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Hardy-Weinberg Theorem

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  1. Hardy-Weinberg Theorem x2 diploid 320 20

  2. Hardy-Weinberg Theorem

  3. Hardy-Weinberg Theorem Note Same

  4. H.-W. Frequencies (2 alleles) • Note how Genotype Frequencies are 100% a function of previous-generation Allele Frequencies. • This is precisely what the H.W. equation tells us. • It is the default evolutionary assumption • (i.e., no evolution is occuring)

  5. To assume Hardy-Weinberg equilibrium all of the following must be true: • The population must be very large (no sampling error/genetic drift) • There must be no net mutation • There must be no natural selection (though as we will see that this assumption can be temporarily suspended in the course of using the Hardy-Weinberg theorem) • No migration between populations • Random mating (equivalent to mixing all sperm and eggs in population into a common bucket to foster fertilization) • In other words, no mechanisms that can affect genetic structure—i.e., allele or genotype frequencies—may be operating H.-W. Assumptions

  6. H.-W. Equilibrium • If no mechanisms that can affect genetic structure are operating, then • Hardy-Weinberg genotype frequencies will be established in a single generation… • And these frequencies will persist indefinitely • (I.e., so long as there are no mechanisms operating that can affect genetic structure)

  7. Work with Decimals, not percentages, not fractions, not absolute numbers • Convert Phenotypes to Genotypes, whenever you are given phenotype information you should be pondering (i) how can I convert phenotypes to genotypes? and (ii) how can I convert known phenotype frequencies to genotype frequencies? • Convert Genotypes to Alleles, once you know genotype frequencies it should be trivial to convert to allele frequencies: don’t let this step trip you up • Convert Alleles to Genotypes, if you know allele frequencies, but not genotype frequencies, then chances are you will need to figure out the latter • Incorporating Selection, usually selection only operates at the diploid stage  make sure frequencies always add up to one • Practice, Practice, Practice, Practice, Practice! Solving H.-W. Problems

  8. Convert percentages to decimals (I.e., by dividing by 100): 25%  0.25 • Convert fractions to decimals (I.e., by dividing by the denominator): ¼  0.25 • Convert absolute numbers to decimals (I.e., by dividing number by total): 60/240  0.25 • Many a Hardy-Weinberg solution has been tripped up by not employing decimals, i.e., by not employing frequencies • E.g., 25% x 25% = 625%! (which is incorrect) • E.g., 0.25 x 0.25 = 0.0625! (which is correct) • Yes, 25/100 x 25/100 = 625/100/100 = 0.0625 • But isn’t that absurdly complicating??? Working with Decimals

  9. Phenotype to Genotype conversions are going to depend on the genetics of your locus • Always in these problems genotypes will be diploid • If alleles have a dominance-recessive relationship, then the heterozygote will have the same phenotype as the dominant homozygote • Therefore, if the relationship is dominant-recessive you will know with certainty only the genotypes of recessive homozygotes • If the relationship is codominant or incomplete dominant, however, then there will be a one-to-one mapping of genotype to phenotype • That is, for the latter (& only for the latter) genotype frequencies will be the same as phenotype frequencies Phenotype  Genotype

  10. If a population is in Hardy-Weinberg equilibrium then the frequency of all genotypes, even dominant genotypes, may be estimated • Start with the frequency of the recessive homozygote  this equals q2 • q therefore is equal to the square root of the frequency of the recessive homozygote • p, the frequency of the dominant allele, therefore (if 2-alleles) can be assumed to be equal to 1 – q • The dominant homozygote therefore can be assumed to have a frequency of (1 – q)2 • The heterozygote therefore can be assumed to have a frequency simply of 2*p*q • Always assume Hardy-Weinberg equilibrium unless you have a compelling reason not to Dominant Genotypes

  11. Once you know genotype frequences, going from genotype frequencies to allele frequencies is easy • Don’t let it trip you up! • There are two formulas one can use and which one you use depends on whether you are working with absolute numbers versus genotype frequencies • f(A) = [2*f(AA) + 1*f(Aa) + 0*f(aa)] / 2 • [note that 2 = 2*f(AA) + 2*f(Aa) + 2*f(aa) since all frequencies should add up to 1] • Note that this is just a ratio of number of alleles of a one type to total number of alleles present in a population • Alternatively, with X= # AA, Y= # Aa, & Z= # aa: • f(A) = (2*X + 1*Y + 0*Z) / 2*(X + Y + Z) • Note also that f(A) = 1 – f(a) (for 2 allele system) • [for ABO (3-allele) system, f(IA) = 1 - f(IB) - f(i)] Genotype  Allele

  12. Genotype frequencies can be estimated from allele frequencies • First, you must assume Hardy-Weinberg equilibrium • Then simply calculate genotype frequencies from allelic frequencies using the Hardy-Weinberg theorem • (recall that p and q are allele frequencies) • If you had 70 A alleles and 120 a alleles, then what are the expected frequencies of AA, Aa, and aa? • f(A) = 70 / (70 + 120) = 0.37  f(a) = 0.63 • f(AA) = 0.372 = 0.14; f(aa) = 0.632 = 0.40; f(Aa) = 2 * 0.37 * 0.63 = 0.47; • Check your answer  0.14 + 0.40 + 0.47 = 1.01, which is pretty close to 1.0 (rounding error?) Allele  Genotype

  13. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn,ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  14. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  15. Non-Random Mating • Non-Random mating violates statistical independence, which would complicate our math • Recall the “Rule of Multiplication” from Chapter 14 • “How do we determine the chance that two or more independent events will occur together in some specific combination? The solution is in computing the probability for each independent event, then multiplying these individual probabilities to obtain the overall probability of the two events occurring together.” (p. 254 C & R, 2002) • It is because matings are random that the odds, e.g., of one A allele (from mom) being paired with another A allele (from dad) is p * p or p2 • If matings were not random then the probability of the above pairing could be >p2 or <p2, depending on whether “opposites” repel or “opposites” attract (respectively)

  16. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  17. Sampling Error: Genetic Drift Errors Get Bigger (as fraction of sample) as Samples Get Smaller!

  18. This image resembling Vincent van Gogh's painting, "Starry Night," is Hubble's latest view of an expanding halo of light around a distant star, named V838 Monocerotis (V838 Mon). This Hubble image was obtained with the Advanced Camera for Surveys on February 8, 2004. The illumination of interstellar dust comes from the red supergiant star at the middle of the image, which gave off a flashbulb-like pulse of light two years ago. V838 Mon is located about 20,000 light-years away from Earth in the direction of the constellation Monoceros, placing the star at the outer edge of our Milky Way galaxy.

  19. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift — Bottleneck • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  20. Sampling Error: Bottleneck

  21. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift — Founder Effect • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  22. Sampling Error: Founder Effect

  23. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  24. Migration (Gene Flow) Makes allele frequencies become more similar

  25. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift • Mutation (particularly net mutation) • Migration • Non-Random mating Non-Darwinian Evolution

  26. Mutation & Neutral Variation

  27. Generally Natural Selection is the evolutionary force most closely associated with Darwinism (i.e., Darwinian evolution) • Keep in mind, though, that selection cannot operate without genetic variation • Genetic variation, in turn, ultimately is a consequence of mutation • Non-Darwinian mechanisms generally are not adaptive and include: • Genetic drift • Mutation • Migration • Non-Random mating Non-Darwinian Evolution

  28. Natural Selection Make sure that you understand that… • Natural selection acts on phenotypes • Genotypes underlie phenotypes • Alleles underlie genotypes • Therefore, natural selection ultimately acts on allele frequencies, though selection occurs through the filter of both phenotype and genotype

  29. Incorporating Selection

  30. Darwinian Fitness/Natural Selection

  31. Modes of Selection

  32. Directional Selection (in macroevolution) Note: This example is Macroevolutionary, not Micro…

  33. Sexual Selection • Sexual selection are forces that impact on mate procurement • If you don’t mate, you don’t make babies • Mate procurement involves competing with same gender individuals (e.g., other males) and attracting other-gender individuals • Intrasexual selection is a consequence of direct competition (e.g., fighting) with one’s own gender • Intersexual selection (mate choice) is competition for the other gender’s “eye” • How these mechanisms operate can differ greatly from gender to gender • Basically, for some species (e.g., us), procuring a mate can be a very complicated experience

  34. Sexual Selection

  35. Sexual Dimorphism

  36. Sexual Selection

  37. Polymorphism

  38. Balanced Polymorphism • Stably maintained multiple alleles at a given locus • Heterozygous Advantage, a.k.a., balancing selection • E.g., Sickle Cell Anemia but otherwise probably not too important • Hybrid Vigor a product of heterozygous advantage and the masking of deleterious alleles • E.g., Hybrid Corn, but can this maintain polymorphisms in the wild? • Frequency-Dependent Selection  selection for alleles because they are rare, e.g., Major Histocompatibility Complex • Neutral variation  selection not strong enough to remove alleles (unless environment changes) • There is more neutral variation in larger populations due reduced strength of genetic drift

  39. Environmental Variation: A Cline

  40. Link to Next Presentation

  41. Acknowledgements http://207.233.

  42. Definition of Planetary Nebula Go to… http://www.google.com/search?q=define:planetary+nebula

  43. Definition of Planetary Nebula Go to… http://www.google.com/search?q=define:white+dwarf Let's have a reading quiz tomorrow, covering chapter 24

  44. With no selection: calculations proceed whereby allelic frequency is used to calculate genotype frequency (I.e., following fertilization) which, in turn, is used to calculate allelic frequency (I.e., following meiosis) • With selection: calculations are identical except that selection modifies genotype frequency prior to the calculation of allelic frequency • The trick is properly modifying genotype frequency • We use selection coefficients which simply are numbers multiplying phenotype frequencies • E.g., if all aa and AA individuals are killed then the resulting genotype frequency must be 1.0 Aa or 0.5 = f(A) and 0.5 = f(a) Incorporating Selection

  45. What would the genotype frequency be following selection if all aa individuals are killed but no AA or Aa individuals, and the population started with 0.5 a alleles • (remember to otherwise assume H.-W. equilibrium) • A: genotype frequencies prior to selection are 0.25, 0.5, and 0.25 for AA, Aa, and aa • Following selection f(AA) = 0.25 / (0.25 + 0.5) = 0.33  f(Aa) = 1 – 0.33 = 0.67 • Can you see where the new genotype frequency came from? • What is the new allele frequency? • A: f(A) = (2*0.33 + 1*0.67 + 0*0)/2 = 0.67  f(a) = 0.33 Incorporating Selection

  46. Non-Random Mating

  47. The fossil lineage of the horse provides a remarkable demonstration of directional succession. The full lineage is quite complicated and is not just a simple line from the tiny dawn horse Hyracotherium of the early Eocene, to today's familiar Equus. Overall, though, the horse has evolved from a small-bodied ancestor built for moving through woodlands and thickets to its long- legged descendent built for speed on the open grassland. This evolution has involved well- documented changes in teeth, leg length, and toe structure. Directional Selection (in macroevolution)