5,655 research outputs found
Tree Contractions and Evolutionary Trees
An evolutionary tree is a rooted tree where each internal vertex has at least
two children and where the leaves are labeled with distinct symbols
representing species. Evolutionary trees are useful for modeling the
evolutionary history of species. An agreement subtree of two evolutionary trees
is an evolutionary tree which is also a topological subtree of the two given
trees. We give an algorithm to determine the largest possible number of leaves
in any agreement subtree of two trees T_1 and T_2 with n leaves each. If the
maximum degree d of these trees is bounded by a constant, the time complexity
is O(n log^2(n)) and is within a log(n) factor of optimal. For general d, this
algorithm runs in O(n d^2 log(d) log^2(n)) time or alternatively in O(n d
sqrt(d) log^3(n)) time
Inferring Species Trees from Incongruent Multi-Copy Gene Trees Using the Robinson-Foulds Distance
We present a new method for inferring species trees from multi-copy gene
trees. Our method is based on a generalization of the Robinson-Foulds (RF)
distance to multi-labeled trees (mul-trees), i.e., gene trees in which multiple
leaves can have the same label. Unlike most previous phylogenetic methods using
gene trees, this method does not assume that gene tree incongruence is caused
by a single, specific biological process, such as gene duplication and loss,
deep coalescence, or lateral gene transfer. We prove that it is NP-hard to
compute the RF distance between two mul-trees, but it is easy to calculate the
generalized RF distance between a mul-tree and a singly-labeled tree. Motivated
by this observation, we formulate the RF supertree problem for mul-trees
(MulRF), which takes a collection of mul-trees and constructs a species tree
that minimizes the total RF distance from the input mul-trees. We present a
fast heuristic algorithm for the MulRF supertree problem. Simulation
experiments demonstrate that the MulRF method produces more accurate species
trees than gene tree parsimony methods when incongruence is caused by gene tree
error, duplications and losses, and/or lateral gene transfer. Furthermore, the
MulRF heuristic runs quickly on data sets containing hundreds of trees with up
to a hundred taxa.Comment: 16 pages, 11 figure
Reconstructing Gene Trees From Fitch's Xenology Relation
Two genes are xenologs in the sense of Fitch if they are separated by at
least one horizontal gene transfer event. Horizonal gene transfer is asymmetric
in the sense that the transferred copy is distinguished from the one that
remains within the ancestral lineage. Hence xenology is more precisely thought
of as a non-symmetric relation: is xenologous to if has been
horizontally transferred at least once since it diverged from the least common
ancestor of and . We show that xenology relations are characterized by a
small set of forbidden induced subgraphs on three vertices. Furthermore, each
xenology relation can be derived from a unique least-resolved edge-labeled
phylogenetic tree. We provide a linear-time algorithm for the recognition of
xenology relations and for the construction of its least-resolved edge-labeled
phylogenetic tree. The fact that being a xenology relation is a heritable graph
property, finally has far-reaching consequences on approximation problems
associated with xenology relations
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