Related papers: Branch length statistics in phylogenetic trees und…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…
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…
In molecular systematics, evolutionary trees are reconstructed from sequences at the tips under simple models of site substitution. A central question is how much sequence data is required to reconstruct a tree accurately? The answer…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
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…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
We calculate the density and expectation for the number of lineages in a reconstructed tree with $n$ extant species. This is done with conditioning on the age of the tree as well as with assuming a uniform prior for the age of the tree.
We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have $n$ extant species today, we look at the tree distribution of the reconstructed trees-- i.e. the trees…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth-death polytomy resolver is a method of…
We study the role of phylogenetic trees on correlations in mutation processes. Generally, correlations decay exponentially with the generation number. We find that two distinct regimes of behavior exist. For mutation rates smaller than a…
A phylogenetic birth-and-death model is a probabilistic graphical model for a so-called phylogenetic profile, i.e., the size distribution for a homolog gene family at the terminal nodes of a phylogeny. Profile datasets are used in…
We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the…
With advances in sequencing technologies, there are now massive amounts of genomic data from across all life, leading to the possibility that a robust Tree of Life can be constructed. However, "gene tree heterogeneity", which is when…