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which simpli es to: p (1/2)( pm p f)
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15. a. Hardy-Weinberg proportions are achieved in one generation of random mating (multiple-allelic extension) if the locus is autosomal. If the locus is autosomal but there are different frequencies in the two sexes, then Hardy-Weinberg proportions are achieved in two generations. If the locus is sex linked, with different initial frequencies in the two sexes, then approach to equilibrium is gradual. b. If the loci are not in equilibrium to begin with (linkage disequilibrium), then equilibrium is achieved asymptotically. 17. 0.63 type A, 0.08 type B, 0.28 type AB, 0.01 type O. Since the population is in equilibrium, the genotypic frequencies can be calculated as ( p q r)2 p2 2pq q2 2pr 2qr r2. Let p 0.7, q 0.2, and r 0.1. Blood types will be represented by the following: A: p2 0.49 2pr 0.14 B: q2 0.04 2qr 0.04 AB: 2pq 0.28 O: r2 0.01
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In other words, after one generation of random mating, the allelic frequencies in each sex are the averages for both sexes. Now the frequency is the same in both sexes, and a second generation of random mating will achieve Hardy-Weinberg proportions.The population is not in equilibrium after one generation because the proportion of genotypes is not p2, 2pq, and q2 if pm does not equal p f. In other words, pmp f does not equal p2. 20 Population Genetics: Processes That Change Allelic Frequencies 1. a. The equilibrium frequency of a is q q (6 10 5)/(6 10 5 0.00006/0.0000607 (
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Tamarin: Principles of Genetics, Seventh Edition
Back Matter
App. A: Brief Ans. to Selected Exercises, Problems, and Critical Thinking Ques.
The McGraw Hill Companies, 2001
Appendix A Brief Answers to Selected Exercises, Problems, and Critical Thinking Questions
A-23
3. 0.714. q 5 10 10 2
5. We use equation 20.12 to calculate the migration rate, m: m In this case, qC m (0.45 (qC qN)/(qM qN) 0.03. Thus 0.288
0.45, qN
0.62, and qM 0.62)
0.62)/(0.03
( 0.17)/( 0.59)
7. Fast: 0.56; slow: 0.44.With 900 butter ies we have 1,800 alleles. 0.6 (1,800) 1,080 fast alleles, and 0.4 (1,800) 720 slow alleles. In the migrant population, (0.8)(180) 144 slow and (0.2)(180) 36 fast alleles. Therefore, the frequency of the fast allele is (1,080 36)/1,980 0.56. The frequency of the slow allele is 1 f(fast allele) 1 0.56 0.44. 9. 0.47. We again use equation 20.12: m where m 0.1, qC qC qM qN qN 0.25. qN qN 0.45 0.45 0.425 0.47 And p qN qN p pn pn
1 2 1
AA Before selection Fitnesses (W ) Frequencies after selection p2 1 p2(1 s s)/ W 2pq 1 s s)/ W Aa aa q2 1 q2/ W W 1 Total 1 p2s 1 2pqs
0.45, and qM 0.1 0.45 0.25 qN) 0.1qN 0.9qN qN
2pq(1
0.1(0.25 0.025
( p2[1 ( p [1
s] s]
pq[1 pq[1 sp( p
s]) W s]) W 2p pW W 1) W
sp( p
1) W
0.425 0.9
0 or 1 (from the root of the quadratic). Only zero is stable.
11. In stabilizing selection, extremes of a distribution are selected against. In directional selection, one extreme is favored over the other. In disruptive selection, both extremes are favored over the middle of the distribution. 13. Heterozygote disadvantage:
AA Before selection Fitnesses (W) Frequencies after selection p2 1 2pq 1 s
aa q2 1 s)/W q2/ W 1
Total
p2/ W 2pq(1
2pqs
17. Since only heterozygotes survive, q from equation 20.24: q s1 (s1
0.5. This can also be derived
Then qn q qn
s2) 1/2
( pq[1 ( pq[1 s] q
s] s] q[1
q2) W q )W
If s1 qW W
1, then q
( pq[1 which simpli es to q
2pqs]) W
spq(2q
1) W
At q 0, q 0, 1, or 0.5 (2q 1 0, therefore q 0.5).The equilibrium points of zero and one are stable if perturbed slightly (less than 0.5), the population will return to these values.The value q 0.5 is, however, unstable if perturbed, it will continue away from the equilibrium point. This can be seen by either substituting into or graphing the q equation.
19. The ST inversion seems to do best at lower elevations and the AR at higher elevations. CH (and others) do not appear to be affected by altitude. To test this hypothesis, we would grow caged populations of ies with different initial frequencies of the various inversions at different simulated elevations, simulated by temperature, pressure, oxygen content, or other. We predict that, regardless of initial conditions, they would eventually equilibrate at the values in the table for the given parameter of the altitude (temperature, pressure, oxygen content, or other) that is acting as a selective agent. We would thus identify the selective agent. Since the inversions isolate various allelic combinations, our next step (a potentially long-term step) would be to determine which loci the selective agent is acting on.
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