Estimating genetic variation within families

Transcription

1 Estimating genetic variation within families Peter M. Visscher Queensland Institute of Medical Research Brisbane, Australia 1

2 Overview Estimation of genetic parameters Variation in identity Applications mean and variance of genome-wide IBD sharing for sibpairs estimation of heritability of height genome partitioning of genetic variation 2

3 Estimation of genetic parameters Model expected covariance between relatives Genetics Environment Data correlation/regression of observations between relatives Statistical method ANOVA regression maximum likelihood Bayesian analysis 3

4 [Galton, 1889] 4

5 The height vs. pea debate (early 1900s) Biometricians Mendelians Do quantitative traits have the same hereditary and evolutionary properties as discrete characters? 5

6 Trait Qq qq QQ m-a m+d m+a RA Fisher (1918). Transactions of the Royal Society of Edinburgh 52:

7 Genetic covariance between relatives cov G (y i,y j ) = a ij σ A2 + d ij σ D 2 a = additive coefficient of relationship = 2 * coefficient of kinship (= E(π)) d = coefficient of fraternity = Prob(2 alleles are IBD) 7

8 Examples (no inbreeding) Relatives a d MZ twins 1 1 Parent-offspring ½ 0 Fullsibs ½ ¼ Double first cousins ¼ 1 / 16 8

9 Controversy/confounding: nature vs nurture Is observed resemblance between relatives genetic or environmental? MZ & DZ twins (shared environment) Fullsibs (dominance & shared environment) Estimation and statistical inference Different models with many parameters may fit data equally well 9

10 Total mole count for MZ and DZ twins MZ twins pairs, r = 0.94 DZ twins pairs, r = Twin Twin Twin 2 Twin 2 10

11 Sources of variation in Queensland school test results of 16-year olds 10% 78% 12% Additive genetic Shared environment Non-shared environment 11

12 An unbiased approach Estimate genetic variance within families 12

13 Actual or realised genetic relationship = proportion of genome shared IBD (π a ) Varies around the expectation Apart from parent-offspring and MZ twins Can be estimated using marker data 13

14 x 1/4 1/4 1/4 1/4 14

15 IDENTITY BY DESCENT Sib 1 Sib 2 4/16 = 1/4 sibs share BOTH parental alleles IBD = 2 8/16 = 1/2 sibs share ONE parental allele IBD = 1 4/16 = 1/4 sibs share NO parental alleles IBD = 0 15

16 Single locus Relatives E(π a ) var(π a ) Fullsibs ½ 1 / 8 Halfsibs ¼ 1 / 16 Double 1 st cousins ¼ 3 / 32 16

17 Several notations IBD Probability Actual IBD0 k 0 0 or 1 IBD1 k 1 0 or 1 IBD2 k 2 0 or 1 Σ=1 Σ=1 Realisations k 0 k 1 k π a = ½k 1 + k 2 = R = 2θ π d = k 2 = xy 17 [e.g., LW Chapter 7; Weir and Hill 2011, Genetics Research]

18 n multiple unlinked loci Relatives E(π a ) var(π a ) Fullsibs ½ 1 / 8n Halfsibs ¼ 1 / 16n Double 1 st cousins ¼ 3 / 32n 18

19 Loci are on chromosomes Segregation of large chromosome segments within families increasing variance of IBD sharing Independent segregation of chromosomes decreasing variance of IBD sharing 19

20 Theoretical SD of π a Relatives 1 chrom (1 M) genome (35 M) Fullsibs Halfsibs Double 1 st cousins [Stam 1980; Hill 1993; Guo 1996; Hill & Weir 2011]

21 Fullsibs: genome-wide (Total length L Morgan) var(π a ) 1/(16L) 1/(3L 2 ) [Stam 1980; Hill 1993; Guo 1996] var(π d ) 5/(64L) 1/(3L 2 ) var(π d )/ var(π a ) 1.3 if L = 35 Genome-wide variance depends more on total genome length than on the number of chromosomes 21

22 Fullsibs: Correlation additive and dominance relationships r(π a, π d ) = σ(π a ) / σ(π d ) [1/(16L) / (5/(64L))] 0.5 = Using β(π a on π d ) = 1 Difficult but not impossible to disentangle additive and dominance variance NB Practical 22

23 Summary Additive and dominance (fullsibs) SD(π a ) SD(π d ) Single locus One chromsome (1M) Whole genome (35M) Predicted correlation 0.89 (genome-wide π a and π d ) 23

24 Application (1) Aim: estimate genetic variance from actual relationships between fullsib pairs Two cohorts of Australian twin families Adolescent Adult Families Individuals Sibpairs with genotypes Markers per individual Average marker spacing 6 cm 5 cm 24

25 Phenotype = height Application (1) Number of sibpairs with phenotypes and genotypes Adolescent cohort 931 Adult cohort 2444 Combined

26 Mean IBD sharing across the genome for the jth sib pair was based on IBD estimated from Merlin every centimorgan and averaged at all 3491 points additive ˆ 3491 = ( j) i= 1 ˆ π a π a( ij) / 3491 dominance 3491 ( j) i= 1 πˆ = p d 2( ij) /

27 And for the c th chromosome of length l c cm additive dominance ˆ π l c c = πˆ c / a ( j ) a ( ij ) c i= 1 l c ( j ) ˆ = p / d π i= 1 2( ij) l l c c 27

28 Mean and SD of genome-wide additive relationships 28

29 Mean and SD of genome-wide dominance relationships 29

30 Empirical and theoretical SD of additive relationships correlation = 0.98 (n = 4401) 30

31 Empirical and theoretical SD of dominance relationships correlation = 0.98 (n = 4401) 31

32 Additive and dominance relationships correlation = 0.91 (n= 4401) 32

33 Phenotypes After adjustment for sex and age: σ p = 7.7 cm σ p = 6.9 cm 33

34 Phenotypic correlation between siblings Raw After age & sex Adolescents Adults

35 Models C = A = E = Family effect Genome-wide additive genetic Residual Full model Reduced model C + A + E C + E 35

36 Estimation Maximum Likelihood variance components Likelihood-ratio-test (LRT) to calculate P- values for hypotheses H 0 : A = 0 H 1 : A > 0 36

37 Estimates: null model (CE) Cohort Family effect (C) Adolescent 0.40 ( ) Adult 0.39 ( ) Combined 0.39 ( ) 37

38 Estimates: full model (ACE) Cohort C A P Adolescent Adult Combined All family resemblance due to additive genetic variation 38

39 Sampling variances are large Cohort A (95% CI) Adolescent 0.80 ( ) Adult 0.80 ( ) Combined 0.80 ( ) 39

40 F+A more accurately estimated Cohort C+A (95% CI) Adolescent 0.80 ( ) Adult 0.80 ( ) Combined 0.80 ( ) Prediction of MZ correlation from fullsibs! 40

41 Power and SE of estimates True parameters (t) Sample size (n) Variance in genome-wide IBD sharing (var(π)) var( h ˆ2 ) (1 t 2 ) 2 / + [ ] (1 t 2 )( n var( π )) NCP = nh 4 var(π)(1+t 2 ) / (1-t 2 ) 2 41

42 Application (2) Genome partitioning of additive Aims genetic variance for height Estimate genetic variance from genome-wide IBD in larger sample Partition genetic variance to individual chromosomes using chromosome-wide coefficients of relationship Test hypotheses about the distribution of genetic variance in the genome 42

43 Sample # Sibpairs Sib Correlation AU US NL Total 11,

44 Realised relationships Mean Range SD

45 Estimates from genome-wide additive and dominance coefficients ACE model Heritability 0.86 ( ) P< Family 0.03 ( ) P=0.38 ADCE model Additive component 0.70 Dominance component 0.16 (P=0.35) 45

46 46

47 Estimates of chromosomal heritabilities 0.12 From combined chromosome analysis y = 1.006x R 2 = No epistasis? From single chromosome analyses 47

48 Longer chromosomes explain more additive genetic variance: ~0.03 per 100 cm Estimate of heritability WLS analysis: P<0.001; intercept NS Length of chromosome (cm) 48

49 Estimates are consistent across countries y = x R 2 = Heritability USA Heritability AU 49

50 Stepwise analyses: at least 6 chromosomes are needed to explain the additive genetic variance Scaled AIC Number of chromosomal additive genetic variance components 50

51 Hypothesis test Model h 2 c 2 df LRT Full (22 chrom.) Genome-wide Additive genetic variance in proportion to lenght not rejected 51

52 Data consistent with published QTL results Estimate of heritability Rank test: P= Number of publications with LOD >

53 Conclusions Empirical variation in genome-wide IBD sharing follows theoretical predictions Genetic variance can be estimated from genome-wide IBD within families results for height consistent with estimates from between-relative comparisons no assumptions about nature/nurture causes of family resemblance Genetic variance can be partitioned onto chromosomes 53

54 Conclusions With large sample sizes it will become possible to estimate dominance variance epistatic variance genome-wide parent-of-origin variance genetic relative risk to disease 54

55 Genetic architecture for height Additive genetic variance No QTL of large effects Chromosomes explain ~10% of genetic variance Consequences for genome-wide association 55

56 Other applications: breeding programmes Exploit variance in genome-wide IBD by using the realised A-matrix large increase in accuracy of selection if variance in identity is large family size is large Genomic Selection 56

57 Using the realised A-matrix: Reliability of EBV for an unphenotyped individual from n-1 phenotyped relatives (a simulation study) 57