Community and gradient analysis:
Matrix approaches in macroecology
The world comes in fragments
Biogeography
Species occurrences across a
fragmented landscape
1.
2.
3.
4.
Islands
Lakes
River bed and irrigation systems
Mainlands
continental distributions
habitat islands
mountain tops and valleys
fragmented landscapes
scattered distributed host plants
5. Cities and anthropogenic habitats
6. Routes of species invasion
7. Experimental plots (natural, macro-,
mesocosm experiments)
Galapagos Islands
The Darwin finches
The Darwin finches (Sanderson, Am. Scient. 2000)
Species
Seymour
Baltra
Isabella
Fernandina
Santiago
Rabida
Pinzon
Santa Cruz
Sante Fe
San
Cristobal
Espanola
Floreana
Genovesa
Marchena
Pinta
Darwin
Wolf
Islands
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
A presence – absence matrix reflects
the distribution of species across sites
The distribution of ground beetles across Mazurian lake islands
Species/Sites
Pterostichus nigrita (Paykull)
Platynus assimilis (Paykull)
Amara brunea (Gyllenhal)
Agonum lugens (Duftshmid)
Loricera pilicornis (Fabricius)
Pterostichus vernalis (Panzer)
Amara plebeja (Gyllenhal)
Badister unipustulatus Bonelli
Lasoitrechus discus (Fabricius)
Poecilus cupreus (Linnaeus)
Amara aulica (Panzer)
Anisodatylus binotatus (Fabricius)
Bembidion articulatum (Panzer)
Clivina collaris (Herbst)
Panagaeus cruxmajor (Linnaeus)
Poecilus versicolor (Sturm)
Pterostichus gracilis Dejean)
Stenolophus mixtus
Pseudoophonus rufipes (De Geer)
Harpalus latus (Linnaeus)
Agonum duftshmidi Shmidt
Harpalus solitaris Dejean
Colums totals
wros wron wil ter swi sos mil
0
1 1 1 0
1 1
0
0 1 0 0
1 0
1
1 0 0 1
1 0
1
1 1 1 0
0 0
0
0 1 0 0
0 1
1
1 1 1 0
1 1
0
0 0 0 1
1 0
0
0 0 0 1
1 0
0
0 0 1 0
0 1
0
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
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 1 0
0 0
0
0 1 0 0
1 1
0
0 0 0 0
1 0
0
0 1 0 0
0 0
0
0 0 0 0
0 0
3
4
7
5
3
9
lip kor hel guc
1 0 0
1
1 1 1
1
1 0 1
1
0 0 0
0
0 0 0
0
0 0 0
0
1 0 0
0
1 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
1 0 0
0
1 0 0
0
0 0 0
0
0 0 0
0
1 1 1
1
1 1 0
0
0 0 0
0
0 0 0
0
8 9
4
3
gil
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
ful dab 3pog 2pog 1pog Row totals
1
1
1
1
1
13
1
1
1
1
0
11
1
1
0
0
0
9
0
1
0
0
1
7
1
1
0
1
0
6
0
0
0
0
0
6
0
1
0
0
0
5
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
13
1
0
1
1
0
7
0
0
1
0
1
3
1
0
0
0
0
2
4 10 7
7
6
5
4
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.
98
Biogeographic matrices are static descriptions of colonization patterns.
Species/Sites
Pterostichus nigrita (Paykull)
Platynus assimilis (Paykull)
Amara brunea (Gyllenhal)
Agonum lugens (Duftshmid)
Loricera pilicornis (Fabricius)
Pterostichus vernalis (Panzer)
Amara plebeja (Gyllenhal)
Badister unipustulatus Bonelli
Lasoitrechus discus (Fabricius)
Poecilus cupreus (Linnaeus)
Amara aulica (Panzer)
Anisodatylus binotatus (Fabricius)
Bembidion articulatum (Panzer)
Clivina collaris (Herbst)
Panagaeus cruxmajor (Linnaeus)
Poecilus versicolor (Sturm)
Pterostichus gracilis Dejean)
Stenolophus mixtus
Pseudoophonus rufipes (De Geer)
Harpalus latus (Linnaeus)
Agonum duftshmidi Shmidt
Harpalus solitaris Dejean
wros wron wil ter swi sos mil
0
1 1 1 0
1 1
0
0 1 0 0
1 0
1
1 0 0 1
1 0
1
1 1 1 0
0 0
0
0 1 0 0
0 1
1
1 1 1 0
1 1
0
0 0 0 1
1 0
0
0 0 0 1
1 0
0
0 0 1 0
0 1
0
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
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 1 0
0 0
0
0 1 0 0
1 1
0
0 0 0 0
1 0
0
0 1 0 0
0 0
0
0 0 0 0
0 0
lip kor hel guc
1 0 0
1
1 1 1
1
1 0 1
1
0 0 0
0
0 0 0
0
0 0 0
0
1 0 0
0
1 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
1 0 0
0
1 0 0
0
0 0 0
0
0 0 0
0
1 1 1
1
1 1 0
0
0 0 0
0
0 0 0
0
gil
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
ful dab 3pog 2pog 1pog
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
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
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
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
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
Pterostichus nigrita (Paykull)
Platynus assimilis (Paykull)
Amara brunea (Gyllenhal)
Agonum lugens (Duftshmid)
Loricera pilicornis (Fabricius)
Pterostichus vernalis (Panzer)
Amara plebeja (Gyllenhal)
Badister unipustulatus Bonelli
Lasoitrechus discus (Fabricius)
Poecilus cupreus (Linnaeus)
Amara aulica (Panzer)
Anisodatylus binotatus (Fabricius)
Bembidion articulatum (Panzer)
Clivina collaris (Herbst)
Panagaeus cruxmajor (Linnaeus)
Poecilus versicolor (Sturm)
Pterostichus gracilis Dejean)
Stenolophus mixtus
Pseudoophonus rufipes (De Geer)
Harpalus latus (Linnaeus)
Agonum duftshmidi Shmidt
Harpalus solitaris Dejean
Colums totals
wros wron wil ter swi sos mil
0
1 1 1 0
1 1
0
0 1 0 0
1 0
1
1 0 0 1
1 0
1
1 1 1 0
0 0
0
0 1 0 0
0 1
1
1 1 1 0
1 1
0
0 0 0 1
1 0
0
0 0 0 1
1 0
0
0 0 1 0
0 1
0
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
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 1 0
0 0
0
0 1 0 0
1 1
0
0 0 0 0
1 0
0
0 1 0 0
0 0
0
0 0 0 0
0 0
3
4 7 5 3
9 8
lip kor hel guc gil
1 0 0
1 1
1 1 1
1 1
1 0 1
1 0
0 0 0
0 1
0 0 0
0 1
0 0 0
0 0
1 0 0
0 1
1 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
1 0 0
0 0
1 0 0
0 0
0 0 0
0 1
0 0 0
0 0
1 1 1
1 1
1 1 0
0 1
0 0 0
0 0
0 0 0
0 1
9 4 3
4 10
ful dab 3pog 2pog 1pog Row totals
1
1
1
1
1
13
1
1
1
1
0
11
1
1
0
0
0
9
0
1
0
0
1
7
1
1
0
1
0
6
0
0
0
0
0
6
0
1
0
0
0
5
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
13
1
0
1
1
0
7
0
0
1
0
1
3
1
0
0
0
0
2
7
7
6
5
4
98
Species/Sites
Pterostichus nigrita (Paykull)
Platynus assimilis (Paykull)
Amara brunea (Gyllenhal)
Agonum lugens (Duftshmid)
Loricera pilicornis (Fabricius)
Pterostichus vernalis (Panzer)
Amara plebeja (Gyllenhal)
Badister unipustulatus Bonelli
Lasoitrechus discus (Fabricius)
Poecilus cupreus (Linnaeus)
Amara aulica (Panzer)
Anisodatylus binotatus (Fabricius)
Bembidion articulatum (Panzer)
Clivina collaris (Herbst)
Panagaeus cruxmajor (Linnaeus)
Poecilus versicolor (Sturm)
Pterostichus gracilis Dejean)
Stenolophus mixtus
Pseudoophonus rufipes (De Geer)
Harpalus latus (Linnaeus)
Agonum duftshmidi Shmidt
Harpalus solitaris Dejean
Colums totals
wros wron wil ter swi sos mil
0
1 1 1 0
1 1
0
0 1 0 0
1 0
1
1 0 0 1
1 0
1
1 1 1 0
0 0
0
0 1 0 0
0 1
1
1 1 1 0
1 1
1
0 1 0 1
1 0
1
1 1 0 1
1 0
0
1 1 1 0
0 1
1
1 1 1 1
1 0
1
1 1 0 1
0 0
1
0 1 1 1
0 1
1
1 1 1 0
0 1
1
1 0 0 1
0 1
0
1 1 1 1
0 0
1
1 1 1 1
0 0
1
1 1 1 1
0 0
1
1 0 1 0
0 0
1
1 1 0 1
1 1
1
1 0 0 1
1 0
0
0 1 0 1
1 1
0
0 0 0 1
1 1
15
16 17 11 14 11 10
lip kor hel guc gil
1 0 0
1 1
1 1 1
1 1
1 0 1
1 0
0 0 0
0 1
0 1 1
1 1
0 1 1
1 0
1 1 1
1 1
1 1 1
1 1
0 1 1
1 0
0 1 1
1 0
0 1 1
1 0
0 1 1
1 0
0 1 1
1 0
0 1 1
1 0
1 0 1
1 0
1 0 1
1 0
0 0 1
1 1
0 0 1
1 0
1 1 1
1 1
1 1 0
0 1
1 1 1
1 1
1 0 1
0 1
11 14 19 19 11
ful dab 3pog 2pog 1pog Row totals
1
1
1
1
1
13
1
1
1
1
0
11
1
1
0
0
0
9
0
1
1
0
1
8
1
1
1
1
0
10
0
0
1
1
0
11
1
1
1
1
1
14
1
0
1
1
1
14
1
0
1
1
1
11
1
0
0
0
1
11
1
0
1
0
1
10
1
1
0
1
0
11
1
1
1
1
1
13
1
1
1
1
1
12
1
1
1
1
1
12
1
1
1
1
1
13
1
1
1
1
1
13
1
1
1
1
1
10
1
1
1
1
1
16
1
0
1
1
0
10
1
0
1
0
1
12
1
0
0
0
0
7
20 14
18
16
15
251
Dispersion
Extinction
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
Species/Sites
Pterostichus nigrita (Paykull)
Platynus assimilis (Paykull)
Amara brunea (Gyllenhal)
Agonum lugens (Duftshmid)
Loricera pilicornis (Fabricius)
Pterostichus vernalis (Panzer)
Amara plebeja (Gyllenhal)
Badister unipustulatus Bonelli
Lasoitrechus discus (Fabricius)
Poecilus cupreus (Linnaeus)
Amara aulica (Panzer)
Anisodatylus binotatus (Fabricius)
Bembidion articulatum (Panzer)
Clivina collaris (Herbst)
Panagaeus cruxmajor (Linnaeus)
Poecilus versicolor (Sturm)
Pterostichus gracilis Dejean)
Stenolophus mixtus
Pseudoophonus rufipes (De Geer)
Harpalus latus (Linnaeus)
Agonum duftshmidi Shmidt
Harpalus solitaris Dejean
wros wron wil ter
0
2 61 53
0
0
1 0
1
1
0 0
1
1
2 2
0
0
1 0
1
1 21 2
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
0 0
0
0
0 0
0
0
0 0
0
0
0 0
0
0
0 0
0
0
0 1
0
0 13 0
0
0
0 0
0
0
1 0
0
0
0 0
swi sos mil lip kor
0 18 39 2
0
0
9
0 117 76
19 40 0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
7
0
0
1
2
0
4
0
4
1
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
3
2
90
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
hel guc gil
0
1 58
9
2 39
3
4
0
0
0
3
0
0
5
0
0
0
0
0
5
0
0
3
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
1
0
0
0
3
1
5
0
0 20
0
0
0
0
0
1
ful dab 3pog 2pog 1pog
1
5
2
2
30
48 4
25
7
0
10 5
0
0
0
0
2
0
0
1
5
1
0
1
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
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
1
2
1
6
3
3
0
7
11
0
0
0
2
0
1
1
0
0
0
0
Abundance matrices contain additional information. Abundance matrices might be
based on point or averaged time series data.
Mutual interaction matrices
1.
2.
3.
4.
5.
6.
7.
Food web example
P a ra site s
L a rg e
h e rb iv o re s
H yp e rp a ra sito id s
P a ra sito id s
L a rg e
ca rn iv o re s
L a rg e
o m n iv o re s
L a rg e r
ca rn iv o re s
S m a ll
ca rn iv o re s
S m a ll
h e rb iv o re s
P la n t
p ro d u ce rs
L a rg e r
d e co m p o se r
M e d iu m
o m n iv o re s
B a cte rio phages
B a cte ria l
p ro d u ce rs
Typical terrestrial food web
S m a lle r
d e co m p o se r
Food webs
Host – parasite networks
Plant – herbivore networks
Pollination networks
Predator – prey networks
Competition networks
Species impact networks
Translation of a food web into a matrix.
Ones denote direct links.
Prey/Predators
A
B
C
D
E
F
G
H
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
3
1
1
1
0
0
0
1
0
4
1
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
Generalist predator
Specialist predator
P re d a ce o u s b ird s a n d sn a ke s
P a ra sito id sp id e r w a sp s
S o n g b ird s
P re d a ce o u s
in se cts
S co rp io n s
L iza rd s
S p id e rs
R o d e n sts
H e rb ivo ro u s
in se cts
S ca ve n g in g
in se cts
D e trito vo ro u s
in se cts
S e a b ird
e cto p a ra site s
L a n d p la n d s , se e d d e tritu s
F ish a n d b ird ca rca sse s
S e a b ird g u a n o
A lg a l d e tritu s
S e a b ird s
M a rin ce p la n cto n ic fo o d w e b
M a rin e m a cro a lg a e
Lower/higher level
A quantitative
food web
A
B
C
D
E
F
G
H
1
0.8
0.6
0.9
0.7
0.3
0
0.7
0.2
2
3
4
5
0.2 0.3 0.1 0.5
0.6 0.6 0 0.7
0 0.9 0
0
0
0 0.4 0
0.7 0 0.1 0
0.6 0
0
0
0
0
0
0
0
0 0.8 0
Interaction
strength is
expressed by
probabilities or by
frquencies of
interaction
Interaction matrices
Pollination networks
Plants
From Kratochwil et
al. 2009
Bees
Plant
Asclepias AsclepiasAspidonepsis
Miraglossum
Miraglossum
PachycarpusSisyranthusXysmalobium
Xysmalobium
Pollinators
cucullata
woodii diploglossa verticillare pilosum natalensistrichostomus gerrardii involucratum
Hemipepsis
0
0
0
18
9
20
2
41
1
Pompilidae sp. 2
0
0
0
0
0
0
0
1
0
Tiphia
0
1
0
0
0
0
0
0
0
Arge
0
0
0
0
0
0
1
0
0
Apis
0
0
1
0
0
0
1
3
0
Halictidae sp. 1
0
0
2
0
0
0
0
0
0
Halictidae sp. 2
1
0
0
0
0
0
0
0
0
Other wasps
0
1
1
0
0
0
0
1
3
Other bees
0
0
0
0
0
0
0
1
1
Other solitary bees
0
1
2
0
0
9
0
0
0
Atrichelaphinis
0
15
0
1
0
0
35
15
6
Cyrtothyrea
0
8
0
1
0
0
42
6
0
Lycidae sp.
0
0
0
0
0
0
0
2
0
Cantharidae sp.
0
0
0
0
0
0
0
2
0
Elateridae sp.
0
0
0
0
0
0
0
0
4
Chrysomelidae sp. 1
0
0
0
0
0
1
0
0
1
Chrysomelidae sp. 2
0
0
0
0
0
0
1
1
1
Scarabaeinae sp. 1
0
0
0
0
0
0
0
3
0
Scarabaeinae sp. 2
0
0
0
0
0
0
0
3
1
Scarabaeinae sp. 3
0
0
0
0
0
0
0
1
0
Curculionidae sp. 1
0
0
0
0
0
0
10
4
1
Curculionidae sp. 2
0
2
0
0
0
0
0
0
0
Coleoptera sp. 3
0
0
0
0
0
0
0
2
0
Coleoptera sp. 8
0
0
0
0
0
0
1
0
0
Other Coleoptera
0
0
0
0
0
0
0
4
4
Aspilocoryphus
1
0
0
1
0
4
1
139
1
Lygaeidae sp. 2
0
0
0
1
0
1
0
8
2
Coreidae sp.
0
0
0
0
0
0
0
1
0
Spilostethus
0
0
0
0
0
1
0
0
0
Homoecerus
0
0
0
0
0
1
0
0
0
Pentatomoidea sp.
0
0
0
0
0
0
0
1
0
Other Heteroptera
0
0
0
0
0
0
0
1
0
Calliphoridae genus 1
0
0
0
0
0
0
0
1
0
Calliphoridae genus 2
0
0
0
0
0
0
2
6
0
Calliphoridae genus 3
0
0
0
0
0
0
0
1
0
Sarcophaga sp.
0
1
0
6
0
11
0
53
1
Musca
0
0
2
0
0
0
0
3
0
Muscidae genus 2
0
0
1
0
0
0
0
0
0
Empididae sp. 1
2
0
0
0
0
1
0
0
0
Empididae sp. 2
0
0
0
0
0
0
0
1
0
Chloropidae
0
0
1
0
0
0
0
1
0
Microphthalma
0
0
0
0
0
1
0
0
0
Microphthalma
0
0
0
0
0
0
0
1
0
Tachinidae subfamily Goniinae
0
0
0
0
0
0
0
1
0
Tachinidae genus 2
0
0
0
0
0
0
0
1
0
Actea
0
0
0
0
0
0
0
1
0
Sepsidae sp. 1
0
0
0
0
0
0
0
3
1
Sepsidae sp. 2
0
0
0
0
0
0
0
0
1
Sepsidae sp. 3
0
0
0
1
0
0
0
0
0
Dacus
0
0
0
0
0
1
0
0
0
Bibionidae
0
0
0
0
0
0
0
1
0
Diptera sp. 3
0
0
0
0
0
0
1
0
0
Diptera sp. 22
0
0
0
0
0
1
0
0
0
Other Diptera
0
1
0
1
0
1
0
15
0
Unidentified butterfly
0
0
0
0
0
0
1
0
0
Unidentified micromoth
2
0
0
0
0
0
0
0
0
From Ollerton et
al. 2003
How to present a presence – absence matrix?
Unsorted raw data
S
1
2
3
4
5
6
7
8
9
10
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
3
0
0
1
1
0
1
0
0
0
0
4
1
0
1
0
1
0
0
1
1
0
5
0
0
0
0
0
1
0
1
1
0
6
0
1
1
0
0
0
0
1
0
0
7
0
1
0
0
0
1
0
0
1
1
8
1
0
0
0
0
0
1
1
0
0
S
3
4
3
5
3
3
4
3
Sorted according to marginal totals
S
3
3
4
2
1
3
1
5
4
2
S
8
3
9
1
2
6
4
10
5
7
4
1
1
1
1
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
7
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
5
1
0
1
0
0
1
0
0
0
0
6
1
1
0
0
1
0
0
0
0
0
8
1
0
0
1
0
0
0
0
0
1
S
5
4
4
3
3
3
3
3
S
5
4
4
3
3
3
2
2
1
1
Sorted to maximize species turnover
S
7
1
10
2
5
8
9
3
6
4
8
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
7
0
0
1
1
0
0
1
0
1
0
4
0
1
0
0
1
1
1
1
0
0
6
0
0
0
1
0
1
0
1
0
0
5
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
1
0
1
3
0
0
0
0
0
0
0
1
1
1
S
3
3
4
5
3
3
4
3
S
1
3
2
3
1
5
4
4
3
2
Correspondence
analysis
Reciprocal averaging
(seriation)
Ecological gradients
Species
ful
guc 3pog sos 2pog
dabwros gil ter 1pogwil mil swi kor hel lip
wron Sum
Pterostichus nigrita (Paykull)
1
1
2 18 2 5
0 58 53 30 61 39 0 0 0
2
2
Platynus assimilis (Paykull)
48
2
25
9 7 4
0 39 0
0 1
0 0 76 9 117
0
Amara brunea (Gyllenhal)
10
4
0 40 0 5
1 0 0
0 0
0 19 0 3
1
1
Agonum lugens (Duftshmid)
0
0
0
0 0 2
1 3 2
1 2
0 0 0 0
0
1
Loricera pilicornis (Fabricius)
5
0
0
0 1 1
0 5 0
0 1
3 0 0 0
0
0
Pterostichus vernalis (Panzer)
0
0
0
1 0 0
1 0 2
0 21
7 0 0 0
0
1
Amara plebeja (Gyllenhal)
0
0
0
2 0 1
0 5 0
0 0
0 1 0 0
4
0
Badister unipustulatus Bonelli
0
0
0
1 0 0
0 3 0
0 0
0 4 0 0
3
0
Lasoitrechus discus (Fabricius)
0
0
0
0 0 0
0 0 1
0 0
1 0 0 0
0
0
Poecilus cupreus (Linnaeus)
0
0
0
2 0 0
0 0 0
0 0
0 0 1 0
0
0
Sum
4
3
2
7 3 6
3 6 4
2 5
4 3 2 2
5
4
Area
Isolation
Habitat heterogeneity
13
11
9
7
6
6
5
4
2
2
10
10 2.1 20 1 7 0.2 10 0
0 1 0.2 2.1 2 1 4.19 0.15
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 0.09
10
10 8.4 8 7 7 6.8 6 4 4.3 4 3.1 3.1 3 1 1.23 0.91
Spatial or ecological Distance
Sorting of matrix columns according to ecological gradients allows for an
assessment of the the importance of environmental variables.
Basic patterns
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.
Raw matrix
Species
ful
guc 3pog sos 2pog
dabwros gil ter 1pogwil mil swi kor hel lip
wron
Pterostichus nigrita (Paykull)
1
1
2 18 2 5
0 58 53 30 61 39 0 0 0
2
2
Platynus assimilis (Paykull)
48
2
25
9 7 4
0 39 0
0 1
0 0 76 9 117
0
Amara brunea (Gyllenhal)
10
4
0 40 0 5
1 0 0
0 0
0 19 0 3
1
1
Agonum lugens (Duftshmid)
0
0
0
0 0 2
1 3 2
1 2
0 0 0 0
0
1
Loricera pilicornis (Fabricius)
5
0
0
0 1 1
0 5 0
0 1
3 0 0 0
0
0
Pterostichus vernalis (Panzer)
0
0
0
1 0 0
1 0 2
0 21
7 0 0 0
0
1
Amara plebeja (Gyllenhal)
0
0
0
2 0 1
0 5 0
0 0
0 1 0 0
4
0
Badister unipustulatus Bonelli
0
0
0
1 0 0
0 3 0
0 0
0 4 0 0
3
0
Lasoitrechus discus (Fabricius)
0
0
0
0 0 0
0 0 1
0 0
1 0 0 0
0
0
Poecilus cupreus (Linnaeus)
0
0
0
2 0 0
0 0 0
0 0
0 0 1 0
0
0
Ordinated presence – absence matrix
.
kor swi lip
sos hel guc3poggil ful dab 2pogwil wronwros1pogmil
Poecilus_cupreus_(Linnaeus)
1
0
0
1 0 0
0 0 0
0 0
0 0 0 0
Badister_unipustulatus_Bonelli
0
1
1
1 0 0
0 1 0
0 0
0 0 0 0
Amara_plebeja_(Gyllenhal)
0
1
1
1 0 0
0 1 0
1 0
0 0 0 0
Platynus_assimilis_(Paykull)
1
0
1
1 1 1
1 1 1
1 1
1 0 0 0
Amara_brunea_(Gyllenhal)
0
1
1
1 1 1
0 0 1
1 0
0 1 1 0
Pterostichus_nigrita_(Paykull)
0
0
1
1 0 1
1 1 1
1 1
1 1 0 1
Loricera_pilicornis__(Fabricius)
0
0
0
0 0 0
0 1 1
1 1
1 0 0 0
Pterostichus_vernalis_(Panzer)
0
0
0
1 0 0
0 0 0
0 0
1 1 1 0
Agonum_lugens_(Duftshmid)
0
0
0
0 0 0
0 1 0
1 0
1 1 1 1
Lasoitrechus_discus_(Fabricius)
0
0
0
0 0 0
0 0 0
0 0
0 0 0 0
Unexpected occurrences
ter
0
0
0
0
0
1
1
1
0
1
Ecological distance
between sites
0
0
0
0
0
1
0
1
1
1
Spatial
distance
between
species
Nested subset patterns
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
B
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
C
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
D
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
E
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
F
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
G
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
H
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
I
J
K
L
M
N
O
P
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
S um 1 5 1 4 1 3 1 2 1 1 1 1 1 0 1 0
9
9
9
9
8
6
5
5
Random matrix ordered
according to row/colum totals
S um
14
11
9
9
9
9
8
8
8
8
7
7
7
7
7
6
6
6
5
5
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
B
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
C
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
D
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
E
F
G
H
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
Sum 20 18 14 12
9
9
7
I
J
K
L
M
N
O
P
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
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
1
1
1
1
0
0
0
0
0
0
0
0
0
0
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
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
5
5
4
4
3
3
2
2
Unexpected
absence
Unexpected
presence
A nested matrix ordered
according to row/colum totals
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.
Sum
16
16
14
11
10
8
7
6
5
4
4
4
3
3
3
2
2
3
1
1
Causes of nestedness
Mechanism
Assumption/Precondition
Predictions
Gradient of site
properties
Carrying
capacities of
sites
Gradient of
species properties
Regional
abundance
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 environmental 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.
Passive sampling
Regional abundance predicts occupancy
The mass effect
Regional abundance Colonization of
within the
sites with different
metacommunity
carrying capacities
(areas)
Abundance
Species
A
B
C
D
E
F
G
H
I
J
K
L
M
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
3
1
1
1
1
1
1
1
0
1
1
1
0
0
4
1
1
1
1
1
1
1
1
1
0
0
0
0
5
1
1
1
1
1
1
0
1
1
1
0
0
0
6
1
1
0
1
1
1
1
1
0
0
0
0
0
7 8 9 10 11 12 13
1 1 1 1 1 1 1
1 1 1 0 1 0 0
1 1 1 1 0 0 0
1 1 0 0 0 0 0
1 0 1 0 0 0 0
0 1 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 0 0 0 0 0
Capacity
Abundance
A
B
C
D
E
F
G
H
I
J
K
L
M
across all
sites
103940
50432
34092
18433
11786
5943
1005
597
386
164
107
65
43
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.
Ecologists are mainly interested in process beyond mass
effects. They are interested in ecological interactions.
Negative species associations
Aggregated matrix
Checkerboard matrix
S
1
2
3
4
5
6
7
8
9
10
1
1
0
1
0
1
0
1
0
1
0
2
0
1
0
1
0
1
0
1
0
1
3
1
0
1
0
1
0
1
0
1
0
4
0
1
0
1
0
1
0
1
0
1
5
1
0
1
0
1
0
1
0
1
0
6
0
1
0
1
0
1
0
1
0
1
7
1
0
1
0
1
0
1
0
1
0
8
0
1
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.
Reciprocal
averaging
S
1
3
5
7
9
6
4
8
2
10
1
1
1
1
1
1
0
0
0
0
0
3
1
1
1
1
1
0
0
0
0
0
5
1
1
1
1
1
0
0
0
0
0
7
1
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
6
0
0
0
0
0
1
1
1
1
1
4
0
0
0
0
0
1
1
1
1
1
8
0
0
0
0
0
1
1
1
1
1
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.
Which matrix is expected under severe
competition?
Positive species associations
Compartmented matrices
S
1
2
3
4
5
6
7
8
9
10
1
1
1
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
3
1
1
1
1
1
1
1
0
0
0
4
0
0
0
1
1
1
1
0
0
0
5
0
0
0
1
1
1
1
0
0
0
6
0
0
0
0
0
0
0
1
1
1
7
0
0
0
0
0
0
0
1
1
1
8
0
0
0
0
0
0
0
1
1
1
Boundary clumping.
Species ranges are
coherent.There are no gaps
(embedded absences) in
the sequence of occurrence.
S
4
5
6
7
2
3
1
8
9
10
1
1
1
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
6
1
1
1
0
0
0
0
0
0
0
7
1
1
1
0
0
0
0
0
0
0
8
1
1
1
0
0
0
0
0
0
0
5
0
0
0
1
1
1
1
1
1
1
4
0
0
0
1
1
1
1
1
1
1
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.
Patterns in biogeographic presence – absence matrices
The competition view of nature
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.”
Jared Diamond
A neutral view of nature
The Tallahassee mafia and his followers
(particularly Steven Hubbell and other
neutralists ) argued that patterns of
species co-occurrence (associations) are
mainly random.
Dan Simberloff
The frequency of segregated matrices in ecological meta-communities
Frequency (%)
35
30
25
20
15
10
5
0
0.3
0.2
n=10
n=20
0.18
0.25
0.12
n=50
0.1
0.16
-6
0.14
0.2
0.1
0.08
0.1
0.06
0.04
0
2
4
6
8
10
12
Standardized effect size
0.04
0.06
0.05
-2
Gotelli,
McCabe 2002
f(x )
f(x )
0.15
-4
0.08
0.12
f(x )
34 of a total of 96 meatcommunities
(35%) were significantly (two sided
95% confidence limits) segregated.
0.02
0.02
0
0
0
2
0
Standardized effect size
4
6
8
10
0
3
X
6
9 12 15 18
X
0 6 12 18 24 30 36 42 48
X
0.06
Zi 
xi  x
s
0.05
f(x )
0.04
0.03
0.02
0.01
0
0
0.5
1
1.5
2
2.5
X
3
3.5
4
4.5
5
P( - 1.96 < X <  + 1.96) = 95%
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
Equiprobable random Proportional random, nested
S
26
49
46
20
5
34
32
35
40
33
38
41
13
11
6
21
10
9
25
19
30
1
47
17
12
43
28
50
8
23
48
18
39
15
2
16
4
31
7
29
27
37
22
42
36
14
24
45
3
44
27
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
17
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
28
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
29
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
15
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
30
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
23
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
24
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
22
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
S
50
48
49
47
46
45
44
42
40
43
41
38
36
22
39
31
34
35
37
27
15
29
28
8
6
24
26
1
12
2
3
9
5
16
33
18
25
7
32
10
4
30
20
21
11
23
14
17
19
13
50
1
1
1
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
26
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
22
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
39
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
35
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
28
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
9 18 27
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 1 0
1 1 0
1 1 0
1 1 1
0 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 0 1
1 0 1
1 1 0
1 1 1
0 0 1
1 0 1
0 1 0
1 0 1
0 1 1
1 0 1
0 1 0
0 1 0
1 0 1
0 1 1
0 1 0
0 0 1
0 1 0
1 0 0
1 1 0
0 0 1
0 1 0
0 0 0
0 0 0
1 0 1
1 0 0
0 0 0
1 1 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
S
50
43
41
40
49
33
31
39
34
42
37
35
36
29
32
24
27
26
23
21
2
47
5
3
11
15
14
13
12
10
8
9
16
6
4
1
7
17
25
45
38
28
46
44
18
48
19
20
30
22
50
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
0
0
0
44
0
1
0
0
0
0
0
0
0
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
46
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
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
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
5 33 16
1 0 1
0 0 0
0 1 0
1 1 1
1 1 1
1 1 1
1 0 0
1 0 1
0 1 1
1 0 0
0 0 1
1 1 0
1 1 1
1 0 1
1 0 0
0 0 1
1 1 1
0 1 0
0 0 1
1 0 0
0 1 0
0 1 1
1 0 0
1 0 0
0 1 1
0 1 0
1 0 1
0 0 0
1 0 0
0 1 0
1 0 0
0 1 0
0 1 0
1 1 1
0 0 0
1 0 0
0 1 1
0 0 1
0 1 0
0 0 1
0 0 0
1 0 0
1 0 1
0 0 0
0 1 1
1 0 0
1 0 1
0 0 0
0 0 0
0 0 0
42
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
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0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
Species turnover
2 10 6 23 7 20 24
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
1 0 0 0 0 0 0
1 1 0 0 0 0 0
1 1 1 0 0 0 0
1 1 1 1 0 0 0
1 1 1 1 0 1 1
1 1 1 1 1 0 0
1 1 1 1 1 1 0
1 0 1 1 1 1 1
1 1 1 1 1 1 1
1 0 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 0 1 0 1
1 1 0 1 1 1 1
0 0 1 1 1 1 0
1 1 1 1 0 1 1
1 1 1 0 1 1 0
1 1 0 0 1 0 1
0 1 1 0 1 0 0
1 1 1 0 1 0 0
0 1 1 1 1 1 0
1 1 0 0 1 1 0
1 0 1 1 0 0 1
1 0 1 0 1 0 1
0 0 0 0 1 0 1
0 1 1 1 1 1 1
0 1 1 0 0 1 1
0 0 1 0 1 0 0
1 0 0 1 0 1 1
0 0 0 1 1 1 0
0 0 0 1 0 1 0
0 1 0 0 1 0 1
0 1 0 0 1 0 0
1 1 1 0 1 1 0
1 0 0 0 0 0 1
0 0 0 0 0 0 1
0 0 1 0 0 0 0
0 0 0 0 0 1 0
1 0 1 0 0 1 0
1 0 1 1 0 0 0
1 0 0 1 0 0 1
0 0 0 0 0 1 0
0 0 0 1 0 0 0
0 1 0 0 0 0 1
0 0 0 0 1 0 0
0 0 0 0 1 0 0
4 15 11
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
1 0 0
1 0 0
1 1 0
1 1 0
0 0 1
1 1 1
1 1 1
1 1 1
1 0 1
1 1 0
1 1 1
1 1 1
0 1 1
1 1 0
1 1 1
1 1 1
1 0 1
0 1 1
1 0 1
1 1 1
0 1 1
1 0 1
0 1 1
0 0 0
0 1 1
1 1 0
1 1 1
1 1 0
0 0 1
1 0 1
0 0 1
0 0 0
1 1 0
1 1 0
1 0 1
0 0 0
0 1 0
0 0 0
0 0 1
1 0 0
8 16 3 30 5
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 0 0 0 0
0 0 0 0 0
1 1 0 1 0
1 0 0 0 1
1 1 1 0 1
0 1 1 0 0
1 0 0 0 0
1 0 1 1 1
1 1 1 0 0
1 1 1 0 1
1 0 1 1 1
0 1 1 1 1
1 1 0 1 1
1 1 1 1 1
1 1 1 1 1
1 0 1 1 1
0 1 1 0 0
0 0 1 1 1
0 1 1 1 1
1 1 0 1 0
1 0 1 1 1
0 1 1 1 0
1 0 1 0 1
1 0 1 0 0
1 0 1 1 1
0 1 1 0 1
0 0 0 0 1
0 1 1 0 1
1 1 1 1 0
0 1 1 0 0
1 0 0 1 1
0 1 1 0 1
1 1 1 1 0
1 0 1 0 0
0 0 0 0 1
0 0 0 1 0
0 1 0 0 1
1 0 0 0 1
1 1 1 1 1
1 0 1 1 1
1 1 0 0 1
1 17 25
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
1 0 0
1 0 0
1 0 0
0 1 0
1 1 1
1 0 1
1 1 1
0 1 0
0 1 0
1 0 1
1 1 1
1 1 1
1 0 1
0 0 1
1 1 1
1 1 1
0 0 1
1 1 0
1 0 0
1 1 0
1 1 1
1 0 1
0 1 0
1 1 1
1 1 0
1 1 0
1 1 0
1 1 1
1 0 1
1 1 1
1 0 1
0 0 1
1 1 0
1 1 1
0 0 0
1 1 1
0 0 0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
37
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
44
0
0
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
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
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
1
1
1
0
0
0
0
0
0
0
0
0
0
5 15 25
0 0 0
1 0 0
1 0 0
1 0 0
0 0 0
1 1 0
1 1 1
1 1 0
1 1 0
1 0 0
1 0 0
1 1 0
1 1 0
1 1 0
1 1 0
1 0 1
1 0 1
1 0 1
1 0 1
1 0 1
1 1 1
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
1 1 1
1 1 1
1 1 1
1 1 0
0 1 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
1 0 0
0 0 0
24
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
23
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
32
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
30
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
28
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
8 31 11
0 0 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 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 0 1
1 0 1
1 0 1
1 0 1
1 0 1
1 1 1
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
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
0 0 0
1 0 1
1 1 1
0 0 0
0 0 0
1 0 1
0 0 0
1 0 1
1 0 1
1 0 1
1 0 1
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
19
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
1
0
0
1
0
1
1
0
1
16
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
20
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
18
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
3
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
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
4
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7 14 8 12 15
0 0 0 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 0 0 1
1 0 0 1 0
1 1 1 1 1
0 0 0 0 0
0 0 1 0 0
1 1 1 1 1
1 1 1 0 0
1 0 1 1 1
0 1 1 1 1
1 0 0 0 0
0 1 0 0 0
1 1 0 1 1
1 0 1 1 1
1 1 1 1 1
1 1 0 0 0
1 1 1 1 1
1 1 1 1 0
0 0 0 0 0
1 1 1 1 1
1 1 1 1 1
1 0 1 1 1
0 0 0 0 0
1 1 1 1 1
1 0 1 1 1
0 0 1 0 0
1 1 1 1 1
1 1 1 1 1
1 0 1 1 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 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 1 1 1
1 1 1 1 1
11
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
10
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
13
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9 27 21
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 1 1
0 0 0
0 0 0
1 0 0
0 0 1
0 0 1
1 1 0
1 0 0
1 0 0
1 1 0
1 1 1
1 0 0
0 0 1
1 1 0
1 0 1
0 0 0
1 0 1
1 0 0
1 0 1
0 0 0
1 0 1
1 1 1
1 0 0
1 1 1
1 1 0
1 0 0
1 1 1
1 1 1
1 1 1
1 0 0
1 1 1
1 1 1
1 0 0
1 1 1
1 0 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 0 1
1 1 1
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
19
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
23
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
22
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
26
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
20
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
25
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
24
0
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
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
29
0
0
0
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
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
36
0
0
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
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
33
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
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
34
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
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
30
0
0
0
0
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
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
41
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
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
32
0
0
0
0
0
0
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
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
35
0
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
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
40
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
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
39
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
1
0
0
0
1
1
0
0
1
0
0
1
0
1
38
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
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
37
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
44
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
1
0
0
0
0
0
0
0
0
0
0
1
43
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
1
0
0
0
0
0
1
0
1
0
42
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
1
0
0
0
0
0
0
0
1
0
0
1
1
47
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
1
0
0
0
45
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
0
1
0
0
50
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
0
1
0
0
Unequal abundances
46
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
0
0
1
0
48
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
0
0
0
1
S
47
45
40
41
28
30
21
37
35
33
14
19
20
18
24
8
4
7
13
12
29
39
3
1
6
5
2
9
11
38
10
32
23
25
15
48
17
43
16
26
22
27
36
44
42
34
31
46
49
50
19
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
50
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
1
0
0
0
0
0
0
S
48
42
44
50
45
13
33
8
31
38
5
24
26
32
34
39
15
21
22
36
35
12
18
7
37
16
29
11
23
2
25
49
9
46
43
10
30
3
17
4
20
40
19
6
47
1
14
28
41
27
48
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
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
49
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
3 31 35
1 1 0
1 1 1
1 0 0
0 1 0
0 0 1
1 0 1
1 1 1
1 1 1
1 1 1
1 0 1
1 0 0
1 0 1
1 1 0
1 1 0
1 1 0
0 1 1
0 0 1
0 1 0
1 0 0
1 0 0
1 0 1
0 1 1
1 0 0
1 0 1
0 1 0
0 1 1
0 0 0
0 0 1
1 1 0
1 0 1
0 1 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
1 0 0
0 0 0
1 0 1
0 0 0
1 1 0
0 0 0
0 0 1
0 0 0
0 1 1
0 0 0
0 0 0
S
45
47
44
50
49
42
48
43
39
41
35
40
38
36
46
31
34
33
37
29
32
27
25
28
30
26
24
21
23
17
22
18
20
19
14
16
15
13
12
10
8
11
7
6
4
3
9
1
2
5
7
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
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
0
1
1
1
0
0
0
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
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
0
0
0
0
0
1
0
1
1
1
1
1
1
1
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
0
1
1
1
0
0
1
0
0
Proportional segregated
Compartmented
4
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
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
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
25
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
35
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
43
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
38
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
6 13 34
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
1 1 0
0 0 0
0 0 0
0 0 0
1 0 1
0 0 0
1 0 0
0 0 1
1 0 1
1 1 0
1 1 0
0 1 1
0 1 1
0 1 1
0 0 1
0 0 0
1 1 1
1 1 1
1 1 0
1 1 1
1 1 1
1 1 1
1 1 0
0 0 0
1 1 1
0 0 0
1 0 0
1 0 0
1 0 1
0 0 0
1 1 1
0 0 0
0 1 1
1 1 0
1 1 0
1 1 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
16
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
20
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
28
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
29
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
21
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
34
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
46
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
44
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
Equiprobably segregated
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5 12 14
1 1 1
1 0 1
1 1 1
0 1 0
1 1 1
1 1 1
1 1 1
0 0 0
0 0 1
1 0 0
1 1 1
1 1 0
1 1 0
1 0 1
0 0 0
0 0 1
1 0 1
1 1 0
0 1 1
0 1 0
0 0 0
1 1 0
0 1 0
1 0 0
1 0 0
1 1 0
0 1 1
1 0 1
0 1 1
0 0 1
0 1 1
0 0 0
1 1 1
0 0 1
0 0 0
0 0 0
1 0 0
1 0 1
0 0 0
0 0 0
0 1 0
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 1
21
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
36
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
32
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
17
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
33
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
4 45 22
0 0 0
1 0 1
1 1 0
1 1 0
1 0 1
1 0 0
0 0 0
1 1 1
1 0 1
0 1 1
1 1 0
0 0 1
0 0 1
1 0 1
0 1 0
0 0 0
0 0 0
0 0 1
1 0 1
1 0 1
1 0 0
0 1 0
1 1 0
0 0 1
1 0 0
0 1 0
0 1 0
1 0 1
0 1 0
0 1 0
1 0 0
1 1 0
0 0 0
0 1 0
1 0 1
0 0 1
1 0 1
0 0 1
0 1 1
1 0 1
0 1 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 1
1 1 1
0 0 0
1 0 0
1 0 0
Equiprobably aggregated
44
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
28
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
49
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
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
7 24 15
0 0 0
1 0 0
0 0 1
0 0 0
0 0 0
1 1 1
1 0 0
0 1 1
0 0 0
0 1 1
0 1 0
1 1 0
0 0 0
1 0 1
1 1 1
0 0 0
1 1 0
0 1 0
1 0 1
0 0 1
1 1 1
1 1 1
1 1 0
1 0 0
1 0 0
1 1 1
1 1 0
0 0 1
0 0 1
1 1 1
1 0 0
0 0 1
0 0 0
1 0 0
1 0 1
0 1 1
0 1 1
0 0 0
0 1 1
0 0 1
1 0 1
1 0 1
0 0 0
0 0 0
1 1 0
0 1 0
0 0 0
0 1 0
1 0 0
0 0 0
20
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
30
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
47
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
28
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
9 29 16
1 1 1
0 0 0
0 0 1
1 0 0
0 0 0
1 0 1
1 0 1
0 1 1
0 0 1
1 1 0
0 0 1
0 1 0
0 0 0
0 1 0
1 1 0
1 1 1
0 0 1
1 1 0
0 0 0
1 0 0
0 0 0
1 1 0
0 0 0
1 0 0
1 0 0
0 1 1
0 1 0
0 0 0
0 0 0
0 1 1
0 0 1
0 0 0
1 0 1
1 0 0
1 0 0
0 1 0
1 1 1
0 0 1
1 0 1
1 0 0
1 1 0
0 1 0
1 1 1
0 0 0
1 0 1
0 1 1
0 1 0
0 1 1
1 0 1
1 0 1
19
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
23
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
41
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
26
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
50
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
2 10 38
0 0 0
0 0 0
0 0 0
0 0 0
1 1 0
0 1 0
0 1 0
0 0 1
1 0 1
0 0 0
0 0 1
1 0 0
0 1 0
1 0 1
0 1 0
1 0 0
1 0 0
0 0 0
0 0 1
1 0 0
1 0 0
1 1 0
0 0 1
1 0 0
1 1 1
1 1 0
0 1 1
1 0 0
0 1 1
0 1 1
1 0 0
0 1 0
1 1 0
0 1 1
1 1 0
0 0 0
0 0 0
1 0 1
1 0 1
1 1 0
0 0 0
1 1 0
1 1 1
1 1 1
1 1 0
0 0 1
0 1 0
0 0 1
1 1 1
1 0 0
8 37 13
0 0 0
0 0 1
0 0 0
0 0 0
0 1 0
1 0 0
0 1 0
1 0 0
1 0 0
0 1 1
1 1 0
0 0 0
0 0 0
0 0 0
1 0 1
1 0 0
1 1 1
0 1 0
0 0 0
0 0 0
0 0 1
0 0 1
0 0 1
1 0 1
0 1 1
0 0 0
0 1 0
1 1 1
0 0 0
1 0 1
1 0 0
0 1 0
1 0 0
0 0 1
0 0 1
1 0 1
1 0 1
1 1 1
0 1 0
1 0 1
1 0 0
1 1 0
1 1 0
1 1 0
0 1 1
1 1 0
0 0 1
1 1 1
0 0 1
1 1 1
39
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
40
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
27
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
18
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
11
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
31
0
0
0
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34
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38
0
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36
0
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0
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0
0
0
0
0
0
0
0
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48
0
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25
0
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Nested
5
0
0
1
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1
1
1
1
1
1
1
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1
1
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0
1
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0
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8 11 6
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
1 0 0
1 1 1
1 0 1
1 1 1
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0 1 1
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0 0 0
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9 10 13
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0 0 1
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1 1 0
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12
0
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0
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0
0
1
1
0
1
1
0
1
1
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1
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1
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1
1
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1
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1
1
1
1
1
1
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14
0
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16
0
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1
1
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0
18
0
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17
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15
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1
1
1
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1
1
1
1
1
1
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1
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19
0
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0
0
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0
0
0
0
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0
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1
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1
1
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1
1
1
1
1
1
1
1
1
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22
0
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0
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1
1
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
20
0
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0
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1
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1
1
1
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1
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1
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1
1
1
1
1
1
1
1
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21
0
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1
1
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1
1
1
1
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23
0
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1
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1
1
1
1
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24
0
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0
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1
1
1
1
1
1
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1
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1
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1
1
1
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25
0
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0
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0
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0
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0
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1
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1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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1
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0
0
1
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0
1
1
1
1
1
1
1
1
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1
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30
0
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0
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0
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1
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1
1
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1
1
1
1
1
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26
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
1
1
1
1
1
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1
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1
1
1
1
1
1
1
1
1
1
1
28
0
0
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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
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1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
29
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
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
32
0
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
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
33
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
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
Nine types of theoretical matrices to mimic observed patterns.
What pattern do we expect under intense competition.
37
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
1
0
1
0
0
1
0
1
1
1
1
1
1
1
35
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
1
1
1
1
1
1
1
1
1
1
1
43
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
40
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
1
0
0
0
0
1
1
0
0
1
1
1
1
1
49
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
0
1
0
0
50
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
0
1
0
0
45
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
0
1
1
1
46
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
0
1
1
1
47
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
0
1
0
1
Which matrix type is expected under severe competition?
Metric for species segregation
110
1800 matrices with different structure,
fill and size.
Two metrics to identify species
segregation and species clumping
(aggregation).
90
70
50
30
10
Competition should result in a low
degree of aggregation and a higher
degree of segregation.
-10
-10
0
10
20
30
40
50
60
70
Metric of species aggregation
0.35
0.3
Metric
0.25
0.2
Aggregation
Segregation
0.15
0.1
0.05
0
Compart
EquiAggr
EquiSegr EquiRandom
Nested
Matrix type
PrPrRand
PrEquRand
PropSegr
Turnover
Equiprobable random
S
26
49
46
20
5
34
32
35
40
33
38
41
13
11
6
21
10
9
25
19
30
1
47
17
12
43
28
50
8
23
48
18
39
15
2
16
4
31
7
29
27
37
22
42
36
14
24
45
3
44
27
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
17
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
28
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
29
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
15
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
30
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
23
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
24
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
22
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
5 33 16
1 0 1
0 0 0
0 1 0
1 1 1
1 1 1
1 1 1
1 0 0
1 0 1
0 1 1
1 0 0
0 0 1
1 1 0
1 1 1
1 0 1
1 0 0
0 0 1
1 1 1
0 1 0
0 0 1
1 0 0
0 1 0
0 1 1
1 0 0
1 0 0
0 1 1
0 1 0
1 0 1
0 0 0
1 0 0
0 1 0
1 0 0
0 1 0
0 1 0
1 1 1
0 0 0
1 0 0
0 1 1
0 0 1
0 1 0
0 0 1
0 0 0
1 0 0
1 0 1
0 0 0
0 1 1
1 0 0
1 0 1
0 0 0
0 0 0
0 0 0
42
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
8
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
9 36 13
1 1 1
1 1 0
1 0 0
1 1 1
0 1 1
1 0 1
1 0 0
1 0 0
0 0 0
0 1 0
0 0 1
0 0 1
0 1 0
1 1 1
0 1 1
1 1 0
0 0 1
1 0 1
0 0 1
1 0 1
1 0 0
1 1 1
0 0 0
0 0 1
1 0 0
0 1 0
1 1 0
0 0 1
1 0 0
1 1 0
0 0 0
0 0 1
1 0 0
0 0 1
0 0 1
1 1 0
0 0 1
1 1 0
0 1 0
0 0 1
1 1 1
0 0 0
0 0 0
0 0 1
1 1 0
0 0 0
1 0 0
0 0 0
1 1 0
0 0 1
45
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
20
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
40
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
12
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
32
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
7 39 1 11 21
0 0 0 0 0
1 0 1 1 0
1 0 0 1 0
0 1 1 0 0
0 0 1 0 0
1 0 0 1 1
0 0 0 0 1
0 1 1 0 1
1 0 1 0 0
1 0 1 0 1
1 0 1 1 0
0 0 1 0 0
0 0 0 0 0
0 1 0 0 1
1 1 0 1 1
1 1 0 1 1
0 0 1 1 1
0 1 1 0 0
1 1 1 0 0
0 0 0 1 1
0 1 1 0 0
1 1 0 1 1
0 0 0 1 0
1 0 0 0 1
0 1 1 1 0
1 0 1 0 0
0 0 1 1 0
1 0 0 1 0
0 0 0 0 1
1 1 1 1 1
0 0 0 1 0
1 1 1 1 0
1 0 0 0 0
1 0 1 0 1
1 1 1 1 0
0 0 1 0 0
1 1 0 0 0
1 0 0 1 1
0 1 0 0 0
0 0 1 0 0
0 1 1 0 1
1 1 0 1 0
1 0 1 0 1
1 0 1 0 0
0 0 0 0 1
0 1 1 1 0
1 0 1 1 0
0 0 1 0 1
0 0 0 1 1
0 0 1 1 1
4 14 44
0 1 1
0 0 0
0 0 0
0 0 0
1 1 0
1 1 0
0 0 1
0 0 0
1 1 0
1 0 0
0 0 0
0 0 1
1 1 0
0 0 0
1 1 1
0 1 0
1 0 1
1 0 0
0 1 0
1 0 1
0 0 1
0 0 0
1 0 0
0 1 0
1 0 1
1 0 1
1 1 1
1 0 0
1 1 0
0 1 1
0 1 0
0 0 0
0 0 0
0 1 0
1 1 1
0 1 0
0 1 0
0 0 0
1 1 0
1 0 1
1 1 1
0 0 0
1 0 1
1 1 0
0 0 1
1 1 1
0 1 0
1 0 0
1 1 1
0 0 0
3 10 26
1 0 0
0 0 0
0 0 0
0 0 0
0 1 1
1 0 0
1 0 1
0 0 0
0 1 1
0 0 0
0 0 0
1 1 0
1 1 0
0 0 1
0 1 0
1 1 0
0 1 0
0 1 1
1 0 1
1 0 0
0 0 0
0 1 1
1 0 0
0 0 0
1 1 0
0 1 1
1 0 1
0 0 1
1 1 0
0 0 0
1 0 0
1 1 0
0 0 1
1 0 1
1 1 0
0 0 1
1 1 0
0 1 0
0 1 1
1 1 1
0 0 1
1 0 1
1 1 1
1 0 1
1 1 0
0 1 0
1 1 0
1 0 0
0 0 1
0 1 0
18
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
19
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
2 31 41
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
1 0 1
1 1 0
0 0 1
1 1 0
1 0 0
0 0 0
0 1 1
1 1 1
1 0 1
0 0 1
1 0 0
1 0 0
0 1 0
0 1 0
1 0 0
1 0 1
1 1 0
1 1 0
1 1 0
0 0 1
1 1 0
0 1 0
0 1 0
1 0 0
1 0 0
1 0 1
1 0 1
1 1 1
1 0 0
0 1 0
0 0 1
0 1 1
1 0 0
0 1 0
1 0 0
1 1 1
1 0 1
0 0 1
1 1 1
1 1 0
34
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
46
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
25
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
49
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
6 48 50
0 0 0
0 0 0
0 0 0
1 0 0
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
1 1 0
1 0 0
0 0 0
1 0 0
1 0 0
1 1 0
0 0 0
0 1 0
0 1 1
1 0 0
1 0 0
1 0 1
0 0 0
0 0 0
0 0 1
0 0 0
0 1 1
0 0 0
1 1 1
1 0 1
0 1 0
1 1 0
1 0 0
1 0 0
0 0 1
1 1 1
0 0 1
1 0 1
1 0 1
1 1 1
1 1 0
1 1 0
1 0 1
0 1 1
1 0 0
1 1 0
1 1 0
Proportional segregated
37
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
35
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
S
50
48
45
40
46
47
44
32
38
35
36
37
39
13
27
41
18
42
19
33
28
29
25
30
43
17
34
21
5
49
8
22
24
20
12
26
9
10
11
3
31
16
14
4
15
2
7
23
1
6
27
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
29
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
11
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
9 10 8
0 0 0
1 1 0
1 0 0
0 0 1
0 1 1
1 1 0
1 1 0
1 1 1
0 0 0
1 0 0
1 1 1
1 0 0
1 1 1
1 0 1
0 0 1
1 1 0
0 1 1
1 0 0
0 1 1
0 1 0
1 0 1
0 1 1
1 0 1
0 0 1
0 0 0
1 1 0
0 1 1
0 1 0
1 0 1
0 0 0
0 0 1
1 1 1
0 1 1
0 0 1
0 0 1
1 0 0
0 1 1
1 1 1
1 1 0
1 1 1
0 0 0
1 0 0
0 1 1
1 0 1
1 1 0
0 1 0
0 0 0
0 0 0
0 0 0
1 0 0
6 33 14
1 0 0
1 0 0
1 1 0
1 1 1
0 1 0
0 0 0
0 0 0
0 0 1
0 1 1
1 0 1
1 0 1
0 0 1
1 0 0
1 1 0
0 0 0
0 1 0
1 1 1
0 1 0
1 0 1
0 1 0
1 0 1
0 0 1
1 0 0
0 0 1
1 0 1
1 0 0
1 0 1
0 0 0
1 1 1
0 0 0
1 1 0
0 0 1
0 1 1
0 1 0
1 0 1
0 1 1
0 1 1
1 0 1
0 0 1
1 1 0
0 1 0
0 0 1
1 0 1
0 0 0
0 0 0
0 1 1
1 0 0
1 0 0
1 1 0
1 0 0
24
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
16
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
5 20 44
0 0 0
0 0 0
0 0 0
1 1 0
1 1 0
1 1 0
0 0 1
1 1 1
1 0 0
1 0 0
0 0 1
0 1 1
0 1 0
1 1 1
1 0 0
1 0 0
1 0 0
0 1 0
1 1 0
0 0 0
0 1 1
1 1 1
1 0 0
1 0 0
1 0 1
0 0 0
0 0 0
0 0 0
1 0 1
0 1 0
0 0 0
0 0 0
1 1 0
0 1 1
1 1 1
1 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 1 1
0 1 0
1 1 0
1 1 1
1 0 0
1 0 0
0 0 1
1 1 0
1 1 1
1 0 0
4 15 3 13 19
0 0 0 0 0
0 0 0 1 0
0 1 1 0 0
1 0 1 0 0
1 0 0 0 0
0 0 0 0 0
1 0 1 0 0
1 1 1 0 1
1 1 1 1 0
0 1 0 0 1
0 0 0 1 0
1 0 1 0 0
0 1 0 0 1
0 1 0 0 0
1 0 1 0 1
0 1 1 1 1
0 0 0 1 0
0 1 0 0 0
1 1 0 1 1
1 1 1 1 1
1 0 0 1 1
0 1 0 1 1
1 0 1 0 1
1 0 1 1 0
0 0 0 1 0
0 1 0 1 0
1 0 1 1 0
1 1 1 1 0
0 0 1 1 1
0 1 0 0 1
1 0 1 1 1
0 0 1 1 1
0 0 0 0 1
1 1 1 0 0
1 0 1 1 0
0 0 1 0 1
1 1 1 0 0
1 0 1 0 1
1 0 0 0 1
1 1 1 0 0
1 0 1 1 0
0 1 1 0 0
1 1 1 1 0
0 0 0 1 0
0 0 1 0 1
1 0 0 1 1
1 1 1 0 0
0 1 0 0 1
1 1 0 1 1
0 1 1 1 0
17
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
18
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
23
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
22
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
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0
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7 26 31
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 0 1
0 0 0
1 0 1
0 0 0
1 0 0
1 0 1
0 1 1
1 0 0
1 0 0
0 1 0
0 1 0
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1 1 0
0 1 0
1 0 0
0 0 1
1 0 0
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0 0 0
0 0 0
1 0 1
1 0 1
1 1 0
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0 0 1
0 0 0
1 0 0
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34
0
0
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0
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1
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0
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32
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0
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28
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37
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Equiprobably segregated
49
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48
42
44
50
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13
33
8
31
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5
24
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32
34
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15
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35
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37
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29
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49
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40
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47
1
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28
41
27
48
1
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1
0
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1
1
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0
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3 31 35
1 1 0
1 1 1
1 0 0
0 1 0
0 0 1
1 0 1
1 1 1
1 1 1
1 1 1
1 0 1
1 0 0
1 0 1
1 1 0
1 1 0
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1 0 0
1 0 0
1 0 1
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1 0 0
1 0 1
0 1 0
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0 0 0
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1 1 0
1 0 1
0 1 0
0 0 0
0 0 0
1 0 0
0 0 0
0 0 0
0 0 0
1 0 0
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1 0 0
0 0 0
1 0 1
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1
1
1
1
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0
1
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1
0
1
1
1
1
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1
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1
1
1
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1
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1
1
1
0
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0
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5 12 14
1 1 1
1 0 1
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0 1 0
1 1 1
1 1 1
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0 0 0
0 0 1
1 0 0
1 1 1
1 1 0
1 1 0
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0 0 0
0 0 1
1 0 1
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0 0 0
1 1 0
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1 0 0
1 0 0
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0 0 0
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0 0 1
0 0 0
0 0 0
1 0 0
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0 0 0
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21
1
1
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0
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1
1
1
1
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0
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36
0
1
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0
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1
1
1
1
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0
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32
1
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17
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33
1
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4 45 22
0 0 0
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7 24 15
0 0 0
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20
0
0
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9 29 16
1 1 1
0 0 0
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1 0 0
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19
0
1
0
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0
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1
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0
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0
0
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1
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0
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1
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23
0
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0
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1
1
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0
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41
0
0
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1
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0
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1
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26
0
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50
0
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2 10 38
0 0 0
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8 37 13
0 0 0
0 0 1
0 0 0
0 0 0
0 1 0
1 0 0
0 1 0
1 0 0
1 0 0
0 1 1
1 1 0
0 0 0
0 0 0
0 0 0
1 0 1
1 0 0
1 1 1
0 1 0
0 0 0
0 0 0
0 0 1
0 0 1
0 0 1
1 0 1
0 1 1
0 0 0
0 1 0
1 1 1
0 0 0
1 0 1
1 0 0
0 1 0
1 0 0
0 0 1
0 0 1
1 0 1
1 0 1
1 1 1
0 1 0
1 0 1
1 0 0
1 1 0
1 1 0
1 1 0
0 1 1
1 1 0
0 0 1
1 1 1
0 0 1
1 1 1
39
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
40
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
27
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
18
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
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.
11
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
25
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
43
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
42
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
34
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
46
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
44
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
A meta analysis of 471 empirical presence – absence matrices.
60
50
40
30
20
10
0
-10 -10 0
10
20
Clumping metric
Segregation metric
Raw score
0.2
0.15
0.1
0.05
0
Segregation
metric
Aggregation
metric
471 empirical matrices
In 273 matrices the segregation
metric was higher than the
aggregation metric (58%).
30
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.
1
1000
Matrix size
346 matrices were nested.
Only 3 empirical matrices were more
nested than expected from passive
sampling.
1000000
Only 73 empirical matrices
had significant turnover.
Nestedness metric
Turnover metric
15
10
5
0
-5
-10
-15
Nested
5
0
-5
-10
-15
-20
-25
AntiNested
1
1000
Matrix size
1000000
Are interaction matrices different?
From Bastola
et al. 2009
FW: food webs, P: pollination webs, SD:
seed dispersers.
Open dots: not significant at the 5%
error level
Significantly
nested
networks
From
Bascompte et
al. 2003
Observed degrees of
nestedness in empirical
mutualistic networks increase
biodiversity and minimizes the
degree of competition.
Not significantly
nested
networks
Nestedness and specialization
Part of generalist
species
Species
A
B
C
D
E
F
G
H
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
3
1
1
1
1
1
0
0
0
4
1
1
1
1
0
0
0
0
Generalists
5
1
1
1
0
0
0
0
1
6
1
0
0
0
0
0
0
0
7
1
1
0
0
0
0
1
0
8
0
0
0
1
0
0
0
1
Generalists
Specialists
Specialists
Part of specialist
species
Generalist species interact mainly with other generalists.
Specialists interact either with generalists or with specialists.