Population Genetics

• m:f ratio = q:q 2(or 1:q • if red-green

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Unformatted text preview: ) • M:F ratio = q:q 2 , (or 1:q) • If red-green colour-blindness occurs in 8% of European males, which of the following most closely approximates the expected frequency of this trait in European females? a) 92% b) 64% c) 8% d) 4% e) 1% Properties of Genetic Equilibrium 1) maximum heterozygosity,H, is attained when p=q Take dH=2(1-q)q, with regard to q dH/dq=d(2q-2q 2 )/dq=2-4q, Set d=0 (maximum likelihood function) Solve for q, Then q=.50 Properties of Genetic Equilibrium 2) As p,q values move away from equality, H class diminishes Where 2pq=p 2 , 2p(1-p)=p 2 , then p=2/3 Beyond which p 2 >2pq >q 2 Properties of Genetic Equilibrium 3) As rarer allele becomes less frequent, H class carries greater proportion of that allele than do homozygotes. H/R = 2pq/q2, = 2p/q Who has Q? q q 2 2pq 2pq/q 2 .5 .25 .50 2 .1 .01 .20 20 .01 .0001 .02 200 .001 .000001 .002 2000 Properties of Genetic Equilibrium 4) Among 3 parental matings that produce aa offspring, the relative proportions of aa produced are in same proportions as the zygote frequencies predicted by the square law. aa GT Among Relative Parent Mating All offspring frequencies Aa x Aa p 2 q 2 p 2 Aa x aa 2pq 3 2pq aa x aa q 4 q 2 Total q 2 1.0 What Assumptions? • Large population • Random mating • No mutation • No migration • No selection Effects on allele/gt frequencies when there are deviations from H-W assumptions • Non-random mating – population substructure – inbreeding (increases homozygosity) • Mutation – introduction of new alleles – new allele frequencies affected by selection, drift • Migration – drift – founder effects • Small population size – random drift • Selection – can alter relative allele frequencies Mutation Rate • A large breeding population of goats is found to have a frequency of achondroplasia of 5/12,500 liveborns. Which of the following best approximates the mutation rate for this locus? • A) 1/250 • B) 2.5/500 • C) 1/2,500 • D) 1/5000 • E) 25/6,250 Effects of Mutation on Allele Frequencies • In a population in which a wild type allele, A , is fixed with p=1.0, which of the following most closely approximates the frequency of this allele after 10,000 generations of mutation to a at u=10-5 ? a) 1.0 b) .90 c) .77 d) .37 e) 10-6 Effects of Mutation on Allele Frequencies Δ p = p t-p t-1 = -up t-1 • A decreases and a increases in proportion to u, ¡ Δ p gets smaller as p itself decreases • After n generations, p n = p e-nu (where e=nlog) • After 10,000 generations of u=10-5 , • p= p e-(10 4 )x(10-5 ) = p e-0.1 = 0.904p Effects of Selection on Allele Frequencies p’ = p (W A /W) ¡ Δ p =pq (W A – W a ) W Where W = “fitness” (chance of survival to adulthood) See Kimura, Population Genetics Effects of Selection on Allele Frequencies • Difficult to reduce frequency of allele that is already rare – Preventing mating of aa individuals does not work (if Aa did not mate, allele could be eliminated in 1 generation) • When alternative allele, a , is not rare, selection can cause rapid changes in allele frequency Balance Between Selection and Mutation on Allele Frequencies q 2 = u /s Where s = 1-W, and u = mutation rate Balance Between Selection...
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• M:F ratio = q:q 2(or 1:q • If red-green...

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