數(shù)量遺傳學(xué)原理-參數(shù)估計(jì)理論

1、數(shù)量遺傳學(xué)原理-參數(shù)估計(jì)理論親屬間相似性遺傳力(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（狹義和廣義）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.遺傳力-遺傳力是指性狀的總表型方差中，遺傳方差所占的比例。 Sample heritabilities in human性狀遺傳力性狀遺傳力身材0.81IQ(Otis)0.80坐高0.76糖尿病0.75體重0.78精神分裂癥0.8口才0.68高血壓0.62理科天賦0.34冠狀動(dòng)脈病0.65數(shù)學(xué)天賦0.12先天性幽門(mén)狹窄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個(gè)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（估計(jì)方差組分）: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（遺傳力的上限）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/半同胞設(shè)計(jì)，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(渴望的方差組分) 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（期望得到的斜率為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.（只能應(yīng)用到研究群體）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（與特定環(huán)境相關(guān)）Measure