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1、ThePopulationofTheShillCraneAbstractWeconstructthreemodelstostudythepopulationoftheshillcraneunderthreedifferentgrowthratesdeterminedbytheenvironmentconditionsdemographicstochasticity.Model1dealswiththepopulationwithouta

2、nyromelements.Firstwehavesomeassumptionssuchastheinitialpopulationtheaveragereproductionratetheaveragedeathrate.Sothisisadeteministicmodelwechoosetoproduceatablegraphrepresentingafiveyeardeterministicmodelofthecranepopul

3、ation.Model2studiesthepopulationwiththeeffectsofenvironmentalstochasticity.Wefirstassumethattherearealso100cranesinitiallyweconsideronlytheeffectsoftheenvironmentalstochasticity.Thenweusesomesoftwarestogenerateaunifmromv

4、ariabletocompletethesimulationofthecatastrophe.Finallyweusebothtablesgraphstodescribetheresultingmodel.Model3discussesthepopulationconsideratedwiththedemographicstochasticity.Firstweassumethattherearealso100cranesinitial

5、lyweconsideronlytheeffectsofthedemographicstochasticity.Accdingtotheproblemthebirthdeathratesaregenerallyconsideredtobenmallydistributed.Sowegeneratenmalromvariablesfthebirthdeathrateparametersateachtimestep.Atlastwealso

6、choosetousesometablesgraphstodescribethefinalmodel.IntroductionWetacklethreemainsubproblems:?thepopulationoftheshillcranewithsomedeterministicdata?thepopulationoftheshillcranewithenvironmentalstochasticity?thepopulationo

7、ftheshillcranewithdemographicstochasticity.Assumptions?ThereisonlyenvironmentalstochasticitytobeconsideredwhenbuildingModel2theshillcranesarealwayslivingintheinvariantgeographicspace.?Thereisonlydemographicstochasticityt

8、obeconsideredwhenbuildingModel3thatistosaytheshillcranescannotbeinfluencedbyanyothervariables.?Theshillcranes’livingenvironment’sgeographicalconditionisnmalsoistheotheranypotentialvariables.01234560100200300400500600Year

9、sCranePopulationFIGURE2GraphoftheCranePopulationwithoutStochasticity.Model2:EnvironmentalStochasticityFirstweconsiderhowtheenvironmentalstochasticityaffecttheshillcranepopulation.Environmentalstochasticityfthecranepopula

10、tionwilltakethefmofacatastrophesuchasflooddroughtfireetcthusbringsoutvariationsinbirthdeathrate.Wehaveknownthatacatastropheaffectscranesbyloweringthebirthrateby40%increasingthedeathrateby25%.Thesecatastrophesoccurromlyon

11、averageonceevery25years.Westillassumethatthereare100cranesinitiallyweconsideronlytheeffectsoftheenvironmentalstochasticity.Sincetheenvironmentalstochasticityoccursonaverageonceevery25yearswegenerateaunifmlydistributedrom

12、variablefeachtimestepfromtheinterval(01).Wesaythatacatastropheoccursifthevalueofthisromvariableislessthanequalto0.04doesn’toccurifthevalueisgreaterthan0.04.HereweuseRNtorepresenttheromnumbersintheinterval(01).Ifthebirthr

13、atewillreduceby40%thedeathratewillincreasebyRN≤0.0425%Ifthebirthratethedeathrateareequaltotheinitialvalue.RN0.04bothTABLE2shows40simulationrunsoftheCranePopulationwithenvironmentalstochasticity.TABLE3showsthecranepopulat

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