Biodiversity isunevenly distributed

Erik Rauch (NECSI, MIT)

Yaneer Bar-Yam (NECSI)ICCS 2004

• Species diversity not distributed uniformly

• Within-species diversity also important

– Resistance to disease

– Future environmental changes: diversity = evolutionary potential

Overview

• Simple genealogical model:– Genetic distinctiveness is unevenly

distributed in populations

• Prediction compared with experimental data

• Implications for conservation

How is the diversity in a population distributed within it?

A

time

How is the diversity in a population distributed within it?

time

How is the diversity in a population distributed within it?

A

time

uniqueness u

Diversity model

• Descendants become increasingly different from their ancestors

Model genome(bit string) Generation 1

2

3

Measuring diversity

• Any mutation not already found in the population should increase diversity

• Measure: number of loci that have more than one allele

Generation 1

2

3

• Assume mutations are random, constant rateEach link is a chance for mutation

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are needed to see this picture.

Generation 1

2

3

4

5

Divergence is proportional to number of links back to common ancestor

Generation 1

2

3

4

5

Total diversity: number of links traced back from living population

Generation 1

2

3

4

5

Related work: coalescent theory

Account for repeated mutationsif mutation rate large relative to state space

number of links in the tree

Smaller stateSpace (106)

large statespace (107)

1 mutationper generation

dive

rsity

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)

time

common ancestor

A

time

Measure of genetic distinctiveness

uniqueness u

Uniqueness:Number of generations to common ancestor with most closely related group

Well-mixed and spatial:P(U>u) ~ u-2

uniqueness u

uniqueness u

g: number of independently inherited parts of genome

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

22

Prediction compared with experimental data

gene

tic d

iver

genc

e r

Data from genealogical tree of Pseudomonas soil bacteria

(Cho & Tiedje 2000)

Simulation of sampled population

• Lineage of each sample simulated backward in time as random walk

• Placed at geographic coordinate corresponding to sample

Uniqueness - comparison with experimental data

U(u): number of samples with uniqueness u

Distribution is long-tailed

uniqueness u

U(u)

Implications for conservation

Distribution of diversity by redundancy just after population loss

D(k): number of mutations carried by k members of population

101

Most of the remaining diversity has low redundancyk

D(k): number of mutations carried by k members of population

101

just after reduction

after ~20 generations

Much of the remaining diversity disappears within 20 generations

Effect of population decline

after ~20 generations

reduced population size

just after reduction

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