Related papers: Williams' decomposition of the L\'evy continuous r…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
We introduce flows of branching processes with competition, which describe the evolution of general continuous state branching populations in which interactions between individuals give rise to a negative density dependence term. This…
We consider a neutral haploid population whose generations are not overlapping and whose size is large and constantly of $N$ individuals. Any generation is replaced by a new one and any individual has a single parent. We do not choose the…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or "driver," mutations from "passenger" mutations that have no selective effect. Toward this end, we prove results concerning the…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Test-time scaling has emerged as a promising direction for enhancing the reasoning capabilities of Large Language Models in last few years. In this work, we propose Population-Evolve, a training-free method inspired by Genetic Algorithms to…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced…
We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…
We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
In this paper, we study the speed of extinction of continuous state branching processes in subcritical L\'evy environments. More precisely, when the associated L\'evy process to the environment drifts to $-\infty$ and, under a suitable…
A randomly interacting N-species Lotka-Volterra system in the presence of a Gaussian multiplicative noise is analyzed. The investigation is focused on the role of this external noise into the statistical properties of the extinction times…
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate \lambda. We…