2.2 A Fixed Value I for the Number of Distinct Alleles

Kapitel in diesem Buch

1. Frontmatter i
2. CONTENTS vii
3. PREFACE ix
4. ACKNOWLEDGMENTS xiii
5. 1 Mathematical and Biological Introduction
6. 1.1 Interpreting Population-Genetic Statistics 1
7. 1.2 A Note about Assumed Background 3
8. 1.3 Definitions 3
9. 1.4 Standard Inequalities 7
10. 1.5 Genetic Diversity and Genetic Homogeneity 8
11. 1.6 Genetic Differentiation and Genetic Similarity 13
12. 1.7 Do Statistics “Depend” on Allele Frequencies? 18
13. 1.8 Exercises 19
14. 2 Homozygosity and the Most Frequent Allele
15. 2.1 Arbitrarily Many Distinct Alleles 21
16. 2.2 A Fixed Value I for the Number of Distinct Alleles 33
17. 2.3 Example from Human Populations 40
18. 2.4 Implications 43
19. 2.5 Exercises 46
20. 3 Variations on Homozygosity: J_A, J_B, and J_C
21. 3.1 Boundson J_C/J_B in Terms of J_A 48
22. 3.2 Example from Drosophila 58
23. 3.3 Implications 60
24. 3.4 Exercises 61
25. 4 The ith Most Frequent Allele
26. 4.1 Lower Bound on J in Terms of pi 62
27. 4.2 Upper Bound on J in Terms of pi 66
28. 4.3 Lower and Upper Bounds on pi in Terms of J 75
29. 4.4 Example from Human Populations 85
30. 4.5 Implications 86
31. 4.6 Exercises 90
32. 5 α-homozygosity
33. 5.1 Convexity Inequalities 92
34. 5.2 Arbitrarily Many Distinct Alleles 94
35. 5.3 A Fixed Value I for the Number of Distinct Alleles 99
36. 5.4 Example from Human Populations 103
37. 5.5 Implications 105
38. 5.6 Exercises 106
39. 6 Estimated Homozygosity
40. 6.1 Samples 108
41. 6.2 Number of Distinct Alleles Constrained by Sample Size 111
42. 6.3 A Fixed Value I for the Number of Distinct Alleles 117
43. 6.4 Example from Human Populations 119
44. 6.5 Implications 120
45. 6.6 Exercises 122
46. 7 Conclusions
47. 7.1 Summary of Mathematical Results 124
48. 7.2 Summary of Mathematical Methods 126
49. 7.3 Benefits of the Mathematical Bounds Approach 128
50. 7.4 The Continuing Importance of Summary Statistics 137
51. 7.5 Strategies for Improved Use of Summary Statistics 138
52. NOTATION 141
53. SOLUTIONS TO EXERCISES 145
54. BIBLIOGRAPHY 155
55. AUTHOR INDEX 163
56. SUBJECT INDEX 167