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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 徐书华 金 力 中科院-马普学会计算生物学伙伴研究所 第五讲 遗传漂变效应及有效群体大小的估计 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. 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。 mutations create new alleles evolutionary fate of alleles is governed by 3 other forces: -selection - migration - random drift The influence of evolutionary forces on populations: Genetic Drift All populations are finite in size. AB A Generation: n A B B A B Gene Pool A B B B A A A A B BA B A B A Each generation is a random sample of the previous generation A A A A A B B A Next Generation B B A A A A B Generation: n + 1 A B A AB A A B B A B Gene Pool A B B B A A A A B BA B A B A f(A) = p = 0.48 f(B) = q = 0.52 A A A A A B B A Next Generation B B A A A A B A B A f(A) = p = 0.67 f(B) = q = 0.33 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. Situations in natural populations that magnify drift: 1. Continuously small populations. 2. Founder effect. 3. Bottleneck effect. Consequences of continuously small populations The bottleneck effect Founder Effect ► 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! 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. 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. 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. The Founder Effect 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 generation 0 f(“white’) 0.50 0.50 1 0.60 0.60 2 0.80 0.80 3 0.40 Genetic Drift: Population Size Matters 4 populations 2 at N=25 2 at N=250 From Li (1997) Molecular Evolution, Sinauer Press, via A. Sidow BIOSCI 203 Simulation 演示 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 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) How much variation will there be in allele frequency from one population to the next as a consequence of genetic drift? How much variation will there be in allele frequency from one population to the next as a consequence of genetic drift? p x q Variance = Sp2 = 2 N e Standard error = Sp = pxq 2 Ne Important point – influence of drift increases as Ne gets smaller. For a binomial distribution Applying this to our situation 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. Genetic drift drives the decay of heterozygosity ► Genetic drift removes genetic variation from the population. Ht = (1 - 1 )tH0 2N if 2N is large, 1/2N ~ 0, and (1 - 1 ) ~ 1, Ht ~ H0 2N if 2N is small, 1/2N ~ ‘very , and (1 large 1 ) 2N ~ 0, Ht ~ 0 The decay of heterozygosity 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.” The influence of genetic drift is directly related to the size of a population. 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. 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 Ne = Nf + Nm 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 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 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 Effective population size affected by fluctuating population size Influence of fluctuating population size on the effective number individuals in each generation 1 1 ( 1/N1 + 1/N2 + N = .....1/Nt) e t # generations Effective Number 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 1 ( 1/100 + 1/100 + = N 10 .....1/25) e From this example it’s clear that a single generation with a low population size has a large negative influence on the effective number Effective population size affected by bottlenecks and founder effects 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 Effective population size Effective size and census size fluctuations 1 1 t 1 1 Ne t i 0 N(i) 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? Census size 100 kyears Effective size Answer: Less than 20’000 (assuming a generation time of 20 years) Generations The diversity of the human species much depends on its past demography, and not much on its present size Effective population size affected by reproductive sex ratio Effective Population Size Made the assumption that the number of males and females contributing to each subsequent generation is the same If the sex ratio is not 1:1 for each generation then the population loses genetic variability more rapidly This is because the “effective number” of individuals is smaller than the actual number of individuals in the population Effective Number can be calculated as follows: Effective Number # breeding females in pop. Ne = 4Nm Nf Nm + Nf # breeding males in pop. For a sex ratio of 1 male:9 females in a population of 100 individuals 4(10 X 90) Ne = = 36 10 + 90 Which means that a population of 100 individuals, consisting of 10 breeding males and 90 breeding females would lose genetic variability as rapidly as a population consisting of only 18 males and 18 females or 36 individuals Effective population size Effective population size and reproductive sex ratio 4N m N f Ne Nm N f Effective size of a population of census size 100 as a function of the number of males in the population The effective population size is strongly influenced by the rarer of the two sexes. Examples: A flock of Geese: 50 males 50 females (N = 100) 4 x Nf x Nm Ne = N f + Nm A harem of Elephant seals: 4 males 96 females (N = 100) Examples: 4 x Nf x Nm Ne = N f + Nm A flock of Geese: 50 males 50 females (N = 100) A harem of Elephant seals: 4 males 96 females (N = 100) Will be over represented in the next generation. Examples: A flock of Geese: 50 males 50 females (N = 100) 4 x Nf x Nm Ne = N f + Nm 4 x 50 x 50 Ne = = 100 50 + 50 A harem of Elephant seals: 4 males 4 x 96 x 4 96 females N = = 15.36 e 96 + 4 (N = 100) Effective population size affected by family size Influence of family size on the effective number Actual # of breeding individuals 4N - 4 Ne = Vk + 2 Effective Variance in number of number Offspring Rearrange equation Ne/N ~ 4/(Vk + 2) Ne/N ~ 4/(2+2) = 1.0N Ne/N ~ 4/(4+2) = 0.67N Factors that affect effective population size (Ne): Factors that affect effective population size (Ne): 1. Bias in male/female sex ratios Factors that affect effective population size (Ne): 1. Bias in male/female sex ratios 2. Differential production of offspring Factors that affect effective population size (Ne): 1. Bias in male/female sex ratios 2. Differential production of offspring 3. Fluctuating population size (As might occur from periodic catastrophes) Factors that affect effective population size (Ne): 1. Bias in male/female sex ratios 2. Differential production of offspring 3. Fluctuating population size (As might occur from periodic catastrophes) 4. Overlapping generations Estimate effective population size Effective Population Size A variable in the following equation: = 4Ne ( = mutation rate) Using as an estimator of Ne, the effective population size of humans is ~ 10,000 Human recombination rate (C) =4Ner =4 x 10000 x 1cM/Mb =4 x 10000 x 0.01 M/1000000 bp =0.0004/bp =0.4/kb Estimate Ne from LD Populations for Genetic Studies ►Outbred + Easy to recruit + Directly relevant to patients ►Inbred Isolation ►Why does it matter? ►Specific example: Kosrae Consanguinity Isolates are Intensively Studied Québequois Icelanders Finns Sardinians Ashkenazim Hutterites Bedouins Polynesians Amish Ticuna Afrikaners Aborigines Indirect (LD-based) Association ►A new mutation is in LD with its background ► Recombination bounds co-inherited LD segment Time to Most Recent Common Ancestor Matters ► Phylogenetic LD segment history in tmrca ► If all samples from a sub-phylogeny: longer LD Effects of Population Bottleneck ► Elimination variation: of Recombinants Effects of Population Bottleneck ► Elimination variation: of Recombinants Polymorphic sites Mild Bottlenecks Affect Rare Alleles ► Elimination variation: of rare Recombinants Polymorphic sites “memory” of ancestral state Isolated Populations & Association Studies ► Reduced diversity bottleneck eliminates rare alleles ► Rare alleles become common (detectable) ► Longer LD ► Characteristic phenotype frequencies good candidates for association studies Genetics in Kosrae, Micronesia ► Non genetics: Isolated Inhabited: 2000 ya European exposure: 19th century ► High prevalence of common metabolic diseases Kosraen HapMap (100k x 30 trios) towards genome scan Less common variation on Kosrae Slower decay of LD in Kosrae 常用软件 ►Arlequin 3.01 http://anthro.unige.ch/software/arlequin/ 练习 ► 利用HapMap数据进行有效群体大小估计; http://www.hapmap.org