PRACTICE PROBLEMSIN POPULATIONGENETICS
1. In astudyof theHopi, aNativeAmericantribeof centralArizona,Woolfand Dukepoo (1959) found 26 albinoindividualsinatotalpopulationof 6000. Thisformof albinismiscontrolledby asinglegenewithtwoalleles:albinismisrecessivetonormal skincoloration.
a) Whycan’tyou calculatetheallelefrequenciesfromthisinformationalone?
b) Calculatetheexpectedallelefrequenciesandgenotypefrequenciesifthepopulation wereinHardy-Weinbergequilibrium.How manyof theHopi areestimatedtobecarriers of therecessivealbinoallele?
2. A wildflowernativetoCalifornia,thedwarf lupin(Lupinus nanus) normallybearsblue flowers. Occasionally,plantswithpinkflowers areobservedinwildpopulations.Flower coloriscontrolledatasinglelocus,withthepinkallelecompletelyrecessivetotheblue allele.Harding(1970) censusedseverallupinpopulationsintheCaliforniaCoastRanges. In onepopulationof lupinsatSpanishFlat,California,hefound 25 pinkflowers and
3291 blueflowers, for atotalof 3316 flowers.
a) Calculatetheexpectedallelefrequenciesandgenotypefrequenciesifthepopulation wereinHardy-Weinbergequilibrium.
b) Hardingstudiedthefertilityof lupinsby countingnumberof seedpods producedper plantinasubsampleof theSpanishFlatpopulation.He found thefollowing:
mean# pods / numberof plantsexaminedblue / 19.33 / 39
pink / 13.08 / 24
Assume thatheterozygotesareas fitas homozygousbluelupins,andthatseeds fromboth pinkandbluelupinsallsuffer aboutthesamemortalityrateaftergerminating.Calculate therelativefitnessof eachgenotype.
c)Predictquantitativelytheeffectof naturalselectionon thefrequenciesof phenotypes inthenextgenerationof lupins.
3. CookeandRyder(1971) studiedthenestlingsof Ross’s goose, asmallArcticnesting goose. Goslings (babygeese)existintwo colormorphs, greyor yellow.Cookeand Ryderreportedthatapopulationof geeseatKarrackLake,Canadaincluded263 yellow goslingsand413 greygoslings(676 total).Theyassumedthatcoloriscontrolledby two allelesatasinglelocus.
a) Calculatethefrequenciesof allthreepossiblegenotypes,assumingthatgreyis dominantandthatthepopulationisinHardy-Weinbergequilibrium.Thenrepeat, assumingthatyellowisdominant.
b) Assume thatgreyisdominant.(In reallife,CookeandRyderwereunabletodetermine whichallelewas dominant.)Thereisno differencebetweenyellowandgreygoslings
oncetheyhavematured.However, yellowgoslingsareatanincreasedriskof predation by apredatorybird,theArcticskua. If 303 greygoslingssurvivetoadulthood,butonly
150 yellowones do, calculatethefitnessof theyellowphenotyperelativetothegreyone.
c)Now calculatethemeanfitness("w-bar"). Use thattopredicttheeffectof selectionon thenextgeneration.
4. A 1970 studyof 93 house mice(Mus musculus) inasinglebarninTexasfocusedon a singlelocus(thegenefor acertainenzyme)withtwo alleles,A andA’. Thegenotype frequenciesfound were:
AA / 0.226AA' / 0.400
A'A' / 0.374
a) Calculatetheallelefrequencies.
b) How does thispopulationdifferfromthepredictionsof Hardy-Weinbergequilibrium? Show your work.
c)In thisspecificcase,whatfactoror factorsaremostlikelytobecausingdeviations fromHardy-Weinbergequilibrium?How canyou tell?
5. ThegeneticistP. M. Sheppard(1959) carriedoutaselectionexperimenton a laboratory populationof thefruitflyDrosophila melanogaster.Thestubbleallele,which affectsbristleshapeof thefly,isdominanttothewild-typeallele.Fliesthatare homozygousfor stubblealwaysdieduringembryonicdevelopment.
a) Sheppardstartedoutwith86% normalfliesand14% stubbleflies.Calculatetheallele frequencies.
b) Assumingfor now thatwild-typeandstubblefliesdo notdifferinfitness,use the allelefrequenciestocalculatethemeanfitness.Thenpredictthepercentagesof normal andstubblefliesinthenextgeneration.Show allwork.
c)Sheppardintroducedanadditionalsourceof selection:heremoved60% of thewild- typefliesbeforetheycouldbreedineachgeneration.Repeatpartb takingthisinto account.
6. TheOld GermanBaptistBrethren,informallyknown as the"Dunkers", isasmall religiousdenominationfoundedinGermanyin1708. Beginningin1719, anumberof Dunkers emigratedfromGermanytoPennsylvania.As of 1950, therewereabout3500
Dunkers intheUnitedStates.Dunkers arenotas strictabouttheirlifestyleas other similarreligiousgroups, such as theAmish.However, Dunkers usuallymarrywithin theircommunity.Dunkers who marrynon-Dunkers oftenleavethecommunity,and convertstotheDunker denominationarerelativelyrare.
In 1950, geneticistBentleyGlass studiedapopulationof over200 Dunkers in southernPennsylvania.Glass used theMN bloodgroup, abloodtypecontrolledby a singlegenewithtwo loci.IndividualsmaybetypeM (homozygousfor theM allele),N (homozygousfor theN allele),or MN (heterozygous).TheMN bloodtypehas little clinicalsignificance,andas faras isknown thereisno survivaladvantageinhavingone MN bloodtypeovertheother.
a) Glass found 102 Dunkers withtypeM blood,96 withtypeMN, and31 withtypeN. Calculatetheallelefrequencies.
b) Calculatetheexpectednumbersof peoplewho would haveeachbloodtypeifthe populationwereinHardy-Weinbergequilibrium.If theexpectedfiguresdon’tmatch whatisobserved,suggest why thismightbethecase.
c)In Germanytoday,about30% of thepopulationhas typeM blood,50% has typeMN, and20% has typeN. In theeasternUnitedStates,thefiguresarealmostidentical(29% M, 50% MN, 21% N.) Discuss why bothof thesesets of allelefrequenciesmightdiffer fromthefrequenciesintheDunkers. (Therecouldbemanyreasons, butrestrictyourself tothemostlikely.)
7.P. D. N. Hebertstudiedthefrequenciesof allelesfor thegenethatcodesfor the
enzymemalatedehydrogenase(Mdh) inthe"waterflea,"Daphnia magna, livingin
ponds nearCambridge,England.Therearethreeallelesof theMdh gene,abbreviatedS, M andF. Hebertfound thefollowinggenotypes:
genotype / observednumberSS / 3
SM / 8
SF / 19
MM / 15
MF / 37
FF / 32
total / 114
a) Calculatetheallelefrequencies.
b) Is thepopulationinHardy-Weinbergequilibrium?
8. Avenafatuaisaspeciesof wildoat(atypeof grass). JainandMarshallstudiedwild
oatpopulationgeneticsinCalifornia.One of thetraitstheyexaminedwas thepubescence
(hairiness)of theleafsheath,whichiscontrolledby asinglelocuswithtwo alleles, writtenLandl.Theyfound thatthefrequenciesof genotypesinonepopulationwere:
LL57.1%Ll7.1%ll35.8%
a) Calculatetheallelefrequencies.
b) PredictwhatthegenotypefrequenciesshouldbeunderHardy-Weinbergequilibrium. If thereisadifferencebetweenactualandpredictedfrequencies,explainbrieflywhy the differencesmightexist.
c)CalculateF.
9. ThebiologistB.BattagliaraisedthemarinecopepodTisbereticulata(asmallfree- swimmingmarinecrustacean)undercrowdedconditions.T. reticulatahas onegenewith two alleles,VvandVm,showing incompletedominance.In oneof histanks,Battaglia counted1751 copepods:353 VvVv,1069 VvVm,and329 VmVm.
a) Show thatthepopulationisnotinHardy-Weinbergequilibrium.
b) Discuss why itmightnotbeinHardy-Weinbergequilibrium.
10. Truestory:In 1912, thegeneticistW.H. Goddard suggestedthatfeeble-mindedness
was causedby Mendelianinheritanceatasinglelocuswithtwo alleles.Persons
homozygousfor therecessive,feeble-mindedallele(callitf) weredopes, dummies,and dimwits-- "incapableof managingtheiraffairswithordinaryprudence",as Goddard said. Heterozygotes(Ff) andhomozygousdominants(FF) wereof normalintelligence.This is not actuallytrue-- butpretendthatitis,for thepurposes of working thisproblem.
a) Accordingtothe1910 census, thepopulationof theUnitedSteteswas 91,972,266. Goddard estimatedthat1% of thepopulationwas feeble-minded.Assume thatthe populationof theUS was inHardy-Weinbergequilibrium.Calculatetheallele frequencies,andthencalculatethepercentagesof thepopulationthatwould be heterozygousandhomozygousdominant.
b) Atonetimeor another,thirtystateshadlaws mandatingthecompulsorysurgical sterilizationof thefeebleminded.(As of 1996, Arkansas andnineotherstatesstilldid havesuch alawon thebooks.) Therewereorganizationsintheearly20thcenturythat lobbiedfor theirenactmentnationwide.
Imaginethat,insomealternate-realityUSA, amandatory,nationwidelawreallywas put intoeffectthatforcedthesterilizationof allfeeblemindedindividualsbeforetheycould reproduce.Assume thattheauthoritieswereso efficientthattheywereabletotrackdown andsterilize90% of thefeebleminded—andthattheynever,eversterilizedanyonewho wasn’t feebleminded.Whatwould bethefrequenciesof genotypes,andof alleles,after one generation?
11.Fundus heteroclitus is a small fish that lives in bays andestuariesalongtheeastcoastof North America,fromNewfoundlandtoFlorida.It’sbeenextensivelyused inevolutionarystudies.
Northernpopulationsof F.heteroclitusarevirtuallycompletelyhomozygousfor an alleleof aliverenzymecalledLdh-B(lactatedehydrogenaseB), anallelewhichisjust calledLdh-Ba.Southernpopulationsarevirtuallycompletelyhomozygousfor theother majoralleleof Ldh-B,referredtoas Ldh-Bb.
Ldh-Bhas aneffecton thesurvivalof fish embryoswhen exposedtotemperature stress. In anexperimentaltestof thissurvival,Fundulusheteroclituseggs fromdifferent populationswereincubatedat30°C,underheatstress. 57% of theeggs fromasouthern populationhatchedsuccessfullyat30°C.Only 22% of theeggs fromanorthern populationhatched.Interestinglyenough,87% of theeggs thatwereheterozygousatthe Ldh-Blocussuccessfullyhatched.
a) Suppose you put500 northernFundulusfish and500 southernfish inalargetank, allowedthemtobreedfreely,andthenincubatedalltheeggs at30°C.Predictthe frequenciesof both allelesand genotypesafteronegeneration.
b) Predictthefrequenciesof both allelesand genotypesafterasecondgeneration.
c)Suppose that,when you actuallydo thisexperiment,you discoverthattheactual heterozygotefrequencyis0.55. CalculateF.
12. In 1973, FranciscoAyalaandcolleaguessampledapopulationof deep-seastarfishof thespeciesNearchasteraciculosus,livingatadepthof 1244 metersoff thecoastof San Diego,California.Theyused electrophoresistodeterminethefrequenciesof various alleles.One genethattheylookedat,for theenzymetetrazoliumoxidase(abbreviated To), hadfour alleles(abbreviatedTo-100, To-107, To-114, andTo-120.) Theyfound that thefrequencyof eachallelewas as follows:
To-100 / 0.206To-107 / 0.147
To-114 / 0.353
To-120 / 0.294
Ayalaetal.observedthatinthispopulation,70.6% of thestarfishwereheterozygous. Does thisobservationmatchthepredictionfor apopulationinHardy-Weinberg equilibrium?