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The neutral model approach. Stephen P. Hubbell (1942-. Motoo Kimura (1924-1994). Neutral theory of macroecology. Ecological drift Zero sum multinomial Species equivalence.

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The neutral model approach

Stephen P. Hubbell (1942-

MotooKimura (1924-1994)


Neutral theory of macroecology

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

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

  • 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

Neutral models are individual based!

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

Diversities refer to evolutionary lineages


How does a neutral model work?

  • 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

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

Zero sum multinomial


The speciation modes

5 patches with individuals of different lineages

Point mutation

Peripheral isolate

Fission track

I

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One individual transforms into a new lineage with probability n

A randomly chosen part of one lineage of a local unity transforms into a new lineage with probability n

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

Fundamental biodiversity number Q

No analytical solutions yet

The metacommuityhas a log-seriesspeciesabundancedistribution.

a-diversity


10000

Core species

1000

100

Abundance

10

1

0

5

10

15

20

25

30

Rank order

100

Satellite species

10

Abundance

1

0.1

0

5

10

15

20

25

30

Rank order

Neutral models make explicit predictions about

Abundance rank order relationships

Diversity and evenness

Leistus rufomarginatusPhotos by Roy Anderson

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


45

40

35

30

25

S

20

15

10

5

0

0.01

0.1

1

10

100

Area

Neutral models make explicit predictions about

Species - area relationships

Individuals – area relationships

Carabus granulatus

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


35

30

25

20

Species

15

10

5

0

1

2

4

8

15

Sites occupied

Neutral models make explicit predictions about

Local and regional species distributions

Regional diversity patterns

Dyschirius globosus

Core and satellite species

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


16

16

Predicted

Observed

14

14

12

12

10

10

8

8

Occurrences

Occurrences

6

6

4

4

2

2

0

0

0.01

1

100

0.01

1

100

Mean site abundance

Mean site abundance

Neutral models make explicit predictions about

Abundance - range size relationships

Spatial species turnover

Patrobus atrorufus

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


Species per genus relations

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

Local data

Sampling 5000 times the observed local number of species and compare observed with expect S/G ratios

Regional data


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

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

S/G = 7/4


Family

Genus

Species

Time

Predictions from neutral theory

Phylogenetic trees

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

27


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


Today’s reading

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


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