Hlotye Frequencies nd Linkge isequilirium iosttistics 666
Lst Lecture Genotye Frequencies llele Frequencies Phenotyes nd Penetrnces Hrdy-Weinerg Equilirium Simle demonstrtion
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
Hlotye or Gmete Frequencies
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
Linkge Equilirium In lrge rndom mting oultion hlotye frequencies converge to simle function of llele frequencies (The reverse is lwys true!)
Linkge Equilirium
new muttion efore Muttion G C G fter Muttion G C G C C Muttion
For new muttion One hlotye frequency is zero Linkge disequilirium does not hold In contrst, linkge disequilirium How is linkge equilirium reched?
Recomintion C C efore Recomintion G G C fter Recomintion G C G C C G Recominnt Hlotye
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
Linkge isequilirium
isequilirium Coefficient
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
Rnge of Must e greter thn Mx(-,- ) Must e smller thn Min( -, - ) These constrints ensure tht no hlotyes hve negtive frequencies
lterntive Mesures The most oulr mesures nd ² Other common mesures Chi-squred P-vlue
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
' 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
Rw dt from Chr22 1.00 0.80 0.60 ' 0.40 0.20 0.00 0 200 400 600 800 1000 Physicl istnce (k)
Rw ² dt from Chr22 1.00 0.80 0.60 r 2 0.40 0.20 0.00 0 200 400 600 800 1000 Physicl istnce (k)
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
Recomintion Frequency Recomintion frequency <= 0.50 For loci on the sme chromosome Oserved recomintion refers to n odd numer of crossovers
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
Without Recomintion Hlotye Frequencies Remin Stle Over Time P=1-
With Recomintion Hlotye Frequencies re Function of llele Frequencies P=
Overll Chnge ) (1 ) (1 ) (1 ) (1 isequilirium ecreses
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
Strtifiction isequilirium ncestor Present-dy Poultion Poultion
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