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Monte Carlo integration over stepping stone models for spatial genetic inference using approximate Bayesian

Stuart J E Baird1, Filipe Santos

  • 1Centro de Investigação em Biodiversidade e Recursos Genéticos (CIBIO/UP), Campus Agrário de Vairão, 4485-661 Vairão, Portugal Centre de Biologie et de Gestion des Populations (CBGP), Campus International de Baillarguet CS 30 016, 34988 Montferrier/Lez cedex. France.

Molecular Ecology Resources
|May 14, 2011
PubMed
Summary
This summary is machine-generated.

Approximate Bayesian computation (ABC) improves spatial genetic inference by simulating Kimura's stepping stone model (KSS). Bayesian averaging over mapping field data to stepping stones enhances model fit and provides new analytical resources.

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Area of Science:

  • Population Genetics
  • Computational Biology
  • Bayesian Inference

Background:

  • Analytical solutions for spatial genetic models like Kimura's stepping stone model (KSS) are often intractable.
  • Approximate Bayesian computation (ABC) offers a simulation-based alternative for Bayesian inference.
  • Mapping field observations to discrete spatial models presents significant challenges.

Purpose of the Study:

  • To develop and evaluate a Bayesian strategy for mapping continuous field data onto discrete stepping stones in spatial genetic models.
  • To enhance the inference capabilities of the KSS model using ABC.
  • To provide novel computational tools for spatial genetic data analysis.

Main Methods:

  • Utilized Approximate Bayesian computation (ABC) for Bayesian inference under the KSS.
  • Developed and applied 'Sundial' for projecting field data onto a 2D plane.
  • Generalized KSS to regular tilings and employed Bayesian averaging over stepping stone mappings using 'Tiler Durden'.
  • Introduced a novel KSS parameterization ('m Vector') based on neighborhood size.
  • Generalized spatial coalescence recursions to solve KSS coalescence numerically.

Main Results:

  • Bayesian averaging over the mapping of continuous areas to discrete stepping stones improved the fit between KSS and isolation-by-distance expectations.
  • New parameterizations and computational tools (Sundial, Tiler Durden, m Vector) were developed and made available.
  • Numerical solutions for KSS coalescence were derived, complementing simulation-based approaches.

Conclusions:

  • The developed Bayesian strategy and accompanying tools enhance the application of stepping stone models in spatial genetics.
  • The methods provide a robust framework for comparing simulation-based KSS predictions with empirical field data.
  • This work offers significant applied and analytical resources for researchers in population genetics and evolutionary biology.