Related papers: Trees within trees: Simple nested coalescents
We study a simple solvable model describing the genesis of monomer sequences for hetero-polymers (such as proteins), as the result of the equilibration of a slow stochastic genetic selection process which is assumed to be driven by the…
It is far well accepted that the morphology of nanoparticles and nanoalloys is of paramount importance to understand their properties. Furthemore, the morphology depends on the growth mechanism with coalescence generally accepted as one the…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
We introduce a general diploid population model with self-fertilization and possible overlapping generations, and study the genealogy of a sample of $n$ genes as the population size $N$ tends to infinity. Unlike traditional approach in…
Ice nucleation plays a significant role in a large number of natural and technological processes, but it is challenging to investigate experimentally because of the small time (ns) and short length scales (nm) involved. On the other hand,…
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller…
Representation of coalescent process using pruning of trees has been used by Goldschmidt and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the $\beta(3/2,1/2)$-coalescent. By considering a pruning procedure on…
In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
Given a gene tree topology and a species tree topology, a coalescent history represents a possible mapping of the list of gene tree coalescences to associated branches of a species tree on which those coalescences take place. Enumerative…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $\sigma$-space, a moduli space of fully…
Coalescent histories provide lists of species tree branches on which gene tree coalescences can take place, and their enumerative properties assist in understanding the computational complexity of calculations central in the study of gene…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both…
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
We review recent progress in the understanding of the role of multiple- and simultaneous multiple merger coalescents as models for the genealogy in idealised and real populations with exceptional reproductive behaviour. In particular, we…
One of the goals of phylogenetic research is to find the species tree describing the evolutionary history of a set of species. But the trees derived from geneti data with the help of tree inference methods are gene trees that need not…