University of Oulu

Muff, S., Niskanen, A. K., Saatoglu, D., Keller, L. F., & Jensen, H. (2019). Animal models with group-specific additive genetic variances: extending genetic group models. Genetics Selection Evolution, 51(1).

Animal models with group-specific additive genetic variances : extending genetic group models

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Author: Muff, Stefanie1,2; Niskanen, Alina K.3,4; Saatoglu, Dilan3;
Organizations: 1Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, Zurich, Switzerland
2Department of Biostatistics, Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Hirschengraben 84, Zurich, Switzerland
3Department of Biology, Centre for Biodiversity Dynamics, Norwegian University of Science and Technology, Høgskoleringen 5, Trondheim, Norway
4Department of Ecology and Genetics, University of Oulu, P.O. Box 3000, Oulu, Finland
5Zoological Museum, University of Zurich, Karl-Schmid-Strasse 4, Zurich, Switzerland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.4 MB)
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Language: English
Published: Springer Nature, 2019
Publish Date: 2019-09-04


Background: The animal model is a key tool in quantitative genetics and has been used extensively to estimate fundamental parameters, such as additive genetic variance or heritability. An implicit assumption of animal models is that all founder individuals derive from a single population. This assumption is commonly violated, for instance in crossbred livestock or when a meta-population is split into genetically diferentiated subpopulations. Ignoring that base populations are genetically heterogeneous and thus split into diferent ‘genetic groups’ may lead to biased parameter estimates, especially for additive genetic variance. To avoid such biases, genetic group animal models, which account for the presence of more than one genetic group, have been proposed. Unfortunately, the method to date is only computationally feasible when the breeding values of the groups are allowed to difer in their means, but not in their variances.

Results: We present an extension of the animal model that permits estimation of group-specifc additive genetic variances. This is achieved by employing group-specifc relatedness matrices for the breeding value components to diferent genetic groups. We derive these matrices by decomposing the full relatedness matrix via the generalized Cholesky decomposition, and by scaling the respective matrix components for each group. We propose a computationally convenient approximation for the matrix component that encodes for the Mendelian sampling variance, and show that this approximation is not critical. In addition, we explain why segregation variances are often negligible when analyzing the complex polygenic traits that are frequently the focus of evolutionary ecologists and animal breeders. Simulations and an example from an insular meta-population of house sparrows in Norway with three distinct genetic groups illustrate that the method is successful in estimating group-specifc additive genetic variances, and that segregation variances are indeed negligible in the empirical example.

Conclusions: Quantifying diferences in additive genetic variance within and among populations is of major biological interest in ecology, evolution, and animal and plant breeding. The proposed method allows to estimate such differences for subpopulations that form a connected set of populations, and may thus also be useful to study temporal or spatial variation of additive genetic variances.

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Series: Genetics selection evolution
ISSN: 0999-193X
ISSN-E: 1297-9686
ISSN-L: 0999-193X
Volume: 51
Article number: 7
DOI: 10.1186/s12711-019-0449-7
Type of Publication: A1 Journal article – refereed
Field of Science: 1184 Genetics, developmental biology, physiology
Funding: SM and LFK were funded by the Faculty of Science of the University of Zurich. This study was supported by grants from the Research Council of Norway (programmes STORFORSK, Strategic University Program in Conservation Biology, projects 221956 and 274930), the Norwegian Directorate for Nature Management, the EU-commission (project METABIRD), and the Academy of Finland (project 295204 to AN). This work was also partly supported by the Research Council of Norway through its Centres of Excellence funding scheme, project 223257).
Academy of Finland Grant Number: 295204
Detailed Information: 295204 (Academy of Finland Funding decision)
Copyright information: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.