Related papers: Splitting trees with neutral mutations at birth
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…
The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the "individuals" in…
Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
We consider a Moran model with recombination in a haploid population of size $N$. At each birth event, with probability $1-\rho_N R$ the offspring copies one parent's chromosome, and with probability $\rho_N R$ she inherits a chromosome…
Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory,…
Here we present the first genome wide statistical test for recessive selection. This test uses explicitly non-equilibrium demographic differences between populations to infer the mode of selection. By analyzing the transient response to a…
An important parameter in the study of population evolution is $\theta=4N\nu$, where $N$ is the effective population size and $\nu$ is the rate of mutation per locus per generation. Therefore, $\theta$ represents the mean number of…
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian…
We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions.…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampled from a fixed distribution. At each death…
In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…