589 research outputs found
The agreement distance of unrooted phylogenetic networks
A rearrangement operation makes a small graph-theoretical change to a
phylogenetic network to transform it into another one. For unrooted
phylogenetic trees and networks, popular rearrangement operations are tree
bisection and reconnection (TBR) and prune and regraft (PR) (called subtree
prune and regraft (SPR) on trees). Each of these operations induces a metric on
the sets of phylogenetic trees and networks. The TBR-distance between two
unrooted phylogenetic trees and can be characterised by a maximum
agreement forest, that is, a forest with a minimum number of components that
covers both and in a certain way. This characterisation has
facilitated the development of fixed-parameter tractable algorithms and
approximation algorithms. Here, we introduce maximum agreement graphs as a
generalisations of maximum agreement forests for phylogenetic networks. While
the agreement distance -- the metric induced by maximum agreement graphs --
does not characterise the TBR-distance of two networks, we show that it still
provides constant-factor bounds on the TBR-distance. We find similar results
for PR in terms of maximum endpoint agreement graphs.Comment: 23 pages, 13 figures, final journal versio
Rearrangement operations on unrooted phylogenetic networks
Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree prune and regraft), and TBR (tree bisection and reconnection). Recently, these operations have been extended to unrooted phylogenetic networks, which are generalisations of phylogenetic trees that can model reticulated evolutionary relationships. Here, we study global and local properties of spaces of phylogenetic networks under these three operations. In particular, we prove connectedness and asymptotic bounds on the diameters of spaces of different classes of phylogenetic networks, including tree-based and level-k networks. We also examine the behaviour of shortest TBR-sequence between two phylogenetic networks in a class, and whether the TBR-distance changes if intermediate networks from other classes are allowed: for example, the space of phylogenetic trees is an isometric subgraph of the space of phylogenetic networks under TBR. Lastly, we show that computing the TBR-distance and the PR-distance of two phylogenetic networks is NP-hard
Rooted NNI moves on tree-based phylogenetic networks
We show that the space of rooted tree-based phylogenetic networks is
connected under rooted nearest-neighbour interchange (rNNI) moves.Comment: Fixed typos and references to labels in the last subsectio
On Patchworks and Hierarchies
Motivated by questions in biological classification, we discuss some
elementary combinatorial and computational properties of certain set systems
that generalize hierarchies, namely, 'patchworks', 'weak patchworks', 'ample
patchworks' and 'saturated patchworks' and also outline how these concepts
relate to an apparently new 'duality theory' for cluster systems that is based
on the fundamental concept of 'compatibility' of clusters.Comment: 17 pages, 2 figure
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