Quantifying the difference between phylogenetic diversity and diversity indices.

Phylogenetic diversity is a popular measure for quantifying the biodiversity of a collection Y of species, while phylogenetic diversity indices provide a way to apportion phylogenetic diversity to individual species. Typically, for some specific diversity index, the phylogenetic diversity of Y is not equal to the sum of the diversity indices of the species in Y. In this paper, we investigate the extent of this difference for two commonly-used indices: Fair Proportion and Equal Splits.

Counting and optimising maximum phylogenetic diversity sets.

In conservation biology, phylogenetic diversity (PD) provides a way to quantify the impact of the current rapid extinction of species on the evolutionary 'Tree of Life'. This approach recognises that extinction not only removes species but also the branches of the tree on which unique features shared by the extinct species arose. In this paper, we investigate three questions that are relevant to PD.

Trinets encode orchard phylogenetic networks.

Rooted triples, rooted binary phylogenetic trees on three leaves, are sufficient to encode rooted binary phylogenetic trees. That is, if [Formula: see text] and [Formula: see text] are rooted binary phylogenetic X-trees that infer the same set of rooted triples, then [Formula: see text] and [Formula: see text] are isomorphic. However, in general, this sufficiency does not extend to rooted binary phylogenetic networks.

Defining phylogenetic networks using ancestral profiles.

Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is to consider its 'ancestral profile' (the number of paths from each ancestral vertex to each leaf). In general, this information does not uniquely determine the underlying phylogenetic network.

Caterpillars on three and four leaves are sufficient to reconstruct binary normal networks.

While every rooted binary phylogenetic tree is determined by its set of displayed rooted triples, such a result does not hold for an arbitrary rooted binary phylogenetic network. In particular, there exist two non-isomorphic rooted binary temporal normal networks that display the same set of rooted triples. Moreover, without any structural constraint on the rooted phylogenetic networks under consideration, similarly negative results have also been established for binets and trinets which are rooted subnetworks on two and three leaves, respectively.

A class of phylogenetic networks reconstructable from ancestral profiles.

Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set X of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate processes (for example, hybrid evolution, endosymbiosis, and lateral gene transfer). A major goal in systematic biology is to infer evolutionary relationships, and while phylogenetic trees can be uniquely determined from various simple combinatorial data on X, for networks the reconstruction question is much more subtle.

Tree-based networks: characterisations, metrics, and support trees.

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic tree T, called a base tree, and adding arcs between arcs of T. The class of phylogenetic networks that can be obtained in this way is called tree-based networks and includes the prominent classes of tree-child and reticulation-visible networks.

When is a Phylogenetic Network Simply an Amalgamation of Two Trees?

Phylogenetic networks generalise phylogenetic (evolutionary) trees by allowing for the representation of reticulation (non-treelike) events. The structure of such networks is often viewed by the phylogenetic trees they embed. In this paper, we determine when a phylogenetic network [Formula: see text] has two phylogenetic tree embeddings which collectively contain all of the edges of [Formula: see text].

Quarnet Inference Rules for Level-1 Networks.

An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set X of species from a collection of trees, each having leaf-set some subset of X. In the 1980s, Colonius and Schulze gave certain inference rules for deciding when a collection of 4-leaved trees, one for each 4-element subset of X, can be simultaneously displayed by a single supertree with leaf-set X.

Recovering normal networks from shortest inter-taxa distance information.

Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf vertex is the parent of a tree vertex or a leaf. Up to a certain equivalence, it has been recently shown that, under two different types of weightings, edge-weighted tree-child networks are determined by their collection of distances between each pair of taxa.

On the information content of discrete phylogenetic characters.

Phylogenetic inference aims to reconstruct the evolutionary relationships of different species based on genetic (or other) data. Discrete characters are a particular type of data, which contain information on how the species should be grouped together. However, it has long been known that some characters contain more information than others.

Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks.

Over the last fifteen years, phylogenetic networks have become a popular tool to analyse relationships between species whose past includes reticulation events such as hybridisation or horizontal gene transfer. However, the space of phylogenetic networks is significantly larger than that of phylogenetic trees, and how to analyse and search this enlarged space remains a poorly understood problem. Inspired by the widely-used rooted subtree prune and regraft (rSPR) operation on rooted phylogenetic trees, we propose a new operation-called subnet prune and regraft (SNPR)-that induces a metric on the space of all rooted phylogenetic networks on a fixed set of leaves.

On the quirks of maximum parsimony and likelihood on phylogenetic networks.

Maximum parsimony is one of the most frequently-discussed tree reconstruction methods in phylogenetic estimation. However, in recent years it has become more and more apparent that phylogenetic trees are often not sufficient to describe evolution accurately. For instance, processes like hybridization or lateral gene transfer that are commonplace in many groups of organisms and result in mosaic patterns of relationships cannot be represented by a single phylogenetic tree.

Phylogenetic Networks with Every Embedded Phylogenetic Tree a Base Tree.

We show that the class of tree-child networks is precisely the class of tree-based networks with the property that every embedded phylogenetic tree is a base tree.

Determining phylogenetic networks from inter-taxa distances.

We consider the problem of determining the topological structure of a phylogenetic network given only information about the path-length distances between taxa. In particular, one of the main results of the paper shows that binary tree-child networks are essentially determined by such information.

Phylogenetic networks that display a tree twice.

In the last decade, the use of phylogenetic networks to analyze the evolution of species whose past is likely to include reticulation events, such as horizontal gene transfer or hybridization, has gained popularity among evolutionary biologists. Nevertheless, the evolution of a particular gene can generally be described without reticulation events and therefore be represented by a phylogenetic tree. While this is not in contrast to each other, it places emphasis on the necessity of algorithms that analyze and summarize the tree-like information that is contained in a phylogenetic network.

Cherry picking: a characterization of the temporal hybridization number for a set of phylogenies.

Recently, we have shown that calculating the minimum-temporal-hybridization number for a set [Formula: see text] of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when [Formula: see text] consists of exactly two trees. In this paper, we give the first characterization of the problem for [Formula: see text] being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence.

Amalgamating source trees with different taxonomic levels.

Supertree methods combine a collection of source trees into a single parent tree or supertree. For almost all such methods, the terminal taxa across the source trees have to be non-nested for the output supertree to make sense. Motivated by Page, the first supertree method for combining rooted source trees where the taxa can be hierarchically nested is called AncestralBuild.

Budgeted Nature Reserve Selection with diversity feature loss and arbitrary split systems.

Arising in the context of biodiversity conservation, the Budgeted Nature Reserve Selection (BNRS) problem is to select, subject to budgetary constraints, a set of regions to conserve so that the phylogenetic diversity (PD) of the set of species contained within those regions is maximized. Here PD is measured across either a single rooted tree or a single unrooted tree. Nevertheless, in both settings, this problem is NP-hard.

Quantifying hybridization in realistic time.

Recently, numerous practical and theoretical studies in evolutionary biology aim at calculating the extent to which reticulation-for example, horizontal gene transfer, hybridization, or recombination-has influenced the evolution for a set of present-day species. It has been shown that inferring the minimum number of hybridization events that is needed to simultaneously explain the evolutionary history for a set of trees is an NP-hard and also fixed-parameter tractable problem. In this article, we give a new fixed-parameter algorithm for computing the minimum number of hybridization events for when two rooted binary phylogenetic trees are given.

Quantifying the extent of lateral gene transfer required to Avert a 'genome of Eden'.

The complex pattern of presence and absence of many genes across different species provides tantalising clues as to how genes evolved through the processes of gene genesis, gene loss, and lateral gene transfer (LGT). The extent of LGT, particularly in prokaryotes, and its implications for creating a 'network of life' rather than a 'tree of life' is controversial. In this paper, we formally model the problem of quantifying LGT, and provide exact mathematical bounds, and new computational results.

Analyzing and reconstructing reticulation networks under timing constraints.

Reticulation networks are now frequently used to model the history of life for various groups of species whose evolutionary past is likely to include reticulation events such as horizontal gene transfer or hybridization. However, the reconstructed networks are rarely guaranteed to be temporal. If a reticulation network is temporal, then it satisfies the two biologically motivated timing constraints of instantaneously occurring reticulation events and successively occurring speciation events.

Hybridization in nonbinary trees.

Reticulate evolution--the umbrella term for processes like hybridization, horizontal gene transfer, and recombination--plays an important role in the history of life of many species. Although the occurrence of such events is widely accepted, approaches to calculate the extent to which reticulation has influenced evolution are relatively rare. In this paper, we show that the NP-hard problem of calculating the minimum number of reticulation events for two (arbitrary) rooted phylogenetic trees parameterized by this minimum number is fixed-parameter tractable.

Selecting taxa to save or sequence: desirable criteria and a greedy solution.

Three desirable properties for any method of selecting a subset of evolutionary units (EUs) for conservation or for genomic sequencing are discussed. These properties are spread, stability, and applicability. We are motivated by a practical case in which the maximization of phylogenetic diversity (PD), which has been suggested as a suitable method, appears to lead to counterintuitive collections of EUs and does not meet these three criteria.

Nature reserve selection problem: a tight approximation algorithm.

The Nature Reserve Selection Problem is a problem that arises in the context of studying biodiversity conservation. Subject to budgetary constraints, the problem is to select a set of regions to conserve so that the phylogenetic diversity of the set of species contained within those regions is maximized. Recently, it was shown in a paper by Moulton et al.