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This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied…
In a recent paper, McDiarmid, Semple, and Welsh (2015) showed that the number of tree-child networks with $n$ leaves has the factor $n^{2n}$ in its main asymptotic growth term. In this paper, we improve this by completely identifying the…
Networks are fundamental building blocks for representing data, and computations. Remarkable progress in learning in structurally defined (shallow or deep) networks has recently been achieved. Here we introduce evolutionary exploratory…
In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first…
The goal of this note is to present a general approach to define the net reproduction function for a large class of nonlinear physiologically structured population models. In particular, we are going to show that this can be achieved in a…
Phylogenetic trees play a key role in the reconstruction of evolutionary relationships. Typically, they are derived from aligned sequence data (like DNA, RNA, or proteins) by using optimization criteria like, e.g., maximum parsimony (MP).…
Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms,…
Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree `shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
The reconstruction of phylogenetic networks is an important but challenging problem in phylogenetics and genome evolution, as the space of phylogenetic networks is vast and cannot be sampled well. One approach to the problem is to solve the…
Phylogenetic networks provide a framework for representing evolutionary histories involving reticulate events such as hybridization or horizontal gene transfer. A central problem is to infer such networks from local structural information.…
Phylogenetic networks are a generalization of phylogenetic trees to leaf-labeled directed acyclic graphs that represent ancestral relationships between species whose past includes non-tree-like events such as hybridization and horizontal…
Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree…
Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant…
A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…
Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set $\mathcal{T}$ of binary binets or…
Polyploidization is an evolutionary process by which a species acquires multiple copies of its complete set of chromosomes. The reticulate nature of the signal left behind by it means that phylogenetic networks offer themselves as a…