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Mutualistic networks have been shown to involve complex patterns of interactions among animal and plant species. The architecture of these webs seems to pervade some of their robust and fragile behaviour. Recent work indicates that there is…

In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…

Recently, the minimum number of reticulation events that is required to simultaneously embed a collection P of rooted binary phylogenetic trees into a so-called temporal network has been characterized in terms of cherry-picking sequences.…

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…

The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…

Phylogenetic networks are rooted acyclic directed graphs in which the leaves are identified with members of a set X of species. The cluster of a vertex is the set of leaves that are descendants of the vertex. A network is "distinct-cluster"…

Interest in the inference of evolutionary networks relating species or populations has grown with the increasing recognition of the importance of hybridization, gene flow and admixture, and the availability of large-scale genomic data.…

The hybridization number problem requires us to embed a set of binary rooted phylogenetic trees into a binary rooted phylogenetic network such that the number of nodes with indegree two is minimized. However, from a biological point of view…

Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…

Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary timescales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains…

Head moves are a type of rearrangement moves for phylogenetic networks. They have mostly been studied as part of more encompassing types of moves, such as rSPR moves. Here, we study head moves as a type of moves on themselves. We show that…

Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the…

Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area of phylogenetic networks…

Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their…