the r book references and further reading

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1、28SimulationModelsSimulationmodellingisanenormoustopic,andallIintendhereistodemonstrateafewverysimpletemporalandspatialsimulationtechniquesthatgivetheflavourofwhatispossibleinR.Simulationmodelsareusedforinvestigatingdynamicsintime,inspace,orinbothspaceandtimetogether.Fortemporaldynamicswem

2、ightbeinterestedin:
thetransientdynamics(thebehaviourafterthestartbutbeforeequilibriumisattained–ifindeedequilibriumiseverattained);
equilibriumbehaviour(afterthetransientshavedampedaway);
chaos(random-looking,butactuallydeterministictemporaldynamicsthatareextremelysensitivetoinitialcondi

3、tions).Forspatialdynamics,wemightusesimulationmodelstostudy:
metapopulationdynamics(wherelocalextinctionandrecolonizationofpatchescharacterizethelong-termbehaviour,withconstantturnoverofoccupiedpatches);
neighbourrelations(inspatiallyexplicitsystemswheretheperformanceofindividualsisdeterm

4、inedbytheidentityandattributesoftheirimmediateneighbours);
patterngeneration(dynamicalprocessesthatleadtothegenerationofemergent,butmoreorlesscoherentpatterns).28.1Temporaldynamics:ChaoticdynamicsinpopulationsizeBiologicalpopulationstypicallyincreaseexponentiallywhentheyaresmall,butindivi

5、dualsperformlesswellaspopulationdensityrises,becauseofcompetition,predationordisease.Inaggregate,theseeffectsonbirthanddeathratesarecalleddensity-dependentprocesses,anditisthenatureofthedensity-dependentprocessesthatdeterminesthetemporalpatternofpopulationdynamics.Thesimplestdensity-depen

6、dentTheRBook,SecondEdition.MichaelJ.Crawley.©2013JohnWiley&Sons,Ltd.Published2013byJohnWiley&Sons,Ltd.894THERBOOKmodelofpopulationdynamicsisknownasthequadraticmap.Itisafirst-ordernon-lineardifferenceequation,N(t+1)=λN(t)[1−N(t)],whereN(t)isthepopulationsizeattimet,N(t+1)isthepopulationsize

7、attimet+1,andthesingleparameter,λ,isknownastheper-capitamultiplicationrate.Thepopulationcanonlyincreasewhenthepopulationissmallifλ>1,theso-calledinvasioncriterion.Buthowdoesthesystembehaveasλincreasesabove1?Webeginbysimulatingtimeseriesofpopulationsfordifferentvalue