lecture-16得克萨斯生态学课件

PopulationGrowthandLimits(Ch.52)Populationgrowth:(Pg.1158) Whatispopulationgrowth?Populationgrowth:(Pg.1158)Whatispopulationgrowth? Thechangeinthenumberofindividuals inapopulationthroughtime.Populationgrowth:(Pg.1158)Twomajorfactorsthataffectpopulationgrowth: 1)Birthrates 2)DeathratesDescribingPopulationGrowthwithMathematicalModels(Pg.1158-1163)DescribingPopulationGrowthwithMathematicalModels(Pg.1158-1163)Weconsiderchangesinpopulationsizeover time-therefore,therehastobeatimeinterval2)Forsimplicity,wewillassumeimmigrationandemigrationareequal3)BirthratesanddeathratesareourvariablesSimpleVerbalModel:(Pg.1159)Changeinpopulation Birthsduring DeathsduringSizeduringtimeinterval=timeinterval-timeintervalSimpleVerbalModel:(Pg.1159)Changeinpopulation Birthsduring DeathsduringSizeduringtimeinterval=timeinterval-timeintervalN=PopulationSize

N=changeinpopulation sizet=time

t=timeinterval (appropriatetolifespan andgenerationtimeof species)changeSimpleVerbalModel:(Pg.1159)Changeinpopulation Birthsduring DeathsduringSizeduringtimeinterval=timeinterval-timeintervalRewriteVerbalmodelas,N/t=B-D B=absolute D=absolute #ofbirths #ofdeaths intimeintervalintime intervalN/t=B-DB=bNwhereb=thenumberofoffspring producedperyearbyan averagememberofthe population =(theannualpercapitabirthrate)Absolute#ofbirthsPopulationsizeN/t=B-DB=bNEx. 1)Ifpopulationsize=1000 2)thispopulationexperiences34births/year Whatisthepercapitabirthrate?

B=bNEx. 1)Ifpopulationsize=1000 2)thispopulationexperiences34births/yearPlugintoequation: B=bN

34=(b)1000 34/1000=b

b=0.034percapita birthrateN/t=B-D

IfB=bN,

WhatdoesDequal?

N/t=B-DB=bN WhatdoesDequal? D=dN

wheredisthepercapita deathrateAbsolute#ofdeathsN/t=B-DGivenB=bN andD=dNWecanwrite…N/t=bN -dN

N/t=B-DGivenB=bN andD=dNWecanwrite…N/t=bN -dN

Howcouldwesimplifythisexpression?

N/t=B-DN/t=bN -dN

Howcouldwesimplifythisexpression?

PullNout,N(b–d)

N/t=bN -dNPullNout,N(b–d) r=b-d

r=differenceinpercapita birthanddeathrates

(r=percapitapopulationgrowth)Ecologistsareinterestedinoverallchangesinpopulationsize,so“r”isusedinmodelsr=b-d r=differenceinpercapita birthanddeathrates (r=percapitapopulationgrowth)“r”tellsuswhetherapopulationisgrowing(+values)ordeclining(-values)Zeropopulationgrowth(ZPG)iswhenb=d.Rewritepopulationgrowthequationas…N/t=bN -dNN/t=

N(b–d) usingr=b–dN/t=rNN/t=rNEcologistsusuallyusethedifferentialcalculusexpression

dN/dt=rNwhichexpressesinstantaneousgrowthrates=growthrateatanygivenpointintime.Draw–slopedN/dt=rNThemaximumpopulationgrowthrateiscalledthe

Intrinsicrateofincrease(rmax)Themaximumpopulationgrowthrateiscalledthe Intrinsicrateofincrease(rmax)Populationgrowthatrmaxiscalled

exponentialpopulationgrowthIfresourcesarenotlimited,anidealpopulationgrowsexponentiallyrmax=1rmax=0.5Pg.1160J-shapedcurvermaxisinfluencedbylifehistoryfeatures: 1)Ageatfirstreproduction 2)numberofoffspringproduced 3)howwelloffspringsurvivermaxisinverselyproportionaltogenerationtimeDosmallerorlargerorganismshavehigherrmax?Dosmallerorlargerorganismshavehigherrmax?SMALLERExponentialgrowthischaracteristicofpopulations…thatareintroducedintoneworunfilledenvironmentsthatarereboundingfromacatastrophiceventButwhataboutallotherpopulations? Dotheygrowexponentially?Butwhataboutallotherpopulations? Dotheygrowexponentially?

NONextModelofpopulationgrowth:(Pg.1160) “Logisticpopulationgrowth”which incorporatescarryingcapacityNextModelofpopulationgrowth: Logisticpopulationgrowthwhich incorporatescarryingcapacityCarryingcapacity(K)–themaximumpopulationsizethataparticularenvironmentcansupportwithnonetincreaseordecreaseoverarelativelylongperiodoftime(Pg.1160)“K”isnotanabsolute;Itvariesovertimeandspacewiththeabundanceoflimitingresources(ENVIRONMENTDEPENDENT!!!)Logisticpopulationgrowth: 1)incorporateschangesin“r”asNapproachesK 2)allowsrtovaryfromrmaxtozero 3)populationgrowthisrapidwhenN<<K 4)populationgrowthslowswhenNisclosetoKBuildingthemathematicalmodel:Startwith:

dN/dt=rNNewexpressions:IfK=maximumpopulationsizeforagivenenvironmentthen,K–N=the#ofadditionalindividualstheenvironmentcansustain

Buildingthemathematicalmodel:

Startwith:

dN/dt=rNNewexpressions: K–NTherefore,(K–N)/Ktellsuswhatfraction

ofKisstillavailableforpopulationgrowth

ex.Using(K–N)/KEx. IfK=1000,andN=10, ThenwhatfractionofKis stillavailableforpopulation growth?Using(K–N)/KEx. IfK=1000,andN=10, ThenwhatfractionofKis stillavailableforpopulation growth? (1000–10)/1000=.99or99%

ex.Using(K–N)/KEx. IfK=1000,andN=900,

ThenwhatfractionofKis stillavailableforpopulation growth?Using(K–N)/KEx. IfK=1000,andN=900,

ThenwhatfractionofKis stillavailableforpopulation growth?

(1000–900)/1000=.10or10%Using(K–N)/Kin

dN/dt=rN

Weget… Pg.1161

dN/dt=rN(K–N)/KThismodelreducesrasNincreasetowardK

ex.Pg.1161x=Pg.1161x=PercapitagrowthrateLogisticPopulationGrowth(Pg.1162):S-shapedcurveNaturalorlaboratorypopulationsfitthismodelreasonablywellHowever,thismodeldoesnotconsidertheeffectsofpredatorsandcompetitors,somanynaturalpopulationsdeviatefromthismodelSomeassumptionsofthelogisticmodel:1)populationsapproachKsmoothly–thereisusuallyaLAGTIMEinbetweenresourcedepletionanddecreasedbirthrates,somostpopulationsovershootK.ThisresultsinpopulationsoscillatingaroundKTimeNKovershootoscillationsSomeassumptionsofthelogisticmodel:1)populationsapproachKsmoothly–thereisusuallyaLAGTIMEinbetweenresourcedepletionanddecreasedbirthrates,somostpopulationsovershootK.ThisresultsinpopulationsoscillatingaroundK2)NotallpopulationreachorexistnearK.Manyinsectsandothersmall,rapidlyreproducingorganismsthataresensitivetoenvironmentalfluctuationsareinfluencedbyphysicalvariablesliketemperatureandmoisturewellbeforetheyreachKPopulationgrowthmodelsinfluencelifehistorycharacteristics(generalguidelinesasmostorganismsexhibitintermediatetraits) (Pg.1163)K–selectedpopulations:equilibriumpopulationsr-selectedpopulations:opportunisticpopulationsKnowTableNKKNK-selectedr-selectedWhatlimitspopulations?(Pg.1163)Whatlimitspopulations?Twobasictypesoffactors: 1)densitydependent

2)densityindependentdensitydependentfactors=populationregulationfactorsthatintensifyaspopulationdensityincreases (Pg.1164)Intraspecificcompetition–therelianceofindividualsofthesamespeciesonthesamelimitedresourcesSo,aspopulationsizeincreases,theavailableresourcesdecrease,andcompetitionforresourcesincreasesEx.CompetitionforresourcesCompetitioninfluencessurvivalCompetitionincreasesHighDensitycanresultin: 1)crowding 2)fewerresourcesforeachindividual 3)weakoffspring(duetoresourcesputintotheirproduction) 4)Build-upoftoxinsandwasteinenvironmentwhich negativelyinfluencesindividuals 5)Increase