Related papers: Genealogies in Expanding Populations
Branching Brownian Motion describes a system of particles which diffuse in space and split into offsprings according to a certain random mechanism. In virtue of the groundbreaking work by M. Bramson on the convergence of solutions of the…
Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that…
A core tension in the study of plurality elections is the clash between the classic Hotelling-Downs model, which predicts that two office-seeking candidates should position themselves at the median voter's policy, and the empirical…
We consider a problem of ecological inference, in which individual-level covariates are known, but labeled data is available only at the aggregate level. The intended application is modeling voter preferences in elections. In Rosenman and…
The purpose of this Note is twofold: First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete-time. In the process, we…
We consider a growing planar network where a tip grows at constant speed, branches at constant rate and inactivates when it meets a branch already created. We only consider here orthogonal branching occurring always in the same direction.…
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both…
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…
We present a general framework which can be used to prove that, in an annealed sense, rescaled spatial stochastic population models converge to generalized propagating fronts. Our work is motivated by recent results of Etheridge, Freeman,…
We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population subject to sporadic mass extinction events. By exploiting a separation of timescales property of Wright's island model,…
We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach…
Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a…
To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences…
We introduce a new class of stochastic partial differential equations (SPDEs) with seed bank modeling the spread of a beneficial allele in a spatial population where individuals may switch between an active and a dormant state.…
We dedicate this paper to Sir John Kingman on his 70th Birthday. In modern mathematical population genetics the ancestral history of a population of genes back in time is described by John Kingman's coalescent tree. Classical and modern…
We study evolving genealogies, i.e. processes that take values in the space of (marked) ultra-metric measure spaces and satisfy some sort of "consistency" condition. This condition is based on the observation that the genealogical distance…
We review recent progress in the understanding of the role of multiple- and simultaneous multiple merger coalescents as models for the genealogy in idealised and real populations with exceptional reproductive behaviour. In particular, we…
We generalize the celebrated coagulation-fragmentation duality of Pitman (1999), originally established for the PD$(\alpha,\theta)$ laws of Pitman and Yor (1997), resolving a two-decade open problem. Our framework extends the duality to…
We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the…
We consider one-dimensional biased voter models, where 1's replace 0's at a faster rate than the other way round, started in a Heaviside initial state describing the interface between two infinite populations of 0's and 1's. In the limit of…