Genetics Selection Evolution 2009, 41:35 http://www.gsejournal.org/content/41/1/35 of huge SNP panels feasible. For example, in human genetics, assays with > 500,000 SNP are routinely used, and in cattle, pigs and sheep ~50,000 SNP chips are com- mercially available. These dense marker genotypes can be used to predict genome-wide breeding values using genomic selection (e.g. [1,2]). Genomic selection consists of the following steps: (i) estimation of the effects of all markers in a 'train- ing data set', where the individuals are phenotyped and genotyped; (ii) prediction of the breeding values of other 'evaluation' individuals by combining their marker geno- types with the estimates obtained in step (i). These steps implicitly assume that there is substantial linkage disequi- librium (LD) between the markers and the QTL, and, ide- ally, for every QTL there is a marker in perfect LD, i.e. R2 = 1, where R2 is the square of the correlation between the allele frequencies at two loci. Habier et al. [3] have dem- onstrated that breeding values can also be predicted in the absence of linkage between markers and QTL, since the markers can predict family relationships between the indi- viduals. However, substantial LD requires strong linkage, especially for the prediction of unrelated individuals, and thus dense marker genotyping. The ideal of having a marker in perfect LD with each QTL is complicated by the fact that recently, it has been shown in human genetics studies, that nearly all the genetic vari- ation of quantitative traits is due to genes with a small effect [4]. This implies that (i) there are very many QTL, and thus that the effect of a single marker may be due to a number of QTL in the region; (ii) the estimation of single gene effects will be complicated by their small size and LD with other genes; (iii) assuming a constant genetic vari- ance across the genome when estimating marker effects may be quite realistic, as was shown by Visscher et al. [5] for height in humans. The latter favours the BLUP model for the estimation of marker effects relative to non-linear models, which give more weight to positions that appear to have large effects (e.g. the BayesB model [1]). In the step estimating marker effects, the estimation of effects of very many markers is hampered by the LD, i.e. collinearity, between the marker effects. Fortunately, sim- ilar combinations of marker alleles will be found in the evaluation data set (step (ii)), especially if the individuals of steps (i) and (ii) are related (e.g. parents and offspring as in [2]). The latter implies that it is not necessary to esti- mate the effect of single markers accurately, as long as the effects of distinct haplotypes are estimated accurately by summing the effects of their marker alleles. The prediction of breeding values of 'unrelated' individuals is a particu- larly poor case, since the haplotypes in the evaluation data set can be very different from those in the training data set. Here, 'unrelated' individuals means that they are from the same population, but not structurally related to the train- ing data individuals. However, the prediction of breeding values of unrelated individuals is exactly what is required in many and perhaps the most promising applications of genomic selection, for example when using field data to predict breeding values of elite breeding stocks, the selec- tion of individuals for markers whose effects were esti- mated in an experiment on a unrelated subset of individuals, and in the case of genetic risk prediction for human diseases [6]. The aim of this study is to assess whether the breeding val- ues of unrelated individuals could be predicted with high accuracy, and what resources are required in terms of marker density and number of records in the training data set. The results are based on computer simulations of rel- atively small populations, but will be generalised using the scaling by effective size (Ne) argument from coales- cence theory [7,8]. Methods The scaling by Ne argument From the coalescence theory it is well known that, for a population in recombination-drift equilibrium, the LD between marker and QTL and amongst markers is a func- tion of Ne*c, where c is the recombination rate between the loci and Ne is the effective population size. For instance, the LD structure will be the same for a popula- tion with Ne = 100 and 1000 SNPs per Morgan (M), com- pared to a population with Ne = 1000 and 10,000 SNPs per M, i.e. for both populations, the marker density is 10 * Ne /M [9]. However, the second population requires the estimation of 10 times as many markers, which may be achieved with a similar accuracy if we have 10 times as many training data. The latter is also seen from recent predictions of the accuracy of selection [10-12]: r 2 = Nh2 Nh2 +4N eLν (1) where r is accuracy of selection; N is the number of phe- notypic training records; h2 is the trait heritability; L is genome size in Morgan; 4 NeLν is the effective number of QTL loci in the genome, which each equals the effective number of segments in the genome when the infinitesi- mal model is assumed (i.e. BLUP is used for the estima- tion of SNP effects). In the latter case, ν may be interpreted as the ratio of the effective number of segments and the actual number of segments, which is expected to be 4 NeL. Goddard [11] derived that the effective number of seg- Page 2 of 9 (page number not for citation purposes)