- Describe the transition probabilities for the Moran process with neutral drift.
- Obtain the transition probability matrix for the Moran process with neutral drift with $N=4$ individuals.
- State and prove the theorem for fixation probabilities in a birth death process.
- Extend the formulae of question 3 to the case of a Moran process on a game.
- For the following games, obtain the fixation probability $x_1$ for $N=4$:
- $A=\begin{pmatrix}1 & 1 \\ 1 & 1\end{pmatrix}$
- $A=\begin{pmatrix}1 & 2 \\ 3 & 1\end{pmatrix}$

- Consider the game $A=\begin{pmatrix}r & 1 \\ 1 & 1\end{pmatrix}$ for $r>1$ and $N$, and obtain $x_1$ as a function of $r$. How does $r$ effect the chance of fixation?

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