Related papers: A branching process with coalescence to model rand…

Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…

We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the…

Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network,…

Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…

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 are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An…

Phylogenetic networks represent evolutionary history of species and can record natural reticulate evolutionary processes such as horizontal gene transfer and gene recombination. This makes phylogenetic networks a more comprehensive…

The rich and varied ways that genetic material can be passed between species has motivated extensive research into the theory of phylogenetic networks. Features that align with biological processes, or with desirable mathematical…

A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the…

Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can…

We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…

Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…

We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…

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…

Biological networks such as gene regulatory networks possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated…

Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule…

Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…

Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their `level', i.e. based on…