Community and gradient analysis: Matrix approaches in macroecology

Nicolaus Copernicus University – Department of Animal Ecology

Community and gradient analysis: Matrix approaches in macroecology

The world comes in fragments

Biogeography

Species occurrences across a fragmented landscape

1. Islands2. Lakes3. River bed and irrigation systems4. Mainlands

continental distributionshabitat islandsmountain tops and valleysfragmented landscapesscattered distributed host plants

5. Cities and anthropogenic habitats6. Routes of species invasion7. Experimental plots (natural, macro-,

mesocosm experiments)

Galapagos Islands

The Darwin finches

The Darwin finches (Sanderson, Am. Scient. 2000)

Species

Sey

mou

r

Bal

tra

Isab

ella

Fer

nand

ina

San

tiago

Rab

ida

Pin

zon

San

ta C

ruz

San

te F

e

San

C

risto

bal

Esp

anol

a

Flo

rean

a

Gen

oves

a

Mar

chen

a

Pin

ta

Dar

win

Wol

f

Geospiza magnirostris 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1

Geospiza fortis 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0

Geospiza fulignosa 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0

Geospiza difficilis 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1

Geospiza scandens 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0

Geospiza conirostris 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0

Camarhynchus psittacula 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0

Camarhynchus pauper 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

Camarhynchus parvulus 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0

Platyspiza crassirostris 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0

Cactospiza pallida 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0

Cactospiza heliobates 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Cerrthidea olivacea 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Islands

A presence – absence matrix reflects the distribution of species across sites

The distribution of ground beetles across Mazurian lake islands

Species/Sites wros wron wil ter swi sos mil lip kor hel guc gil ful dab 3pog 2pog 1pogPterostichus nigrita (Paykull) 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1Platynus assimilis (Paykull) 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0Amara brunea (Gyllenhal) 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0Agonum lugens (Duftshmid) 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1Loricera pilicornis (Fabricius) 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0Pterostichus vernalis (Panzer) 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0Amara plebeja (Gyllenhal) 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0Badister unipustulatus Bonelli 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0Lasoitrechus discus (Fabricius) 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0Poecilus cupreus (Linnaeus) 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0Amara aulica (Panzer) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0Anisodatylus binotatus (Fabricius) 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0Bembidion articulatum (Panzer) 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0Clivina collaris (Herbst) 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0Panagaeus cruxmajor (Linnaeus) 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0Poecilus versicolor (Sturm) 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0Pterostichus gracilis Dejean) 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0Stenolophus mixtus 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0Pseudoophonus rufipes (De Geer) 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1Harpalus latus (Linnaeus) 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0Agonum duftshmidi Shmidt 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1Harpalus solitaris Dejean 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0

Row totals13119766542211111111

13732

Colums totals 3 4 7 5 3 9 8 9 4 3 4 10 7 7 6 5 4 98

In presence – absence matrices zeros denote species absence, ones denote species presences.

Absences might be caused either by real absences of species or by incomplete detection.


Biogeographic matrices are static descriptions of colonization patterns.

Colonization and extinction are permanent processes. In reality presence – absence pattern change whole the time.

It makes therefore a difference if we use temporal point data to construct our matrices or a time series.

Time series data contain much more entries but might be ecologically unrealistic.

Species/Sites wros wron wil ter swi sos mil lip kor hel guc gil ful dab 3pog 2pog 1pog Row totalsPterostichus nigrita (Paykull) 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 13Platynus assimilis (Paykull) 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 11Amara brunea (Gyllenhal) 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 9Agonum lugens (Duftshmid) 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 7Loricera pilicornis (Fabricius) 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 6Pterostichus vernalis (Panzer) 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 6Amara plebeja (Gyllenhal) 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 5Badister unipustulatus Bonelli 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 4Lasoitrechus discus (Fabricius) 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 2Poecilus cupreus (Linnaeus) 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 2Amara aulica (Panzer) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1Anisodatylus binotatus (Fabricius) 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1Bembidion articulatum (Panzer) 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1Clivina collaris (Herbst) 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1Panagaeus cruxmajor (Linnaeus) 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1Poecilus versicolor (Sturm) 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1Pterostichus gracilis Dejean) 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1Stenolophus mixtus 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1Pseudoophonus rufipes (De Geer) 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 13Harpalus latus (Linnaeus) 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 7Agonum duftshmidi Shmidt 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 3Harpalus solitaris Dejean 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 2Colums totals 3 4 7 5 3 9 8 9 4 3 4 10 7 7 6 5 4 98

Dispersion

Extinction

Species/Sites wros wron wil ter swi sos mil lip kor hel guc gil ful dab 3pog 2pog 1pog Row totalsPterostichus nigrita (Paykull) 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 13Platynus assimilis (Paykull) 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 11Amara brunea (Gyllenhal) 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 9Agonum lugens (Duftshmid) 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 8Loricera pilicornis (Fabricius) 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 10Pterostichus vernalis (Panzer) 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0 11Amara plebeja (Gyllenhal) 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 14Badister unipustulatus Bonelli 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 14Lasoitrechus discus (Fabricius) 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 11Poecilus cupreus (Linnaeus) 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 11Amara aulica (Panzer) 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 10Anisodatylus binotatus (Fabricius) 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 11Bembidion articulatum (Panzer) 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 13Clivina collaris (Herbst) 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 12Panagaeus cruxmajor (Linnaeus) 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 12Poecilus versicolor (Sturm) 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 13Pterostichus gracilis Dejean) 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 13Stenolophus mixtus 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 10Pseudoophonus rufipes (De Geer) 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 16Harpalus latus (Linnaeus) 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 10Agonum duftshmidi Shmidt 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 12Harpalus solitaris Dejean 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 7Colums totals 15 16 17 11 14 11 10 11 14 19 19 11 20 14 18 16 15 251

Time axis

Time series matrices have too many entries and do not reflect real ecological patterns.

They do not give information on real species interactions

For a proper assessment of

ecological patterns we need point

data.

The comparison of point and time series

matrices gives information about dispersion rates.

The distribution of ground beetles across Mazurian lake islands


Abundance matrices contain additional information. Abundance matrices might be based on point or averaged time series data.

Mutual interaction matrices

Food web example

1. Food webs2. Host – parasite networks3. Plant – herbivore networks4. Pollination networks5. Predator – prey networks6. Competition networks7. Species impact networks

Bacterial producers

Small herbivores

Small carnivores

Larger carnivores

Large carnivores

Medium omnivores

Large omnivores

Large herbivores

Parasitoids

Hyperpara-sitoids

Parasites

Smaller decomposer

Larger decomposer

Plant producers

Bacterio-phages

Prey/Predators 1 2 3 4 5A 1 1 1 1 0B 1 0 1 0 1C 1 1 1 0 0D 1 0 0 0 0E 1 0 0 0 0F 1 0 0 0 0G 1 1 1 0 0H 1 0 0 1 0

Translation of a food web into a matrix. Ones denote direct links.

Generalist predatorSpecialist predator

Typical terrestrial food web

Predaceous birds and snakes Parasitoid spider wasps Songbirds

Lizards

Predaceous insects

Scorpions

Spiders

Herbivorous insects

Land plands, seed detritus

Rodensts

Scavenging insects

Detritovorous insects

Seabird ectoparasites

Algal detritusSeabird guanoFish and bird carcasses

Seabirds

Marince planctonic food web Marine macroalgae

Interaction strength is

expressed by probabilities or by

frquencies of interaction

A quantitative food web

Lower/higher level 1 2 3 4 5A 0.8 0.2 0.3 0.1 0.5B 0.6 0.6 0.6 0 0.7C 0.9 0 0.9 0 0D 0.7 0 0 0.4 0E 0.3 0.7 0 0.1 0F 0 0.6 0 0 0G 0.7 0 0 0 0H 0.2 0 0 0.8 0

Interaction matrices

Pollination networks

Plants

BeesFrom Kratochwil et al. 2009

Plant Asclepias AsclepiasAspidonepsisMiraglossumMiraglossumPachycarpusSisyranthusXysmalobiumXysmalobiumPollinators cucullata woodii diploglossa verticillare pilosum natalensistrichostomus gerrardii involucratumHemipepsis 0 0 0 18 9 20 2 41 1Pompilidae sp. 2 0 0 0 0 0 0 0 1 0Tiphia 0 1 0 0 0 0 0 0 0Arge 0 0 0 0 0 0 1 0 0Apis 0 0 1 0 0 0 1 3 0Halictidae sp. 1 0 0 2 0 0 0 0 0 0Halictidae sp. 2 1 0 0 0 0 0 0 0 0Other wasps 0 1 1 0 0 0 0 1 3Other bees 0 0 0 0 0 0 0 1 1Other solitary bees 0 1 2 0 0 9 0 0 0Atrichelaphinis 0 15 0 1 0 0 35 15 6Cyrtothyrea 0 8 0 1 0 0 42 6 0Lycidae sp. 0 0 0 0 0 0 0 2 0Cantharidae sp. 0 0 0 0 0 0 0 2 0Elateridae sp. 0 0 0 0 0 0 0 0 4Chrysomelidae sp. 1 0 0 0 0 0 1 0 0 1Chrysomelidae sp. 2 0 0 0 0 0 0 1 1 1Scarabaeinae sp. 1 0 0 0 0 0 0 0 3 0Scarabaeinae sp. 2 0 0 0 0 0 0 0 3 1Scarabaeinae sp. 3 0 0 0 0 0 0 0 1 0Curculionidae sp. 1 0 0 0 0 0 0 10 4 1Curculionidae sp. 2 0 2 0 0 0 0 0 0 0Coleoptera sp. 3 0 0 0 0 0 0 0 2 0Coleoptera sp. 8 0 0 0 0 0 0 1 0 0Other Coleoptera 0 0 0 0 0 0 0 4 4Aspilocoryphus 1 0 0 1 0 4 1 139 1Lygaeidae sp. 2 0 0 0 1 0 1 0 8 2Coreidae sp. 0 0 0 0 0 0 0 1 0Spilostethus 0 0 0 0 0 1 0 0 0Homoecerus 0 0 0 0 0 1 0 0 0Pentatomoidea sp. 0 0 0 0 0 0 0 1 0Other Heteroptera 0 0 0 0 0 0 0 1 0Calliphoridae genus 1 0 0 0 0 0 0 0 1 0Calliphoridae genus 2 0 0 0 0 0 0 2 6 0Calliphoridae genus 3 0 0 0 0 0 0 0 1 0Sarcophaga sp. 0 1 0 6 0 11 0 53 1Musca 0 0 2 0 0 0 0 3 0Muscidae genus 2 0 0 1 0 0 0 0 0 0Empididae sp. 1 2 0 0 0 0 1 0 0 0Empididae sp. 2 0 0 0 0 0 0 0 1 0Chloropidae 0 0 1 0 0 0 0 1 0Microphthalma 0 0 0 0 0 1 0 0 0Microphthalma 0 0 0 0 0 0 0 1 0Tachinidae subfamily Goniinae 0 0 0 0 0 0 0 1 0Tachinidae genus 2 0 0 0 0 0 0 0 1 0Actea 0 0 0 0 0 0 0 1 0Sepsidae sp. 1 0 0 0 0 0 0 0 3 1Sepsidae sp. 2 0 0 0 0 0 0 0 0 1Sepsidae sp. 3 0 0 0 1 0 0 0 0 0Dacus 0 0 0 0 0 1 0 0 0Bibionidae 0 0 0 0 0 0 0 1 0Diptera sp. 3 0 0 0 0 0 0 1 0 0Diptera sp. 22 0 0 0 0 0 1 0 0 0Other Diptera 0 1 0 1 0 1 0 15 0Unidentified butterfly 0 0 0 0 0 0 1 0 0Unidentified micromoth 2 0 0 0 0 0 0 0 0

From Ollerton et al. 2003

S 8 1 7 4 6 5 2 3 S

7 1 0 0 0 0 0 0 0 11 1 1 0 1 0 0 0 0 3

10 0 1 1 0 0 0 0 0 22 0 1 1 0 1 0 0 0 35 0 0 0 1 0 0 0 0 18 1 0 0 1 1 1 1 0 59 0 0 1 1 0 1 1 0 43 0 0 0 1 1 0 1 1 46 0 0 1 0 0 1 0 1 34 0 0 0 0 0 0 1 1 2

S 3 3 4 5 3 3 4 3

How to present a presence – absence matrix?

Unsorted raw data Sorted according to marginal totals

Sorted to maximize species turnover

S 4 2 7 1 3 5 6 8 S

8 1 1 0 0 0 1 1 1 53 1 1 0 0 1 0 1 0 49 1 1 1 0 0 1 0 0 41 1 0 0 1 0 0 0 1 32 0 0 1 1 0 0 1 0 36 0 0 1 0 1 1 0 0 34 0 1 0 0 1 0 0 0 2

10 0 0 1 1 0 0 0 0 25 1 0 0 0 0 0 0 0 17 0 0 0 0 0 0 0 1 1

S 5 4 4 3 3 3 3 3

Correspondence analysis

Reciprocal averaging (seriation)

S 1 2 3 4 5 6 7 8 S

1 1 0 0 1 0 0 0 1 32 1 0 0 0 0 1 1 0 33 0 1 1 1 0 1 0 0 44 0 1 1 0 0 0 0 0 25 0 0 0 1 0 0 0 0 16 0 0 1 0 1 0 1 0 37 0 0 0 0 0 0 0 1 18 0 1 0 1 1 1 0 1 59 0 1 0 1 1 0 1 0 4

10 1 0 0 0 0 0 1 0 2

S 3 4 3 5 3 3 4 3

Ecological gradients

Species ful guc 3pog sos 2pogdabwrosgil ter 1pogwil mil swi kor hel lip wron SumPterostichus nigrita (Paykull) 1 1 2 18 2 5 0 58 53 30 61 39 0 0 0 2 2 13Platynus assimilis (Paykull) 48 2 25 9 7 4 0 39 0 0 1 0 0 76 9 117 0 11Amara brunea (Gyllenhal) 10 4 0 40 0 5 1 0 0 0 0 0 19 0 3 1 1 9Agonum lugens (Duftshmid) 0 0 0 0 0 2 1 3 2 1 2 0 0 0 0 0 1 7Loricera pilicornis (Fabricius) 5 0 0 0 1 1 0 5 0 0 1 3 0 0 0 0 0 6Pterostichus vernalis (Panzer) 0 0 0 1 0 0 1 0 2 0 21 7 0 0 0 0 1 6Amara plebeja (Gyllenhal) 0 0 0 2 0 1 0 5 0 0 0 0 1 0 0 4 0 5Badister unipustulatus Bonelli 0 0 0 1 0 0 0 3 0 0 0 0 4 0 0 3 0 4Lasoitrechus discus (Fabricius) 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 2Poecilus cupreus (Linnaeus) 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 2Sum 4 3 2 7 3 6 3 6 4 2 5 4 3 2 2 5 4

Area 10 10 2.1 20 1 7 0.2 10 0 0 1 0.2 2.1 2 1 4.19 0.15Isolation 0.01 0.01 0.1 0.1 0 0 0.1 0 0 0.1 0 0.1 0.1 0 0 0.09 0.09Habitat heterogeneity 10 10 8.4 8 7 7 6.8 6 4 4.3 4 3.1 3.1 3 1 1.23 0.91

Sorting of matrix columns according to ecological gradients allows for an assessment of the the importance of environmental variables.

Spatial or ecological Distance

Species turnover

Species turnover or beta diversity is a special case of species segregation where there is an ordering change in species composition across the sites.

Species ful guc 3pog sos 2pogdabwrosgil ter 1pogwil mil swi kor hel lip wronPterostichus nigrita (Paykull) 1 1 2 18 2 5 0 58 53 30 61 39 0 0 0 2 2Platynus assimilis (Paykull) 48 2 25 9 7 4 0 39 0 0 1 0 0 76 9 117 0Amara brunea (Gyllenhal) 10 4 0 40 0 5 1 0 0 0 0 0 19 0 3 1 1Agonum lugens (Duftshmid) 0 0 0 0 0 2 1 3 2 1 2 0 0 0 0 0 1Loricera pilicornis (Fabricius) 5 0 0 0 1 1 0 5 0 0 1 3 0 0 0 0 0Pterostichus vernalis (Panzer) 0 0 0 1 0 0 1 0 2 0 21 7 0 0 0 0 1Amara plebeja (Gyllenhal) 0 0 0 2 0 1 0 5 0 0 0 0 1 0 0 4 0Badister unipustulatus Bonelli 0 0 0 1 0 0 0 3 0 0 0 0 4 0 0 3 0Lasoitrechus discus (Fabricius) 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0Poecilus cupreus (Linnaeus) 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0

. kor swi lip sos hel guc3poggil ful dab 2pogwil wronwros1pogmil terPoecilus_cupreus_(Linnaeus) 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0Badister_unipustulatus_Bonelli 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0Amara_plebeja_(Gyllenhal) 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0Platynus_assimilis_(Paykull) 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0Amara_brunea_(Gyllenhal) 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0Pterostichus_nigrita_(Paykull) 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1Loricera_pilicornis__(Fabricius) 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0Pterostichus_vernalis_(Panzer) 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1Agonum_lugens_(Duftshmid) 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1Lasoitrechus_discus_(Fabricius) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

Raw matrix

Ordinated presence – absence matrix

Unexpected occurrences

Spatial distance between species

Ecological distance between sites

Basic patterns

Nested subset patterns

A B C D E F G H I J K L M N O P Sum1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 142 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 113 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 94 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 95 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 96 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 97 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 88 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 89 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 8

10 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 811 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 712 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 713 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 714 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 715 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 716 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 617 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 618 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 619 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 520 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 5

Sum 15 14 13 12 11 11 10 10 9 9 9 9 8 6 5 5

A B C D E F G H I J K L M N O P Sum1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 162 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 163 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 144 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 115 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 106 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 87 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 78 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 69 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 5

10 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 411 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 412 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 413 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 314 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 315 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 316 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 218 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 319 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 120 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

Sum 20 18 14 12 9 9 7 6 5 5 4 4 3 3 2 2

Random matrix ordered according to row/colum totals

A nested matrix ordered according to row/colum totals

Unexpected presence

Unexpected absence

A pattern where the species composition of species poorer assemblages form true samples of the species composition of species

richer assemblages is called a nested subset pattern.

Nestedness is common among biogeographical and interaction matrices.

Causes of nestedness

Mechanism Assumption/Precondition Predictions

Gradient of site properties

Gradient of species properties

Passive sampling Carrying capacities of sites

Regional abundance

Regional abundance predicts occupancy

Selective colonization

Isolation Dispersal ability Selective occupancy of sites according to isolation

Selective extinction Carrying capacities of sites

Extinction susceptibility (faunal relaxation)

Selective occupancy of sites according to area of sites

Nested habitats Habitat heterogeneity

Degrees of specialization

Higher proportion of generalist species in smaller and/or resource poor patches

Selective environ-mental tolerances

Environmental harshness

Environmental tolerances

Selective occupancy of sites according to tolerance to environmental stress

Habitat quality Environmental harshness

- Site occupancy in accordance to the ideal free distribution model.

The mass effect

SpeciesAbundance

across all sites

A 103940B 50432C 34092D 18433E 11786F 5943G 1005H 597I 386J 164K 107L 65M 43

Regional abundance within the

metacommunity

Colonization of sites with different carrying capacities

(areas)

Proportional colonization of sites according to metacommunity

abundance and carrying capacities

Passive sampling causes a nested subset pattern.

The mass effect is fundamental to all neutral models in ecology.

1 2 3 4 5 6 7 8 9 10 11 12 13A 1 1 1 1 1 1 1 1 1 1 1 1 1B 1 1 1 1 1 1 1 1 1 0 1 0 0C 1 1 1 1 1 0 1 1 1 1 0 0 0D 1 1 1 1 1 1 1 1 0 0 0 0 0E 1 1 1 1 1 1 1 0 1 0 0 0 0F 1 1 1 1 1 1 0 1 0 0 0 0 0G 1 1 1 1 0 1 1 0 0 0 0 0 0H 1 1 0 1 1 1 0 0 0 0 0 0 0I 1 0 1 1 1 0 0 0 0 0 0 0 0J 1 1 1 0 1 0 0 0 0 0 0 0 0K 1 0 1 0 0 0 0 0 0 0 0 0 0L 0 1 0 0 0 0 0 0 0 0 0 0 0M 1 0 0 0 0 0 0 0 0 0 0 0 0

Capacity

Ab

un

da

nce

Ecologists are mainly interested in process beyond mass effects. They are interested in ecological interactions.

Checkerboard matrixS 1 2 3 4 5 6 7 81 1 0 1 0 1 0 1 02 0 1 0 1 0 1 0 13 1 0 1 0 1 0 1 04 0 1 0 1 0 1 0 15 1 0 1 0 1 0 1 06 0 1 0 1 0 1 0 17 1 0 1 0 1 0 1 08 0 1 0 1 0 1 0 19 1 0 1 0 1 0 1 0

10 0 1 0 1 0 1 0 1

Checkerboards are 2x2 submatrices with

perfect species exclusion.

Classical competiton theory predicts high

numbers of checkerboards under intense competition of

species.

S 1 3 5 7 2 6 4 81 1 1 1 1 0 0 0 03 1 1 1 1 0 0 0 05 1 1 1 1 0 0 0 07 1 1 1 1 0 0 0 09 1 1 1 1 0 0 0 06 0 0 0 0 1 1 1 14 0 0 0 0 1 1 1 18 0 0 0 0 1 1 1 12 0 0 0 0 1 1 1 1

10 0 0 0 0 1 1 1 1

Reciprocal averaging

Any perfectly segregated matrix can be reordered by reciprocal

averaging to appear highly aggregated.

Aggregation and segregation are in fact two

sites of the same coin.

Aggregated matrix

Which matrix is expected under severe competition?

Negative species associations

S 1 2 3 4 5 6 7 81 1 1 1 0 0 0 0 02 1 1 1 0 0 0 0 03 1 1 1 0 0 0 0 04 0 0 1 1 1 0 0 05 0 0 1 1 1 0 0 06 0 0 1 1 1 0 0 07 0 0 1 1 1 0 0 08 0 0 0 0 0 1 1 19 0 0 0 0 0 1 1 1

10 0 0 0 0 0 1 1 1

S 1 2 3 6 7 8 5 44 1 1 1 1 1 1 0 05 1 1 1 1 1 1 0 06 1 1 1 1 1 1 0 07 0 0 0 0 0 0 1 12 0 0 0 0 0 0 1 13 0 0 0 0 0 0 1 11 0 0 0 0 0 0 1 18 0 0 0 0 0 0 1 19 0 0 0 0 0 0 1 1

10 0 0 0 0 0 0 1 1

Compartmented matrices

The existence of well defined compartments points always to the fact that the species assemblage under study is not homogeneous (a true community) but an artificial sample of species. In these cases we should deal with the compartments

as separate communities.

Matrix analysis is able to identify natural ecological entities.Tools are either cluster analysis of ordination.

Positive species associations

Boundary clumping.Species ranges are

coherent.There are no gaps (embedded absences) in

the sequence of occurrence.

Patterns in biogeographic presence – absence matrices

Jared Diamond’s 1975 assembly rules

1. „If one considers all combinations that can be formed from a group of related species, only certain

ones of these combinations exist in nature.”

5. „Some pairs of species never coexist, either by themselves or as part of a larger combination.”

Dan Simberloff

The Tallahassee mafia and his followers (particularly Steven Hubbell and other neutralists ) argued that patterns of

species co-occurrence (associations) are mainly random.

The competition view of nature

A neutral view of nature

Jared Diamond

http://en.wikipedia.org/wiki/Image:Jared_diamond.jpg

05

101520253035

-6 -4 -2 0 2 4 6 8 10 12

Freq

uenc

y (%

)

Standardized effect sizeGotelli, McCabe 2002

The frequency of segregated matrices in ecological meta-communities

34 of a total of 96 meatcommunities (35%) were significantly (two sided 95% confidence limits) segregated.

Standardized effect size

00.020.040.060.08

0.10.120.140.160.18

0.2

0 3 6 9 12 15 18X

f(x)

n=20

0

0.02

0.04

0.06

0.08

0.1

0.12

0 6 12 18 24 30 36 42 48X

f(x)

n=50

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10X

f(x)

n=10

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5X

f(x)

2

2

( )

21( )

2

x

f x e

P(m - 1.96s < X < m + 1.96s) = 95%

sxx

Z ii

The distribution of Z should have a mean of zero and a standard deviation of one.

Thus under a normal approximation 95% of values should range inside

-1.96 < Z < +1.96

S 27 47 17 28 38 29 15 30 23 24 22 5 33 16 42 8 9 36 13 45 20 40 12 32 7 39 1 11 21 4 14 44 3 10 26 18 19 2 31 41 34 46 25 49 6 48 50 37 43 3526 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 049 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 046 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 020 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 05 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 034 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 035 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 040 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 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Equiprobable randomS 49 2 5 1 3 4 6 7 14 8 12 15 11 10 13 9 27 21 17 16 19 23 18 22 26 20 25 28 24 29 31 36 33 34 30 41 32 35 40 39 38 37 44 43 42 47 45 50 46 4846 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 050 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 043 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 047 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 040 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 042 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 045 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 039 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 033 0 1 1 1 1 1 1 1 1 1 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Proportional random, nestedS 19 24 7 3 42 17 18 23 27 8 36 32 49 9 31 1 26 33 11 10 41 14 5 12 30 15 37 2 45 40 44 47 39 48 25 35 43 38 4 6 13 34 16 20 46 50 22 28 29 2147 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 045 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 040 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 041 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 028 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 030 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 021 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 037 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 035 0 1 1 1 0 0 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 05 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1

Nested

Nine types of theoretical matrices to mimic observed patterns.What pattern do we expect under intense competition.

Which matrix type is expected under severe competition?

-10

10

30

50

70

90

110

-10 0 10 20 30 40 50 60 70

Met

ric fo

r spe

cies

seg

rega

tion

Metric of species aggregation

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Compart EquiAggr EquiSegr EquiRandom Nested PrPrRand PrEquRand PropSegr Turnover

Met

ric

Matrix type

AggregationSegregation

1800 matrices with different structure, fill and size.

Two metrics to identify species segregation and species clumping

(aggregation).

Competition should result in a low degree of aggregation and a higher

degree of segregation.

S 27 47 17 28 38 29 15 30 23 24 22 5 33 16 42 8 9 36 13 45 20 40 12 32 7 39 1 11 21 4 14 44 3 10 26 18 19 2 31 41 34 46 25 49 6 48 50 37 43 3526 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 049 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 046 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 020 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 05 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 034 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 032 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 035 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 040 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 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Equiprobable randomS 27 29 11 2 1 9 10 8 6 33 14 24 16 5 20 44 4 15 3 13 19 17 18 23 22 12 7 26 31 34 25 32 38 28 30 21 35 36 46 48 43 41 37 40 42 39 47 45 49 5050 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 048 1 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 045 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 040 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 046 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 047 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 044 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 032 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 038 1 0 0 1 1 0 0 0 0 1 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Proportional segregatedS 48 49 6 3 31 35 1 5 12 14 21 36 32 17 33 4 45 22 7 24 15 20 30 47 28 9 29 16 19 23 41 26 50 2 10 38 8 37 13 39 40 27 18 11 25 43 42 34 46 4448 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 042 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 044 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 050 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 045 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 013 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 033 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 08 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 031 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 038 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 05 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 024 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 126 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 032 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 034 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 039 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 015 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 021 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 022 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 136 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 135 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 012 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 018 0 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 07 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 137 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 016 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 029 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 111 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 023 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 12 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 025 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 049 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 19 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 146 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 043 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 010 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 0 030 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 13 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 117 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 04 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 120 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 140 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 119 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 16 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 047 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 01 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 114 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 028 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 041 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 127 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1

Equiprobably segregated

The null expectation of matrix pattern under intense competition are• A random matrix or• A segregated matrix with pronounced differences in species abundances.

Randomness might be the outcome of strong negative species interactions.

A meta analysis of 471 empirical presence – absence matrices.

In 273 matrices the segregation metric was higher than the aggregation metric (58%).

0

0.05

0.1

0.15

0.2

Segregation metric

Aggregation metric

Raw

scor

e

471 empirical matrices

-100

102030405060

-10 0 10 20 30

Segr

egati

on m

etric

Clumping metric

34 matrices (7%) had negative clumping Z-scores and significantly positive

segregation Z-scores.94 matrices (20%) had negative clumping

and positive segregation Z-scores.

There is no prevalence of segregation (negative species interactions).

These results do not corroborate the assembly rule model.

-25-20-15-10

-505

1 1000 1000000

Nes

tedn

ess m

etric

Matrix size

-15-10

-505

1015

1 1000 1000000

Turn

over

met

ric

Matrix size

Only 73 empirical matrices had significant turnover.

346 matrices were nested.Only 3 empirical matrices were more nested than expected from passive

sampling.

Nested

Anti-Nested

Are interaction matrices different?

FW: food webs, P: pollination webs, SD: seed dispersers.

Open dots: not significant at the 5% error level

From Bascompte et al. 2003

Significantly nested networks

Not significantly nested networks

From Bastola et al. 2009

Observed degrees of nestedness in empirical

mutualistic networks increase biodiversity and minimizes the

degree of competition.

Nestedness and specialization

Part of generalist species

Part of specialist species

Species 1 2 3 4 5 6 7 8A 1 1 1 1 1 1 1 0B 1 0 1 1 1 0 1 0C 1 1 1 1 1 0 0 0D 1 1 1 1 0 0 0 1E 1 1 1 0 0 0 0 0F 1 1 0 0 0 0 0 0G 1 0 0 0 0 0 1 0H 0 0 0 0 1 0 0 1

Generalist species interact mainly with other generalists.Specialists interact either with generalists or with specialists.

Generalists

Specialists

Generalists Specialists

Community and gradient analysis: Matrix approaches in macroecology

Documents

species absence

distribution of species

presence absence matrix

species presences

real absences of species

real ecological patterns

biogeographic matrices

real species interactionsfor