Noisy traveling waves: effect of selection on genealogies

Abstract

For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like ${\log }^{\alpha }N$, where $N$ is the size of the population, in contrast with neutral models for which they scale like $N$. An argument relating this time scale to the diffusion constant of the noisy traveling wave leads to a prediction for $\alpha$ which agrees with our simulations. An exactly soluble case gives trees with statistics identical to those predicted for mean-field spin glasses in Parisi's theory.

4 pages, 2 figures New version includes more numerical simulations and some rewriting of the text presenting our results

Cited by in corpus (32)

• The Color Glass Condensate
• Gene surfing
• Stochastic Models of Evolution in Genetics, Ecology and Linguistics
• Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization
• Summing Pomeron loops in the dipole approach
• The survival probability of a branching random walk in presence of an absorbing wall
• Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• Quantum chromodynamics at high energy and statistical physics
• Quasi-stationary regime of a branching random walk in presence of an absorbing wall
• Universal tree structures in directed polymers and models of evolving populations
• Simulation of quasi-stationary distributions on countable spaces
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• Lecture notes on "Quantum chromodynamics and statistical physics"
• Fluctuations and first-passage properties of systems of Brownian particles with reset
• Branching Brownian motion with selection
• Self-energy corrections to anisotropic Fermi surfaces
• Dense-dilute factorization for a class of stochastic processes and for high energy QCD
• Fluctuations of a swarm of Brownian bees
• Competition in a system of Brownian particles: Encouraging achievers
• F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• Stochastic drift in discrete waves of non-locally interacting-particles
• First correction to JIMWLK evolution from the classical equations of motion
• Negative large deviations of the front velocity of $N$-particle branching Brownian motion
• Spreading speed of locally regulated population models in macroscopically heterogeneous environments
• Probabilities of moderately atypical fluctuations of the size of a swarm of Brownian Bees
• Rank Dependent Branching-Selection Particle Systems
• A geometrical scaling solution to the BFKL Pomeron Calculus in the saturation domain
• Innovation and imitation
• FKPP fronts in quenched random media
• The all-time maximum for branching Brownian motion with absorption conditioned on long-time survival