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)
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_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_incentive_process_k(lim=1e-14):
"""
Compare stationary distribution computations to known analytic form for
neutral landscape for the Moran process.
"""
for k in [1, 2, 10,]:
for n, N in [(2, 20), (2, 50), (3, 10), (3, 20)]:
mu = (n-1.)/n * 1./(N+1)
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
# Neutral landscape is the default
edges = incentive_process.k_fold_incentive_transitions(
N, incentive, num_types=n, mu=mu, k=k)
stationary_1 = stationary_distribution(edges, lim=lim)
# Check that the stationary distribution satisfies balance
# conditions
check_detailed_balance(edges, stationary_1)
check_global_balance(edges, stationary_1)
check_eigenvalue(edges, stationary_1)
# Also check edge_func calculation
edges = incentive_process.multivariate_transitions(
N, incentive, num_types=n, mu=mu)
states = states_from_edges(edges)
edge_func = power_transitions(edges, k)
stationary_2 = stationary_distribution(
edge_func, states=states, lim=lim)
for key in stationary_1.keys():
assert_almost_equal(
stationary_1[key], stationary_2[key], places=5)
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)
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 graph_test():
"""Test yen search on large process -- a two type neutral Moran process on
a cycle."""
def neighbor_function(state):
"""States in this case are a list of ones and zeroes, i.e. a graph
coloring."""
neighbors = []
for i, t in enumerate(state):
neighbor = copy.copy(list(state))
if t == 0:
neighbor[i] = 1
else:
neighbor[i] = 0
neighbors.append(tuple(neighbor))
return neighbors
# print(neighbor_function([0, 1, 0]))
def transition_function(source, target, mu=0.05):
# Find the state that differs
for i, (s, t) in enumerate(zip(source, target)):
if s != t:
break
# i is now the index of the state that differs
# Look at neighboring states (within the cycle) to determine transition
N = len(source)
indices = [i-1, i+1]
transition = 0.
for index in indices:
if source[index % N] == s:
transition += 1 - mu
else:
transition += mu
return transition
state = [0, 1, 0, 1, 0, 0]
e = yen_search(state, neighbor_function, transition_function)
print(e)
state = [0, 1, 0, 1, 1, 1]
e = yen_search(state, neighbor_function, transition_function)
print(e)
# state = [0, 0, 0, 1, 1, 1]
# e = yen_search(state, neighbor_function, transition_function)
# print(e)
# Non-neutral landscape test
m = [[1,2], [2,1]] # Hawk-Dove
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
def transition_function2(source, target, mu=0.01):
"""Non-neutral landscape specified by a game matrix (above)"""
# Find the state that differs
for i, (s, t) in enumerate(zip(source, target)):
if s != t:
break
# i is now the index of the state that differs
s = sum(source)
N = len(source)
population_state = (N - s, s)
inc = incentive(population_state)
denom = float(sum(inc))
indices = [i-1, i+1]
transition = 0.
for index in indices:
rep_type = source[index % N]
r = float(inc[rep_type]) / denom
if rep_type == s:
transition += r * (1 - mu)
else:
transition += r * mu
return transition
state = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0]
e = yen_search(state, neighbor_function, transition_function2)
print(e)
state = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1]
e = yen_search(state, neighbor_function, transition_function2)
print(e)
state = [0, 1] * 8
e = yen_search(state, neighbor_function, transition_function2)
print(e)
state = [0] * 8 + [1] * 8 + [0] * 8 + [1] * 8
e = yen_search(state, neighbor_function, transition_function2)
print(e)
state = [0, 1] * 64
e = yen_search(state, neighbor_function, transition_function2)
print(e)
state = [0] * 256 + [1] * 256
e = yen_search(state, neighbor_function, transition_function2)
print(e)
state = [0, 1] * 64 + [1] * 4
e = yen_search(state, neighbor_function, transition_function2,
extrema='min')
print(e)
state = [0] * 32 + [1, 0] + [1] * 32
e = yen_search(state, neighbor_function, transition_function2,
extrema='min')
print(e)
# transition_function3()
def transition_function3(source, target, mu=0.6):
"""Non-neutral landscape specified by a game matrix (above)"""
# Find the state that differs
for i, (s, t) in enumerate(zip(source, target)):
if s != t:
break
# i is now the index of the state that differs
s = sum(source)
N = len(source)
population_state = (N - s, s)
inc = incentive(population_state)
denom = float(sum(inc))
indices = [i-1, i+1]
transition = 0.
for index in indices:
rep_type = source[index % N]
r = float(inc[rep_type]) / denom
if rep_type == s:
transition += r * (1 - mu)
else:
transition += r * mu
return transition
state = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0]
e = yen_search(state, neighbor_function, transition_function3)
print(e)
state = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1]
e = yen_search(state, neighbor_function, transition_function3)
print(e)
state = [0, 1] * 8
e = yen_search(state, neighbor_function, transition_function3)
print(e)
state = [0, 1] * 64
e = yen_search(state, neighbor_function, transition_function3)
print(e)
state = [0] * 128 + [1] * 128
e = yen_search(state, neighbor_function, transition_function3)
print(e)
N = 10
try:
mu = sys.argv[2]
except IndexError:
mu = 1. / N
#m = [[1,1], [1,1]]
#m = [[1,2], [2,1]]
#m = [[2,1],[1,2]]
#m = [[2,2],[2,1]]
m = [[2, 2], [1, 1]]
print(N, m, mu)
graph = cycle(N)
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_dict = multivariate_graph_transitions(N,
graph,
incentive,
num_types=2,
mu=mu)
edges = [(v1, v2, t) for ((v1, v2), t) in edge_dict.items()]
g = Graph(edges)
print("There are %s configurations and %s transitions" %
(len(set([x[0] for x in edge_dict.keys()])), len(edge_dict)))
print("Local Maxima:", len(find_extrema_yen(g, extrema="max")))
print("Local Minima:", len(find_extrema_yen(g, extrema="min")))
print("Total States:", 2**N)
N = 10
try:
mu = sys.argv[2]
except IndexError:
mu = 1./N
#m = [[1,1], [1,1]]
#m = [[1,2], [2,1]]
#m = [[2,1],[1,2]]
#m = [[2,2],[2,1]]
m = [[2,2],[1,1]]
print(N, m, mu)
graph = cycle(N)
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_dict = multivariate_graph_transitions(N, graph, incentive, num_types=2, mu=mu)
edges = [(v1, v2, t) for ((v1, v2), t) in edge_dict.items()]
g = Graph(edges)
print("There are %s configurations and %s transitions" % (len(set([x[0] for x in edge_dict.keys()])), len(edge_dict)))
print("Local Maxima:", len(find_extrema_yen(g, extrema="max")))
print("Local Minima:", len(find_extrema_yen(g, extrema="min")))
print("Total States:", 2**N)
exit()
print("Computing stationary")
s = stationary_distribution(edges, lim=1e-8, iterations=1000)
print("Local Maxima:", len(find_extrema_stationary(s, g, extrema="max")))
print("Local Minima:", len(find_extrema_stationary(s, g, extrema="min")))
