# Use Moran processes on replacement graphΒΆ

The Moran process method on the `Game`

class can take an
`replacement_stochastic_matrix`

which defines the replacement graph
as described in [Ohtsuki2007]:

```
>>> import nashpy as nash
>>> import numpy as np
>>> A = np.array([[3, 1], [1, 2]])
>>> game = nash.Game(A)
```

In this case, the `moran_process`

method returns a generator of a given
collection of generations where individuals replace individuals as with
probability proportional to the weighted directed replacement graph (in the
example below, there are actually two disconnected components):

```
>>> np.random.seed(0)
>>> replacement_stochastic_matrix = np.array(((1 / 2, 1 / 2, 0, 0), (1 / 2, 1 / 2, 0, 0), (0, 0, 1 / 2, 1 / 2), (0, 0, 1 / 2, 1 / 2)))
>>> generations = game.moran_process(initial_population=(0, 1, 1, 0), replacement_stochastic_matrix=replacement_stochastic_matrix)
>>> for population in generations:
... print(population)
[0 1 1 1]
[0 1 1 1]
[0 1 1 1]
[0 1 1 1]
[0 1 1 1]
[0 1 1 1]
[0 1 1 1]
[0 1 1 1]
[0 0 1 1]
```