From: Understanding the potential bias of variance components estimators when using genomic models
Scenario | Population | MAF | QTL/markers | \({\lim _{\mathrm{n}\rightarrow \infty }}\) | |
---|---|---|---|---|---|
\({\mathbb {E}(\hat{\gamma }_{\mathrm{QM}})}\) | \({\mathbb {E}(\hat{\gamma }_{\mathrm{M}})}\) | ||||
1 | 1 generation\(^{*}\) | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}=\hbox {f}_{\mathrm{MAF}_{_{\mathrm{makers}}}}\) | Complete LE | \(\gamma\) | 0 |
2 | 1 generation\(^{*}\) | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}\ne \hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | Complete LE | \(\gamma\) | 0 |
3 | 1 generation\(^{*}\) | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}=\hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | LD | \(\gamma\) | \(<<< \mathbb {E}(\hat{\gamma }_{\mathrm{QM}})\) |
4 | 2 generations | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}=\hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | LD | \(\gamma\) | \(<< \mathbb {E}(\hat{\gamma }_{\mathrm{QM}})\) |
5 | 10 generations | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}=\hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | LD | \(\gamma\) | \(< \mathbb {E}(\hat{\gamma }_{\mathrm{QM}})^{\dagger }\) |
6 | 1 generation\(^{*}\) | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}\ne \hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | LD | \(<<< \gamma\) | \(<<< \mathbb {E}(\hat{\gamma }_{\mathrm{QM}})\) |
7 | 2 generations | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}\ne \hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | LD | \(<< \gamma\) | \(<< \mathbb {E}(\hat{\gamma }_{\mathrm{QM}})\) |
8 | 10 generations | \(\hbox {f}_{\mathrm{MAF}_{_{\mathrm{QTL}}}}\ne \hbox {f}_{\mathrm{MAF}_{\mathrm{makers}}}\) | LD | \(< \gamma ^{\dagger }\) | \(< \mathbb {E}(\hat{\gamma }_{\mathrm{QM}})^{\dagger }\) |