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FORMULAS TO MEMORIZE genotype frequencies: fr(AA) = AA/total; fr(Aa) = Aa/total; fr(aa) = aa/total allele frequencies: fr(A) = [2AA+Aa]/2*total = fr(AA) + 0.5fr(Aa) fr(a) = [2aa+Aa]/2*total = fr(aa) + 0.5fr(Aa) fr(A) + fr(a) = 1 Hardy-Weinberg equilibrium: if fr(A) = p , fr(a) = q, and p+q = 1 then fr(AA) = p2, fr(Aa) = 2pq, fr(aa) = q2 2 = [(E-O)2/E] where E = expected number of individuals, O = observed number of individuals Linkage disequilibrium: D = fr(AB)fr(ab) – fr(Ab)fr(aB) FORMULAS TO UNDERSTAND p – refers to fr(A) at the time 0 p1 – fr(A) at the next generation p = p1-p p - average p p̂ - fr(A) at equilibrium Natural Selection General case: q = [(q2waa+pqwAa)/( p2wAA+2pqwAa+ q2waa)] - q Directional Selection for the Dominant Phenotype: q = -q2ps/(1-q2s) Directional Selection for the Recessive Phenotype: q = q2ps / (1-p2s-2pqs) Balancing Selection q = pq(s1p-s2q)/(1-p2s1-q2s2) stable equilibrium for balancing selection: q̂ =s1/(s1 + s2) Disruptive Selection: q = qps(2q-1)/(1-2pqs) q – refers to fr(a) at the time 0 q1 – fr(a) at the next generation q = q1-q q̂ - fr(a) at equilibrium q - average q Mutations if fr(A a) = and fr(a A) = then q = pq equilibrium q: q̂ = (+) Mutations+ Selection for the dominant phenotype: q = pq q2ps/(1-q2s)]; since q 0 and 1-q2s 1 ; q p q2ps equilibrium for mutation + the directional selection for the dominant phenotype is reached when: q2s q̂ = /s Genetic Drift N N! P = pkqN-k k k ! ( N k )! P(fixed) = P(all A)+P(all a) = p2N + q2N fixation index: F1 = 1/(2N) + [1 – 1/(2N)] F0 t Ft = 1- (1 - 1/(2N)) Detecting natural selection based on DNA sequence analysis -s ____ Tajima’s D = SD(-s) ____ dN/dS (Hughes and Nei 1988)