Biodiversity is unevenly distributed

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Biodiversity isunevenly distributed

• Erik Rauch (NECSI, MIT)
• Yaneer Bar-Yam (NECSI)
• ICCS 2004

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• Species diversity not distributed uniformly
• Within-species diversity also important
• Resistance to disease
• Future environmental changes diversity
  evolutionary potential

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Overview

• Simple genealogical model
• Genetic distinctiveness is unevenly distributed
  in populations
• Prediction compared with experimental data
• Implications for conservation

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How is the diversity in a population distributed
within it?
A
time
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How is the diversity in a population distributed
within it?
time
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How is the diversity in a population distributed
within it?
A
time
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Diversity model
Model genome (bit string)
Generation 1
2
3
Descendants become increasingly different
from their ancestors
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Measuring diversity
Generation 1
2
3
Any mutation not already found in the
population should increase diversity
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• Assume mutations are random, constant rate
• ?Each link is a chance for mutation

Generation 1
2
3
4
5
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• Divergence is proportional to number of links
  back to common ancestor

Generation 1
2
3
4
5
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• Total diversity number of links traced back from
  living population

Generation 1
2
3
4
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Related work coalescent theory
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Account for repeated mutationsif mutation rate
large relative to state space
large state space (107)
1 mutation per generation
diversity
Smaller state Space (106)
number of links in the tree
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Reproduction

• Fixed number of sites, each with an individual
• Spatial or well-mixed
• At each time step, current population replaced by
  new generation
• New individual is offspring of a random neighbor

(could also have multiple parents)
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time
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common ancestor
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Measure of genetic distinctiveness
A
time
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Uniqueness Number of generations to common
ancestor with most closely related
group Well-mixed and spatial P(Ugtu) u-2
uniqueness u
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g number of independently inherited parts of
genome
uniqueness u
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Distribution of uniqueness

• Probability that no other lineage jumps to a
  site
• where p(T)N number of ancestors at
  time T (well-mixed 2/T), N number of sites
• Probability of uniqueness greater than u

2
2
2
2
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Prediction compared with experimental data
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• Data from genealogical tree of Pseudomonas soil
  bacteria
• (Cho Tiedje 2000)

genetic divergence r
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Simulation of sampled population

• Lineage of each sample simulated backward in time
  as random walk
• Placed at geographic coordinate corresponding to
  sample

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Uniqueness - comparison with experimental data
U(u) number of samples with uniqueness
u Distribution is long-tailed
U(u)
uniqueness u
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Implications for conservation
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Distribution of diversity by redundancy just
after population loss
D(k) number of mutations carried by k members of
population
1
10
k
Most of the remaining diversity has low redundancy
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Much of the remaining diversity disappears within
20 generations
D(k) number of mutations carried by k members of
population
just after reduction
after 20 generations
1
10
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Effect of population decline
just after reduction
after 20 generations
reduced population size
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Conclusion

• Simple model predicts experimental data
• Diversity is unevenly distributed in populations
• Conserve diversity by identifying distinctive
  groups, even just after population loss
• Boundaries arise without specific causes