Genetics Selection Evolution 2009, 41:35 http://www.gsejournal.org/content/41/1/35 ments is ∑i log2(4NNeLeiLi) , where summation is over the chromosomes and Li is the size of chromosome i. From this scaling argument and Equation (1) it is also seen that as genome size doubles, we need twice as many training records (N) to achieve a similar accuracy of pre- dicting breeding value, assuming a constant marker den- sity. Whether the latter expectation holds will be tested in the Results and Discussion section. Also, the LD structure between the QTL is equivalent if the number of QTL per M is 100 and 1000 in populations with Ne = 100 and 1000, respectively. In order to reduce computer time, the effective size used in the simulations described here will be quite low (Ne = 100), but the scaling argument makes it possible to extend the results to bigger population sizes. The use of a rela- tively low Ne does not only reduce the population size to be simulated, but also the number of generations needed to reach equilibrium between mutation, drift and recom- bination. This is because lineages coalesce faster in small populations. The genomic history of the populations In general, the model for the population history mimics that of coalescence simulations [7], however a forward simulation approach is used because this increases the size of the chromosomes that can be handled. Following the coalescence theory, the Fisher-Wright idealised popu- lation model [13] and the infinite-sites mutation model were assumed [14], with a mutation frequency of 2*10-8 per nucleotide per generation. The latter ensured a large number of SNP. The historical effective size of the popu- lation was Ne = 100, and the forward simulations were conducted for 400 generations. The latter is expected to result in a mutation-drift balance, since any sample of alleles at a locus is expected to coalesce into its most recent common ancestor (MRCA) within 200 (= 2Ne) genera- tions. Any mutations before this MRCA lived do not cause a polymorphism (since all present alleles would be of the mutant type). Preliminary simulations showed that an approximate mutation-drift balance was reached before 400 generations (result not shown). Recombinations were sampled according to the Haldane mapping func- tion. The genome consisted of 10 chromosomes of 50 cM each, i.e. the total genome size was 5 M. After these 400 generations, SNP with a Minor Allele Fre- quency (MAF) < 0.02 were discarded. From the remaining SNP, 12 were randomly selected per chromosome to become a QTL, which resulted in a total of 120 QTL. From the remaining, non-QTL SNP, the 1000 SNP per chromo- some with the highest MAF were selected to become a marker. This resulted in a total of 10,000 markers, and a density of 20 Ne/M. For humans, this density corresponds to a total of ~2.3 million markers (= 20*38*3,000; assum- ing a genome of 38 M [15], and Ne ~3,000 [16]), and for cattle 600,000 markers (assuming a 30 M genome and Ne~1,000). Smaller marker densities of 20/x Ne/M were obtained by taking every x-th marker from the original set of 10,000 markers, where x = 2, 4, 10 or 20. Recent history of the populations After these 400 generations, the population was increased to 1000 by sampling parents from the previous genera- tions for 1000 individuals, which formed generation G0. Generation G0 was split into 500 G0t and 500 G0e indi- viduals (e and t indicate that they become the 'evaluation' and 'training' line, respectively). The 500 G0e-individuals were used for the sampling of parents for 500 G1e individ- uals, and similarly the G0t-individuals were used for the sampling of parents for 500 G1t individuals. Setting up different lines for the sampling of the G1e and the G1t individuals ensured that these two groups of individuals shared no close relationships. Subsequently, parents of 100 G2e individuals were sampled at random (with replacement) from the 500 G1e individuals. Similarly, parents of N G2t individuals were sampled from the 500 G1t individuals, where N was 500, 1000 or 2000. The G2t individuals were used for the estimation of marker effects, i.e. they were genotyped and phenotyped. The 100 G2e individuals are only genotyped, and their genetic value is to be predicted. The G0e, G0t, G1e, G1t, G2e and G2t individuals were pedigree recorded, i.e. for the pedigree recording the parents of G0 were treated as founders. The 'training' individuals (G2t) had neither parents nor grand- parents in common with the evaluation individuals (G2e) due to the separation of the two lines. The results were based on 16 replicated simulations, which was computa- tionally advantageous, since the 16 replicates could be run in parallel. Figure 1 summarises the population structure. Genetic and phenotypic values An additive genetic model was assumed, and the allelic effect of the mutant QTL allele at locus j, uj, was sampled from the exponential distribution, and uj was given a neg- ative sign with probability 0.5. The total genetic value of individual i was calculated as: 120 g i = ∑ j=1 qiju j where qij is the number of mutant alleles (0, 1, or 2) that individual i carries at locus j. At the end of the 400 gener- ations of simulation, the allelic effects were standardised so that the total genetic variance was 1. Phenotypes for the G2t individuals were obtained by adding an environmen- tal effect sampled from N(0,0.25) to their genetic value. This resulted in a high heritability of 0.8. The effect of a Page 3 of 9 (page number not for citation purposes)