Analyzing and reconstructing reticulation networks under timing constraints

Reticulation networks are now frequently used to model the history of life for various groups of organisms whose evolutionary past is likely to include reticulation events like 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. On the other hand, if a reticulation network is not temporal, it is always possible to resolve this issue by adding a number of additional unsampled or extinct taxa. In the first half of the paper, we show that deciding whether a given number of additional taxa is sufficient to transform a non-temporal reticulation network into a temporal one is an NP-complete problem. As one is often given a set of gene trees instead of a network in the context of hybridization, this motivates the second half of the paper which provides an algorithm for reconstructing a temporal hybridization network that simultaneously explains the ancestral history of two trees or indicates that no such network exists. We highlight two practical applications of this algorithm and illustrate the second application on a grass data set

Representing Partitions on Trees

In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set X of species from a multiset Π of partitions corresponding to various attributes of these species. One approach that is used to solve this problem is to try instead to associate a tree (or even a network) to the multiset ΣΠ consisting of all those bipartitions {A,X − A} with A a part of some partition in Π. The rational behind this approach is that a phylogenetic tree with leaf set X can be uniquely represented by the set of bipartitions of X induced by its edges. Motivated by these considerations, given a multiset Σ of bipartitions corresponding to a phylogenetic tree on X, in this paper we introduce and study the set P(Σ) consisting of those multisets of partitions Π of X with ΣΠ = Σ. More specifically, we characterize when P(Σ) is non-empty, and also identify some partitions in P(Σ) that are of maximum and minimum size. We also show that it is NP-complete to decide when P(Σ) is non-empty in case Σ is an arbitrary multiset of bipartitions of X. Ultimately, we hope that by gaining a better understanding of the mapping that takes an arbitrary partition system Π to the multiset ΣΠ, we will obtain new insights into the use of median networks and, more generally, split-networks to visualize sets of partitions

Deposition of general ellipsoidal particles

We present a systematic overview of granular deposits composed of ellipsoidal particles with different particle shapes and size polydispersities. We study the density and anisotropy of such deposits as functions of size polydispersity and two shape parameters that fully describe the shape of a general ellipsoid. Our results show that, while shape influences significantly the macroscopic properties of the deposits, polydispersity plays apparently a secondary role. The density attains a maximum for a particular family of non-symmetrical ellipsoids, larger than the density observed for prolate or oblate ellipsoids. As for anisotropy measures, the contact forces show are increasingly preferred along the vertical direction as the shape of the particles deviates for a sphere. The deposits are constructed by means of an efficient molecular dynamics method, where the contact forces are efficiently and accurately computed. The main results are discussed in the light of applications for porous media models and sedimentation processes.Comment: 7 pages, 8 figure

Extremely small amounts of B[a]P residues remobilised in long-term contaminated soils : A strong case for greater focus on readily available and not total-extractable fractions in risk assessment

There is a lack of understanding about the potential for remobilisation of polycyclic aromatic hydrocarbons (PAHs) residues in soils, specifically after the removal of readily available fractions, and the likelihood to cause harm to human and environmental health. Sequential solvent extractions, using butanol (BuOH), dichloromethane/acetone, and methanolic saponification were used to investigate the time-dependent remobilisation of B[a]P residues in aged soils, after removal of readily available or total-extractable fractions. After 120 d of aging, BuOH-remobilised B[a]P were small or extremely small ranging from 2.3 ± 0.1 mg/kg to 4.5 ± 0.5 mg/kg and from 0.9 ± 0.0 mg/kg to 1.0 ± 0.1 mg/kg, after removal of readily available and total-extractable fractions, respectively. After removal of readily available fractions, the remobilisation rates of B[a]P residues were constant over 5 re-equilibration times, as shown by first-order kinetics. The amounts of B[a]P remobilised significantly (p < 0.05) decreased with aging, particularly in hard organic carbon-rich soils. After 4 years of aging, BuOH- and total-remobilised B[a]P were generally < 5% of the initially spiked 50 mg/kg. Based on the findings of this study, the potential or significant potential for B[a]P NERs in soils to cause significant harm to human and environmental health are minimal

Carbon nanomaterials in clean and contaminated soils: environmental implications and applications

The exceptional sorptive ability of carbon nanomaterials (CNMs) for hydrophobic organic contaminants (HOCs) is driven by their characteristically large reactive surface areas and highly hydrophobic nature. Given these properties, it is possible for CNMs to impact on the persistence, mobility and bioavailability of contaminants within soils, either favourably through sorption and sequestration, hence reducing their bioavailability, or unfavourably through increasing contaminant dispersal. This review considers the complex and dynamic nature of both soil and CNM physicochemical properties to determine their fate and behaviour, together with their interaction with contaminants and the soil microflora. It is argued that assessment of CNMs within soil should be conducted on a case-by-case basis and further work to assess the long-term stability and toxicity of sorbed contaminants, as well as the toxicity of CNMs themselves, is required before their sorptive abilities can be applied to remedy environmental issues

Folding and unfolding phylogenetic trees and networks

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network $N$ can be "unfolded" to obtain a MUL-tree $U(N)$ and, conversely, a MUL-tree $T$ can in certain circumstances be "folded" to obtain a phylogenetic network $F(T)$ that exhibits $T$. In this paper, we study properties of the operations $U$ and $F$ in more detail. In particular, we introduce the class of stable networks, phylogenetic networks $N$ for which $F(U(N))$ is isomorphic to $N$, characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network $N$ can be related to displaying the tree in the MUL-tree $U(N)$. To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view $U(N)$ as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in $U(N)$ and reconcilingphylogenetic trees with networks

A Note on Encodings of Phylogenetic Networks of Bounded Level

Driven by the need for better models that allow one to shed light into the question how life's diversity has evolved, phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? In this note, we present a complete answer to this question for the special case of a level-1 (phylogenetic) network by characterizing those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. Given that this type of network forms the first layer of the rich hierarchy of level-k networks, k a non-negative integer, it is natural to wonder whether our arguments could be extended to members of that hierarchy for higher values for k. By giving examples, we show that this is not the case