Subtree prune and regraft: a reversible real tree-valued Markov process
نویسندگان
چکیده
We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and re-graft (SPR)Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov– Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Dirichlet form hinges on a new path decomposition of the Brownian excursion. Short title: Subtree prune and re-graft
منابع مشابه
Ricci-Ollivier Curvature of the Rooted Phylogenetic Subtree-Prune-Regraft Graph
Statistical phylogenetic inference methods use tree rearrangement operations to perform either hillclimbing local search or Markov chain Monte Carlo across tree topologies. The canonical class of such moves are the subtree-prune-regraft (SPR) moves that remove a subtree and reattach it somewhere else via the cut edge of the subtree. Phylogenetic trees and such moves naturally form the vertices ...
متن کاملA 3-approximation algorithm for the subtree distance between phylogenies
In this paper, we give a (polynomial-time) 3-approximation algorithm for the rooted subtree prune and regraft distance between two phylogenetic trees. This problem is known to be NP-complete and the best previously known approximation algorithm is a 5-approximation. We also give a faster fixed-parameter algorithm for the rooted subtree prune and regraft distance than was previously known.
متن کاملOn the Computational Complexity of the Rooted Subtree Prune and Regraft Distance
The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore...
متن کاملExtremal Distances for Subtree Transfer Operations in Binary Trees
Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection (TBR), subtree prune and regraft (SPR) and rooted subtree prune and regraft (rSPR). For a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is n−Θ( √ n), extending a result of Ding, ...
متن کاملEfficiently Inferring Pairwise Subtree Prune-and-Regraft Adjacencies between Phylogenetic Trees
We develop a time-optimal O(mn)-time algorithm for the problem of constructing the subtree prune-regraft (SPR) graph on a collection of m phylogenetic trees with n leaves. This improves on the previous bound of O(mn). Such graphs are used to better understand the behaviour of phylogenetic methods and recommend parameter choices and diagnostic criteria. The limiting factor in these analyses has ...
متن کامل