def test_extrema_moran_5(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 3
N = 60
mu = (3. / 2) * 1. / N
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
maxes = set([(20, 20, 20), (0, 0, 60), (0, 60, 0), (60, 0, 0), (30, 0, 30),
(0, 30, 30), (30, 30, 0)])
fitness_landscape = linear_fitness_landscape(m)
incentive = fermi(fitness_landscape, beta=0.1)
edges = incentive_process.multivariate_transitions(N,
incentive,
num_types=n,
mu=mu)
s = stationary_distribution(edges, lim=lim)
s2 = expected_divergence(edges, q_d=0)
flow = inflow_outflow(edges)
# These sets should all correspond
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s2), set(maxes))
assert_equal(find_local_minima(flow), set(maxes))
# The minima are pathological
assert_equal(find_local_minima(s), set([(3, 3, 54), (3, 54, 3),
(54, 3, 3)]))
assert_equal(find_local_maxima(s2),
set([(4, 52, 4), (4, 4, 52), (52, 4, 4)]))
assert_equal(find_local_maxima(flow),
set([(1, 58, 1), (1, 1, 58), (58, 1, 1)]))
def test_extrema_moran_5(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 3
N = 60
mu = (3./2) * 1./N
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
maxes = set([(20, 20, 20), (0, 0, 60), (0, 60, 0), (60, 0, 0),
(30, 0, 30), (0, 30, 30), (30, 30, 0)])
fitness_landscape = linear_fitness_landscape(m)
incentive = fermi(fitness_landscape, beta=0.1)
edges = incentive_process.multivariate_transitions(
N, incentive, num_types=n, mu=mu)
s = stationary_distribution(edges, lim=lim)
s2 = expected_divergence(edges, q_d=0)
flow = inflow_outflow(edges)
# These sets should all correspond
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s2), set(maxes))
assert_equal(find_local_minima(flow), set(maxes))
# The minima are pathological
assert_equal(find_local_minima(s),
set([(3, 3, 54), (3, 54, 3), (54, 3, 3)]))
assert_equal(find_local_maxima(s2),
set([(4, 52, 4), (4, 4, 52), (52, 4, 4)]))
assert_equal(find_local_maxima(flow),
set([(1, 58, 1), (1, 1, 58), (58, 1, 1)]))
def test_extrema_moran_3(lim=1e-12):
"""
Test for extrema of the stationary distribution.
"""
n = 2
N = 100
mu = 6. / 25
m = [[1, 0], [0, 1]]
maxes = set([(38, 62), (62, 38)])
mins = set([(50, 50), (100, 0), (0, 100)])
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edges = incentive_process.multivariate_transitions(N,
incentive,
num_types=n,
mu=mu)
s = stationary_distribution(edges, lim=lim)
flow = inflow_outflow(edges)
for q_d in [0, 1]:
s2 = incentive_process.kl(edges, q_d=1)
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s), set(mins))
assert_equal(find_local_minima(s2), set([(50, 50), (40, 60),
(60, 40)]))
assert_equal(find_local_maxima(flow), set(mins))
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_extrema_moran_4(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 3
N = 60
mu = 3./ (2 * N)
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
maxes = set([(20,20,20)])
mins = set([(0, 0, 60), (0, 60, 0), (60, 0, 0)])
fitness_landscape = linear_fitness_landscape(m)
incentive = logit(fitness_landscape, beta=0.1)
edges = incentive_process.multivariate_transitions(N, incentive, num_types=n, mu=mu)
s = stationary_distribution(edges, lim=lim)
s2 = expected_divergence(edges, q_d=0)
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s), set(mins))
assert_equal(find_local_minima(s2), set(maxes))
assert_equal(find_local_maxima(s2), set(mins))
def test_extrema_moran_3(lim=1e-12):
"""
Test for extrema of the stationary distribution.
"""
n = 2
N = 100
mu = 6./ 25
m = [[1, 0], [0, 1]]
maxes = set([(38, 62), (62, 38)])
mins = set([(50, 50), (100, 0), (0, 100)])
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edges = incentive_process.multivariate_transitions(N, incentive, num_types=n, mu=mu)
s = stationary_distribution(edges, lim=lim)
flow = inflow_outflow(edges)
for q_d in [0, 1]:
s2 = expected_divergence(edges, q_d=1)
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s), set(mins))
assert_equal(find_local_minima(s2), set([(50,50), (40, 60), (60, 40)]))
assert_equal(find_local_maxima(flow), set(mins))
def test_extrema_moran(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 2
for N, maxes, mins in [(60, [(30, 30)], [(60, 0), (0, 60)]),
(100, [(50, 50)], [(100, 0), (0, 100)])]:
mu = 1. / N
edges = incentive_process.compute_edges(N, num_types=n,
incentive_func=replicator, mu=mu)
s = stationary_distribution(edges, lim=lim)
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s), set(mins))
def test_extrema_moran_2(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 2
N = 100
mu = 1. / 1000
m = [[1, 2], [3, 1]]
maxes = set([(33, 67), (100,0), (0, 100)])
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edges = incentive_process.multivariate_transitions(N, incentive, num_types=n, mu=mu)
s = stationary_distribution(edges, lim=lim)
s2 = expected_divergence(edges, q_d=0)
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s2), set(maxes))
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)
