Polymorphic evolution sequence and evolutionary branching

DOI10.1007/s00440-010-0292-9zbMath1225.92040arXiv0812.1655OpenAlexW3100519101MaRDI QIDQ644791

Sylvie Méléard, Nicolas Champagnat

Publication date: 7 November 2011

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.1655

zbMATH Keywords

adaptive dynamicsevolutionary branchingcompetitive Lotka-Volterra systempolymorphic evolution sequencefitness of invasionmutation-selection individual-based model

Mathematics Subject Classification ID

Related Items (38)

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models ⋮ Stochastic eco-evolutionary model of a prey-predator community ⋮ The polymorphic evolution sequence for populations with phenotypic plasticity ⋮ A rigorous model study of the adaptive dynamics of Mendelian diploids ⋮ The effect of recurrent mutations on genetic diversity in a large population of varying size ⋮ Unnamed Item ⋮ On the establishment of a mutant ⋮ Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks ⋮ Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems ⋮ Measure framework for the pure selection equation: global well posedness and numerical investigations ⋮ Filling the gap between individual-based evolutionary models and Hamilton-Jacobi equations ⋮ A new proof for the convergence of an individual based model to the trait substitution sequence ⋮ Scaling limit of an adaptive contact process ⋮ Existence, uniqueness and ergodicity for the centered Fleming-Viot process ⋮ Random Modeling of Adaptive Dynamics and Evolutionary Branching ⋮ Multiscale eco-evolutionary models: from individuals to populations ⋮ Adaptation in a stochastic multi-resources chemostat model ⋮ On Λ-Fleming–Viot processes with general frequency-dependent selection ⋮ Invasion and fixation of microbial dormancy traits under competitive pressure ⋮ Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer ⋮ The interplay of two mutations in a population of varying size: A stochastic eco-evolutionary model for clonal interference ⋮ Stochastic individual-based models with power law mutation rate on a general finite trait space ⋮ Direct competition results from strong competition for limited resource ⋮ Small jumps asymptotic of the moving optimum Poissonian SDE ⋮ Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex ⋮ The evolutionary limit for models of populations interacting competitively via several resources ⋮ Survival of a recessive allele in a Mendelian diploid model ⋮ An eco-evolutionary approach of adaptation and recombination in a large population of varying size ⋮ The recovery of a recessive allele in a Mendelian diploid model ⋮ Crossing a fitness valley as a metastable transition in a stochastic population model ⋮ A birth-death model of ageing: from individual-based dynamics to evolutive differential inclusions ⋮ Genealogies of two linked neutral loci after a selective sweep in a large population of stochastically varying size ⋮ Fluctuation limits of a locally regulated population and generalized Langevin equations ⋮ From adaptive dynamics to adaptive walks ⋮ Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape ⋮ Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective ⋮ Mutual invadability near evolutionarily singular strategies for multivariate traits, with special reference to the strongly convergence stable case ⋮ The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adaptive dynamics and evolutionary stability
• Adaptive dynamics for physiologically structured population models
• On selection dynamics for continuous structured populations
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Stopping times and tightness
• Evolutionary dynamics of seed size and seedling competitive ability
• Invasion dynamics and attractor inheritance
• Resident-invader dynamics and the coexistence of similar strategies
• A microscopic probabilistic description of a locally regulated population and macroscopic approximations
• The dynamical theory of coevolution: A derivation from stochastic ecological processes
• Stationary distributions of a model of sympatric speciation
• Mathematical modeling for the life sciences
• Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models
• A microscopic interpretation for adaptive dynamics trait substitution sequence models
• The dynamics of adaptation: An illuminating example and a Hamilton--Jacobi approach
• Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics
• On existence and uniqueness of the carrying simplex for competitive dynamical systems
• From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution
• Systems of differential equations which are competitive or cooperative: III. Competing species
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems

This page was built for publication: Polymorphic evolution sequence and evolutionary branching