, and that the amount of molecular change between two species measures how long ago they shared a common ancestor. From this, Kimura concluded that not much selection is going on (because the pattern of regular mutations is not obscured by selection), and that most evolution is influenced by Genetic Drift. Figure: the rate of evolution of hemoglobin. Each point on the graph is for a pair of species, or groups of species. From Kimura (1983). 19 The Neutral Theory of Molecular Evolution • The Neutral theory posits that the vast majority of evolutionary change at the molecular level is caused by random genetic drift rather than natural selection. Motoo Kimura • Neutral theory is not incompatible with Darwin's theory of evolution by natural selection: adaptive changes are acknowledged as present and important, but hypothesized to be a small minority of evolutionary change. • Recent tests of selection have found that in many cases evolution is not neutral, even in non-coding regions of the genome. • Nevertheless, the neutral theory is useful as the null hypothesis, for testing whether natural selection is occurring. 20 I. Random Genetic Drift Definition: Changes in allele frequency from one generation to the next simply due to chance (sampling error). This is a NON ADAPTATIVE evolutionary force. Darwin did not consider genetic drift as an evolutionary force, only natural selection. 21 Genetic Drift Genetic Drift happens when populations are limited in size, violating HW assumption of infinite population size When population is large, chance events cancel each other out When population is small, random differences in reproductive success begin to matter much more 22 Effective Population Size In Evolution, when we talk about population size, we mean effective population size 23 Effective Population Size The concept of effective population size Ne was introduced by Sewall Wright, who wrote two landmark papers on it (Wright 1931, 1938). Sewall Wright defined it as "the number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration” OK, easier definition: Effective population size is the number of individuals in a population that actually contribute offspring to the next generation. 24 Effective Population Size The effective population size is always either equal to or less than the census population size (N). The effective population size is usually smaller than the real census population size because not everyone breeds and leaves offspring. Unequal sex ratio, variation in number of offspring, overlapping generations, fluctuations in population size, nonrandom mating could lead to an effective population size that is smaller than the census size. Ne = 4Nm Nf (Nm + Nf ) where Nm = number of males, Nf = number of females from this equation, you can see that unequal sex ratio would lead to lower Ne 25 Why do we care about effective population size Ne? Because Ne is the actual unit of evolution, rather than the census size N Why? Because only the alleles that actually get passed onto the next generation count in terms of evolution… the individuals that do not mate or have offspring are evolutionary dead ends… 26 Chance Events (no Selection) There is always an element of chance, in: Who leaves Offspring # of Offspring Which Offspring survive (which gametes, which alleles) 27 Example of sampling error Green fur: Blue fur: G (dominant) b (recessive) If Gb x Gb mate, the next generation is expected to have: 3:1 Ratio of Green to blue (GG, Gb, bG, bb) But this might not happen One family could get this unusual frequency just due to chance: You might get: bb, bb, bb, bb And, so you might accidentally lose the G allele not for any reason, but just due to chance The larger the population, the more these effects average out, and frequencies approach HW equilibrium 28 Why is this not Selection? Selection happens when some survive for a reason: better adapted. Genetic Drift is just a numbers game. Which gamete gets fertilized, which allele gets passed on is RANDOM 29 Consequences of Genetic Drift Random fluctuations in allele frequency If population size is reduced: 1. At the Allelic level: Random fixation of Alleles (loss of alleles) 2. At the Genotypic level: Loss of Heterozygosity (because of fewer alleles) 30 Random Shift in Allele Frequencies across Generations 31 Probability of loss of alleles is greater in smaller populations For example, if there are 50 different alleles in population …and a new population is founded by only 10 individuals Then the new population will be unable to capture all 50 alleles, and many of the alleles will be lost 32 Bottleneck Effect 33 Random fixation of alleles FIXATION: When an allele frequency becomes 100% The other alleles are lost by chance Fluctuations are much larger in smaller populations 34 Probability of fixation of an allele Probability of fixation of an allele = the allele’s starting frequency (Sewall Wright 1931) That is, if the frequency of an allele is 0.10 (10% in the population), then its probability (chances) of fixation (going to 100% in the population) is 0.10, or 10% 35 Probability of fixation of an allele Probability of fixation of an allele = the allele’s starting frequency (Sewall Wright 1931) That is, if the frequency of an allele is 0.10 (10% in the population), then its probability (chances) of fixation (going to 100% in the population) is 10% WHY? 36 Probability of fixation of an allele If a population has 2N alleles The probability of each allele being fixed = 1 2N If there are X # copies of that allele in the population, then the probability of fixation for that allele is X 2N This is the proportion (%) of alleles in the population 37 Genetic Drift: Random Fixation 38 Genetic Drift: Random Fixation After 7 generations, all allelic diversity was lost… the population became fixed for allele #1 just due to chance 39 Genetic Drift: Random Fixation As populations get smaller, the probability of fixation goes up 40 41 Heterozygosity Heterozygosity: frequency of heterozygotes in a population (% of heterozygotes) Often used as an estimate of genetic variation in a population HW expected frequency of heterozygotes in a population = 2p(1-p) As genetic drift drives alleles toward fixation or loss, the reduction in number of alleles causes the frequency of heterozygotes to go down 42 Heterozygosity The Expected Heterozygosity following a population bottleneck (frequency of Heterozygotes in the next generation = Hg+1): g+1 g e Note in this equation that as population size 2Ne gets small, heterozygosity in the next generation Hg+1, goes down 43 Grey line = theoretical expected heterozygosity: g+1 g e Blue line = observed heterozygosity (% heterozygotes in population) 44 Heterozygosity declines faster in smaller populations 45 Loss of Variation Allele frequencies 0.36 Lots of Alleles: 0.16 0.20 0.24 0.04 46 Lots of alleles --> Lots of genotypes: Possible genotype combinations 47 Loss of Allelic Variation Allele frequencies Due to Genetic Drift 0.53 0.067 0.20 0.20 0 48 Loss of Allelic Variation due to Genetic Drift results in Increased Homozygosity Fewer possible genotype combinations Increase in homozygosity 49 No Genetic Variation = No Natural Selection 50 No Genetic Variation = No Natural Selection Selection has nothing to act on 51 Genetic Drift and Natural Selection Because of the randomness introduced by Genetic Drift, Natural Selection is less efficient when there is genetic drift Thus, Natural Selection is more efficient in larger populations, and less effective in smaller populations 52 Allele A1 Demo • Impact of Effective Population Size • Impact of starting allele frequency • Interaction between Natural Selection and Genetic Drift 53 How do you detect Genetic Drift? Random fluctuations in allele frequencies Fluctuations in non-coding and non-functional regions of the genome The same pattern of fluctuations across these regions of the genome (same demographic factors would act across the genome) - but mtDNA not same Fluctuations in allele frequencies correspond to demography of the population (population size) 54 Consequences of Genetic Drift ---> Random fluctutations in allele frequency If population size is reduced and Drift acts more intensely, we get: 1. At the Allelic level: Random fixation of Alleles (loss of alleles) 2. At the Genotypic level: Inbreeding, Reduction in Heterozygosity (because of fewer alleles) 55 Dilemma for Conservationists • It is easier to remove genetic diversity than create it… especially variation that is potentially adaptive Census size: Roughly 2000-3000 cheetahs live in Namibia today The effective population size is much lower 56 2. Genetic Drift often leads to Inbreeding Inbreeding is a consequence of Genetic drift in small populations, resulting from loss of alleles Due to loss of alleles, there is an increase in homozygosity 57 With small population size, heterozygosity goes down, homozygosity goes up 58 Inbreeding Mating among genetic relatives, often because of small population size Alleles at a locus will more likely become homozygous A consequence of loss of alleles due to genetic drift (reduction in population size) 59 Calculations like these are used in genetic counseling and animal breeding to calculate F, the coefficient of inbreeding (developed by Sewall Wright) Fx = ∑[(1/2)n+1(1 + FA)] FA is the inbreeding coefficient for the common ancestor F = fixation index, a measure of homozygosity; the probability that two alleles at any locus in an individual are identical by descent from the common ancestor(s) of the two parents (homozygous, rather than heterozygous). (F=1 means individuals are genetically identical) 60 Probability of getting the same allele from the grandmother Mate between full-siblings Probability for identity by descent for both alleles Textbook 7.36 Probability of getting grandma’s allele Probability of getting grandpa’s allele Mate between full-siblings Textbook 7.36 The probability of getting grandma or grandpa’s allele small population size genetic drift loss of alleles decrease in heterozygosity increase in homozygosity increase of exposure of deleterious alleles 63 Consequences of Inbreeding Increase in Homozygosity: Exposure of recessive alleles (that could be subjected to selection) Inbreeding Depression (reduction in survival and fitness) Lower genotypic diversity (poor response to natural selection) 64 Consequences of Inbreeding • Deleterious recessive alleles are exposed as homozygotes (and less masked in the heterozygous state) • These deleterious recessive alleles get removed out of an inbred population more rapidly, because they are exposed to natural selection ---> this process is aided by Sex, discussed in Next Lecture (on Variation) 65 Mechanism: Most deleterious alleles are recessive Alleles On average each of us carries 35 lethal recessive alleles Locus1 A a These deleterious alleles are expressed in inbred individuals Locus2 B b Locus3 C c In Heterozygotes, these deleterious recessives are masked, and not exposed to selection 66 Increasing genetic distance Fitness Inbreeding Depression Hybrid Vigor Outbreeding Depression 67 Examples of Inbreeding 68 69 Inbreeding and Conservation Vexing Problem: How do we prevent extinctions? How do we maximize genetic variance in a population? What should we preserve? (species, populations, habitats, ecosystems???) 70 Inbreeding and Agriculture: Because we have focused excessively on a few breeds, effective population sizes of many crops are incredibly small 600 breeds of livestock have disappeared ~78 breeds lost each year 1000-1500 breeds of livestock are considered at risk of extinction (30% of current breeds) 71 8 million Holstein cows are descendents of 37 individuals!!! Neurological disorders Autoimmune diseases Fertility problems 72 Recent efforts have focused on outcrossing to increase fitness in agricultural stocks Duvick, D. N. 2002. Biotechnology in the 1930s: the development of hybrid maize. Nature Reviews Genetics. 2: 69-74. Bruce, W. B., G. O. Edmeades, and T. C. Barkre. 2002. Review Article: Molecular and physiological approaches to maize improvement for drought tolerance. Journal 73 of Experimental Botany. 53: 13-25. Inbreeding depression in humans 74 Genetic Diseases due to Inbreeding have afflicted many Royal Families George III Insane due to Porphyria Examples: Porphyria: accumulation of porphyrin precursors, causes insanity; Dominant, but more intense in the homozygous form Mary, Queen of Scots George III, loss of American colony Acromegaly: Overproduction of GH by the pituitary gland; recessive Charles II, King of Spain (1665-1700) Hemophilia: “Victoria’s Secret” Charles II “Hapsburg Jaw” X-linked, shows up in males Cognitively disabled Daughters spread it among the royals, impotent downfall of Russian monarchy 75 Porphyria in the Royal Families of Europe George III Dominant, but more intense in the homozygous form 76 Royal Pedigree of the “Hapsburg Jaw” In small populations, individuals tend to mate with relatives = expression of the disorder 77 Royal Pedigree of Hapsburg Jaw = expression of the disorder = marriage with close relative Inbreeding within the Royal Families of Europe was genetically “disasterous” 78 Inbreeding within Royal Families has been reduced in recent years Diana was a 7th cousin of Charles, rather than a first or second cousin (which was the normal practice previously) Kate Middleton is neither an aristocrat nor a royal, but the marriage was approved given the modern recognition of the perils of inbreeding… this marriage is an example of genetic immigration (Migration) 79 into an enclosed population Articles on British Royalty and Inbreeding: News Article: http://www.telegraph.co.uk/news/worldnews/e urope/spain/5158513/Inbreeding-causeddemise-of-the-Spanish-Habsburg-dynastynew-study-reveals.html Original Scientific Article: http://www.plosone.org/article/info:doi/10.1371/jou rnal.pone.0005174 80 Amish in Lancaster County, PA Descendents of ~200 Swiss who emigrated mid-1700s. Closed genetic population for 12+ generations. Host to 50+ identified inherited disorders (many more uncharacterized) 81 Examples of Diseases that Afflict Amish Populations High levels of infant mortality High Incidence of brain damage Large number of metabolic disorders, such as PKU Ellis-van Creveld (dwarfism) syndrome 1/14 in Amish Glutaric aciduria type I 1/200 in Amish High incidence of bipolar disorder Polydactyly (6 fingers) 82 There is nothing special about the Amish, genetically speaking (or Royal Families). • There are about ~200 of you here, similar to the size of the founding Amish population in Lancaster county, Pennsylvania. • If all of you were stranded on a desert island, eventually your descendents would be related and mating with one another. • Each of us carries 3-5 lethal recessive alleles. • If 200 people each had 3-5 different recessive lethals and started forming a closed population, eventually, hundreds of genetic disorders would emerge. 83 Dating Service FIND Your Genetically Most Distant Mate!!!! (GenePartner, “Love is no coincidence!” http://www.genepartner.com/ Instant Chemistry, SingldOut) 84 Summary (1) Genetic Drift occurs when a population is small, and leads to random loss of alleles due to sampling error (2) Inbreeding, an extreme consequence of Genetic Drift, results in increases in homozygosity at many loci, including recessive lethals 85 CONCEPTS Genetic Drift Effective population size Fixation Heterozygosity Inbreeding Inbreeding Depression Heterozygote advantage 86 1. When is Genetic Drift LEAST likely to operate? (A) When there are migrants between populations (B) When populations are fragmented and isolated (C) When population size is small (D) When population size is very very large 87 2. Which of the following is FALSE regarding inbreeding? (A) Inbreeding could result as a consequence after genetic drift has acted on a population (B) Populations with lower allelic diversity tend to have lower genotypic diversity (more homozygous) (C) Selection acts more slowly in inbred populations to remove deleterious recessive alleles (D) One way to reduce inbreeding in a population is to bring in migrants from another population 88 3. Which of the following is FALSE regarding Genetic Drift? (A) Genetic Drift occurs more rapidly in smaller populations (B) In populations of finite size, random changes in allele frequency occur at each generation (C) Genetic Drift could lead to inbreeding due to loss of alleles (D) Genetic Drift occasionally leads to the generation of favorable alleles 89 Answers to sample exam questions: 1D 2C 3D 90