数量遗传学原理-参数估计理论

1、数量遗传学原理-参数估计理论亲属间相似性遗传力(Heritability)P=G+E=A+D+EVP = VG + VE = VA + VD + VE OutlineHeritability definitionHeritability estimation One-way ANOVA Parent-offspring regression Variance components methodsHeritability characteristicsOutlineHeritability definitionHeritability estimation One-way ANOVA Paren

2、t-offspring regression Variance components methodsHeritability characteristicsHeritability definitionNarrow vs. board sense（狭义和广义）Narrow sense: h2 = VA/VP Board sense: H2 = VG/VP When one refers to heritability, the default is narrow-sense, h2Heritability is the proportion of phenotypic variation in

3、 a population that is due to genetic variation between individuals.遗传力-遗传力是指性状的总表型方差中，遗传方差所占的比例。 Sample heritabilities in human性状遗传力性状遗传力身材0.81IQ(Otis)0.80坐高0.76糖尿病0.75体重0.78精神分裂症0.8口才0.68高血压0.62理科天赋0.34冠状动脉病0.65数学天赋0.12先天性幽门狭窄0.75Heritability estimationOne-way ANOVAParent-offspring regressionVarian

4、ce components methodsEstimation: One-way ANOVASimple (balanced) full-sib design: N full-sib families, each with n offspring（N个家系）One-way ANOVA model:zij = m + fi + wijTrait value in sib j from family iCommon MeanEffect for family i =deviation of mean of i from the common meanDeviation of sib j from

5、the family means2f = between-family variance = variance among family meanss2w = within-family variances2P = Total phenotypic variance = s2f + s2w One-way ANOVACovariance between members of the same group equals the variance among (between) groupsThe variance among family effects equals the covarianc

6、e between full sibs The within-family variance s2w = s2P - s2f,Cov(FullSibs)=(zij;zik)=(+fi+wij);(+fi+wik)=(fi;fi)+(fi;wik)+(wij;fi)+(wij;wik)=2f2f=2A/2+2D/4+2Ec 2w(FS)=2P(2A/2+2D/4+2Ec)=2A+2D+2E(2A/2+2D/4+ 2Ec)=(1/2)2A+(3/4)2D+2E2EcOne-way ANOVAOne-way Anova: N families with n sibs, T = NnFactorDFS

7、ums ofSquares (SS)Mean sum of squares (MS)E MS Among-familyN-1SSf/(N-1)s2w + n s2fWithin-familyT-NSSw/(T-N)s2wOne-way ANOVAEstimating the variance components（估计方差组分）:2Var(f) is an upper bound for the additive variance（ 2Var(f) 是加性方差的上限）Var(f)=MSfMSwnVar(w)=MSwVar(z)=Var(f)+Var(w)Since2f= 2A/2+2D/4+2

8、EcOne-way ANOVAEstimating heritabilityHence, h2 2 tFStFS=Var(f)Var(z)=12h2+2D/4+2Ec2z（遗传力的上限）One-way ANOVAWorked exampleFactorDfSSMSEMSAmong-familes9SSf = 40545s2w + 5 s2fWithin-families40SSw = 80020s2w10 full-sib families, each with 5 offspring are measuredVA 10h2 2 (5/25) = 0.4Var(f)=MS fMS wn=452

9、05=5One-way ANOVAFull sib-half sib design: Nested ANOVAFull-sibsHalf-sibsEstimation: Nested ANOVABalanced full-sib / half-sib design: N males (sires)are crossed to M dams each of which has n offspring（平衡的全同胞/半同胞设计，N M n）Nested ANOVA model:zijk = m + si + dij+ wijkValue of the kth offspringfrom the j

10、th dam for sire iOverall meanEffect of sire i = deviationof mean of is family fromoverall mean Effect of dam j of sire i = deviationof mean of dam j from sire and overallmean Within-family deviation of kthoffspring from the mean of theij-th family s2s = between-sire variance = variance in sire famil

11、y meanss2d = variance among dams within sires = variance of dam means for the same sires2w = within-family variances2T = s2s + s2d + s2wOne-way ANOVANested ANOVA: N sires crossed to M dams, each with n sibs, T = NMnFactorDfSSMSEMSSiresN-1SSs/(N-1)Dams (Sires)N(M-1)SSd /(NM-1)Sibs (Dams)T-NMSSw/(T-NM

12、)One-way ANOVAEstimation of sire, dam, and family variances:Translating these into the desired variance components(渴望的方差组分) Var(Total) = Var(between FS families) + Var(Within FS) s2w = s2z - Cov(FS)Var(s)=MS s MS dMnVar(d)=MS dMS wnVar(e)=MS w2d= 2z2s2w= (FS) (PHS) Var(Sires) = Cov(Paternal half-sib

13、s)= s2s = s(PHS)One-way ANOVASummarizing,Expressing these in terms of the genetic and environmental variances,2s=(PHS)2w=2z(FS)2d=2z2s2w=(FS)(PHS)2s2A42d2A4+2D4+2Ec2w2A2+32D4+2EsOne-way ANOVA4tPHS = h2h2 2tFSIntraclass correlations and estimating heritabilityNote that 4tPHS = 2tFS implies no dominan

14、ce or shared family environmental effectsOne-way ANOVAWorked Example: N=10 sires, M = 3 dams, n = 10 sibs/damFactorDfSSMSEMSSires94,230470Dams(Sires)203,400170Within Dams2705,400202w+102d+302s2w+102d2w2w=MS w=202d=MS dMS wn=1702010=152s=MS sMS dNn=47017030=102P=2s+2d+2w=452d=15=(1/4)2A+(1/4)2D+2Ec=1

15、0+(1/4)2D+2Ec2A=42s=40h2=2A2P=4045=0.892D+42Ec=20One-way ANOVASingle parent - offspring regressionzoi=+b o | p(zpi)+e iThe expected slope of this regression is:E(bo|p)=(zo;zp)2(zp)(2A/2)+(Eo;Ep)2z=h22+(Eo;Ep)2zParent-offspring regression2bO|P = h2The expected slope of this regression is h2（期望得到的斜率为h

16、2 ）, as ()Midparent - offspring regressionzoi=+b o | M Pz mi+z fi2+e ibo|MP=Covzo;(zm+zf)/2 Var(zm+zf)/2=Cov(zo;zm)+Cov(zo;zf)/2Var(z)+Var(z) /4=2Cov(zo;zp)Var(z)=2b o | pKey: Var(MP) = (1/2)Var(P)bo |MP=Covzo;(zm+zf) /2 Var(zm+zf)/2=Cov(zo;zm)+Cov(zo;zf) / 2Var(z)+Var(z) /4=2Cov(zo;zp)Var(z)=2b o |

17、 pParent-offspring regressionbO|MP = h2The vertical axis is the offspring heights while the horizontal axis is their corresponding mid-parents heightHeritabilities are functions of populationsHeritability measures the standing genetic variation of a population, A zero heritability DOES NOT imply tha

18、t the trait is not genetically determinedHeritability values only make sense in the content of the population for which it was measured.（只能应用到研究群体）Heritability characteristicsAn example of low heritability: a population with genotypes coding for only one hair colourA crowd with variance in hair colourHeritabilities are functions of the distribution of environmental valuesDecreasing VP increases h2.Heritability values measured in one environment(or distribution of environments) may not be valid under another（与特定环境相关）Measure