群體遺傳 課件

PopulationGenetics群體遺傳HumanOriginsmtDNA——夏娃(Eve)Ychromosome——亞當(dāng)(Adam)BiologicalEvolutionHumandiversityOverviewsz

Medicalpopulationgeneticsmainlystudiesthebehaviorofgeneinhumanpopulation,includingtheestimationofgenefrequenciesandheterozygotefrequencies(雜合子頻率).z

--Broadsensepopulation(廣義群體):allpersons(6

billions)intheworld.z

--Narrowsensepopulation(狹義群體):Mendel

populationinsomeareas.MedicalpopulationgeneticsF1：DDxdd

~Dd

(Dominant)F2：DdxDd

3/4willbeDD/Dd(Dominant)ThefrequencyofDgeneinpopulation↑？Whiledgene↓？Withthedeathofddaffected,dgenewilldisappearfromthepopulation

？Topicsz

TheHardy-Weinbergequilibriumz

ApplicationoftheHardy-Weinbergequilibriumz

FactorsaffectingtheHardy-Weinbergequilibriumz

InbreedingcoefficientTheHardy-WeinbergEquilibriumz

HardyG.H.wasanEnglishmathematicianandWeinbergW.wasaGermanphysician.In1908,theydevelopedindependentlyamathematicalmodel.Theymadethefollowingassumptions:---Thegenotypescouldbedistinguishedunequivocally,meaningthatthefrequenciesofthephenotypeswerethesameasthoseofthegenotypes.---Nomutation,noselection,andnomigration.---Randommatingatthesametimeinapopulationofinfinitesize.EvidenceoftheH-Wlawz

Assumeonelocuswithtwoalleles:A

anda,theformerbeingdominantandthelatterbeingrecessive.z

Lettherelativefrequenciesofthetwoallelesbepandqrespectively.Asthereareonlytwoalleles,p+q=1.Thenthespermsproducedbythemalepopulationandeggsproducedbythefemalepopulationwillcontaintheminthesameproportions.EvidenceoftheH-Wlawz

Withrandommatingthevariousgameticcombinationscanberepresentedas:ThefrequenciesofthreegenotypesamongF1offspringfromsuchmatingsarep2

(AA),2pq(Aa),q2(aa).EvidenceoftheH-Wlawz

GenefrequenciesinF1offspring:AA:p2;Aa:pq+qp=2pq;aa:q2A

=

p2+1/2(2pq)=p2+pq=p(p+q)=pa=q2+1/2(2pq)=q2+pq=q(p+q)=qEvidenceoftheH-Wlawz

NowconsiderthatF1offspringmatewitheachother.Thefrequenciesofvariousmatingscanberepresentedas:AA(p2)

Aa(2pq)

aa(q2)AA(p2)

AA×AA

AA×Aa

AA×aap4Aa(2pq)

Aa×AA

Aa×Aa

Aa×aa2p3q

4p2q2

2pq3aa×AA

aa×Aa

aa×aa2p3qp2q2aa(q2)p2q22pq3q4z

Grouptogetherreciprocalmatings,AA×AaandAa×AA,forexample,andsumuptheirrespectivefrequencies.Wethusobtainsixmatingtypesandtheirfrequencies.z

Theexpectedproportionsofthethreegenotypesamongtheprogenyofthesesixmatingscanbecalculatedaccordingtoapriorisegregationratio.Matingtype

FrequencyAAAa-aaAA×AAAA×AaAa×AaAA×aaAa×aaaa×aap4p4--4p3q4p2q22p2q24pq3q42p3q2p3q2p2q22p2q22pq3-p2q2p2q2----2pq3q4EvidenceoftheH-Wlawz

WehavethepredictedfrequencydistributionofgenotypeamongtheF2progenyofallmatings.z

Frequency

of

AA

=

p4

+2p3q+p2q2=p2(p2+2pq+q2)=p2;z

FrequencyofAa=2p3q+4p2q2

+2pq3=

2pqz

Frequencyofaa=p2q2

+2pq3+q4=q2z

TherelativefrequenciesofthreegenotypesamongF2progenyarethesameasthoseamongF1generation:p2(AA),2pq(Aa)andq2(aa).Soaregenefrequencies.FrequencyofA=p;Frequencyofa=q.TheHardy-Weinbergtheoremz

Apopulationundergoingrandommatingreaches,inonegeneration,adistributionofgenotypefrequenciesgivenbythebinomialexpansionof[p(A)+q(a)]2

=

p2(AA)+2pq(Aa)+q2

(aa)z

OneofthemostimportantfeatureoftheHardy-Weinbergtheoremisthatitenablesustoexpressthedistributionofgenotypesandphenotypesinapopulationentirelyintermsofthegenefrequencies.z

Foralocusoftwoalleles,Aanda,withgenefrequenciespandqrespectively:Relativegenotypefrequencies:p2+2pq+q2=1Relativephenotypefrequencies,assumingcompletedominanceofAovera:(p2+2pq)(”A”)+q2

(”a”)

=1z

TheH-Wtheoremcanbeextendedquiteeasilytocovermultiplealleles.ForthreeallelesoftheABOlocus,IA,IB

andi,withgenefrequenciesp,qandrrespectively:then(p+q+r)2=p2+q2+r2+2pq+2pr+2qrTheHardy-Weinbergtheoremz

Foralocushavingnalleles(A1,A2,...,A

)withgenefrequenciesp

,p

,...,pn1

2nrespectively,thegeneticequilibriumofthislocusunderrandommatingcanbeexpressedas:[p

(A

)+p

(A

)+...,+p

(A

)]21

12

2n

n=∑pi2(AiAi)+∑2pipj(AiAj)ApplicationsoftheH-Wlawz

Estimationofgenefrequencyandheterozygotefrequency:z

Countingmethodforestimatingfrequenciesofcodominantalleles:

suchasMNbloodgroup.z

Phenotypes:M(+)N(-);M(+)N(+);M(-)N(+)z

Genotypes:

MM(M);

MN(MN);NN(N)p=(2M+1MN)/2n=0.4628q=1–p=0.5372ApplicationsoftheH-Wlawz

Squarerootmethodforestimatingfrequencyofrecessivesallelewhenthereiscompletedominance:z

Populationincidenceofalcaptonuria(尿黑酸尿癥):x=1/1000000=q2so

[a]q=

√x=1/1000[A]p=1–q=1,[Aa]2pq=2×1×

(1/1000)=1/500ApplicationsoftheH-Wlawz

ABObloodgrouplocushavethreeallele:accordingtoH-Wlaw,weassumeIA

(p),IB

(q)

,i(r),then(p+q+r)2=p2

+2pq+q2+2qr+r2

+2prwehaver=√

O,

B=q2+2qr,

O=r2

thereforez

B

+

O

=

q2+2qr+r2=(q+r)2=(1-p)2z

Thenwehave

p=1–√B+Oz

Thus

wehave

q=1–p–rThen,wecanestimateIA,IB

andigenefrequency.e.g.

q=0.2115,

p=0.2324,

r=0.5555ApplicationsoftheH-Wlawz

XgbloodgrouplocusisX-linked

andhastwoalleleswithXga

beingdominantoverXg.z

Inmalepopulation,thegenefrequenciesarethesameasthephenotype&genotypefrequencies.z

Infemalepopulation,thegenefrequenciescanbeestimatedwithsquarerootmethod.z

Note:thegenefrequencyfrommale&femalepopulationhasnotsignificantdifference(P>0.05).ApplicationsoftheH-WlawSex

Blood

Genotype

No.

Of

Freq.

Freq.ofgrouppopula

of-tion

pheno-typegeneMale

Xg(a+)

XgaYXg(a-)

XgY1880.631

0.6311100.369

0.369Fema-

Xg(a+)

XgaXgale260310.893

0.6730.107

0.327XgaXgXg(a-)

XgXgSomeconceptsderivedfromtheH-Wtheoremz

Forararedominantgene,p2

is

negligible,then

2pq/p2

+2pq≈

1.Nearlyalloftheaffectedindividualsareheterozygotes.z

Forararerecessivegene,q2

is

very

muchsmallerthanpwhichisclosetoone.2pq=2(1-q)q=2q-2q2≈2q.q≈(2pq)/2=2or(2pq)/q≈2z

Forararerecessivegene,pisclosetoone.Then,

2pq/q2

=2p/q=2/qSomeconceptsderivedfromH-Wtheoremz

ForarareX-linkeddominantgene,pisNegligible,sop/(p2+2pq)=1/(2–p)≈

1/2z

ForarareX-linkedrecessivegene,thereoccurmoreaffectedmalesthanaffectedfemales,q/q2=1/qTestofgenetichypothesisz

Phenylthiocarbamide(PTC)tasting.z

Givingagenetichypothesis:allelesTandt,

then,z

TastergenotypeisTTorTt,nontasteristtz

PTCtastingwithfamilydata:z

a.Observedfamilydataz

b.Expectedphenotypedistributionamongoffspring.IfitisTaster×

Taster,theoverallproportionofrecessivesamongoffspringisp2q2

/p2(1+q)2

=(q/1+q)2.Mating

Freq.of

Freq.

Freq.type

mating

of

ofTaster

Non-taster-TT×TT

p4p433TT×Tt

4p

q

4p

q

-2

22

22

2Tt×Tt

4p

q

3p

q

p

qIfitisTaster×Nontaster,theoverallproportionofrecessivesamongoffspringis2pq3

/2pq2(1+q)=q/1+qMating

Freq.

Freq.

Freq.

oftype

of

of

Non-mating

Taster

taster2

22

2TT×tt

2p

q

4p

q

-333Tt×tt

4pq

2pq

2pqTestofgenetichypothesisz

Estimationofqfrompopulationdata:q=

0.2981=0.5460,

p=0.4540z

Chisquaretestforgoodnessoffitz

---Taster×Taster:χ2

=

|O-E|2

/

E

=

0.0487,z

P>0.05z

---Taster×non-taster:χ2

=

0.5048,

df

=

1,z

P>0.05z

TheobservedfamilydatasupportsthehypothesisInbreedingCoefficient(IorF)z

ICistheprobabilitythatanindividualreceivesatagivenlocustwogenesthatareidenticalbydescent.z

ICforautosomallocusinprogenyoffirst-cousinmarriage:I=1/16Evaluatingthedeleteriouseffectofconsanguineousmarriagesz

Thetotalprobabilitythatafirst-cousinmarriagewillproduceagene“a”withfrequencyq=Theprobabilitythatthegenescometogetherfromtheircommonancestor+theprobabilitythatthegenescometogetherfromsomeothersource=(1/16)q+(15/16)q2.z

Theprobabilitythatarandommarriagewillproduceahomozygousrecessiveforagene“a”withfrequencyq=q2Evaluatingthedeleteriouseffectofconsanguineousmarriagesz

Thedeleteriouseffectofthefirst-cousinmarriage=[(1/16)q+(15/16)q2]/q2z

Suggestionfromthedeleteriouseffectofconsanguineousmarriages.z

Ifadiseaseisrare,ahighincidenceofconsanguineousmarriagesamongtheparentscanbeconsideredquiteconclusiveevidence.Namely:i.Thatitisinherited.ii.Thattheresponsiblegeneisanautosomalrecessive.DeleteriouseffectofconsanguineousmarriagesGenefre.

q2

(1/16)pq

q2+(pq/

1+15q/（q）16)16q0.20

0.0400

0.010

0.050

1.250.10

0.0100

0.0056

0.015

1.560.04

0.0016

0.0024

0.004

2.500.02

0.0004

0.0012

0.002

4.060.01

0.0001

0.0006

0.0007

7.190.001

0.00000

0.00006

0.00006

63.5FactorAffectingtheH-Wlawz

Deviationfromrandommatingz

Assortativemating(positiveornegative):thetendencyforhumanbeingstochoosepartnerswhosharecharacteristicssuchasheightintelligenceandracial.z

Inbreeding:marriagebetweencloselyrelatedindividuals.z

MutationTherateofmutationforanyparticulargeneisprobablyfairlyconstant.FactorAffectingtheH-Wlawz

Selection(s)Itoperatesbyincreasing(positionselection)ordecreasing(negativeselection)the

reproductivefitness(f).

s+f=1.Relativelyhighfrequenciesofsomemutantgenesarebelievedtobemaintainedbyaselectiveadvantage