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Fixed effect variance and the estimation of the heritability: Issues and solutions

View ORCID ProfilePierre de Villemereuil, View ORCID ProfileMichael B. Morrissey, View ORCID ProfileShinichi Nakagawa, View ORCID ProfileHolger Schielzeth
doi: https://doi.org/10.1101/159210
Pierre de Villemereuil
1School of Biological Sciences, University of Auckland, Auckland, New Zealand,
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  • For correspondence: bonamy@horus.ens.fr
Michael B. Morrissey
2School of Evolutionary Biology University of St Andrews, St Andrews, UK, KY16 9TH,
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Shinichi Nakagawa
3Evolution and Ecology Research Centre University of New South Wales, Sydney, NSW 2052, Australia,
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  • For correspondence: s.nakagawa@unsw.edu.au
Holger Schielzeth
4Population Ecology Group, Institute of Ecology, Friedrich Schiller University, Dornburger Str. 159, 07743 Jena, Germany,
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  • For correspondence: holger.schielzeth@uni-jena.de
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Abstract

Linear mixed effects models are frequently used for estimating quantitative genetic parameters, including the heritability, of traits of interest. Heritability is an important metric, because it acts as a filter that determines how efficiently phenotypic selection translates into evolutionary change. As a quantity of biological interest, it is important that the denominator, the phenotypic variance, actually reflects the amount of phenotypic variance in the relevant ecological stetting. The current practice of quantifying heritability from mixed effects models frequently deprives the heritability of variance explained by fixed effects (often leading to upward-bias) and it has been suggested to omit fixed effects when estimating heritabilities. We advocate an alternative option of fitting complex models incorporating all relevant effects, while including the variance explained by fixed effects into the estimation of heritabilities. The approach is easily implemented (an example is provided) and allows corrections for the estimation of heritability, such as the exclusion of variance arising from experimental design effects while still including all biologically relevant sources of variation. We explore the complications arising depending on the nature of the covariates included as fixed effects (e.g. biological or experimental origin, characteristics of biological covariates). Furthermore, we discuss fixed effects in non-linear and generalized linear models when fixed effects. In these cases, the variance parameters depend on the location of the intercept and hence on the scaling of the fixed effects. Integration over the biologically relevant range of fixed effects offers a preferred solution in those situations.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted July 04, 2017.
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Fixed effect variance and the estimation of the heritability: Issues and solutions
Pierre de Villemereuil, Michael B. Morrissey, Shinichi Nakagawa, Holger Schielzeth
bioRxiv 159210; doi: https://doi.org/10.1101/159210
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Fixed effect variance and the estimation of the heritability: Issues and solutions
Pierre de Villemereuil, Michael B. Morrissey, Shinichi Nakagawa, Holger Schielzeth
bioRxiv 159210; doi: https://doi.org/10.1101/159210

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