Asymptotic genealogy of a critical branching process
By Lea Popovic. 2004
90 citations recorded by the source corpus.
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution.
Subfields: Artificial Intelligence, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9a41cf6cae9a823159f5dc79a1275dbaa9a1835d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Amaury Lambert
- David J. Aldous
- S. Johnston
- Simon C. Harris
- Matthew I. Roberts
- Tanja Gernhard
- Denis Villemonais
- S. M'el'eard
In Finance
- Amaury Lambert
- Simon C. Harris
- David J. Aldous
- Matthew I. Roberts
- S. Johnston
- Tanja Gernhard
- Lea Popovic
- Andreas E. Kyprianou
In Mathematical Physics
- Simon C. Harris
- Matthew I. Roberts
- S. Johnston
- Amaury Lambert
- Tanja Gernhard
- David J. Aldous
- Lea Popovic
- Zhan Shi
Citations in the corpus
- The coalescent structure of continuous-time Galton–Watson trees (2017, methodology): “[19] Lambert, A. and Popovic, L. (2013).”
- Population Dynamics and Random Genealogies (2008, methodology): “We use this observation to derive a certain number of properties of these trees, including spine decompositions, a generalization of the coalescent point process of Aldous and Popovic[1,95], and connections between Lévy processes and branching processes previously discovered by Le Gall and Le Jan[86”
- A critical branching process model for biodiversity (2004, methodology): “The continuous-time branching model Tt,n conditioned on having n extant individuals has previously been explored in [17].”
- The conditioned reconstructed process. (2008, background): “Keywords: Phylogenetics, macroevolutionary models, birth-death process, recon- structed process.”