Genomewide association mapping in model organisms such as inbred mouse strains is a promising approach for the identification of risk factors related to human diseases. However, genetic association studies in inbred model organisms are confronted by the problem of complex population structure among strains. This induces inflated false positive rates, which cannot be corrected using standard approaches applied in human association studies such as genomic control or structured association. Recent studies demonstrated that mixed models successfully correct for the genetic relatedness in association mapping in maize and Arabidopsis panel data sets. However, the currently available mixed-model methods suffer from computational inefficiency. In this article, we propose a new method, efficient mixed-model association (EMMA), which corrects for population structure and genetic relatedness in model organism association mapping. Our method takes advantage of the specific nature of the optimization problem in applying mixed models for association mapping, which allows us to substantially increase the computational speed and reliability of the results. We applied EMMA to in silico whole-genome association mapping of inbred mouse strains involving hundreds of thousands of SNPs, in addition to Arabidopsis and maize data sets. We also performed extensive simulation studies to estimate the statistical power of EMMA under various SNP effects, varying degrees of population structure, and differing numbers of multiple measurements per strain. Despite the limited power of inbred mouse association mapping due to the limited number of available inbred strains, we are able to identify significantly associated SNPs, which fall into known QTL or genes identified through previous studies while avoiding an inflation of false positives. An R package implementation and webserver of our EMMA method are publicly available.

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Efficient Control of Population Structure in Model Organism Association Mapping

Estimating and Interpreting Heritability for Plant Breeding: An Update

A strategy of using an average information matrix is shown to be computationally convenient and efficient for estimating variance components by restricted maximum likelihood (REML) in the mixed linear model. Three applications are described. The motivation for the algorithm was the estimation of variance components in the analysis of wheat variety means from 1,071 experiments representing 10 years and 60 locations in New South Wales. We also apply the algorithm to the analysis of designed experiments by incomplete block analysis and spatial analysis of field experiments.

https://www.jstor.org/stable/pdfplus/2533274.pdf

Average information REML: An efficient algorithm for variance parameter estimation in linear mixed models

Variance components due to direct and maternal effects for growth traits of Australian beef cattle

Summary - A method is described for the simultaneous estimation of variance components due to several genetic and environmental effects from unbalanced data by restricted maximum likelihood (REML). Estimates are obtained by evaluating the likelihood explicitly and using standard, derivative-free optimization procedures to locate its maximum. The model of analysis considered is the so-called Animal Model which includes the additive genetic merit of animals as a random effect, and incorporates all information on relationships between animals. Furthermore, random effects in addition to animals’ additive genetic effects, such as maternal genetic, dominance or permanent environmental effects are taken into account. Emphasis is placed entirely upon univariate analyses. Simulation is employed to investigate the efficacy of three different maximization techniques and the scope for approximation of sampling errors. Computations are illustrated with a numerical example. variance components - restricted maximum likelihood - animal model - additional random effects - derivative - free approach

/pdf/restricted-maximum-likelihood-to-estimate-variance-2l1am1o29a.pdf

S.P. Smith

Papers

A Derivative-Free Approach for Estimating Variance Components in Animal Models by Restricted Maximum Likelihood