CHAPTER16TheGeneticAnalysisOfPopulationsAndHowTheyEvolvePART1PopulationGenetics

AnpaintingbytheFrenchartistPaulGauguinCharlesDarwin,1831-1836,5yearsvoyage1859,“OriginofSpecies”,“NaturalSelectionorthePreservationofFavoredRacesintheStruggleforLife”.

1.TheEmergenceOfEvolutionaryTheoryandPopulationGeneticsThemajorgapofDarwin’stheory:Theoriginofvariation?Howparticularvariantsareinherited?1900,therediscoveryofMendel’sprinciples1930,PopulationGeneticswasbornWright,Fisher,Haldane’scontribution

PopulationGeneticsPopulationgeneticsstudiestheoriginofvariation,thetransmissionofvariantsfromparentstooffspringgeneration,andthetemporalchangesthatoccurinapopulationbecauseofsystematicandrandomevolutionaryforces.

2.TheTheoryOfAlleleFrequenciesa.EstimationGenotypeandAlleleFrequencies:LMLM=1787/(1787+3039+1303)=0.2916

LMLN

=3039/(1787+3039+1303)=0.4958

LNLN

=1303/(1787+3039+1303)=0.2126LM

=[(2x1787)+3039]/(2x6129)=0.5395LN=[(2x1303)+3039]/(2x6129)=0.4605

RelatingGenotypeFrequenciestoAlleleFrequencies(1908)

b.

TheHardy-WeinbergPrincipleGenotypeFrequency

AAp2Aa2pqaaq2c.ApplicationsoftheHardy-WeinbergPrinciple

LM

=[(2x1787)+3039]/(2x6129)=0.5395LN=[(2x1303)+3039]/(2x6129)=0.4605i.MNbloodtype-x2testx2=(1787-1784.2)2/1784.2+(3939-3044.8)2/3044.8+(1303-1300.0)2/1300.0=0.0223Degreeoffreedom:3–2=1Thecriticalvalue:3.841

ii.EstimationofthemutantallelefrequencyPKU:thefrequencyofmutanthomozygotes:

q2=0.0001Undertheassumptionofrandommating:q2=0.0001q=0.01p=1-q=1-0.01=0.99Carrierfrequency=2pq=2(0.99)(0.01)=0.019

iii.X-linkedgene-colorblindnesse.g.200men,24haveX-linkedcolorblindnessandalltheotherhavenormalcolorvision.Frequencyofc=24/200=0.12,C=1-0.12=0.88

iv.A-B-Oblood-typingsystem

IA=

p,IB=q,

IO=r

(p+q+r)2=p2+q2+r2+2pq+2qr+2pr

d.ExceptionstotheHardy-Weinberg

Principle---Nonrandommating

GenotypeFrequencywithconsanguineousmating

AAp2+pqFAa2pq–2pqFaaq2+pqFIfF=1,

AApAa0aaq

d.ExceptionstotheHardy-Weinberg

Principle---UnequalsurvivalGenotypeObservednumberHardy-Weinbergprediction

AA335

AD13470

DD335ThefrequencyofAisp=0.5ThefrequencyofDisq=0.5Becausetheheterozygoteshaveamuchbetterchanceofsurviving.

d.ExceptionstotheHardy-Weinberg

Principle---Populationsubdivision

GenotypeAAAaaaFrequencyinpopulation10.040.320.64Frequencyinpopulation20.640.320.04

d.ExceptionstotheHardy-WeinbergPrinciple-Migration

BeforeMigrationAfterMigration

e.UsingAlleleFrequenciesinGeneticCounselingTheincidenceofCFinthenorthernEuropeanancestry=0.0004

q=0.02

p=0.982pq=1/25Examples1ABObloodtypeA=326,B=20,AB=16,O=338,Total=700r2=338/700=0.483r=0.695(p+r)2=p2+2pr+r2

A+O=(p2+2pr)+r2=(326+338)/700=0.949(p+r)2

=0.949p+r=0.974,p=0.974–0.695=0.279p+q+r=1

q=1–p–r=1–0.279–0.695=0.026

Examples22.Patternbaldness(PB)PB=0.3,PB+=0.7GenotypePB/PBPB/PB+PB+/PB+Frequency(0.3)2=0.092(0.3)(0.7)=0.42(0.7)2=0.49Male:0.09+0.42=0.51Female:0.09

3.NaturalSelectionFitness(w):abilitytosurviveandreproduceSelectioncoefficient(s):fitnessdeviationbynaturalselections=1–w,w=1-s

NaturalSelectionattheLeveloftheGenea.Selectionagainstaagenotype

Genotypes

AAAaaatotalfrequencyofaFreq.p22pqq21qFitness111-sAfterSelectionp22pqq2(1-s)p2+2pq+q2(1-s)=1-sq2

RelativeFreq.p2/[1-sq2]2pq/[1-sq2]q2(1-s)/[1-sq2][pq+q2(1-s)]/[1-sq2]=[pq+q2-sq2]/[1-sq2]=[q(p+q-sq)]/[1-sq2]=[q(1-sq)]/[1-sq2]ChangeΔq=q(1-sq)/(1-sq2)–q=q(1-sq)/[1-sq2]–q(1-sq2)/[1-sq2]=[q-sq2–q+sq3]/[1-sq2]=[-sq2+sq3]/[1-sq2]=[-sq2(1-q)]/[1-sq2]

ofaFreq.a.SelectionagainstaagenotypeΔq=[-sq2(1-q)]/[1-sq2]WhenqisverysmallThen1-sq2=1Δq≈-sq2(1-q)

b.SelectionagainstAAandAagenotype

(Selectioninfavorofallelea)GenotypesAAAaaatotalfrequencyofAFreq.p22pqq2

1pFitness1-s1-s1AfterSelectionp2(1-s)2pq(1-s)q2

p2(1-s)+2pq(1-s)+q2

=1-sp(2-p)

RelativeFreq.p2(1-s)/[1-sp(2-p)]2pq(1-s)/[1-sp(2-p)]q2/[1-sp(2-p)][p2(1-s)+pq(1-s)]/[1-sp(2-p)]=(p–sp)/[1-sp(2-p)]

ChangeΔp=(p–sp)/[1-sp(2-p)]–p=-sp(1-p)2/[1-sp(2-p)]ofAFreq.

Δp=-sp(1-p)2/[1-sp(2-p)]Whensisverysmall1-sp(2-p)=1Δp≈-sp(1-p)2Selectioninfavorofallelea

Darkformandlightformofthemoth:SelectioninfavorofAgeneA:dark;a:light

c.SelectioninfavorofAagenotypeGenotypes

AAAaaatotalfrequencyofaFreq.p22pqq2

1qFitness1-s11-tAfterSelectionp2(1-s)2pqq2(1-t)p2(1-s)+2pq+q2(1-t)=1-p2s-q2tRelative

p2(1-s)/[1-p2s-q2t]2pq/[1-p2s-q2t]q2(1-t)/[1-p2s-q2t][pq+q2(1-t)]/[1-p2s-q2t]Freq.=q(1-qt)/[1-p2s-q2t]

ChangeΔq=q(1-qt)/[1-p2s-q2t]–q=pq(ps-qt)/[1-p2s-q2t]ofAFreq.

BalancingSelectionΔq=pq(ps-qt)/[1-p2s-q2t]Whentheallelefrequenciesarenolongerchanging(i.e.atthebalancepoint)Δq=0ps=qt,p=1-qq=s/(s+t)p=t/(s+t)

e.g.1Genotype:HbsHbsHbsHbAHbAHbARelativefitness:1-s11-tWhentheequilibriumfrequencyofHbsisp=0.1,s=1p=t/(s+t)0.1=t/(1+t)t=0.1/0.9=0.11

Distributionofthesickle-cellanemiaalleleandmalariae.g.2Genotype:HbsHbsHbsHbAHbAHbAfrequency:0.0120.3880.600FrequencyofHbsp=0.206WhenwofHbsHbs=0.25

sofHbsHbs=1-w=0.75t=ps/q=0.206x0.75/0.794=0.195

wofHbAHbA=1-t=0.805

Distributionofthesickle-cellanemiaalleleandmalariaNaturalSelectionattheLevelofthePhenotype

4.RandomGeneticDrift

RandomChangesinAlleleFrequencies

TheEffectsofPopulationSize

Mutation-selectionbalanceforadeleteriousrecessiveallelewithfrequencyqA→arate=uSelectioncoefficientfora=su=sq2

q2=

u/s

5.MutationPART2InheritanceofComplexTraits

ACombinationofGeneticandEnvironmentalfactors

CardiovascularDisease:a.QuantitativeTraitse.g.1broadbeansizeByJohannsenin1903,1909e.g.2kernelcolorinwheatByNilsson-Ehlein1909

1.Complexpatternsofinheritance

e.g.3

corollalengthintobaccobyEdwardM.East41mm93mm

Quantitativetraits

Quantitativetraitsareinfluencedbymanygenes.Quantitativetraitsareinfluencedbymanyfactorsintheenvironment.Multifactorialtraits

1.Complexpatternsofinheritanceb.ThresholdTraitse.g.cleftlip

ConcordanceAmong

MZandDZ

FamilyStudiesofCleftLip/CleftPalate

aFrequencyDistributionsanddescriptivestatisticsoftimetomaturityinfourpopulationofwheat

2.StatisticsofQuantitativeGeneticsNormalDistributionb.TheMeanandtheModalClassX=(∑Xi)/ns2=∑(Xi-X)2/(n–1)c.TheVarianceandtheStandardDeviation

3.AnalysisofQuantitativeTraitsa.ThemultiplefactorhypothesisbyR.A.Fisherin1918T=μ+g+e

b.PartitioningthephenotypicVarianceVT=Vg+VeBroad-SenseHeritabilityH2=Vg/VTVg=Va+Vd+ViVT=Va+Vd+Vi+VeNarrow-SenseHeritabilityh2=Va/VT

μ=26,s2

=26.6

b.PartitioningthephenotypicVariance

PartitioningthephenotypicVarianceμ=30,s2=5.3,Vg=0,VT=Ve=5.3μ=28,s2=21.3,Ve=0,VT=Vg=21.3c.Broad-SenseHeritabilityand

Narrow-SenseHeritabilityVT=Vg+Ve26.6=21.3+5.3H2=Vg/VT=21.3/26.6=0.8Corollalengthintobacco:Ve=(VP1+VP2+VF1)

/3=7mm2VT=Vg+VeVg=VT

–VeVg=43mm2

–7mm2

=36mm2H2=36/43=0.84

Narrow-SenseHeritabilityfor

QuantitativeTraits

To=μ+h2[(Tm+Tf)/2–μ]To=μ+h2(Tp–μ)(Tm+Tf)/2=Tp

d.PredictingPhenotypesTo=μ+h2

(Ts–μ)[To–μ]=h2(Ts–μ)[To–μ]=R(Ts–μ)=SR=h2SR:responsetoselectionS:selectiondifferential

e.ArtificialSelectionArtificialSelectionforBodySize

Weightrange:1800-3000μgμ=2400μgS2

=4000