The neutral model approach

1. The neutral model approach Stephen P. Hubbell (1942- MotooKimura (1924-1994)

2. 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

3. 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

4. The speciation modes 5 patches with individuals of different lineages Point mutation Peripheral isolate Fission track I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 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

5. 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)

6. 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)

7. 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)

8. 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)

9. 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

10. 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

11. 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

12. 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

13. 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