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The evolving beta coalescent


 
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1. Title Title of document The evolving beta coalescent
 
2. Creator Author's name, affiliation, country Götz Kersting; Goethe-Universität, Frankfurt; Germany
 
2. Creator Author's name, affiliation, country Jason Schweinsberg; University of California at San Diego; United States
 
2. Creator Author's name, affiliation, country Anton Wakolbinger; Goethe-Universität, Frankfurt; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) beta coalescent, evolving coalescent, total branch length, total external length, number of mergers, stable moving average processes
 
3. Subject Subject classification 60K35; 60F17; 60G52; 60G55; 92D15
 
4. Description Abstract In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time.  As the population evolves over time, the tree that represents the genealogy of the population also changes, leading to a tree-valued stochastic process known as the evolving coalescent.  Here we will consider the evolving coalescent for populations whose genealogy can be described by a beta coalescent, which is known to give the genealogy of populations with very large family sizes.  We show that as the size of the population tends to infinity, the evolution of certain functionals of the beta coalescent, such as the total number of mergers, the total branch length, and the total length of external branches, converges to a stationary stable process.  Our methods also lead to new proofs of known asymptotic results for certain functionals of the non-evolving beta coalescent.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation, Deutsche Forschungsgemeinschaft
 
7. Date (YYYY-MM-DD) 2014-07-20
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3332
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3332
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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