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Genetic Heteroscedasticity for Domestic Animal Traits
Dalarna University, School of Technology and Business Studies, Statistics. Swedish University of Agricultural Sciences. (Komplexa system - mikrodataanalys)
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Animal traits differ not only in mean, but also in variation around the mean. For instance, one sire’s daughter group may be very homogeneous, while another sire’s daughters are much more heterogeneous in performance. The difference in residual variance can partially be explained by genetic differences. Models for such genetic heterogeneity of environmental variance include genetic effects for the mean and residual variance, and a correlation between the genetic effects for the mean and residual variance to measure how the residual variance might vary with the mean.

The aim of this thesis was to develop a method based on double hierarchical generalized linear models for estimating genetic heteroscedasticity, and to apply it on four traits in two domestic animal species; teat count and litter size in pigs, and milk production and somatic cell count in dairy cows.

The method developed is fast and has been implemented in software that is widely used in animal breeding, which makes it convenient to use. It is based on an approximation of double hierarchical generalized linear models by normal distributions. When having repeated observations on individuals or genetic groups, the estimates were found to be unbiased.

For the traits studied, the estimated heritability values for the mean and the residual variance, and the genetic coefficients of variation, were found in the usual ranges reported. The genetic correlation between mean and residual variance was estimated for the pig traits only, and was found to be favorable for litter size, but unfavorable for teat count.

Place, publisher, year, edition, pages
Uppsala: Sveriges Lantbruksuniversitet, 2014. , 54 p.
Series
Acta Universitatis agriculturae Sueciae, ISSN 1652-6880 ; 2014:43
Keyword [en]
Quantitative genetics, genetic heteroscedasticity of residuals, genetic heterogeneity of environmental variation, genetic heterogeneity of residual variance, double hierarchical generalized linear models, teat count in pigs, litter size in pigs, milk yield in cows, somatic cell count in cows
National Category
Animal and Dairy Science Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
URN: urn:nbn:se:du-14310ISBN: 978-91-576-8035-8 (print)ISBN: 978-91-576-8034-1 (print)OAI: oai:DiVA.org:du-14310DiVA: diva2:725229
Public defence
2014-06-11, Room L, Undervisningsplan 8, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2014-06-16 Created: 2014-06-16 Last updated: 2015-06-08Bibliographically approved
List of papers
1. Genetic heterogeneity of residual variance: estimation of variance components using double hierarchical generalized linear models
Open this publication in new window or tab >>Genetic heterogeneity of residual variance: estimation of variance components using double hierarchical generalized linear models
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2010 (English)In: Genetics Selection Evolution, ISSN 0999-193X, E-ISSN 1297-9686, Vol. 42, 8Article in journal (Refereed) Published
Abstract [en]

Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms.

Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.

Conclusions: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

National Category
Probability Theory and Statistics
Research subject
Complex Systems – Microdata Analysis, Statistisk modellering är grunden till en ökad förståelse inom genetik!
Identifiers
urn:nbn:se:du-10497 (URN)10.1186/1297-9686-42-8 (DOI)000277118500001 ()20302616 (PubMedID)
Available from: 2012-08-03 Created: 2012-08-03 Last updated: 2017-12-07Bibliographically approved
2. Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models
Open this publication in new window or tab >>Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models
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2012 (English)In: Genetics Research, ISSN 0016-6723, Vol. 94, no 6, 307-317 p.Article in journal (Refereed) Published
Abstract [en]

The possibility of breeding for uniform individuals by selecting animals expressing a small response to environment has been studied extensively in animal breeding. Bayesian methods for fitting models with genetic components in the residual variance have been developed for this purpose, but have limitations due to the computational demands. We use the hierarchical (h)-likelihood from the theory of double hierarchical generalized linear models (DHGLM) to derive an estimation algorithm that is computationally feasible for large datasets. Random effects for both the mean and residual variance parts of the model are estimated together with their variance/covariance components. An important feature of the algorithm is that it can fit a correlation between the random effects for mean and variance. An h-likelihood estimator is implemented in the R software and an iterative reweighted least square (IRWLS) approximation of the h-likelihood is implemented using ASReml. The difference in variance component estimates between the two implementations is investigated, as well as the potential bias of the methods, using simulations. IRWLS gives the same results as h-likelihood in simple cases with no severe indication of bias. For more complex cases, only IRWLS could be used, and bias did appear. The IRWLS is applied on the pig litter size data previously analysed by Sorensen & Waagepetersen (2003) using Bayesian methodology. The estimates we obtained by using IRWLS are similar to theirs, with the estimated correlation between the random genetic effects being −0·52 for IRWLS and −0·62 in Sorensen & Waagepetersen (2003).

Place, publisher, year, edition, pages
Cambridge University Press, 2012
Keyword
genetic heterogeneity, environmental variation, hierarchical likelihood, DHGLM
National Category
Animal and Dairy Science Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-11811 (URN)10.1017/S0016672312000766 (DOI)000314425400002 ()
Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2015-06-22Bibliographically approved
3. Variance component and breeding value estimation for genetic heterogeneity of residual variance in Swedish Holstein dairy cattle
Open this publication in new window or tab >>Variance component and breeding value estimation for genetic heterogeneity of residual variance in Swedish Holstein dairy cattle
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2013 (English)In: Journal of Dairy Science, ISSN 0022-0302, E-ISSN 1525-3198, Vol. 96, no 4, 2627-2636 p.Article in journal (Refereed) Published
Abstract [en]

Trait uniformity, or micro-environmental sensitivity, may be studied through individual differences in residual variance. These differences appear to be heritable, and the need exists, therefore, to fit models to predict breeding values explaining differences in residual variance. The aim of this paper is to estimate breeding values for micro-environmental sensitivity (vEBV) in milk yield and somatic cell score, and their associated variance components, on a large dairy cattle data set having more than 1.6 million records. Estimation of variance components, ordinary breeding values, and vEBV was performed using standard variance component estimation software (ASReml), applying the methodology for double hierarchical generalized linear models. Estimation using ASReml took less than 7 d on a Linux server. The genetic standard deviations for residual variance were 0.21 and 0.22 for somatic cell score and milk yield, respectively, which indicate moderate genetic variance for residual variance and imply that a standard deviation change in vEBV for one of these traits would alter the residual variance by 20%. This study shows that estimation of variance components, estimated breeding values and vEBV, is feasible for large dairy cattle data sets using standard variance component estimation software. The possibility to select for uniformity in Holstein dairy cattle based on these estimates is discussed.

Place, publisher, year, edition, pages
Elsevier, 2013
Keyword
dairy cattle, genetic heterogeneity, milk yield, somatic cell score
National Category
Probability Theory and Statistics
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-12687 (URN)10.3168/jds.2012-6198 (DOI)000316772000062 ()
Available from: 2013-07-01 Created: 2013-07-01 Last updated: 2017-12-06Bibliographically approved
4. Genetic Heteroscedasticity for Teat Count in Pigs
Open this publication in new window or tab >>Genetic Heteroscedasticity for Teat Count in Pigs
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics Animal and Dairy Science
Research subject
Komplexa system - mikrodataanalys
Identifiers
urn:nbn:se:du-14318 (URN)
Available from: 2014-06-16 Created: 2014-06-16 Last updated: 2014-06-30Bibliographically approved

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