Related papers: The site frequency spectrum for coalescing Brownia…
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…
We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…
A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted…
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 study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial,…
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years…
We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size \varepsilon_NN, usually called peripheral isolates in ecology, where N\to\infty and \varepsilon_N\to 0 in such a way that…
We study the voter model on Z with long-range interactions, as proposed by Hammond and Sheffield. We show a spacetime rescaling converges to a fractional Gaussian free field, which can be viewed as a one-parameter family of fractional…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…
A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We…
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.…
Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated…
We study coalescent processes conditional on the population pedigree under the exchangeable diploid bi-parental population model of \citet{BirknerEtAl2018}. While classical coalescent models average over all reproductive histories, thereby…
We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…
Variation in a sample of molecular sequence data informs about the past evolutionary history of the sample's population. Traditionally, Bayesian modeling coupled with the standard coalescent, is used to infer the sample's bifurcating…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of…