A transition function expansion for a diffusion model with selection.

DOI10.1214/aoap/1019737667zbMath1171.60368OpenAlexW2045980157MaRDI QIDQ1578616

Andrew David Barbour, Robert C. Griffiths, Stewart N. Ethier

Publication date: 4 September 2000

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1019737667

Mathematics Subject Classification ID

Diffusion processes (60J60) Genetics and epigenetics (92D10) Continuous-time Markov processes on discrete state spaces (60J27) Transition functions, generators and resolvents (60J35)

Related Items (17)

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation ⋮ General selection models: Bernstein duality and minimal ancestral structures ⋮ Random evolutionary dynamics driven by fitness and house-of-cards mutations: sampling formulae ⋮ A coalescent dual process in a Moran model with genic selection ⋮ Approximate filtering via discrete dual processes ⋮ A diffusion approach to approximating preservation probabilities for gene duplicates ⋮ The frequency spectrum of a mutation, and its age, in a general diffusion model ⋮ Wright-Fisher diffusion with negative mutation rates ⋮ The site-frequency spectrum of linked sites ⋮ A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit ⋮ Optimal filtering and the dual process ⋮ A dual process for the coupled Wright-Fisher diffusion ⋮ Exact solution of the multi-allelic diffusion model ⋮ A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit ⋮ A coalescent dual process for a Wright-Fisher diffusion with recombination and its application to haplotype partitioning ⋮ Wright-Fisher diffusion bridges ⋮ Dirichlet approximation of equilibrium distributions in Cannings models with mutation

Cites Work

• The transition function of a Fleming-Viot process
• Line-of-descent and genealogical processes, and their applications in population genetics models
• Lines of descent in the diffusion approximation of neutral Wright-Fisher models
• Diffusion processes in population genetics
• The coalescent
• Equations différentielles provenant de la genetique des populations
• A reversibility problem for Fleming-Viot processes
• Ancestral processes with selection
• Genealogical processes for Fleming-Viot models with selection and recombination
• Simulating allele frequencies in a population and the genetic differentiation of populations under mutation pressure
• Weak convergence of Markov processes with extended generators
• A countable representation of the Fleming-Viot measure-valued diffusion
• Some Problems of Stochastic Processes in Genetics
• A transition density expansion for a multi-allele diffusion model
• Geometric aspects of finite and infinite-dimensional Fleming-Viot processes
• SOLUTION OF A PROCESS OF RANDOM GENETIC DRIFT WITH A CONTINUOUS MODEL
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