biodiversity is unevenly distributed
DESCRIPTION
Biodiversity is unevenly 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. - PowerPoint PPT PresentationTRANSCRIPT
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
QuickTime™ and aTIFF (LZW) decompressor
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