关键词：
Ancestral tree
Multi-type branching process
Yule tree
Binary search tree
Tree topology
Parameter reconstruction
摘要：
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.
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