Fig. 1
From: Understanding the potential bias of variance components estimators when using genomic models
Simulation results for scenarios 1 and 2, consisting of one generation of completely unrelated individuals, with QTL and markers in complete linkage equilibrium (LE), for both \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}} = \hbox {f}_{\mathrm{MAF}_{_{\mathrm{markers}}}}\) and \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}} \ne \hbox {f}_{\mathrm{MAF}_{_{\mathrm{markers}}}}\). Simulations were performed with 3000 QTL generating the phenotypes, replicated 500 times. a shows the relationship between \(\lambda _{\mathrm{i}}\) and \(\kappa _{\mathrm{i}}\), for the true model (QTL only) and for both genomic models evaluated (QTL plus markers and markers only); b presents the confidence ellipses for the simulated heritabilities (\(\hbox {h}_{\mathrm{sim}}^{2} = \gamma _{_{\mathrm{sim}}}/(1+\gamma _{_{\mathrm{sim}}})\)), with a simulation parameter \(\hbox {h}^{2}=0.05,0.15,\ldots ,0.95\), and the heritabilities estimated using REML (\(\hbox {h}_{\mathrm{REML}}^{2} = \gamma _{_{\mathrm{REML}}}/(1+\gamma _{_{\mathrm{REML}}})\)), for the true model (QTL only) and for both genomic models evaluated (QTL plus markers and markers only); c presents the confidence ellipses for the simulated heritabilities (\(\hbox {h}_{\mathrm{sim}}^{2} = \gamma _{_{sim}}/(1+\gamma _{_{\mathrm{sim}}})\)), with a simulation parameter \(\hbox {h}^{2}=0.05,0.15,\ldots ,0.95\), and the relative bias of \(\hbox {h}_{\mathrm{REML}}^{2}\) (\(\hbox {RB}(\hbox {h}_{\mathrm{REML}}^{2}) = (\hbox {h}_{\mathrm{REML}}^{2}-\hbox {h}_{\mathrm{sim}}^{2})/\hbox {h}_{\mathrm{sim}}^{2}\))