Lecture 6: Introduction to Quantitative genetics

1 Lecture 6: Introduction toQuantitative geneticsBruce Walsh Lecture notesLiege May 2011 courseversion 25 May 2011 Quantitative GeneticsThe analysis of traits whosevariation is determined by botha number of genes andenvironmental factorsPhenotype is highly uninformative as tounderlying genotypeComplex (or Quantitative ) trait No (apparent) simple Mendelian basis for variation in thetrait May be a single gene strongly influenced by environmentalfactors May be the result of a number of genes of equal (ordiffering)

2 Effect Most likely, a combination of both multiple genes andenvironmental factors Example: Blood pressure, cholesterol levels Known genetic and environmental risk factors Molecular traits can also be Quantitative traits mRNA level on a microarray analysis Protein spot volume on a 2-D gelPhenotypic distribution of a traitConsider a specific locus influencing the traitFor this locus, mean phenotype = , whileoverall mean phenotype = 0 Goals of Quantitative genetics Partition total trait variation into genetic (nature)vs.

3 Environmental (nurture) components Predict resemblance between relatives If a sib has a disease/trait, what are your odds? Find the underlying loci contributing to geneticvariation QTL -- Quantitative trait loci Deduce molecular basis for genetic trait variation eQTLs -- expression QTLs, loci with a quantitativeinfluence on gene expression , QTLs influencing mRNA abundance on a microarrayDichotomous (binary) traitsPresence/absence traits (such as a disease) can (and usually do) have a complex genetic basisConsider a disease susceptibility (DS)

4 Locus underlying a disease, with alleles D and d, where allele D significantly increases your disease riskIn particular, Pr(disease | DD) = , so that thepenetrance of genotype DD is 50%Suppose Pr(disease | Dd ) = , Pr(disease | dd) = individuals can rarely display the disease, largelybecause of exposure to adverse environmental conditions If freq(d) = , what is Prob (DD | show disease) ?freq(disease) = * + 2* * * + * = Bayes theorem, Pr(DD | disease) = Pr(disease |DD)*Pr(DD)/Prob(disease) = * / = (6 %)dd individuals can give rise to phenocopies 5% of the time,showing the disease but not as a result of carrying therisk allelePr(Dd | disease) = , Pr(dd | disease) = about 50% of the diseased individuals are phenocopiesBasic model of Quantitative GeneticsBasic model.

5 P = G + EPhenotypic value -- we will occasionallyalso use z for this valueGenotypic valueEnvironmental valueG = average phenotypic value for that genotypeif we are able to replicate it over the universeof environmental values, G = E[P]Basic model of Quantitative GeneticsBasic model: P = G + EG = average phenotypic value for that genotypeif we are able to replicate it over the universeof environmental values, G = E[P]G x E interaction --- G values are differentacross environments. Basic model nowbecomes P = G + E + GEQ1Q1Q2Q1Q2Q2CC + a(1+k)C + 2aCC + a + dC + 2aC -aC + dC + a2a = G(Q2Q2) - G(Q1Q1) d = ak =G(Q1Q2 ) - [G(Q2Q2) + G(Q1Q1) ]/2 d measures dominance, with d = 0 if the heterozygoteis exactly intermediate to the two homozygotes k = d/a is a scaled measure of the dominanceContribution of a locus to a traitExample.

6 Apolipoprotein E &Alzheimer age of onsetEEEeeeGenotype2a = G(EE) - G(ee) = - --> a = ak =d = G(Ee) - [ G(EE)+G(ee)]/2 = k = d/a = small amount of dominanceExample: Booroola (B) Litter sizeBBBbbbGenotype2a = G(BB) - G(bb) = --> a = ak =d = G(Bb) - [ G(BB)+G(bb)]/2 = k = d/a = s (1918) Decomposition of GOne of Fisher s key insights was that the genotypic valueconsists of a fraction that can be passed from parent tooffspring and a fraction that cannot. G= Gij freq(QiQj)Mean value, withAverage contribution to genotypic value for allele iGij= G+ i+ j+ ijConsider the genotypic value Gij resulting from an AiAj individualIn particular, under sexual reproduction, parents onlypass along SINGLE ALLELES to their offspringSince parents pass along single alleles to theiroffspring, the !

7 I (the average effect of allele i)represent these contributionsGij= G+ i+ j+ ij Gij= G+ i+ jThe genotypic value predicted from the individualallelic effects is thusThe average effect for an allele is POPULATION-SPECIFIC, as it depends on the types and frequencies of alleles that it pairs withGij= G+ i+ j+ ij Gij Gij= ijDominance deviations --- the difference (for genotypeAiAj) between the genotypic value predicted from thetwo single alleles and the actual genotypic value, Gij= G+ i+ jThe genotypic value predicted from the individualallelic effects is thusGij= G+2 1+( 2 1)N+ ijGij= G+ i+ j+ ijFisher s decomposition is a RegressionPredicted valueResidual errorA notational change clearly shows this is a regression,Independent (predictor) variable N = # of Q2 allelesGij= G+2 1+( 2 1)N+ ij2 1+( 2 1)

8 N= 2 1forN=0, ,Q1Q1 1+ 2forN=1, ,Q1Q22 2forN=2, ,Q2Q2 Regression slopeIntercept012 NGG22G11G21 Allele Q2 common, !1 > !2012 NGG22G11G21 Allele Q1 common, !2 > !1 Slope = !2 - !1 012 NGG22G11G21 Both Q1 and Q2 frequent, !1 = !2 = 02aa(1+k)0 GenotypicvalueQ2Q2Q2Q1Q1Q1 GenotypeConsider a diallelic locus, where p1 = freq(Q1) G=2p2a(1+p1k)MeanAllelic effects 2=p1a[1+k(p1 p2)] 1= p2a[1+k(p1 p2)]Dominance deviations ij=Gij G i jAverage effects and Additive genetic ValuesA(Gij)= i+ jA=n k=1( (k)i+ (k)k)The !

9 Values are the average effects of an alleleA key concept is the Additive genetic Value (A) ofan individualA is called the Breeding value or the Additive geneticvalueA=n k=1( (k)i+ (k)k)Why all the fuss over A?Suppose father has A = 10 and mother has A = -2for (say) blood pressureExpected blood pressure in their offspring is (10-2)/2 = 4 units above the population mean. Offspring A =average of parental A sKEY: parents only pass single alleles to their , they only pass along the A part of their genotypicvalue GGenetic VariancesGij= g+( i+ j)+ ij 2(G)=n k=1 2( (k)i+ (k)j)+n k=1 2( (k)ij) 2(G)= 2( g+( i+ j)+ ij)= 2( i+ j)+ 2( ij)As Cov(!)

10 ,") = 0 genetic Variances 2(G)=n k=1 2( (k)i+ (k)j)+n k=1 2( (k)ij) 2G= 2A+ 2 DAdditive genetic Variance(or simply Additive Variance)Dominance genetic Variance(or simply dominance variance)Key concepts (so far) !i = average effect of allele i Property of a single allele in a particular population (depends ongenetic background) A = Additive genetic Value (A) A = sum (over all loci) of average effects Fraction of G that parents pass along to their offspring Property of an Individual in a particular population Var(A) = additive genetic variance Variance in additive genetic values Property of a population Can estimate A or Var(A) without knowing any of theunderlying genetical detail (forthcoming)