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Basic metrics of food webs. A pitcher plant ( Nepenthes albomarginata ) food web . Nepenthes albomarginata. S = 19 species L max = 19*18/2 = 171 possible links between two species L = 35 realized links between two species Connectance : C = 35/171

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Basic metrics of foodwebs

  • A pitcher plant (Nepenthes albomarginata) food web

Nepenthes albomarginata

S = 19 species

Lmax = 19*18/2 = 171 possiblelinksbetweentwospecies

L = 35 realizedlinksbetweentwospecies

Connectance: C = 35/171

Ch = 100 totallength of allfoodchains

Li = 40 isthetotalnumber of chains

ChL = 100/40 = 2.5 istheaveragechainlength

L/S = 35/19 = 1.8 isthemeannumber of links per species


Foodwebmetricstranslatedintomatrixmetrics

N = 28

Fill = 28/80=0.35

Dm=28/10=2.8

Dn=28/8=3.5


Metrics of speciesassociationsinbiogeographicmatrices

TheC-score as a metric of negativeassociations

Checkerboards

TheClumping-score as a metric of positiveassociations

TheTogetherness-score as a metric of nicheoverlap


Theadditivenature of theC-score

Numbers of checkerboards for entrieswithinthearea AT are a measure of spatialspeciesturnover.

Numbers of checkerboards for entrieswithinthearea ATC are a measure of turnover independent speciessegregation.

CMixed = CS – CTurn - CSegr.

Therankcorrelation of matrixentriesis a metric of spatialturnover.

  • 11 21 32 12 2…….7 108 10

R2is a moreliberalmetricthanCturn.

R2 = 0.347

Thecorrelation of ordinationscoresisalso a metric of turnover but even less selective.


Rangesizecoherence

Coherentrangesize

Scatteredrangesize

Thereare 17 embeddedabsences.

Thenumber of embeddedabsencesis a measure of speciesrangesizecoherence.

Themetricdependsstrongly on theordering of rows and columns


Themeasurement of nestedness

Thedistanceconcept of nestedness.

Sort thematrixrows and olumnsaccording to some gradient.

Define an isoclinethatdividesthematrixinto a perfectlyfilled and an empty part.

Thenormalizedsquared sum of relativedistances of unexpectedabsences and unexpectedpresencesisnow a metric of nestednessis.


Nestedness based on Overlap and Decreasing Fill (NODF)

NODF is a gap basedmetric and moreconservativethantemperature.


The disorder measure of Brualdi and Sanderson

Ho many cellsmust be filledoremptied to achieve a perfectlyorderedmatrix.

TheBrualdiSandersonmeasureis a count of thisnumber

Discrepancyis a gap countingmetric.


How to measurespeciesaggregation?

dij

Nearestneighbormetrics

Nearestneighbouris a presence – absencemetric

Compartmentedmatrix

NND hasweakpowerathighermatrixfill

Joincountstatistics

Othermetricsproposed:

Morisita

Simpson

Soerensen

Block variance

Ordinationscorevariance

Marginalvariances

A sum of cellentriesaround a focalcellmultiplied by theentry of thefocalcell

Joincountoperates on presence – absence and abundancematrices

Thesemetricshaveverylowpower a moderate to smallmatrixsize and high orlowmatrixfill.


Abundancebasedmetrics

TheC-scoreextension

The metric CA is a count of the number of abundance checkerboards in the matrix.

Other 2x2 submatricescatchmatrixpropertiesthathave not welldefinedecologicalmeaning.


Nestednessinabundancematrices

Themetricis a sum of allpairsinthematrix (first sortedaccoding to speciesrichnessthensortedaccording to weights), wheretheweightintherow/column of lowerspeciesrichnessissmallerthantheweightintherow/column of higherspeciesrichness


A completetable of methods for co-occurrenceanalysis


Patterndetectioninlargematrices

Pajek: software for socialnetworkanalysis

WAND: ecologicalnetworkanalysis

Theseprogramsuseclusteranalysis and ordination to sort thematrixaccording to numbers of occurrences. Didstancemetricsarethenused to identifycompartments.

Theygeneratehypothesesaboutmatrixstructure.

They do not fullyallow for statisticalinference.

KliqueFinder: software for compartmentanalysis


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