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Concordance between species trees and gene trees with multiple mergers of ancestral lineages

Presented by: 
B Eldon [Oxford]
Monday 20th June 2011 - 16:30 to 16:50
INI Seminar Room 1
Concordance between species trees and gene genealogies are considered for gene genealogies allowing multiple mergers of ancestral lineages. Donnelly and Kurtz, Pitman, and Sagitov independently introduced coalescent processes (Lambda coalescent) that allow asynchronous multiple mergers of ancestral lineages. Kingman's coalescent allows only two ancestral lineages to merge at a time. Lambda coalescents may be more appropriate than Kingman's coalescent for some marine organisms with high fecundity and broadcast spawning. Multiple mergers, ie allowing any number of ancestral lineages present each time to coalesce, complicates computations. Two methods will be presented to compute the concordance, one relies on enumeration of all possible sequences of mergers, and the other is the spectral decomposition of the rate matrix. Results will be presented for species trees consisting of two to four species, and for different Lambda coalescents.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons