Solving the selection-recombination equation: ancestral lines and dual processes

DOI10.25537/dm.2021v26.743-793zbMath1478.92126arXiv2003.06831MaRDI QIDQ2035567

Frederic Alberti, Ellen Baake

Publication date: 25 June 2021

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06831

zbMATH Keywords

dualitypopulation geneticsinteractive particle systemancestral selection-recombination graphMoran model with selection and recombinationselection-recombination differential equation

Mathematics Subject Classification ID

Problems related to evolution (92D15) Random graphs (graph-theoretic aspects) (05C80) Continuous-time Markov processes on general state spaces (60J25) Combinatorial probability (60C05) Genetics and epigenetics (92D10)

Related Items

Evolution with recombination as Gibbs sampling ⋮ Selection, recombination, and the ancestral initiation graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partitioning, duality, and linkage disequilibria in the Moran model with recombination
• The common ancestor type distribution of a \(\Lambda\)-Wright-Fisher process with selection and mutation
• A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent
• Haldane linearisation done right: solving the nonlinear recombination equation the easy way
• Common ancestor type distribution: a Moran model and its deterministic limit
• Ancestral processes for non-neutral models of complex diseases
• The selection mutation equation
• Cycling in simple genetic systems
• General two-locus selection models: Some objectives, results and interpretations
• Convergence of multilocus systems under weak epistasis or weak selection
• Multilocus dynamics under haploid selection
• Ancestral processes with selection
• Genealogical processes for Fleming-Viot models with selection and recombination
• The fixation probability and time for a doubly beneficial mutant
• Lines of descent under selection
• Evolutionary dynamics in the two-locus two-allele model with weak selection
• Properties of a neutral allele model with intragenic recombination
• The concept of duality and applications to Markov processes arising in neutral population genetics models
• Probabilistic structures in evolution
• Chromosome painting: how recombination mixes ancestral colors
• Effect of epistasis and linkage on fixation probability in three-locus models: an ancestral recombination-selection graph approach
• On the notion(s) of duality for Markov processes
• The general recombination equation in continuous time and its solution
• Tractable diffusion and coalescent processes for weakly correlated loci
• Closed-Form Asymptotic Sampling Distributions under the Coalescent with Recombination for an Arbitrary Number of Loci
• ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS
• Probability Models for DNA Sequence Evolution
• Haldane Linearisation of Baric Algebras
• Stable cycling in discrete-time genetic models.
• Markov Chains
• The deterministic limit of the Moran model: a uniform central limit theorem
• An Exactly Solved Model for Mutation, Recombination and Selection