Practice Set Answer Key. Q1: In a population of insects, all the individuals reproduce once a year at the same time, and then die.
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1 PracticeSetAnswerKey GeometricPopulationGrowth Q1:Inapopulationofinsects,alltheindividualsreproduceonceayearatthesame time,andthendie. Whattypeofreproductionisseeninthiscase? Semelparous,pulsed Whatistheappropriatemodelofgrowthforthistypeoforganism? Geometricgrowth Thepopulationsizeisinitially478,oneyearlateritis600.Whatisthegeometric rateofincreaseforthispopulation? Nt=478 Nt+1=600 λ=nt+1/nt =600/478 = 1.26 Whatwillthepopulationbeafter20years,assumingnolimitstogrowth? Nt=N0λ t N20=478(1.26) 20 =48622individuals LogisticPopulationGrowth Theblack footedferret(mustelanigripes),anendangeredspeciesinnorthamerica, wasintroducedtograsslandsnationalpark,saskatchewanin2008.youhavebeen hiredbyparkscanadatodocumenthowwelltheseferretsareadaptingtotheirnew home,andifandhowtheirpopulationisgrowing. YouwanttofollowacohortofthefirstferretsbornintheParkoverafive year period.usinganon invasivemethodthatdoesnotcompromisethesurvivalofthe ferrets,youtagthefemalekits(babyferrets),releasethembackintothewild,and thenmonitortheirprogramforaperiodoffiveyears. Youattainthefollowingdata: Year Numberof Average Average female numberof numberof ferretsin littersper femalekits thecohort female perlitter N/A
2 N/A Q1:Whatisthenetreproductiverate(RO)forafemaleferretinthispopulation? Whatexactlydoesthisvaluemean?Explain. A: X Bx Mx BxMx X(BxMx) R0=Σbxmx RO= RO=4.93 Thisvaluemeansthatafemaleferretinthispopulationwillproduce4.93kitsinher lifetime. Q2:Whatisthegenerationtimeforafemaleferretinthispopulation?Whatdoes thisvaluemean? A:T=Σxlxmx/R0 T=( )/4.93 T=1.85 Thisvaluemeansthatitwilltakeaferret1.85yearsfromthetimesheisborntothe timesheproducesanotherferret(aka replaceherself). Q3:Whatisthepercapitarateofincreaseinthispopulation?Whatdoesthervalue mean?isthispopulationgrowingordeclining? A:r=lnR0/T r=ln(4.9)/1.85 r=1.59/1.85 r=0.86 Ther valuerepresentsthenumberofbirthsminusthenumberofdeathsina population.thispopulationisgrowing,becausethervalueislargerthanzero.
3 Q4:Plotasurvivorshipcurveforthisferretcohort(Agevs.Survivorship).Whattype ofgrowthcurvedoferretpopulationshave? &!!"!"#$%&'()')%&&%*+'./'-'0(1(&*'!"#$%&'()')%&&%*+' %#!" %!!" $#!" $!!" #!"!"!" $" %" &" '" #" (",%-&+' Q5:Imaginetheintrinsicrateofincrease(rmax)inthispopulationis0.8,andthatthe environmenthasacarryingcapacityof350ferrets.howmanyferretswilltherebe inthefollowingyear,iftheinitialpopulationsizeis256? A:dN/dt=rmaxN(1 (N/K)) dn/dt=(0.8)x256(1 (256/350)) dn/dt=(0.8)x256(0.269) dn/dt=(0.8)x68.86 dn/dt=55.09 Inthenextyear,therewillbe311ferrets(256+55)inthepopulation. Lotka VoltaraInterspeciesCompetition DuringtheLateCretaceousofNorthAmerica(~74Ma),thereweretwolarge predatorsfromthefamilytyrannosauridaepresent:gorgosauruslibratusand Daspletosaurustorosus.Imaginethatbothspeciesarehighlyterritorialandthatboth speciessharethesamemainfoodsource,theduckbilleddinosaurlambeosaurus. **Recallthat α (canalsobewrittenα12)asistheeffectofspecies2onspecies1. Similarly,β(canalsobewrittenα21)isastheeffectofspecies1onspecies2.** "TheGorgosauruspopulationhasanrmaxof0.25,acarryingcapacity(K)of85,and acompetitiveability(β)of0.6.theinitialpopulationsizeis65.
4 TheDaspleotosauruspopulationhasanrmaxof0.32,acarryingcapacity(K)of80, andcompetitiveability(α)of0.5.theinitialpopulationsizeis35." Q1:WhatisthedN/dtforeachspecies? A:dN1/dt=r1maxN1[(K1 N1 αn2)/k1 =(0.25x65)x(85 65 (0.5x35)) 85 =0.478 dn2/dt=r2maxn2[(k2 N2,βN1)/K2] =(0.32x35)x(80 35 (0.6x65)) 80 =0.840 Q2:Drawagraphthatillustratesthepossibleoutcomesofthiscompetition(Seepg. 167ofKreb). K 1 /" = 170 N 2 K 2 =80 K 1 =85 K 2 /! = Q3:Istherecompetitiveexclusiongoingoninthispopulationatthispoint?Ifnot, whattypeofequilibriumisthis stableorunstable? N 1
5 A:Thisisastableequilibrium,becauseneitherspeciescangrowlargeenoughto excludetheother.(k2/β)is133,k1is85,(k1/α)is170,andk2is80. Q4:Rearrangetheequationtodeterminethepopulationsizeina)the Daspleotosaursandb)theGorgosaurs,atthepointinwhichtheisoclinesofzero populationgrowthcrossonthegraph. A:K1 N1 an2=k2 N2 bn1 (K1 N1)/a=K2 bn1 K1 N1=aK2 abn1 N1 abn1=k1 ak2 N1 0.3N1=85 (0.5)80 0.7N1=45 N1=~64 N2=80 (0.6)64=~42 Predator/PreyEquations Q1.SupposethedynamicsbetweenGodzilla(predator)andthecitizensof Metropolis(prey)canbemodeledbyLotka VolterraEquations. Part1.WhatconstantdetermineshowmanycitizensareconvertedtoGodzillas? A.Theconstantcisthepreytopredatorconversionrate. Part2.Ifthedeathrate,dpofGodzillasis0.2andthereare20GodzillasattimeT0, howmanywilltherebeatt1? *ThisquestionisonlyaskingaboutthedeathrateofGodzilla,notofthecitizensof Metropolis.* A. dpnp (0.2)*(20)=4 20 4=16 Part3.Ifc=0.5,dp=0.2andthepredationrate,p=0.05,howmanyGodzillaswill therebeifattimet1ifatt0thereare50godzillasand100citizens? A. dnp/dt=cpnhnp dpnp (0.5)*(0.05)*(50)*(100) (0.2)(50) =115 NGodzillas=115(atNt+1)+50(atN0)=165. Q2:Howmanycatsmustbepresentifapopulationof300micewithapercapita rateofincreaseof1.5declinestoapopulationof150micewhencatsthathavea capturemiceataratep=0.05areintroducedtothesystem?
6 (Lotka Volterrapredatorpreyequation) dnh/dt=rhnh pnhnp 150=(1.5)(300) (0.05)(300)Np 150=450 15(Np) 600= 15(Np) 40=Np TrophicLevels Q1.Inafoodchainwithfourtrophiclevels(primaryproducer,primaryconsumer, secondaryconsumer,tertiaryconsumer,primaryproducersproduce3500 kcal/m 2 /yr.iftheecologicalefficienciesareasfollows: EE1:primaryproducertoprimaryconsumer:0.15 EE2:Primaryconsumertosecondaryconsumer:0.09 EE3:Secondaryconsumertotertiaryconsumer:0.07 Howmanykcal/m 2 /yraretransferredtothesecondaryconsumer?tothetertiary consumer?whatisthetotalecologicalefficiencyofthesystem? Totheprimaryconsumer:EE1*Pn 1=0.15*3500=525kcal/m 2 /yr Tothesecondaryconsumer:EE2*Pn=0.09*525=47.25kcal/m 2 /yr Tothetertiaryconsumer:EE3*Pn+1=0.07*47.25=3.31kcal/m 2 /yr TotalEE=3.31/3500= (i.e.theproductofalltheEEs(0.15*0.09*0.07)) EcologicalEfficiencyandEnergyTransfer Q1.Onewaytostudyecosystemsistofocusontheenergytheycontain.Asenergy istransferredfromonetrophicleveltoanother,someofitislost.theefficiency withwhichthistransferoccursiscalled ecologicalefficiency or trophic efficiency.itisgenerallyexpressedas: ProductionfortrophiclevelN/ProductionfortrophiclevelN 1 a)whatistheapproximatepercentenergytransferusuallyobservedbetween trophiclevels? A:10%(canvaryfrom5 20%) b)whatarethethreecomponentsofecologicalefficiencyandhowaretheyusedto calculatetheoverallecologicalefficiency?
7 Consumptionefficiency(In/Pn 1):Theproportionofthetotalavailableproductionin onetrophiclevelthatisactuallyconsumedbythenexttrophiclevel. Assimilationefficiency(An/In):Theproportionoftheconsumedproductionthatis assimilatedacrossthegutwall(ratherthanexcreted). Productionefficiency=(Pn/An):Theproportionofassimilatedproductionthatis transformedintobiomass(asopposedtolostasheat). Ecologicalefficiencyistheproductofthesethreeefficiencies: CE*AE*PE=Pn/Pn 1 c)youarestudyingagrasslandfoodwebwhereprimaryproductionis1000 kcal/m 2 /year.agrazinganimalconsumes258kcal/m2/year,excretes75%ofthis consumption,andtransformstheremainderintobiomasswithanefficiencyof2%. Whatistheecologicalefficiencyofthetransferfromtheprimaryproducertothe primaryconsumer? CE= (In/Pn 1)In=258,Pn 1= /1000=0.258 AE= =0.25 PE= (Pn/An)=0.02(directlyfromquestion) EE= CE*AE*PE=0.258*0.25*0.02= (i.e.lessthan1%oforiginalNPPgoes intothesecondtrophiclevel). Q2.Asyoustudyforthisexam,youdrank2cupsofcoffeeinthefirsthour,and1 cupofcoffeeeveryhourafterthat.thereareabout80mgofcaffeinepercupof coffee,andyourbodyeliminatescaffeineatarateof80mgperhour.thismeans that,atanygiventime,youhave80mgofcaffeineinyourbody.suddenly,you realizethatthisisanalogoustoanecologicalconceptregardingnutrientcycling. a)whatisthisconcept?whatareyourbody,thelengthoftimeagivencaffeine moleculestaysinitandtherateatwhichcaffeineisleavingyourbodyanalogousto? Thisisanalogoustotheconceptofreservoirs,residencetimeandfluxes(when consideringnutrientcycles,forexample).yourbodyisareservoirofcaffeine,the lengthoftimeacaffeinemoleculeisinyourbodyistheresidencetimeandtherate atwhichitisleavingyourbodyisaflux. b)afteryoursixhoursofstudying,whatistheamountofcaffeineinyourbody?
8 Thisisthe reservoir :Itisalways80mg. c)whatisthatrateatwhichcaffeineenters/leavesyourbodyandwhatdoesthis represent? TheFlux=mass/time=80mgenteringorleavingyourbody/hour d)howlongdoesagivencaffeinemoleculestayinyourbody? ThisistheMeanResidenceTime=reservoir(mass)/flux(mass/time) =80/80=1hour
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