Table 1 The Q Matrix form for the new Subfunctionalization + Dosage Model, given in equation set 10
From: Dosage balance acts as a time-dependent selective barrier to subfunctionalization
| Â | 0 | 1 | 2 | 3 | S | Y |
|---|---|---|---|---|---|---|
0 | \(- \frac{{1 - \left( {\frac{{f_{0} }}{{f_{1} }}} \right)}}{{1 - \left( {\frac{{f_{0} }}{{f_{1} }}} \right)^{{N_{e} }} }} \cdot N_{e} \cdot u_{b} \cdot l_{r} \cdot 2z\)Â Â \(- 2*\frac{{1 - \left( {\frac{{f_{0} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{0} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot N_{e} \cdot u_{h} \cdot l_{c}\)Â Â | \(\frac{{1 - \left( {\frac{{f_{0} }}{{f_{1} }}} \right)}}{{1 - \left( {\frac{{f_{0} }}{{f_{1} }}} \right)^{{N_{e} }} }} \cdot N_{e} \cdot u_{b} \cdot l_{r} \cdot 2z\)Â Â | \(0\) | \(0\) | \(0\) | \(2* \frac{{1 - \left( {\frac{{f_{0} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{0} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{h}}\cdot {l}_{\mathrm{c}}\)Â Â |
1 | \(0\) | \(- \frac{{1 - \left( {\frac{{f_{1} }}{{f_{2} }}} \right)}}{{1 - \left( {\frac{{f_{1} }}{{f_{2} }}} \right)^{{N_{e} }} }} \cdot N_{e} \cdot u_{b} \cdot l_{r} \cdot (z - 1)\)Â Â \(- \frac{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{S}}} }}} \right)}}{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{S}}} }}} \right)^{{N_{e} }} }} \cdot N_{e} \cdot u_{b} \cdot l_{r} \cdot (z - 1)\)Â Â \(- \frac{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot N_{e} \cdot u_{h} \cdot l_{c}\)Â Â | \(\frac{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{2}}} }}} \right)}}{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{2}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot (z-1)\)Â Â | \(0\) | \(\frac{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{S}}} }}} \right)}}{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{S}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot (z-1)\)Â Â | \(\frac{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{1} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{h}}\cdot {l}_{\mathrm{c}}\)Â Â |
2 | \(0\) | \(0\) | \(- \frac{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{3}}} }}} \right)}}{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{3}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot \left(z-2\right)\)Â Â \(- \frac{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{S}}} }}} \right)}}{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{S}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot \left(z-2\right)\)Â Â \(- \frac{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{h}}\cdot {l}_{\mathrm{c}}\)Â Â | \(\frac{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{3}}} }}} \right)}}{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{3}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot (z-2)\)Â Â | \(\frac{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{S}}} }}} \right)}}{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{S}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot (z-2)\)Â Â | \(\frac{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{2} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{h}}\cdot {l}_{\mathrm{c}}\)Â Â |
3 | \(0\) | \(0\) | \(0\) | \(- \frac{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{S}}} }}} \right)}}{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{S}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot \left(z-3\right)\)  \(- \frac{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{h}}\cdot {l}_{\mathrm{c}}\)  \(- \frac{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\)  | \(\frac{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{S}}} }}} \right)}}{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{S}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\cdot (z-3)\)  | \(\frac{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{h}}\cdot {l}_{\mathrm{c}}\)   + \(\frac{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)}}{{1 - \left( {\frac{{f_{3} }}{{f_{{\text{Y}}} }}} \right)^{{N_{e} }} }} \cdot {N}_{\mathrm{e}}\cdot {u}_{\mathrm{b}}\cdot {l}_{\mathrm{r}}\)  |
S | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
Y | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |