Moran Processes

Modelling evolution in a discrete population: motivating the Moran process - YouTube - Private
The definition of the Moran process - YouTube - Private
Moran processes and games: fitness functions from games. - YouTube - Private
Selection probabilities for the Moran process on a game - YouTube - Private
The Moran process with mutation - YouTube - Private
The Moran process on 2 types: a mathematically tractable model. - YouTube - Private
A formula for the fixation probability for Moran processes with 2 types. - YouTube - Private
Using Python to simulate the Moran Process with Nashpy - YouTube - Private

Typical Programming Exercises

For each of the following matrices \(A\) and initial populations \(x_0\), for the corresponding normal form game:

create a variable initial_population which has value the corresponding nashpy initial population.
create a variable probabilities which has value the fixation probabilities of the simulated Moran process (using the given repetitions and random seed).

a. \(A = \begin{pmatrix}1 & 2 \\ 2 & 1\end{pmatrix} \qquad x_0 = \begin{pmatrix}10 & 0\end{pmatrix}\)

repetitions=500 and seed=0

b. \(A = \begin{pmatrix}1 & 2 \\ 2 & 1\end{pmatrix} \qquad x_0 = \begin{pmatrix}3 & 0\end{pmatrix}\)

repetitions=350 and seed=4

c. \(A = \begin{pmatrix}1 & 2 & 3 \\ 2 & 1 & 4 \\ 2 & 3 & 1\end{pmatrix} \qquad x_0 = \begin{pmatrix}3 & 1 & 2\end{pmatrix}\)

repetitions=1 and seed=2

d. \(A = \begin{pmatrix}1 & 2 & 3 \\ 2 & 1 & 4 \\ 2 & 3 & 1\end{pmatrix} \qquad x_0 = \begin{pmatrix}6 & 2 & 4\end{pmatrix}\)

repetitions=350 and seed=0

Class notes: Moran Processes