title: Genome-wide selection by mixed model ridge regression and extensions based on geostatistical models.
abstract: BACKGROUND
  The success of genome-wide selection (GS) approaches will depend crucially on the availability of efficient and easy-to-use computational tools. Therefore, approaches that can be implemented using mixed models hold particular promise and deserve detailed study. A particular class of mixed models suitable for GS is given by geostatistical mixed models, when genetic distance is treated analogously to spatial distance in geostatistics.
  
  
  METHODS
  We consider various spatial mixed models for use in GS. The analyses presented for the QTL-MAS 2009 dataset pay particular attention to the modelling of residual errors as well as of polygenetic effects.
  
  
  RESULTS
  It is shown that geostatistical models are viable alternatives to ridge regression, one of the common approaches to GS. Correlations between genome-wide estimated breeding values and true breeding values were between 0.879 and 0.889. In the example considered, we did not find a large effect of the residual error variance modelling, largely because error variances were very small. A variance components model reflecting the pedigree of the crosses did not provide an improved fit.
  
  
  CONCLUSIONS
  We conclude that geostatistical models deserve further study as a tool to GS that is easily implemented in a mixed model package.
authors.affiliation: Bioinformatics Unit, Institute for Crop Production and Grassland Research, Universität Hohenheim, Fruwirthstrasse 23, 70599 Stuttgart, Germany. torben.schulz-streeck@uni-hohenheim.de.
authors.forename: Torben
authors.initials: T
authors.lastname: Schulz-Streeck
authors.forename: Hans-Peter
authors.initials: HP
authors.lastname: Piepho