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Neutral evolution in spatially continuous populations.

Nick H Barton1, Frantz Depaulis, Alison M Etheridge

  • 1Institute of Cell, Animal and Population Biology, University of Edinburgh, King's Building, West Mains Road, Edinburgh, EH9 3JT, United Kingdom.

Theoretical Population Biology
|March 16, 2002
PubMed
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This study presents a new model for genetic identity in continuous populations, considering mutation, migration, and density-dependent regulation. The classical Malécot formula is accurate only for large neighborhood sizes.

Area of Science:

  • Population Genetics
  • Mathematical Biology
  • Ecology

Background:

  • Understanding genetic structure in continuous populations is crucial for evolutionary studies.
  • Previous models often simplify population interactions and spatial structures.
  • Density-dependent regulation is a key factor in real-world populations.

Purpose of the Study:

  • To develop a general recursion for the probability of identity in state for individuals in a continuous population.
  • To incorporate density-dependent regulation into population genetic models.
  • To evaluate the accuracy of the Malécot formula under these general conditions.

Main Methods:

  • Derivation of a general recursion for identity in state.
  • Development of series expansions for large neighborhood size and low mutation rates.

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  • Comparison with the classical Malécot formula.
  • Validation through simulations.

    • Main Results:

    • A novel recursion accurately models identity in state in continuous populations with mutation, migration, drift, and density-dependence.
    • The classical Malécot formula is shown to be inaccurate for small neighborhood sizes.
    • For large neighborhood sizes, the Malécot formula provides an accurate approximation, defined by effective dispersal rate, effective population density, and local scale.

    Conclusions:

    • The developed recursion provides a more comprehensive framework for studying genetic structure in continuous populations.
    • The accuracy of the Malécot formula is context-dependent, highlighting the importance of neighborhood size.
    • The study quantifies local population structure using effective dispersal, density, and scale parameters.