The Tangled Nature model: a study of community structure, species area relation and species diversit

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The Tangled Nature model a study of
community structure, species area relation and
species diversity within a model of
co-evolution.

• Henrik Jeldtoft Jensen, Dept of Mathematics
• Collaborators
• Paul Anderson
• Kim Christensen
• Simone A. di Collobiano
• Matt Hall
• Daniel Lawson
• Simon Laird
• Paolo Sibani

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• Motivation
• ?How far can a minimal model go?
• ?Input mutation prone reproduction at
  
• level of individuals.
• ?Output Species formation, macro
• dynamics, SAD, SAR, etc.
• ?Check Trend in broad range of data.

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Motivation - Examples

• ?Lifetime of taxa
  

Fossil record Frequency distribution of
lifetimes of marine genus. From Newman and
Sibani, Proc. Roy. Soc. B. 266, 1593 (1999)
kk k
K

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Motivation - Examples

• ?Time dependent extinction rate
  

Fossil record Decreasing extinction
rate. From Newman and Sibani, Proc. Roy. Soc. B.
266, 1593 (1999)



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Motivation - Examples

• ?Species area relation
  

Bird species versus area Czech Republic.
From A Stizling and D Storch Ecol. Lett. 7, 60
(2004)
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Motivation - Examples
?Interaction and diversity

Kashiwag et al, J. Molec. Evol. 52, 502-509
(2001).
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List of Content

• ?Definition of the model
• ?Results
• Uncorrelated genotype space
• Structure in Genotype space
• Nature of dynamics
• Species Abundance Distribution
• Species Area Relation
• Diversity Interaction
• Error threshold
• Correlated genotype space
• ?Conclusion

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Definition Individuals
, where
and

L 3
Dynamics a time step
Annihilation Choose indiv. at
random, remove with probability
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Reproduction

• ? Choose indiv. at random
• ? Determine

occupancy at the location
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reproduction probability

from
1


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Asexual reproduction
Replace
by two copies

with probability
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Mutations

• Mutations occur with probability
• , i.e.

See also work on simplified version of model by
Rikvold Zia
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RESULTS
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Segregation in genotype space Initiation
Only one genotype Jn term 0
N(t) adjusts

Total population
Diversity

Time steps
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Intermittency
q-ESS quasi-Evolutionary Stable Strategy

of transitions in window
1 generation
generations
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Stability of the q-ESS

Consider simple adiabatic approximation.
Stability of genotype S assuming Consider Stat
ionary solution Fluctuation Fulfil

i.e.
stability



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Transitions between q-ESS caused by
co-evolutionary collective fluctuations




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Time dependence
(Average behaviour)
Total population N(t)

• 800

90 100
Diversity
Time in Generations
0
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Origin of drift? Effect of mutation
Let
convex
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N(t)
t
Not the whole explanation evolution not smooth.
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Durations
Lifetime Of individual genotype

q-ESS

Transitions
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Distribution of durations
hectic periods
q-ESS
occup. of pos.
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What is fitness? Fitness survival of the
fittest ?? (Darwin
Huxley) What does evolution do? Evolution and
adaptation increases the
fitness, the complexity, the
diversity or what ???
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Within the TaNa model

reproductive fitness
fixed But then what ?
Neglecting mutations
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Increasing complexity ?
x1
Simulation
Random
T0.25
Significant shift for correlated genotype space.
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Time evolution of Distribution of active
coupling strengths
T0.005
T0.25
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? Is something being optimised? And in what
manner?
Average behaviour
generations
Number of transitions
generations
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Single realisation and record dynamics



Extracting records from the population size

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Record dynamics


Jumping through collective adaptation space
Transition between q-ESS


Motion within one q-ESS

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the
record
Record dynamics

stochastic signal
Paolo Sibani and Peter Littlewood (in relation
to spin glass relaxation)

exponentially distributed ? Poisson process in
ln(t)


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Record dynamics

Ratio r remains non-zero
Cumulative Distribution



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Question?
It can be difficult to spot which
quantity controls the record dynamics?

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• Ecological Aspects
• Species Abundance Distribution
• Species Area Relation
• Diversity and Interaction

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Networks in genotype spaces and Species
Abundance Distribution.
Low ?
High ?
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Species Abundance species with n
individuals

T0.005
T0.25
Nature is high ?
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Species area relation
Dispersion by random walk
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Species area relation
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Species area relation
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Diversity and interaction Weight function
Density dependent Density independent Fujiyama
lanscape
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Diversity and interaction
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Origin of threshold in k A balance between
inter-species and intra-species Interaction.
Mean field sketch
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Parameter dependence
? 1 and J const No
segregation in genotype space,
i.e., no distinct species
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The Error Threshold The q-ESS are lost for
no q-ESS
q-ESS
1/k
width of distrib. of couplings
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Estimate of
hectic q-ESS
Allows q-ESS to be established
from flow balance on pos.

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Correlated type space Use a VERY large type
space 10000161080 VERY smooth
variation in Also include a conserve
resource
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Correlated type space Distribution of
couplings strengths
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Correlated type space Lifetime distribution
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Correlated type space Degree distribution
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Correlated type space Connectance
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Summary

• And conclusion

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Tangle Nature model

• Output
• Speciation
• Intermittency
• Gradual collective adaptation
• Species Abundance Distri.
• Species Area Relation
• Diversity - Interaction

• Input
• Interacting genotypes
• Frequency dependent
• selection

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• Tangled Nature Model
• Jensen
• Physica A 340, 697 (2004)
• Anderson and Jensen
• J of Theor Biol. 232/4, 551 (2004)
• Christensen, Collobiano, Hall and Jensen
• J of Theor. Biol. 216, 73 (2002)
• Hall, Christensen, Collobiano Jensen
• Phys. Rev. E 66, 011904 (2002)
• Collobiano, Christensen Jensen
• J Phys. A 36, 883 (2003)