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1、Lecture10:PopulationGrowthtjhlqz起重机立体停车设备电动葫芦hygy1688衬塑复合管涂塑复合管钢塑复合管消防涂覆钢管WorldpopulationPopulationgrowthDefinition:howthenumberofindividualsinapopulationincreasesordecreaseswithtimeGrowthiscontrolledbyratesofbirth,immigrationanddeathandemigration.Openorclosedpopulation:noimmigrationandemigration,o
2、rimmig.=emig.Inclosedpopulation,growthisdeterminedbybirthrateanddeathrate.10.1PopulationgrowthreflectsthedifferencebetweenratesofbirthanddeathModeldevelopmentApopulationoffreshwaterhydragrowinginanaquariuminthelaboratory.PopulationsizeN(t)whentimeist.Thisisaclosedpopulation.Populationsizechangeisre
3、latedtobirthrate(b)anddeathrate(d)dN/dt=(b-d)N=rNThedifferencebetweenbirthrateanddeathrateistheintrinsicgrowthrate(r)(instantaneouspercapitarateofgrowth).r=b-dInaclosedpopulation,populationsizechangeisrelatedtobirthrate(b)anddeathrate(d)Thedifferencebetweenbirthrateanddeathrateistheintrinsicgrowthr
4、ate(r)(instantaneouspercapitarateofgrowth).r=b-dPopulationgrowthisrelatedtothisintrinsicgrowthrate(r).ExponentialpopulationgrowthEquations:1)dN/dt=rN(differentialequationform)2)N(t)=N(0)exp(rt)(exponentialgrowthmodel)Conditions:InitialpopulationissmallNofoodorresourcelimitationAnexampleReindeer,St.
5、Paul,Alaska.Startedin1910withonly4malesand22femalesIn1940,therewerenearly2000Whoopingcrane,anendangeredspecies recoveredfromnearextinctionin1941Howtocalculater?Software,Excel(trendline)AransasNationalWildlifeRefugePropertiesofexponentialgrowthrdeterminestheshapeofthegrowth.r=0,nochangeinpopulation
6、sizer<0,decreaseinpopulationsize;r>0,increaseinpopulationsize.PropertiesofexponentialgrowthWidelyusedinbiologyN(t)=N(0)Exp(rt)Giveatimet,wecanpredictthepopulationsize.AnExample:Deerpopulation:N(0)=300,r=0.5,after5years,what’sthepopulationsize?N(5)=N(0)Exp(rt)=300*exp(0.5*5)=3655(495,815,1344,2216,3
7、655)t=10,?Predictionofpopulationgrowth4452410.2LifetableLifetableisanage-specificaccountofmortality.Purposeoflifetable:toprovideaclearandsystematicpictureofmortalityandsurvivalwithinapopulationHowtoconstruc
