title: Topology and inference for Yule trees with multiple states.
abstract: We introduce two models for random trees with multiple states motivated by studies of trait dependence in the evolution of species. Our discrete time model, the multiple state ERM tree, is a generalization of Markov propagation models on a random tree generated by a binary search or 'equal rates Markov' mechanism. Our continuous time model, the multiple state Yule tree, is a generalization of the tree generated by a pure birth or Yule process to the tree generated by multi-type branching processes. We study state dependent topological properties of these two random tree models. We derive asymptotic results that allow one to infer model parameters from data on states at the leaves and at branch-points that are one step away from the leaves.
authors.affiliation: Department of Mathematics and Statistics, Concordia University, Montreal, QC, H3G 1M8, Canada. lea.popovic@concordia.ca.
authors.forename: Lea
authors.initials: L
authors.lastname: Popovic
authors.affiliation: Department of Mathematics and Statistics, Concordia University, Montreal, QC, H3G 1M8, Canada.
authors.forename: Mariolys
authors.initials: M
authors.lastname: Rivas
mesh_terms: D002965:Classification / Q000379:methods*; D008390:Markov Chains; D008957:Models, Genetic; D010802:Phylogeny
keywords: Ancestral tree; Binary search tree; Multi-type branching process; Parameter reconstruction; Tree topology; Yule tree