CourseCourse 2.1.1:2.1.1: BasicsBasics ofof EcosystemEcosystem AnalysisAnalysis

HierarchyHierarchy TheoryTheory

PawePawełł LeLeśśniewskiniewski Szczecin University of Technology, Poland

1 IntroductionIntroduction WhatWhat isis hierarchyhierarchy theorytheory ?? • A theory of system organization (King 1997) System: A collection of objects joined in a constitutive relationship of interactions that forms a whole • Originally designed to understand middle – number systems (Allen & Starr 1982)

AndAnd whatwhat areare hierarchicalhierarchical systemssystems ?? • A system organized as a system of systems within systems (King 1997) • A system composed of subsystems nested within other subsystems Nestedness: An important attribute of hierarchies

2 IntroductionIntroduction

MiddleMiddle––numbernumber systemssystems -- (hmm…?)(hmm…?)

•• HaveHave tootoo manymany componentscomponents toto describedescribe eacheach withwith itsits ownown equation…equation… •• …… andand tootoo fewfew componentscomponents toto obtainobtain reliablereliable meanmean propertiesproperties byby averagingaveraging •• IncludesIncludes mostmost ofof biologybiology !! •• SystemsSystems andand phenomenaphenomena thatthat areare idiosyncraticidiosyncratic andand difficultdifficult toto understandunderstand andand predictpredict

3 IntroductionIntroduction

TwoTwo (luckily…)(luckily…) kindskinds ofof hierarchieshierarchies

1a.1a. Costitutive:Costitutive: UnitsUnits atat eacheach levellevel areare physicalphysical partsparts ofof thethe unitsunits atat nextnext higherhigher levellevel 1b.1b. CumulativeCumulative constitutiveconstitutive hierarchieshierarchies 2.2. AggregativeAggregative:: UnitsUnits areare physicalphysical entitiesentities organizedorganized intointo collections,collections, butbut theythey areare physicallyphysically independentindependent andand

remainremain soso 4 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

TheThe SomaticSomatic HierarchyHierarchy (Eldredge(Eldredge 1985)1985)

•• SubatomicSubatomic particleparticle // atomatom // moleculemolecule // organelleorganelle // cellcell // tissuetissue // organorgan // organorgan systemsystem // individualindividual organismorganism •• UnicellularUnicellular organismsorganisms havehave nono levelslevels betweenbetween thethe cellcell levellevel andand thethe organismorganism levellevel •• NoteNote thatthat thethe hierarchyhierarchy stostopsps atat thethe organismorganism levellevel andand doesdoes notnot proceedproceed toto thethe populationpopulation levellevel !! •• ThisThis isis aa constitutiveconstitutive hierarchyhierarchy

5 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

TheThe EcologicalEcological HierarchyHierarchy • Individual organism / population / community • This is an aggregative hierarchy • Should not be combined with the constitutive somatic hierarchy !! TheThe GeneticGenetic HierarchyHierarchy • Nucleotide bases / chromosomes / genome / gene pool / collection of gene pools • This is a mixed hierarchy with both systems • Should not be combined with the constitutive somatic hierarchy

6 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

7 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

AndAnd finallyfinally thethe mostmost interesting…interesting… TheThe EcosystemEcosystem HierarchyHierarchy

•• EcosystemEcosystem // Ecoregion Ecoregion ProvincesProvinces // EcoregionEcoregion DivisionsDivisions // Ecoregion Ecoregion DomainsDomains // BiosphereBiosphere

•• ThisThis isis aa landland –– basedbased constitutiveconstitutive hierarchyhierarchy •• EcosystemEcosystem isis aa dualdual organizationorganization determineddetermined byby :: 1.1. StructuralStructural constraintsconstraints onon organismsorganisms && 2.2. FunctionalFunctional constraintsconstraints onon processesprocesses

8 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

TheThe EcosystemEcosystem HierarchyHierarchy

•• EcosystemEcosystem cancan bebe conceptualizedconceptualized asas aa nestednested spatialspatial hierarchyhierarchy (holarchy)(holarchy) ofof geographicgeographic unitsunits (holons)(holons) allall embeddedembedded withinwithin thethe biospherebiosphere •• EcosystemEcosystem hashas structurestructure andand function.function. EachEach levellevel ofof thethe ecosystemecosystem hierarchyhierarchy displaysdisplays emergentemergent propertiesproperties •• TheirTheir geographygeography isis sufficisufficientlyently homogenoushomogenous toto bebe ecologicallyecologically consistent,consistent, e.g.,e.g., aa watershedwatershed

9 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

TheThe EcosystemEcosystem HierarchyHierarchy

•• AtAt thethe basebase ofof anan ecosystem’secosystem’s hierarchyhierarchy areare individualindividual organismsorganisms •• TheseThese makemake upup speciesspecies whichwhich inin turnturn makemake upup thethe assemblageassemblage ofof speciesspecies foundfound inin thethe ecosystemecosystem (ecological(ecological community)community) •• ThereThere areare alsoalso aggregationsaggregations ofof ecosystems,ecosystems, withwith thethe largestlargest aggregationaggregation ofof allall beingbeing allall ofof thethe ecosystemsecosystems foundfound onon aa planetplanet

10 ExamplesExamples ofof HierarchiesHierarchies inin BiologyBiology

HolonsHolons

•• SelfSelf--organisingorganising entitiesentities ofof interestinterest •• WatershedWatershed,, oror perhapsperhaps aa communitycommunity,, oror thethe homehome rangerange ofof aa speciesspecies,, etc.etc. •• AA delineationdelineation isis requiredrequired •• KeyKey relationshipsrelationships betweenbetween holonsholons mustmust bebe establishedestablished •• TheThe contextcontext ofof thethe holonholon mustmust bebe exploredexplored

11 HierarchyHierarchy structurestructure

L L L

12 HierarchyHierarchy structurestructure

L L L

L+1

L+1

L L L

13 HierarchyHierarchy structurestructure L-1

L L

L+1

L+1

L L L

14 HierarchyHierarchy structurestructure

So (as we’ve seen)

•• HierarchiesHierarchies havehave aa triodictriodic structure:structure: focalfocal levellevel (L)(L),, higherhigher (L+1)(L+1) && lowerlower (L(L--1)1) •• FullyFully ordered,ordered, ranked,ranked, nestednested

•• EachEach levellevel isis mademade upup ofof unitsunits

15 HierarchicalHierarchical TheoryTheory && GeographicGeographic RepresentationRepresentation

MayMay YuanYuan Title: Professor; Associate Dean; Director of Center for Spatial Analysis Dept: Geog Phone: (405) 325-4293 E-mail: [email protected]

16 HierarchicalHierarchical TheoryTheory && GeographicGeographic RepresentationRepresentation

„Hierarchical„Hierarchical theorytheory cancan provideprovide conceptualconceptual andand logicallogical frameworksframeworks toto organizeorganize GISGIS datadata basedbased onon thethe underlineunderline processesprocesses andand theirtheir relationships,relationships, toto enhanceenhance thethe levelslevels ofof spatialspatial andand temporaltemporal informationinformation thatthat cancan bebe extractedextracted fromfrom aa GISGIS database,database, andand furthermore,furthermore, toto offeroffer aa theoreticaltheoretical foundationsfoundations forfor thethe designdesign ofof GISGIS representations.”representations.”

May Yuan

17 HierarchicalHierarchical TheoryTheory && GeographicGeographic RepresentationRepresentation

„Hierarchical„Hierarchical theorytheory isis aa ththeoryeory thatthat appliesapplies hierarchyhierarchy toto organizeorganize conceptsconcepts andand interpretinterpret ecologicalecological complexity”complexity” Ahl & Allen (1996) „„AnyAny complexcomplex systemsystem inin thethe worldworld mustmust bebe hierarchical,hierarchical, oror otherwiseotherwise wewe wouldwould havehave nono wayway toto acquireacquire it.”it.” Simon (1973)

18 HierarchyHierarchy ProcessesProcesses

SpatialSpatial patternspatterns producedproduced throughthrough timetime (t)(t) byby hierarchyhierarchy processesprocesses

t = 0 t = 1 t = 2 t = 3

Source

19 HierarchyHierarchy ProcessesProcesses

•• TheseThese occuroccur whenwhen interactioninteraction betweenbetween regionsregions isis controlledcontrolled byby thethe positionposition ofof eacheach regionregion inin aa structuralstructural dependencedependence basedbased uponupon levellevel inin aa „hierarchy”„hierarchy” •• HowHow suchsuch systemssystems generategenerate notnot onlyonly centralcentral place,place, butbut alsoalso shoppingshopping triptrip andand otherother interactiveinteractive phenomenaphenomena (Ravenstein(Ravenstein <1885>,<1885>, BerryBerry <1962>)<1962>) •• HowHow somesome stagesstages ofof thethe mmeasleseasles diffusiondiffusion processprocess inin SouthernSouthern EnglandEngland areare controlledcontrolled byby hierarchyhierarchy effectseffects

20 AA SummarySummary ofof TheThe PrinciplesPrinciples ofof HierarchyHierarchy TheoryTheory

TimothyTimothy F.F. H.H. AllenAllen

ProfessorProfessor ofof BotanyBotany andand EnvironmentalEnvironmental StudiesStudies Ph.D. (1968) University College of North Wales, University of Wales

21 AA SummarySummary ofof TheThe PrinciplesPrinciples ofof HierarchyHierarchy TheoryTheory

Robert V. O'Neill

Pioneer researcher in ecosystem theory, ecological modeling, error analysis, hierarchy theory, and landscape ecology and the development of basic applications in risk assessment and regional environmental analysis.

22 AA ShortShort AnnotatedAnnotated BibliographyBibliography ofof HierarchyHierarchy TheoryTheory

•• AllenAllen,, T.T. F.F. H.H. andand T.T. B.B. StarrStarr.. 1982.1982. Hierarchy:Hierarchy: perspectivesperspectives forfor ecologicalecological complexitycomplexity.. UniversityUniversity ChicagoChicago PressPress.. •• SaltheSalthe,, S.S. 1985.1985. EvolvingEvolving HierarchicalHierarchical SystemsSystems:: theirtheir structurestructure andand representationrepresentation.. ColumbiaColumbia UniversityUniversity PressPress,, NewNew YorkYork •• O'NeillO'Neill,, R.R. V.,V., D.D. DeAngelisDeAngelis,, J.J. WaideWaide andand T.T. F.F. H.H. AllenAllen.. 1986.1986. AA hierarchicalhierarchical conceptconcept ofof ecosystemsecosystems.. PrincetonPrinceton UniversityUniversity PressPress..

23 AA ShortShort AnnotatedAnnotated BibliographyBibliography ofof HierarchyHierarchy TheoryTheory

•• AllenAllen T.T. F.F. H.H. andand T.T. HoekstraHoekstra.. 1992.1992. TowardToward aa unifiedunified ecologyecology.. ColumbiaColumbia UniversityUniversity PressPress.. •• AhlAhl,, V.V. andand T.T. F.F. H.H. AllenAllen.. 1996.1996. HierarchyHierarchy theory,theory, aa visionvision,, vocabularyvocabulary andand epistemologyepistemology.. ColumbiaColumbia UniversityUniversity PressPress..

24 ThankThank youyou forfor youryour attentionattention !!

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