The neutral model approach

Stephen P. Hubbell (1942- Motoo Kimura (1924-1994)

EI

S

All ecological patterns are now triggered by only one fundamental constant, universal biodiversity number that is the product 2pm, with p being the

speciation rate and m being the size of the metacommunity.

Metacommunity

BD

EI

BD

EI

BD

EI

BD

EI

BD

EI

BD

P

P

P

P

Local community

Ecological drift Zero sum multinomial

Neutral models try to explain ecological patterns by five basic stochastic processes:

- Simple birth processes - Simple death processes

- Immigration of individuals - Dispersal of individuals

- Lineage branching

Ecological driftZero sum multinomialSpecies equivalence

Ecological patterns are now triggered by one fundamental constant, the universal biodiversity number Q = 2pm, with p being the lineage branching rate and m the size of the metacommunity

Neutral models are individual based!

Although they make predictions about diversities they do not explicitly refer to species!

Diversities refer to evolutionary lineages

Metacommunity species richness: S= Q ln(Q /m)

Neutral theory of macroecology

• Irrespective of species randomly chosen individuals of an assemblage die with probability d• Irrespective of species randomly chosen individuals of an assemblage are born with probability

b• Irrespective of species randomly chosen individuals immigrate from other assemblages with

probability i• Irrespective of species randomly chosen individuals emigrate from local assemblages to others

with probability e• Irrespective of species randomly chosen individuals mutate into a new species with probability n

How does a neutral model work?

DB

E

I

S

Local community

Metacommunity

0 0 0 0 0 0iJ J iJ bJ eJ dJ J

Zero sum multinomial

Local community structure is determined by three basic parameters

The net reproduction rate r = b - d

The migration rate m = i - e

The metacommunity size J

The speciation rate n

Neutral models lack any specific biological interaction like

• Competition Mutualism

• Regulation Species specific survival

The speciation modes

I

I

I

I I

I

I I

I

I

5 patches with individuals of different lineages

Point mutation

One individual transforms into a new lineage with probability n

I

I

I

I I

I

I I

I

I

Peripheral isolate

A randomly chosen part of one lineage of a local unity

transforms into a new lineage with probability n

I

I

I

I I

I

I I

I

I

Fission track

A randomly chosen part of one lineage of the metacommunity transforms into a new lineage

with probability n

After many time steps an equilibrium is established

Analytical solution exists

2J Fundamental biodiversity number Q

ln 1J

S

a-diversity

No analytical solutions yet

The metacommuity has a log-series species abundance distribution.

1

10

100

1000

10000

0 5 10 15 20 25 30

Rank order

Abu

ndan

ce

Core species

0.1

1

10

100

0 5 10 15 20 25 30Rank order

Abu

ndan

ce

Satellite species

Neutral models make explicit predictions about

Abundance rank order relationships

Diversity and evenness

The study object: ground beetles on lake islands in Lake Mamry (Ulrich and Zalewski 2007)

Leistus rufomarginatusPhotos by Roy Anderson

Neutral models make explicit predictions about

Species - area relationships

Individuals – area relationships

0

5

10

15

20

25

30

35

40

45

0.01 0.1 1 10 100

Area

S

The study object: ground beetles on lake islands in Lake Mamry (Ulrich and Zalewski 2007)

Carabus granulatus

Neutral models make explicit predictions about

Local and regional species distributions

Regional diversity patterns

0

5

10

15

20

25

30

35

1 2 4 8 15Sites occupied

Spe

cie

s

Core and satellite species

The study object: ground beetles on lake islands in Lake Mamry (Ulrich and Zalewski 2007)

Dyschirius globosus

Neutral models make explicit predictions about

Abundance - range size relationships

Spatial species turnover

0

2

4

6

8

10

12

14

16

0.01 1 100

Mean site abundance

Occ

urre

nces

Observed

0

2

4

6

8

10

12

14

16

0.01 1 100

Mean site abundance

Occ

urre

nces

Predicted

The study object: ground beetles on lake islands in Lake Mamry (Ulrich and Zalewski 2007)

Patrobus atrorufus

Species per genus relations

Number Order Suborder SuperfamilyFamily Subfamily Genus Subgenus Species1 HymenopteraSymphyta OrussoideaOrussidae * Orussus * abietinus2 HymenopteraSymphyta Xyeloidea Xyelidae Xyelinae Xyela * longula3 HymenopteraSymphyta Xyeloidea Xyelidae Xyelinae Xyela * obscura4 HymenopteraSymphyta Xyeloidea Xyelidae Xyelinae Xyela * julii5 HymenopteraSymphyta Xyeloidea Xyelidae Xyelinae Xyela * graeca6 HymenopteraSymphyta Xyeloidea Xyelidae PleroneurinaePleroneura* dahli7 HymenopteraSymphyta Xyeloidea Xyelidae PleroneurinaePleroneura* coniferarum8 HymenopteraSymphyta MegalodontoideaPamphiliidae* Caenolyda * reticulata9 HymenopteraSymphyta MegalodontoideaPamphiliidae* Cephalcia * abietis

10 HymenopteraSymphyta MegalodontoideaPamphiliidae* Cephalcia * arvensis11 HymenopteraSymphyta MegalodontoideaPamphiliidae* Cephalcia * lariciphila12 HymenopteraSymphyta MegalodontoideaPamphiliidae* Cephalcia * falleni13 HymenopteraSymphyta MegalodontoideaPamphiliidae* Cephalcia * erythrogaster14 HymenopteraSymphyta MegalodontoideaPamphiliidae* Acantholyda* erythrocephala15 HymenopteraSymphyta MegalodontoideaPamphiliidae* Acantholyda* flaviceps16 HymenopteraSymphyta MegalodontoideaPamphiliidae* Acantholyda* pumilionis17 HymenopteraSymphyta MegalodontoideaPamphiliidae* Acantholyda* posticalis18 HymenopteraSymphyta MegalodontoideaPamphiliidae* Acantholyda* laricis19 HymenopteraSymphyta MegalodontoideaPamphiliidae* Acantholyda* hieroglyphica20 HymenopteraSymphyta MegalodontoideaPamphiliidae* Pamphilius* nemorum

To study whether phylogenetically related species occur more or less often together than expected by chance we compare observed species / genus (S/G) relations with those

obtained from a random sampling out of the respective species pool

Number Order Suborder SuperfamilyFamily Subfamily Genus Subgenus Species499 HymenopteraParasitica Proctotrup Diapriidae * Acanosem * nervosa408 HymenopteraParasitica Chalcidoid Eulophida * Achrysoch * cilla215 HymenopteraIchneumo Ichneumo Ichneumo * Aclastus * micator216 HymenopteraIchneumo Ichneumo Ichneumo * Aclastus * solutus500 HymenopteraParasitica Proctotrup Diapriidae * Aclista * ?analis501 HymenopteraParasitica Proctotrup Diapriidae * Aclista * ?hämorrhoidalis502 HymenopteraParasitica Proctotrup Diapriidae * Aclista * ?janssoni503 HymenopteraParasitica Proctotrup Diapriidae * Aclista * cantianus504 HymenopteraParasitica Proctotrup Diapriidae * Aclista * GW1505 HymenopteraParasitica Proctotrup Diapriidae * Aclista * GW2506 HymenopteraParasitica Proctotrup Diapriidae * Aclista * prolongata507 HymenopteraParasitica Proctotrup Diapriidae * Aclista * rufopetiolata

Local data

Regional data

Sampling 5000 times

the observed local number

of species and compare

observed with expect S/G

ratios

Genus SpeciesFamily

Time

Predictions from neutral theory

Phylogenetic trees

Species / genus S/G ratios are a measure of faunal similarity

Species of the same genus should be ecologically more similar than species of different genera.

Low values in relation to the expected values from the species pool point to ecological separation

S/G = 7/4

Neutral theory predicts local S/G ratios to be lower than expected from the metacommunity

Low S/G ratios are therefore not necessary an outcome of competition

Older lineages are expected to have higher local and regional abundances

More widespread lineages should be older

The total number of lineages is predicted to grow exponentially with evolutionary time

1 3 11 21 270

10

20

30

40

50

0 1 2 3 4 5 6

TimeL

ine

ag

es

z

Predictions from neutral theory

Phylogenetic trees

Genus SpeciesFamily

Time

Genus SpeciesFamily

Time

Predictions from neutral theory

Phylogenetic trees

Phylogenetic trees should look similar irrespective of the taxonomic level

Trees should be self-similar

Metacommunities with low regional diversity (b-diversity) contain higher proportions of evolutionary older lineages

Neutral theory: http://en.wikipedia.org/wiki/Unified_neutral_theory_of_biodiversity

Null and neutral models: www.uvm.edu/~ngotelli/manuscriptpdfs/gotelli_mcgill_ecography.pdf

Neutrality: www.zoology.ufl.edu/rdholt/holtpublications/189.pdf

Today’s reading