人类群体遗传学 基本原理和分析方法

1. 中国科学院上海生命科学研究院研究生课程人类群体遗传学中国科学院上海生命科学研究院研究生课程人类群体遗传学 人类群体遗传学基本原理和分析方法 中科院-马普学会计算生物学伙伴研究所 徐书华 金 力

2. 第五讲 遗传漂变效应及有效群体大小的估计

3. 基本概念 • 遗传漂变（Genetic drift） • 群体内由于抽样误差造成的等位基因频率的随机波动. • 有效群体大小（Effective population size） • 一个理想遗传学群体中繁育群体的大小.

4. 中性突变 –随机漂变学说 • 在分子水平上，仅很少一部分突变是有利的，多数突变是有害的、中性的。 • 自然选择是一种保存有利突变和消灭有害突变的进化过程。 • 大部分新突变都将消失，少量新突变的固定依赖于随机漂变。

5. mutations create new alleles evolutionary fate of alleles is governed by 3 other forces: • selection • migration • random drift

6. The influence of evolutionary forces on populations: Genetic Drift All populations are finite in size.

7. Generation: n A B A B B A A A B B B Gene Pool B A A A A B A B B A B A Each generation is a random sample of the previous generation Next Generation A A A A A B B A B B A A A A B Generation: n + 1 A B A

8. A B A B B A A A f(A) = p = 0.48 f(B) = q = 0.52 B B B Gene Pool B A A A A B A B B A B A Next Generation A A A A A B B A f(A) = p = 0.67 f(B) = q = 0.33 B B A A A A B A B A

9. Genetic drift occurs when changes in gene frequencies from one generation to another occur because of chance events (sampling errors) that occur when populations are finite in size.

10. Situations in natural populations that magnify drift: • Continuously small populations. • Founder effect. • Bottleneck effect.

11. Consequences of continuously small populations

12. The bottleneck effect

13. Founder Effect

14. Bottlenecking is an important concept in conservation biology of endangered species. • Populations that have suffered bottleneck incidents have lost at least some alleles from the gene pool. • This reduces individual variation and adaptability. • For example, the genetic variation in the three small surviving wild populations of cheetahs is very low when compared to other mammals. • Their genetic variation is similar to highly inbred lab mice!

15. Northern Elephant Seal: Example of Bottleneck Hunted down to 20 individuals in 1890’s Population has recovered to over 30,000 No genetic diversity at 20 loci.

16. The Founder Effect is Another Variation of Genetic Drift The South Atlantic island of Tristan da Cunha was colonized by 15 Britons in 1814, one of them carrying an allele for retinitis pigmentosum. Among their 240 descendents living on the island today, 4 are blind by the disease and 9 others are carriers.

17. The Founder Effect Old Order Amish populations are derived from a few dozen colonists who escaped religious persecution in Germany in 1719 to settle in Pennsylvania. The community is closed. Allele and genetic disease frequencies in Amish are significantly different from the German ancestral and the surrounding local populations.

18. The Founder Effect

19. in a population: only a fraction of individuals will produce progeny each generation: - some genes may increase in frequency - others decrease in frequency - some may be lost genetic drift randomly alters gene frequencies

20. generation f(“white’) 0 0.50 • 0.50 • 0.60 • 0.60 • 0.80 0.80 3 0.40

21. 4 populations 2 at N=25 2 at N=250 Genetic Drift: Population Size Matters From Li (1997) Molecular Evolution, Sinauer Press, via A. Sidow BIOSCI 203

22. Simulation 演示

23. How big is big enough?? • As a general rule, an Ne of 50 is necessary to prevent immediate harmful effects of inbreeding, and an Ne of ~500 is necessary to maintain long-term evolutionary potential. 50/500 rule of thumb

24. Genetic drift -Summary • Genetic drift occurs because the population size is not infinite, allowing chance events (sampling error) to occur. • Genetic drift is a random process. The outcome of genetic drift cannot be stated with certainty. • Genetic drift removes genetic variation from the population. • The rate of fixation of a selectively neutral alleles is inversely related to the population size: • P(fixation)=1/2N • The rate of loss is: • P(loss)=1-(1/2N)

25. How much variation will there be in allele frequency from one population to the next as a consequence of genetic drift?

26. How much variation will there be in allele frequency from one population to the next as a consequence of genetic drift? p x q 2 Ne Variance = Sp2 = p x q 2 Ne Standard error = Sp = Important point – influence of drift increases as Ne gets smaller.

27. For a binomial distribution

28. Applying this to our situation

29. Effects of drift on natural populations: • Genetic drift is a random process. • Changes will be non-adaptive. • Will cause isolated populations to diverge. • Will result in loss of genetic diversity over time.

30. very large 1 2N Genetic drift drives the decay of heterozygosity • Genetic drift removes genetic variation from the population. Ht = (1 - )tH0 if 2N is large, 1/2N ~ 0, and (1 - ) ~ 1, Ht~ H0 if 2N is small, 1/2N ~ ‘ , and (1 - ) ~ 0, Ht~ 0 1 2N 1 2N

32. The decay of heterozygosity

35. Effective Population Size (concept) • “The number of individuals in a population who contribute offspring to the next generation.” • “The size of an ideal population which acts the same as the real population in question.” • “The size of an ideal population that has the same properties with respect to genetic drift as our actual population does.”

36. The influence of genetic drift is directly related to the size of a population.

37. How big is that population? Census population size vs. effective population size Effective population size = equivalent number of adults contributing gametes to the next generation.

38. How big is that population? Census population size vs. effective population size Effective population size = equivalent number of adults contributing gametes to the next generation. Formula for calculating Ne when there is a bias in the sex ratio 4 x Nf x Nm Nf + Nm Ne =

39. importance of genetic drift is related to population size maximum effect in small populations effective population size = Ne = theoretical population where every individual has the same probability of contributing genes to the next generation

40. Effective population size (Ne) • the size of a genetically idealized population with which an actual population can be equated genetically, Ne = N , if • equal sex ratio • equal probability of mating • constant dispersal rate • progeny per family randomly distributed

41. Effective population size Ne • Sewall Wright (1931, 1938) • “The number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration". • Usually, Ne < N (absolute population size) • Ne != N can be due to: • fluctuations in population size • unequal numbers of males/females • skewed distributions in family size • age structure in population

42. Effective population size affected by fluctuating population size

43. Influence of fluctuating population size on the effective number individuals in each generation 1 Ne 1 t ( 1/N1 + 1/N2 + .....1/Nt) = # generations Effective Number

44. Influence of fluctuating population size on the effective number • e.g., if a population of 100 individuals drops to only 25 in the tenth generation the effective number during these 10 generations would be 77 1 Ne 1 10 ( 1/100 + 1/100 + .....1/25) =

45. From this example it’s clear that a single generation with a low population size has a large negative influence on the effective number

46. Effective population size affected by bottlenecks and founder effects

47. Effective Population Size • Influenced by bottlenecks and founder effects • Reduced genetic variation from the original population • Founder effect: non-random sample of the genes from the original population

48. Effective population size Effective size and census size fluctuations Current effective size is the harmonic mean of previous population sizes Harmonic mean is strongly influenced by the smallest samples Assuming the size of the ancestral human population was 10’000 , 100’000 years ago and that it grew Exponentially until today, what is the present day effective population size? Answer: Less than 20’000 (assuming a generation time of 20 years) Census size 100 kyears Effective size Generations The diversity of the human species much depends on its past demography, and not much on its present size

49. Effective population size affected by reproductive sex ratio

50. Effective Population Size Made the assumption that the number of males and females contributing to each subsequent generation is the same