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Transcript
Selection Dan Graur 1 Conditions for maintaining Hardy-Weinberg equilibrium: 1. 2. 3. 4. 5. random mating no migration no mutation no selection infinite population size 2 2 mathematical approaches to studying genetic changes in populations: Deterministic models Stochastic models 3 Deterministic models assume that changes in allele frequencies from generation to generation occur in a unique manner and can be unambiguously predicted from knowledge of initial conditions. Strictly speaking, this approach applies only when: (1) the population is infinite in size, and (2) the environment either remains constant with time or changes according to deterministic rules. 4 Stochastic models assume that changes in allele frequencies occur in a probabilistic manner, i.e., from knowledge of the conditions in one generation one cannot predict unambiguously the allele frequencies in the next generation, but can only determine the probabilities with which certain allele frequencies are likely to be attained. 5 Stochastic models are preferable to deterministic ones, since they are based on more realistic assumptions. However, deterministic models are easier mathematically and, under certain circumstances, they yield sufficiently accurate insights. 6 Selection The deterministic approach 7 Natural selection The differential reproduction of genetically distinct individuals (genotypes) within a population. Differential reproduction is caused by differences among individuals in such traits as (1) mortality, (2) fertility (offspring), (3) fecundity (gametes), (4) mating success, and (5) viability of offspring. 8 9 Is the fitness of slim men higher than that of fat men? Dixson et al. 2003. Masculine somatotype and hirsuteness as determinants of sexual attractiveness to women. Archives of Sexual Behavior 32:29–39. 10 Variability Non-Genetic Genetic 11 Arashnia levana Non-genetic variability. 12 Helix aspersa Genetic variability. 13 Variability Non-Genetic Fitness-related Genetic Fitness-unrelated 14 Genetic? No Fitness related? Yes Does selection operate? Hair color 15 Sperm morphology Genetic? Yes Fitness related? Yes Does selection operate? 16 Genetic? Fitness related? Does selection operate? Wealth 17 Darwinian selection requires variation. Lamarkian selection does not require variation. 18 Natural selection is predicated on the availability of genetic variation among individuals in characters related to reproductive success (variation in fitness). 19 20 Synonymous and nonsynonymous genetic variability. 21 Evolutionary Success Ryan Kremer Carlos Slim Helú (richest person on earth) 6 children Linus Pauling (Only person to win 2 unshared Nobel prizes) 4 children The fitness (w) of a genotype is a measure of the individual’s ability to survive and reproduce. The size of a population is constrained by the carrying capacity of the environment. Thus, an individual’s evolutionary success is determined not by its absolute fitness, but by its relative fitness in comparison to the other genotypes in the population. 23 Finite Niche (Carrying) Capacity 24 In nature, the fitness of a genotype is not expected to remain constant for all generations and under all conditions. However, by assigning a constant value of fitness to each genotype, we are able to formulate simple models, which are useful for understanding the dynamics of change in the genetic structure of a population brought about by natural selection. 25 26 • We assume that fitness is determined solely by the genetic makeup. • We assume that all loci contribute independently to fitness (i.e., the different loci do not interact with one another in a manner that affects fitness), so that each locus can be dealt with separately. 27 A very simple model (1): One locus = A Two alleles = A 1 & A2 The old allele = A1 The new allele is = A2 Three genotypes = A 1 A 1 , A1 A 2 & A 2 A 2 Each genotype has a typical fitness (w) We are interested in the fate of A2 28 A very simple model (2): The fitness of the old genotype (A1A1) is set at 1. The relative fitnesses of the two new possible genotypes (A1A2 & A2A2) are defined comparatively as 1 + s or 1 + t, where s and t are the selection coefficients. 29 30 In comparison with A1, A2 may deleterious, neutral, or advantageous, and it will be subject to purifying selection, no selection, or positive Darwinian selection, respectively. 31 Genotype A1A1 Fitness w11 Frequency p2 A1A2 A2A2 w12 w22 2pq q2 32 33 Change in A2 allele frequency per generation pq[ p(w12 w11)+ q(w22 w12 )] q 2 2 p w 2pqw q w 11 12 22 34 Genotype A1A1 A1A2 A2A2 Fitness w11 w12 w22 2pq q2 Frequency p2 These are the variables we fiddle with 35 Dominance & Recessiveness At the phenotypic level At the fitness level 36 A1 dominance Genotype A1A2 A2A2 w11 w11 w22 Frequency p2 2pq q2 Fitness A1A1 37 A1 dominance Genotype Fitness A1A1 1 A1A2 1 A2A2 1+s A2 pq2s q 1 q2s 38 A2 dominance Genotype A1A1 A1A2 A2A2 Fitness w11 w22 w22 2pq q2 Frequency p2 39 codominance A2 dominance Genotype Fitness A1A2 1+s A2A2 1+s 2 p qs 2 1 s p s A2 q A1A1 1 40 Codominance (genic selection) Genotype A1A1 Fitness w11 Frequency p2 A1A2 A2A2 (w11 + w22)/2 w22 2pq q2 41 codominance Genotype Fitness A1A2 1+s A2A2 1 + 2s spq 1 2spq 2sq 2 A2 q A1A1 1 42 codominance A1 dominance A2 dominance A1 = old mutant A2 = new mutant 43 Selection intensities 44 Initial Frequencies 45 Industrial Melanism 46 47 A2 48 Selection against recessive lethal alleles b-hexosaminidase A is a dimeric lysosomal protein consisting of two a-subunits. It is encoded by a gene on chromosome 15. 49 Selection against recessive lethal alleles b-hexosaminidase-A catalyzes the removal of Nacetylgalactosamine from GM2 ganglioside, thereby degrading and removing it from the nervous system. 50 Absence of b-hexosaminidase-A Accumulation of GM2 ganglioside in neurons. 51 Selection against recessive lethal alleles Tay-Sachs disease results from a defect in the HEXA gene encoding the a subunit of b-hexosaminidase A. Warren Tay (1843-1927) Bernard Sachs (1858-1944) 52 Tay-Sachs is a recessive… allele 53 Tay-Sachs is a recessive & lethal alleles Symptoms of classical Tay-Sachs disease first appear at 4 to 6 months of age when an apparently healthy baby gradually stops smiling, crawling or turning over, loses its ability to grasp or reach out and, eventually, becomes blind, paralyzed and unaware of its surroundings. Death occurs by age 3-5. Cherry-red spot from an infant with Tay-Sachs disease. 54 Selection against recessive lethal alleles 55 Inefficiency of selection against recessive allele 56 It is difficult to rid a population of recessive alleles, because they hide behind the back of dominant alleles, and are not exposed to selection. If q = 50%, then 50% of all recessive alleles are in heterozygous state. If q = 10%, then 98% of all recessive alleles are in heterozygous state. If q = 1%, then 99.98% of all recessive alleles are in heterozygous state. 57 Selection against dominant lethal alleles Dr. George Sumner Huntington 1850-1916 Protein: huntingtin Gene: 180 Kb (chromosome 4) Exons: 67 Amino acids: 3,141 Mode: autosomal dominant 58 Selection against dominant lethal alleles 59 It should be easy to rid a population of dominant alleles, because all of them are exposed to selection at all frequencies. So why are there dominant lethal diseases? 60 1. 2. 3. 4. Recurrent mutations. Late age of onset. Variable expressivity. Incomplete penetrance. 61 62 Overdominance Genotype A1A1 Fitness w11 Frequency p2 A1A2 A2A2 w12 > w11,w22 w22 2pq q2 63 Underdominance Genotype A1A1 Fitness w11 Frequency p2 A1A2 A2A2 w12 < w11,w22 w22 2pq q2 64 The change in the frequency of A2 from generation to generation is: pq(2sq- tq - s) q 2 1 2spq tq 65 At equilibrium, i.e., when ∆q = 0. s qˆ 2s t 66 overdominance s = 0.04 and t = 0.02 underdominance 67 s = - 0.02 and t = - 0.01 Overdominant selection is inherently inefficient, even if the two homozygotes are not viable. RIP Powderpuff Chinese Crested 68 The peculiar case of sickle-cell anemia 69 70 Glutamic acid Valine 71 mvhltpeeksavtalwgkvn vdevggealgrllvvypwtq rffesfgdlstpdavmgnpk vkahgkkvlgafsdglahld nlkgtfatlselhcdklhvd penfrllgnvlvcvlahhfg keftppvqaayqkvvagvan alahkyh 147aa 72 mvhltpveksavtalwgkvn vdevggealgrllvvypwtq rffesfgdlstpdavmgnpk vkahgkkvlgafsdglahld nlkgtfatlselhcdklhvd penfrllgnvlvcvlahhfg keftppvqaayqkvvagvan alahkyh 147aa 73 74 75 76 77 78 Intuitive Model normal fitness b b H H normal somewhat reduced fitness b s H H sickle cell trait reduced fitness s s H H sickle cell anemia 79 80 In theory, the end result should have been directional selection — a S drastic reduction in H allele frequency in the population. 81 Worldwide distribution of sickle-cell anemia 82 In practice, the frequency of the S H allele may reach enormous values in some populations. >20% 83 84 Plasmodium falciparum 85 An evolutionary “experiment”: Slave trade 86 West Africa Frequency= >20% Curaçau no malaria HS frequency = 5% Surinam endemic malaria HS frequency = 20% 300 years = 10-15 generations 87 Genotype HH Fitness 1 S H H 1.27 0.25 HH S • With malaria in the background, heterozygotes have a huge advantage over the wild type homozygotes. • In the absence of malaria, the heterozygotes have a slight disadvantage in comparison to wild type homozygotes. • The fitness of the HsHs homozygotes is not affected by the presence or absence of malaria. 88 S Modiano D, Luoni G, Sirima BS, Simpore J, Verra F, Konate A, Rastrelli E, Olivieri A, Calissano C, Paganotti GM, D'Urbano L, Sanou I, Sawadogo A, Modiano G, Coluzzi M. 2001. Haemoglobin C protects against clinical Plasmodium falciparum malaria. Nature 414:305-308. 89 Hemoglobin C E to V = HS E to K = HC codon position 6! Glutamic acid Lysine 90 Genotype HH Fitness 1 Genotype HH Fitness 1 S H H 1.27 0.25 HH S C H H 1.27 0.75 HH C S C “…in the long term and in the absence of malaria control, HbC would replace HbS in central West Africa.” 91 The peculiar case of Rh-blood groups 92 Underdominant selection? Why does Rh– still exist? 93 94 95 Typ e of mutation Typ e of resulting selection Deleterious Purifying selection Detrimental Neutral No selection Advantageous Positive Darwinian Adaptive Selection Beneficial Overdominant Stable balancing selection Underdominant Unstable balancing selection 96 A summary: Selection may lead to changes in allele frequencies over time. A mere change in allele frequencies from generation to generation does not necessarily indicate that selection is at work. A lack of change in allele frequencies does not necessarily indicate that selection is absent. 97 Selection is a very important evolutionary force. At least, in principle… 98