Related papers: The height process of a continuous state branching…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We are interested in the genealogical structure of alleles for a Bienaym\'e-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small.…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results…
We analyze the force-extension curve for a general class of systems, which are described at the mesoscopic level by a free energy depending on the extension of its components. Similarly to what is done in real experiments, the total length…
We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
We consider a population constituted by two types of individuals; each of them can produce offspring in two different islands (as a particular case the islands can be interpreted as active or dormant individuals). We model the evolution of…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…
We study the phenomenon of coming down from infinity - that is, when the process starts from infinity and never returns to it - for continuous-state branching processes with generalized drift. We provide sufficient conditions on the drift…
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 propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman,…
We consider a population growth model given by a two-type continuous-state branching process with immigration and competition, introduced by Ma. We study the relative frequency of one of the types in the population when the total mass is…
In the spirit of Duqesne and Winkel (2007) and Berestycki et al. (2011) we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equal in law to a continuous-time…