def two_dim_wright_fisher_figure(N, m, mu=0.01, incentive_func=replicator):
"""
Plot relative entropies and stationary distribution for the Wright-Fisher
process.
"""
n = len(m[0])
fitness_landscape = linear_fitness_landscape(m)
incentive = incentive_func(fitness_landscape)
if not mu:
mu = 1. / N
edge_func = wright_fisher.multivariate_transitions(N,
incentive,
mu=mu,
num_types=n)
states = list(simplex_generator(N, d=n - 1))
s = stationary_distribution(edge_func, states=states, iterations=4 * N)
s0 = expected_divergence(edge_func, states=states, q_d=0)
s1 = expected_divergence(edge_func, states=states, q_d=1)
# Set up plots
gs = gridspec.GridSpec(2, 1)
ax2 = pyplot.subplot(gs[0, 0])
ax2.set_title("Relative Entropy")
plot_dictionary(s0, ax=ax2)
plot_dictionary(s1, ax=ax2)
ax3 = pyplot.subplot(gs[1, 0])
ax3.set_title("Stationary Distribution")
plot_dictionary(s, ax=ax3)
ax3.set_xlabel("Number of A individuals (i)")
def two_dim_wright_fisher_figure(N, m, mu=0.01, incentive_func=replicator):
"""
Plot relative entropies and stationary distribution for the Wright-Fisher
process.
"""
n = len(m[0])
fitness_landscape = linear_fitness_landscape(m)
incentive = incentive_func(fitness_landscape)
if not mu:
mu = 1./ N
edge_func = wright_fisher.multivariate_transitions(N, incentive, mu=mu, num_types=n)
states = list(simplex_generator(N, d=n-1))
s = stationary_distribution(edge_func, states=states, iterations=4*N)
s0 = expected_divergence(edge_func, states=states, q_d=0)
s1 = expected_divergence(edge_func, states=states, q_d=1)
# Set up plots
gs = gridspec.GridSpec(2, 1)
ax2 = pyplot.subplot(gs[0, 0])
ax2.set_title("Relative Entropy")
plot_dictionary(s0, ax=ax2)
plot_dictionary(s1, ax=ax2)
ax3 = pyplot.subplot(gs[1, 0])
ax3.set_title("Stationary Distribution")
plot_dictionary(s, ax=ax3)
ax3.set_xlabel("Number of A individuals (i)")
def test_extrema_wf(lim=1e-10):
"""
For small mu, the Wright-Fisher process is minimal in the center.
Test that this happens.
"""
for n, N, mins in [(2, 40, [(20, 20)]), (3, 30, [(10, 10, 10)])]:
mu = 1. / N**3
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_func = wright_fisher.multivariate_transitions(N,
incentive,
mu=mu,
num_types=n)
states = list(simplex_generator(N, d=n - 1))
s = stationary_distribution(edge_func,
states=states,
iterations=4 * N,
lim=lim)
s2 = expected_divergence(edge_func, states=states, q_d=0)
assert_equal(find_local_minima(s), set(mins))
er = entropy_rate(edge_func, s, states=states)
assert_greater_equal(er, 0)
def test_wright_fisher(N=20, lim=1e-10, n=2):
"""Test 2 dimensional Wright-Fisher process."""
for n in [2, 3]:
mu = (n - 1.) / n * 1. / (N + 1)
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
# Wright-Fisher
for low_memory in [True, False]:
edge_func = wright_fisher.multivariate_transitions(
N, incentive, mu=mu, num_types=n, low_memory=low_memory)
states = list(simplex_generator(N, d=n - 1))
for logspace in [False, True]:
s = stationary_distribution(edge_func,
states=states,
iterations=200,
lim=lim,
logspace=logspace)
wf_edges = edge_func_to_edges(edge_func, states)
er = entropy_rate(wf_edges, s)
assert_greater_equal(er, 0)
# Check that the stationary distribution satistifies balance conditions
check_detailed_balance(wf_edges, s, places=2)
check_global_balance(wf_edges, s, places=4)
check_eigenvalue(wf_edges, s, places=2)
def test_wright_fisher(N=20, lim=1e-10, n=2):
"""Test 2 dimensional Wright-Fisher process."""
for n in [2, 3]:
mu = (n - 1.) / n * 1. / (N + 1)
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
# Wright-Fisher
for low_memory in [True, False]:
edge_func = wright_fisher.multivariate_transitions(
N, incentive, mu=mu, num_types=n, low_memory=low_memory)
states = list(simplex_generator(N, d=n-1))
for logspace in [False, True]:
s = stationary_distribution(
edge_func, states=states, iterations=200, lim=lim,
logspace=logspace)
wf_edges = edge_func_to_edges(edge_func, states)
er = entropy_rate(wf_edges, s)
assert_greater_equal(er, 0)
# Check that the stationary distribution satistifies balance
# conditions
check_detailed_balance(wf_edges, s, places=2)
check_global_balance(wf_edges, s, places=4)
check_eigenvalue(wf_edges, s, places=2)
def test_extrema_wf(lim=1e-10):
"""
For small mu, the Wright-Fisher process is minimal in the center.
Test that this happens.
"""
for n, N, mins in [(2, 40, [(20, 20)]), (3, 30, [(10, 10, 10)])]:
mu = 1. / N ** 3
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_func = wright_fisher.multivariate_transitions(
N, incentive, mu=mu, num_types=n)
states = list(simplex_generator(N, d=n-1))
s = stationary_distribution(
edge_func, states=states, iterations=4*N, lim=lim)
assert_equal(find_local_minima(s), set(mins))
er = entropy_rate(edge_func, s, states=states)
assert_greater_equal(er, 0)
