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General Methods for Evolutionary Quantitative Genetic Inference from Generalized Mixed Models.

Pierre de Villemereuil1, Holger Schielzeth2,3, Shinichi Nakagawa4

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|September 4, 2016
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Summary
This summary is machine-generated.

This study develops methods to estimate evolutionary quantitative genetic parameters for nonnormal traits using generalized linear mixed models (GLMMs). It provides a framework to derive these parameters on the observed scale, enabling accurate evolutionary predictions.

Keywords:
G matrixadditive genetic varianceevolutiongeneralized linear modelquantitative geneticsstatisticstheory

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Area of Science:

  • Evolutionary biology
  • Quantitative genetics
  • Statistical modeling

Background:

  • Standard quantitative genetic methods assume normal trait distributions, limiting their application to many ecologically relevant traits.
  • Generalized linear mixed models (GLMMs) are increasingly used for nonnormal data but provide inference on a latent scale.
  • Translating latent-scale parameters to the observed scale is crucial for biological interpretation and prediction.

Purpose of the Study:

  • To derive expressions for quantitative genetic parameters (e.g., heritability, variance components) on the observed scale from GLMMs.
  • To develop methods for predicting evolutionary responses to selection for nonnormal traits.
  • To provide a practical implementation of these methods in an R package.

Main Methods:

  • Derivation of formulas for population means, phenotypic and genetic (co)variances, and heritability from fitted GLMMs.
  • Integration and averaging over fixed effects to obtain scale-specific parameters.
  • Numerical integration techniques implemented in the R package QGglmm.
  • Incorporation of GLMM results into evolutionary prediction models.

Main Results:

  • Provides general expressions for quantitative genetic parameters on the observed scale, encompassing known formulas for binomial and Poisson traits.
  • Demonstrates the significant impact of fixed effects on these parameters and offers methods to account for them.
  • Shows that the QGglmm package accurately predicts evolutionary trajectories via simulation.
  • Successfully applies the method to a wild vertebrate population dataset.

Conclusions:

  • The developed framework allows for robust estimation and interpretation of quantitative genetic parameters for nonnormal traits using GLMMs.
  • This approach enhances the prediction of evolutionary trajectories and the understanding of evolutionary processes in natural populations.
  • The QGglmm package offers a valuable tool for researchers studying the evolution of nonnormal traits.