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The infinitesimal model: Definition, derivation, and implications.

N H Barton1, A M Etheridge2, A Véber3

  • 1Institute of Science and Technology, Am Campus I, A-3400 Klosterneuberg, Austria.

Theoretical Population Biology
|July 16, 2017
PubMed
Summary
This summary is machine-generated.

The infinitesimal model accurately describes quantitative traits by separating genetic and non-genetic factors, with genetic variance independent of parental traits. This model is mathematically justified as the limit of Mendelian inheritance with many loci.

Keywords:
EpistasisInfinitesimal modelQuantitative geneticsSelection

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Area of Science:

  • Quantitative genetics
  • Evolutionary biology
  • Population genetics

Background:

  • The infinitesimal model is a cornerstone in quantitative genetics for modeling complex traits.
  • It assumes traits are sums of genetic and environmental components, with normally distributed genetic effects.
  • Previous applications have explored its utility in various evolutionary scenarios.

Purpose of the Study:

  • To identify general conditions for the accuracy of the infinitesimal model.
  • To mathematically justify the infinitesimal model as a limit of Mendelian inheritance.
  • To explore the model's applicability to diverse evolutionary processes.

Main Methods:

  • Review of the historical development of the infinitesimal model.
  • Phenotypic level formulation incorporating evolutionary processes (drift, recombination, selection, mutation, population structure).
  • Mathematical derivation as a limit of a multi-locus model with additive effects, generalizing to epistasis.

Main Results:

  • The genetic component within families is normally distributed with variance independent of parental traits, up to an error of order 1/M (where M is the number of loci).
  • The model's accuracy is demonstrated as M approaches infinity.
  • Simulations indicate rapid convergence, potentially as fast as 1/M in some cases.

Conclusions:

  • The infinitesimal model provides a robust framework for understanding quantitative trait variation under various evolutionary pressures.
  • Its mathematical justification supports its wide applicability in evolutionary quantitative genetics.
  • The model's accuracy is strongly supported, especially with a large number of underlying genetic loci.