Genetics Selection Evolution 2009, 41:35 http://www.gsejournal.org/content/41/1/35 Generation___________________________________________________________ -400 -1 0 1 2 Fisher-Wright population (100) Fisher-Wright population (100) G0t(500) G1t(500) G2t(N) G0e(500) G1e(500) G2e(100)_____________ FAigscuhreem1atic representation of the population structure A schematic representation of the population struc- ture. (population sizes are indicated between brackets). lower heritability is investigated in the Results and Discus- sion section. Estimation of marker effects and prediction of breeding value Estimation of marker effects was performed using three models: (i) BLUP of marker effects, which assumes that every marker effect has a constant variance (G-BLUP); (ii) BayesB, which estimates the variance of every marker using a prior distribution and Bayesian methodology [2]; and (iii) MIXTURE, which assumes that the marker effects come from a mixture of two normal distributions, which differ in variance, i.e. the large marker effects are accom- modated by the distribution with large variance and vice versa. The MIXTURE model was used because it, in a rela- tively simple way, approximates the prior distribution of the marker effects, assuming that any prior distribution can be reasonably well approximated by a mixture of nor- mal distributions [17]. Some preliminary testing of the MIXTURE model showed that a mixture of two normal distributions is sufficient. The prior distribution of BayesB of [2] assumed that some markers had a big effect, the var- iance of which was estimated (a fraction NQTL/Nm of markers), whilst the remaining markers did not have an effect at all, where NQTL is the number of QTL and Nm is the number of markers fitted. However, in the BayesB model implemented here, the prior distribution assumed that the majority of the markers (i.e. the fraction 1- NQTL/ Nm) did have a small effect, the variance of which was assumed equal and was estimated in the model, instead of assuming that these markers had no effect at all (as in [2]). The latter has two advantages: (i) a Gibbs-sampling algo- rithm can be implemented, which reduces computer time; and (ii) since there were many QTL, they will probably not be all clearly detected by a single marker, such that a proportion of the genetic variance will be picked up by allowing for many, small marker effects. The statistical model used to estimate the marker effects by G-BLUP, BayesB, and MIXTURE was: y = μ + ∑ Nm j=1 X ja j + e where y is a Nx1 vector of phenotypes; aj is the effect of marker j; Xj is a Nx1 vector denoting the genotype of the individuals for marker j, where 0 denotes homozygous for the first allele; 1/√Hj denotes heterozygous; 2/√Hj denotes homozygous for the second allele, and Hj is the marker heterozygosity. The √Hj term in Xj standardises the vari- ance of the marker genotype data to 1. The variance of aj is assumed to be 1/Nm for G-BLUP, is estimated by BayesB, and, in MIXTURE it equals σ12 or σ22, depending on whether the marker effect is small or large. The proba- bility of a small or large marker effect is estimated together with the variances of the small and large distribution of marker effects, σ12 and σ22. Given the estimates of the marker effects and the marker genotypes, genetic values for the individuals in set G2e are predicted as: gˆ i = ∑ Nm j=1 X ijaˆ j where Xij is the marker genotype of individual i for marker j coded the same as above; and aˆ j is the estimate of marker effect j. The accuracy of this prediction is calcu- lated as the correlation between gi and gˆ i for the G2e individuals. Traditional BLUP (T-BLUP [18]) breeding values are esti- mated based on the phenotypes of the individuals in G2t and the pedigree of the G0, G1t, G1e, G2t, and G2e indi- viduals using the ASREML package [19]. Testing the effect of an increase in genome size From Equation (1) it may be expected that a doubling of the genome size requires twice as many records. To test this expectation, we compared the situation of a genome with 5 chromosomes with N = 500 G2t individuals, to 10 chromosomes with N = 1000, and to 20 chromosomes with N = 2000. Marker density was kept constant at 20 N / e M. Accounting for relationships Following Habier et al. [3], the accuracy of G-BLUP may be split into a component due to genomic selection and a component that could also be predicted by T-BLUP, i.e.: rG-BLUP = rT-BLUP + (1 − rT-BLUP)ρ G-BLUP (2) Page 4 of 9 (page number not for citation purposes)