Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization

Abstract

We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size.

26 pages

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Cited by in corpus (49)

• Genealogies of rapidly adapting populations
• Predicting evolution from the shape of genealogical trees
• Genetic draft, selective interference, and population genetics of rapid adaptation
• The noisy edge of traveling waves
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• The speed of evolution in large asexual populations
• The genealogy of branching Brownian motion with absorption
• Coalescence, genetic diversity in sexual populations under selection
• Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations
• Asexual Evolution Waves: Fluctuations and Universality
• Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
• 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
• Emergence of clones in sexual populations
• Simulation of quasi-stationary distributions on countable spaces
• A new approach to computing the asymptotics of the position of Fisher-KPP fronts
• Genealogies in simple models of evolution
• Large deviations for the branching Brownian motion in presence of selection or coalescence
• Branching random walk with selection at critical rate
• How genealogies are affected by the speed of evolution
• An invariance principle for branching diffusions in bounded domains
• Recent progress in coalescent theory
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• Fluctuations and first-passage properties of systems of Brownian particles with reset
• Particle-number distribution in large fluctuations at the tip of branching random walks
• The genealogy of a solvable population model under selection with dynamics related to directed polymers
• Mosaic length and finite interaction-range effects in a one dimensional random energy model
• Front propagation and quasi-stationary distributions: the same selection principle?
• $N$-Branching random walk with $\alpha$-stable spine
• An example of Brunet-Derrida behavior for a branching-selection particle system on $\mathbb{Z}$
• Fluctuations of a swarm of Brownian bees
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• F-KPP Scaling limit and selection principle for a Brunet-Derrida type particle system
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• Rank Dependent Branching-Selection Particle Systems
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• A Spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent
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