Related papers: Planar Rooted Phylogenetic Networks
Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…
Galled trees are widely studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into galled networks by relaxing a structural condition. In this work, a linear recurrence formula is given…
Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
Phylogenetic networks describe the evolution of a set of taxa for which reticulate events have occurred at some point in their evolutionary history. Of particular interest is when the evolutionary history between a set of just three taxa…
A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no…
Research shows that gene duplication followed by either repurposing or removal of duplicated genes is an important contributor to evolution of gene and protein interaction networks. We aim to identify which characteristics of a network can…
Segmentation in arthropod embryogenesis represents a well-known example of body plan diversity. Striped patterns of gene expression that lead to the future body segments appear simultaneously or sequentially in long and short germ-band…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum…
Popular methods for exploring the space of rooted phylogenetic trees use rearrangement moves such as rNNI (rooted Nearest Neighbour Interchange) and rSPR (rooted Subtree Prune and Regraft). Recently, these moves were generalized to rooted…
The class of terminal planar networks was recently introduced from a biological perspective in relation to the visualization of phylogenetic networks, and its connection to upward planar networks has been established. We provide a…
Balanced minimum evolution is a distance-based criterion for the reconstruction of phylogenetic trees. Several algorithms exist to find the optimal tree with respect to this criterion. One approach is to minimize a certain linear functional…
Phylogenetic networks are generalizations of trees that allow for the modeling of non-tree like evolutionary processes. Split networks give a useful way to construct networks with intuitive distance structures induced from the associated…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Phylogenetic networks are a flexible model of evolution that can represent reticulate evolution and handle complex data. Tree-based networks, which are phylogenetic networks that have a spanning tree with the same root and leaf-set as the…
We show that the space of rooted tree-based phylogenetic networks is connected under rooted nearest-neighbour interchange (rNNI) moves.
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
A tree-based network $N$ on $X$ is called universal if every phylogenetic tree on $X$ is a base tree for $N$. Recently, binary universal tree-based networks have attracted great attention in the literature and their existence has been…
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…