Haplotype Frequencies and Linkage Disequilibrium. Biostatistics 666

Transcription

1 Hlotye Frequencies nd Linkge isequilirium iosttistics 666

2 Lst Lecture Genotye Frequencies llele Frequencies Phenotyes nd Penetrnces Hrdy-Weinerg Equilirium Simle demonstrtion

3 Exercise: NO2 nd owel isese Leu1007fs Frme shift muttion t osition 1007 Frequency of out 5% isruts gene Penetrnce Genotye +/+ -/+ -/- P(Crohn s G) 0.1% 0.2% 3% Clculte frequency of -/- genotye in oultion nd mong tients

4 Hlotye or Gmete Frequencies

5 Tyicl Genotye t Two lleles for ech individul Chromosome origin for ech llele is unknown Mny hlotye irs might e comtile with oserved dt Will ignore this comlexity for now Oservtion C G Mrker1 T C Mrker2 G Mrker3 Possile Sttes C G C G T C C T G G C G C G C T T C G G

6 Linkge Equilirium In lrge rndom mting oultion hlotye frequencies converge to simle function of llele frequencies (The reverse is lwys true!)

7 Linkge Equilirium

8 new muttion efore Muttion G C G fter Muttion G C G C C Muttion

9 For new muttion One hlotye frequency is zero Linkge disequilirium does not hold In contrst, linkge disequilirium How is linkge equilirium reched?

10 Recomintion C C efore Recomintion G G C fter Recomintion G C G C C G Recominnt Hlotye

11 Equilirium or isequilirium? We will resent simle rgument for why linkge equilirium holds lnce of fctors Genetic drift ( function of oultion size) Rndom mting istnce etween mrkers

12 Linkge isequilirium

13 isequilirium Coefficient

14 is hrd to interret Sign is ritrry We could set, to e the common llele nd, to e the rre llele The rnge of deends on llele frequencies Hrd to comre etween mrkers

15 Rnge of Must e greter thn Mx(-,- ) Must e smller thn Min( -, - ) These constrints ensure tht no hlotyes hve negtive frequencies

16 lterntive Mesures The most oulr mesures nd ² Other common mesures Chi-squred P-vlue

17 ² ² ² 2n (1 2 ) (1 ) Rnges etween 0 nd 1 1 when the two mrkers rovide identicl informtion 0 when they re in erfect equilirium Exected vlue is 1/2n

18 ' mx( min(,, ) ) 0 0 Rnges etween 1 nd +1 More likely to tke extreme vlues when llele frequencies re smll 1 imlies t lest one of the oserved hlotyes ws not oserved

19 Rw dt from Chr ' Physicl istnce (k)

20 Rw ² dt from Chr r Physicl istnce (k)

21 Why Equilirium is Reched Eventully, rndom mting nd recomintion should ensure tht muttions sred from originl hlotye to ll hlotyes in the oultion Simle rgument: ssume fixed llele frequencies over time

22 Recomintion Frequency Recomintion frequency <= 0.50 For loci on the sme chromosome Oserved recomintion refers to n odd numer of crossovers

23 Recomintion Rte () Proility of n odd numer of crossovers etween two loci Proortion of time lleles from two different grnd-rents occur in the sme gmete Increses with hysicl (se-ir) distnce, ut rte of increse vries cross genome

24 Without Recomintion Hlotye Frequencies Remin Stle Over Time P=1-

25 With Recomintion Hlotye Frequencies re Function of llele Frequencies P=

26 Overll Chnge ) (1 ) (1 ) (1 ) (1 isequilirium ecreses

27 Predictions isequilirium will decy ech genertion In lrge oultion fter t genertions t = (1-) 0 etter model should llow for chnges in llele frequencies over time

28 Strtifiction isequilirium ncestor Present-dy Poultion Poultion

29 Strtifiction ue to non-rndom mting Eg. Mting sed on roximity or culture llele frequencies drift rt in ech grou Eg. llele frequency differences t mny genes etween fricn-mericns nd Cucsins isese revlences my lso differ Eg. Glucom hs revlence of ~2% in elderly Cucsins, ut ~8% in fricn-mericns