Related papers: Sample genealogy and mutational patterns for criti…
Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…
We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure…
We define the Sampled Moran Genealogy Process, a continuous-time Markov process on the space of genealogies with the demography of the classical Moran process, sampled through time. To do so, we begin by defining the Moran Genealogy Process…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the…
We introduce and study a model of plane random trees generalizing the famous Bienaym\'e--Galton--Watson model but where births and deaths are locally correlated. More precisely, given a random variable $(B,H)$ with values in $\{1,2,3,…
We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential…
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…
The simple Galton--Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given…
If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model.…