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 two_dim_transitions_figure(N, m, mu=0.01, incentive_func=replicator):
"""
Plot transition entropies and stationary distributions.
"""
n = len(m[0])
fitness_landscape = linear_fitness_landscape(m)
incentive = incentive_func(fitness_landscape)
if not mu:
mu = 1./ N
edges = incentive_process.multivariate_transitions(N, incentive, num_types=n, mu=mu)
s = stationary_distribution(edges, exact=True)
d = edges_to_edge_dict(edges)
# Set up plots
gs = gridspec.GridSpec(3, 1)
ax1 = pyplot.subplot(gs[0, 0])
ax1.set_title("Transition Probabilities")
ups, downs, _ = two_dim_transitions(edges)
xs = range(0, N+1)
ax1.plot(xs, ups)
ax1.plot(xs, downs)
ax2 = pyplot.subplot(gs[1, 0])
ax2.set_title("Relative Entropy")
divs1 = expected_divergence(edges)
divs2 = expected_divergence(edges, q_d=0)
plot_dictionary(divs1, ax=ax2)
plot_dictionary(divs2, ax=ax2)
ax3 = pyplot.subplot(gs[2, 0])
ax3.set_title("Stationary Distribution")
plot_dictionary(s, ax=ax3)
ax3.set_xlabel("Number of A individuals (i)")
def two_dim_transitions_figure(N, m, mu=0.01, incentive_func=replicator):
"""
Plot transition entropies and stationary distributions.
"""
n = len(m[0])
fitness_landscape = linear_fitness_landscape(m)
incentive = incentive_func(fitness_landscape)
if not mu:
mu = 1. / N
edges = incentive_process.multivariate_transitions(N,
incentive,
num_types=n,
mu=mu)
s = stationary_distribution(edges, exact=True)
d = edges_to_edge_dict(edges)
# Set up plots
gs = gridspec.GridSpec(3, 1)
ax1 = pyplot.subplot(gs[0, 0])
ax1.set_title("Transition Probabilities")
ups, downs, _ = two_dim_transitions(edges)
xs = range(0, N + 1)
ax1.plot(xs, ups)
ax1.plot(xs, downs)
ax2 = pyplot.subplot(gs[1, 0])
ax2.set_title("Relative Entropy")
divs1 = expected_divergence(edges)
divs2 = expected_divergence(edges, q_d=0)
plot_dictionary(divs1, ax=ax2)
plot_dictionary(divs2, ax=ax2)
ax3 = pyplot.subplot(gs[2, 0])
ax3.set_title("Stationary Distribution")
plot_dictionary(s, ax=ax3)
ax3.set_xlabel("Number of A individuals (i)")