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The Sackin and Colless indices are two widely-used metrics for measuring the balance of trees and for testing evolutionary models in phylogenetics. This short paper contributes two results about the Sackin and Colless indices of trees. One…
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time…
In this article we propose a new method, which we name 'quartet neighbor joining', or 'quartet-NJ', to infer an unrooted species tree on a given set of taxa T from empirical distributions of unrooted quartet gene trees on all four-taxon…
This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as Xi-coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
We consider a neutral haploid population whose generations are not overlapping and whose size is large and constantly of $N$ individuals. Any generation is replaced by a new one and any individual has a single parent. We do not choose the…
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…
Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is…
P\'olya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate P\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with…
We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…
An important problem in evolutionary genomics is to investigate whether a certain trait measured on each sample is associated with the sample phylogenetic tree. The phylogenetic tree represents the shared evolutionary history of the samples…
The Yule branching process is a classical model for the random generation of gene tree topologies in population genetics. It generates binary ranked trees -- also called "histories" -- with a finite number $n$ of leaves. We study the…
A large class of phylogenetic networks can be obtained from trees by the addition of horizontal edges between the tree edges. These networks are called tree based networks. Reticulation-visible networks and child-sibling networks are all…
As an alternative to parsimony analyses, stochastic models have been proposed (Lewis, 2001), (Nylander, et al., 2004) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A…
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 this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…
By measuring or calculating coalescence times for several models of coalescence or evolution, with and without selection, we show that the ratios of these coalescence times become universal in the large size limit and we identify a few…