A little knowledge is a dangerous thing. So is a lot. Albert Einstein. Distribution of grades: Exam I. Genetics. Genetics. Genetics.

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1 A little knowledge is a dangerous thing. So is a lot. Albert Einstein Percentage Distribution of grades: Exam I A B C D F Grade If Huntington s disease is a dominant trait, shouldn t most people have Huntington s? How can O be the most common blood type if it is a recessive trait? Percent type O blood in Native Americans 7-79% 8-89% 9-99% % Why don t all traits have 3:distribution in populations? Why would we expect a 3: ratio? Mendelian crosses Population Reproduction

2 General model population genetics Gene pool: f(a)=.6, f(a)=.4 Hardy-Weinberg: Derivation Gene pool: f(a)=.6, f(a)=.4 For locus, 2 alleles: f(a)=p f(a)=q =-p Genotype frequencies next generation: f (AA)=pXp (=p2) f (Aa)=pXq + qxp (=2pq) f (aa)=qxq (=q2) (p+q)2 = p2 + 2pq + q2 = Hardy-Weinberg Equilibrium Hardy-Weinberg: continued Allele frequencies next generation: p =p2 +.5(2pq) =p2+ pq =p(p+q) =p No change in allele frequencies A way to predict the genotype frequencies in future generations Assumptions Diploid Sexual Non-overlapping generations Random mating Allele frequencies identical in males and females Infinite population size No migration No mutation No selection 2

3 Implications of Hardy-Weinberg What bloody good is it??? No evolution, no change Recessive traits not wiped out Genotype frequencies can be predicted from allele frequencies (p 2, 2pq and q 2 ) Using Hardy-Weinberg: Can determine frequency of rare recessive alleles in population e.g. PKU (phenylketonuria) can t metabolize phenylalanine frequency in population: /, -assuming HWE, what proportion of population are asymptomatic carriers? HaWeE Why do we use it? It provides us with a representation of how alleles should behave in the absence of evolutionary forces. No evolutionary forces Allele frequencies stay constant. Genotype frequencies stay constant. Can you maintain allele frequencies through generations but still have the genotype frequencies changing If frequencies are changing evolution is occurring. Mendelian inheritance preserves genetic variation HaWeE Using Hardy-Weinberg: Populations may sometimes leave HaWeE by chance. How long does it take to return? generation of random mating Allele frequencies in a population of hamsters with allele frequencies for agouti allele (p=a ) and non-agouti allele (q=a 2 ). Number of genotypes are A A =, A A 2 =6, and A 2 A 2 =3. HaWeE allele frequencies are p=.7 and q=.3. The next generation we find genotypes of are A A =7, A A 2 =95, and A 2 A 2 =35, with p =.5875 and q =.425. This population is not in HaWee. If random mating occurs and there is no selection the allele genotype frequencies in the next generation will be A A = =.345, A A 2 =2*.5875*.425 =.485, A 2 A 2 =.7 Note: if the generations overlap return to HaWee is more gradual Null model (no change) χ 2 test for deviations from HWE deviation indicates assumptions violated e.g. random mating no population structure equal allele frequencies between sexes no selection no migration no genetic drift 3

4 Testing Hardy-Weinberg e.g. scarlet tiger moth (N=62) SS white spots (469) Ss intermediate (38) ss little spotting (5) Calculate allele frequencies: p= q= Testing Hardy-Weinberg e.g. scarlet tiger moth (N=62) SS white spots (469) Ss intermediate (38) ss little spotting (5) Calculate allele frequencies: p= (2*469+38)/(2*62) =.954 q=-.954 Testing Hardy-Weinberg (cont) Calculate genotype frequencies expected under HWE SS (p 2 ) = =.9 Ss (2pq) =2*.954*.46 =.88 ss (q 2 ) =.46 2 =.2 Calculate expected genotype numbers SS =62*.954 Ss =62*.88 ss =62*.2 Testing Hardy-Weinberg (cont) Calculate genotype frequencies expected under HWE SS (p 2 ) = =.9 Ss (2pq) =2*.954*.46 =.88 ss (q 2 ) =.46 2 =.2 Calculate expected genotype #s SS =62*.9= Ss =62*.88= ss =62*.2= Testing Hardy-Weinberg (cont) χ 2 test compares observed, expected numbers χ 2 =sum((obs-exp) 2 /exp) χ 2 crit =3.84 ( ) 2 ( ( )2 )2 Accept null hypothesis The population is in HWE = A) Random mating Inbreeding/assort. Mating heterozygote deficit Outbreeding/negative assortative mating heterozygote excess How could you distinguish between assortative mating at a certain locus, vs inbreeding? 4

5 Nonrandom mating in humans Assortative mating: Height, IQ, ethnicity, dwarfism Disassortative mating (rare): MHC (T-shirt studies) Inbreeding avoidance B) Sexual reproduction Send in the clones Clonaid has been able to find living cells in a body that has been dead for 4 months - there is hope! C) Diploidy Can you do it for others? D) Discrete generations E) Infinite population size -finite pop s = sampling error (genetic drift) -random fluctuations in allele and genotype frequencies -drift strength proportional to /(2N) -eventually one allele fixed, others lost F) Equal allele freqs between sexes G) No selection H) No migration I) No mutation HaWee Mechanisms of evolution Why do we use it? It provides us with a representation of how alleles should behave in the absence of evolutionary forces. Null model for evolution If frequencies are changing evolution is occurring.» Forces of evolution? No evolutionary forces Allele frequencies stay constant. Genotype frequencies stay constant. Can you maintain allele frequencies through generations but still have the genotype frequencies changing? Prove it yes or no In conservation, provides a basis for the following: detecting deviations from random mating tests for selection modeling the effects of inbreeding and selection Mendelian inheritance preserves genetic variation 5

6 Revision: Hardy Weinberg Sources Alleles Allele frequency Genotypes Genotype frequency AA p 2 A p Aa 2pq a q aa q 2 The ultimate source of all new genetic variation at a locus is MUTATION Within a population genetic variation can be added in different ways Mutation Dispersal Transposable elements p 2 + 2pq + q 2 =, p + q = What do you do if you have 3 allele or are a triploid? Mutations Recurrent mutation Mutations are rare for most markers New mutant alleles are by definition rare /2N Increasing frequency of mutant allele Drift Removes low frequency alleles Recurrent mutation Slow /2N, 2/2N, 3/2N Selection Depends upon the strength of selection Frequency of mutant allele N= N= N= Generation Mutation Irreversible.9 HaWeE with µ Allele frequency with mutation p t = p t- (- µ) Only allele which didn t mutate p t- = p t-2 (- µ) Thus p t = p (- µ) t As t infinity p. Frequency m=. m=..5 m=. m= Generation 6

7 Mutation Irreversable Half-life HaWeE with µ Allele frequency with mutation p t = p t- (- µ) Only allele which didn t mutate p t- = p t-2 (- µ) Thus p t = p (- µ) t Mutation half life p t =.5p Thus.5 = (- µ) t ln(.5) = t ln(- µ) t =ln.5/ln(- µ) t = -.693/ln(- µ) ln(- µ) - µ t =.693/µ Half life Reversible A -> a A -> A Probability of A -> a = µ a -> A = ν Mutations HaWeE with reversible mutation P t = p t- (- µ)+q t- ν Do the math p = ν/(µ+ν) Reversible mutations result in an equilibrium of the two (or more) allleles Frequency A(m=.,p=.9) Starting allele a(n=.) frequency doesn t matter for.9 A(m=.,p=.7) the equilibrium point a(n=.5) only the two mutation.8 rates A(m=.,p=.5) a(n=.) Generations Frequency A(m=.) a(n=.5).9 A(m=.) a(n=.5) Infinite Alleles Model (IAM) Mutations Unlikely that only 2 alleles exist. How many alleles exist? Lots a protein with 3 AA 9 nucleotides occupied by of 4 nucs (A,T,C,g) 4 9 = 542!!! Typical microsatelite locus has - 2 alleles Typical allozyme locus has 2-3 Typical RAPD or AFLP? Each mutation should create a novel allele thus there are an infinite number of possible alleles Mutation Always creates a novel allele Any two identical alleles must be Identical By Descent (IBD) Calculating homozygosity Two alleles that must be IBD join in an individual Autozygous Generation 7