def __call__(self, X):
"""
@param X: six params defining mutation and selection
@return: negative log likelihood
"""
# define the hardcoded number of alleles
k = 4
# unpack the params
params = X.tolist()
theta, ka, kb, g0, g1, g2 = params
if any(x < 0 for x in (theta, ka, kb)):
return float('inf')
mutation, fitnesses = kaizeng.params_to_mutation_fitness(
self.N, params)
# get the transition matrix
P = kaizeng.get_transition_matrix(self.N, k, mutation, fitnesses)
v = MatrixUtil.get_stationary_distribution(P)
return -StatsUtil.multinomial_log_pmf(v, self.observed_counts)
def __call__(self, X):
"""
@param X: six params defining mutation and selection
@return: negative log likelihood
"""
# define the hardcoded number of alleles
k = 4
# unpack the params
params = X.tolist()
theta, ka, kb, g0, g1, g2 = params
if any(x < 0 for x in (theta, ka, kb)):
return float('inf')
mutation, fitnesses = kaizeng.params_to_mutation_fitness(
self.N, params)
# get the transition matrix
P = kaizeng.get_transition_matrix(self.N, k, mutation, fitnesses)
v = MatrixUtil.get_stationary_distribution(P)
return -StatsUtil.multinomial_log_pmf(v, self.observed_counts)
def get_response_content(fs):
np.set_printoptions(linewidth=200)
out = StringIO()
nsamples = 1
arr = []
#
nsites = 50000
N = 15*2
k = 4
params = (0.002, 1, 1, 0, 0, 0)
#params = (0.008, 1, 1, 0.5, 1, 1.5)
mutation, fitnesses = kaizeng.params_to_mutation_fitness(N, params)
#
tm = time.time()
P = kaizeng.get_transition_matrix(N, k, mutation, fitnesses)
print 'time to construct transition matrix:', time.time() - tm
#
tm = time.time()
v = MatrixUtil.get_stationary_distribution(P)
print 'time to get stationary distribution:', time.time() - tm
#
tm = time.time()
counts = np.random.multinomial(nsites, v)
print 'time to sample multinomial counts:', time.time() - tm
#
tm = time.time()
logp = StatsUtil.multinomial_log_pmf(v, counts)
print 'time to get multinomial log pmf:', time.time() - tm
#
for i in range(nsamples):
counts = np.random.multinomial(nsites, v)
X0 = np.array(params)
g = G(N, counts)
Xopt = optimize.fmin(g, X0)
arr.append(Xopt)
print >> out, np.array(arr)
return out.getvalue()
def get_response_content(fs):
np.set_printoptions(linewidth=200)
out = StringIO()
nsamples = 1
arr = []
#
nsites = 50000
N = 15 * 2
k = 4
params = (0.002, 1, 1, 0, 0, 0)
#params = (0.008, 1, 1, 0.5, 1, 1.5)
mutation, fitnesses = kaizeng.params_to_mutation_fitness(N, params)
#
tm = time.time()
P = kaizeng.get_transition_matrix(N, k, mutation, fitnesses)
print 'time to construct transition matrix:', time.time() - tm
#
tm = time.time()
v = MatrixUtil.get_stationary_distribution(P)
print 'time to get stationary distribution:', time.time() - tm
#
tm = time.time()
counts = np.random.multinomial(nsites, v)
print 'time to sample multinomial counts:', time.time() - tm
#
tm = time.time()
logp = StatsUtil.multinomial_log_pmf(v, counts)
print 'time to get multinomial log pmf:', time.time() - tm
#
for i in range(nsamples):
counts = np.random.multinomial(nsites, v)
X0 = np.array(params)
g = G(N, counts)
Xopt = optimize.fmin(g, X0)
arr.append(Xopt)
print >> out, np.array(arr)
return out.getvalue()
def get_response_content(fs):
N_small = 10
N_big_diploid = fs.N_big_diploid
N_big_haploid = N_big_diploid * 2
if N_big_haploid < N_small:
raise ValueError('use a larger diploid population size')
if fs.with_replacement:
f_subsample = StatsUtil.subsample_pmf_with_replacement
elif fs.without_replacement:
f_subsample = StatsUtil.subsample_pmf_without_replacement
else:
raise ValueError('subsampling option error')
k = 4
gamma = fs.gamma_1
params_list = [
(0.008, 1, 1, fs.gamma_0, fs.gamma_1, fs.gamma_2),
(0.008, 2, 1, fs.gamma_0, fs.gamma_1, fs.gamma_2)]
allele_histograms = np.zeros((2, N_big_haploid + 1))
for i, params in enumerate(params_list):
mutation, selection = kaizeng.params_to_mutation_fitness(
N_big_haploid, params)
P = kaizeng.get_transition_matrix(
N_big_diploid, k, mutation, selection)
v = MatrixUtil.get_stationary_distribution(P)
for state_index, counts in enumerate(kaizeng.gen_states(
N_big_haploid, k)):
if counts[0] and counts[1]:
allele_histograms[i, counts[0]] += v[state_index]
# Define the r table.
# There are nine columns each corresponding to an allele frequency.
# There are three rows each corresponding to a configuration.
arr = []
# Use the two allele approximation
# from mcvean and charlesworth 1999 referred to by zeng 2011.
# I'm not sure if I am using the right equation.
g0 = fs.gamma_0
g1 = fs.gamma_1
"""
s_0 = -gamma_0 / float(N_big)
s_1 = -gamma_1 / float(N_big)
hist = np.zeros(N_small+1)
for i in range(1, N_small):
x = i / float(N_small)
hist[i] = math.exp(1*N_big*(s_0 - s_1)*x) / (x*(1-x))
h = hist[1:-1]
h /= np.sum(h)
arr.append(h.tolist())
"""
arr.append(diallelic_approximation(N_small, g0, g1).tolist())
# Use the exact two allele distribution.
# Well, it is exact if I understand the right scaling
# of the population size and fitnesses.
f0 = 1.0
f1 = 1.0 - gamma / N_big_haploid
#f0 = 1.0 + gamma / N
#f1 = 1.0
#f0 = 1.0 + 1.5 / (4*N)
#f1 = 1.0 - 1.5 / (4*N)
h = get_two_allele_distribution(
N_big_haploid, N_small, f0, f1, f_subsample)
arr.append(h.tolist())
# Get frequencies for the other two configurations
for hist in allele_histograms:
# Get probabilities conditional on dimorphism.
hist[0] = 0
hist[-1] = 0
hist /= np.sum(hist)
# Get the subsampled pmf.
distn = f_subsample(hist, N_small)
MatrixUtil.assert_distribution(distn)
# Get probabiities conditional on dimorphism of the sample.
distn[0] = 0
distn[-1] = 0
distn /= np.sum(distn)
# Add to the table of densities.
arr.append(distn[1:-1].tolist())
# Get a large population approximation
# when there is mutational bias.
params = (0.008, 2, 1, fs.gamma_0, fs.gamma_1, fs.gamma_2)
mutation, fitness = kaizeng.params_to_mutation_fitness(
N_big_haploid, params)
gammas = np.array([fs.gamma_0, fs.gamma_1, fs.gamma_2, 0])
h = kaizeng.get_large_population_approximation(N_small, k, gammas, mutation)
arr.append(h.tolist())
# define the r script
out = StringIO()
print >> out, 'title.string <- "allele 1 vs allele 2"'
print >> out, 'mdat <-', RUtil.matrix_to_R_string(arr)
print >> out, mk_call_str(
'barplot',
'mdat',
'legend.text=' + mk_call_str(
'c',
'"two-allele large N limit"',
'"two-allele"',
'"four-allele without mutational bias"',
'"four-allele with mutational bias (kappa_{1,2}=2)"',
'"four-allele with mutational bias, large N limit"',
),
'args.legend = list(x="topleft", bty="n")',
'names.arg = c(1,2,3,4,5,6,7,8,9)',
main='title.string',
xlab='"frequency of allele 1"',
ylab='"frequency"',
col=mk_call_str(
'c',
'"red"',
'"white"',
'"black"',
'"gray"',
'"blue"',
),
beside='TRUE',
)
#print >> out, 'box()'
script = out.getvalue().rstrip()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter_no_table(
script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
def get_response_content(fs):
N_small = 10
N_big_diploid = fs.N_big_diploid
N_big_haploid = N_big_diploid * 2
if N_big_haploid < N_small:
raise ValueError('use a larger diploid population size')
if fs.with_replacement:
f_subsample = StatsUtil.subsample_pmf_with_replacement
elif fs.without_replacement:
f_subsample = StatsUtil.subsample_pmf_without_replacement
else:
raise ValueError('subsampling option error')
k = 4
gamma = fs.gamma_1
params_list = [(0.008, 1, 1, fs.gamma_0, fs.gamma_1, fs.gamma_2),
(0.008, 2, 1, fs.gamma_0, fs.gamma_1, fs.gamma_2)]
allele_histograms = np.zeros((2, N_big_haploid + 1))
for i, params in enumerate(params_list):
mutation, selection = kaizeng.params_to_mutation_fitness(
N_big_haploid, params)
P = kaizeng.get_transition_matrix(N_big_diploid, k, mutation,
selection)
v = MatrixUtil.get_stationary_distribution(P)
for state_index, counts in enumerate(
kaizeng.gen_states(N_big_haploid, k)):
if counts[0] and counts[1]:
allele_histograms[i, counts[0]] += v[state_index]
# Define the r table.
# There are nine columns each corresponding to an allele frequency.
# There are three rows each corresponding to a configuration.
arr = []
# Use the two allele approximation
# from mcvean and charlesworth 1999 referred to by zeng 2011.
# I'm not sure if I am using the right equation.
g0 = fs.gamma_0
g1 = fs.gamma_1
"""
s_0 = -gamma_0 / float(N_big)
s_1 = -gamma_1 / float(N_big)
hist = np.zeros(N_small+1)
for i in range(1, N_small):
x = i / float(N_small)
hist[i] = math.exp(1*N_big*(s_0 - s_1)*x) / (x*(1-x))
h = hist[1:-1]
h /= np.sum(h)
arr.append(h.tolist())
"""
arr.append(diallelic_approximation(N_small, g0, g1).tolist())
# Use the exact two allele distribution.
# Well, it is exact if I understand the right scaling
# of the population size and fitnesses.
f0 = 1.0
f1 = 1.0 - gamma / N_big_haploid
#f0 = 1.0 + gamma / N
#f1 = 1.0
#f0 = 1.0 + 1.5 / (4*N)
#f1 = 1.0 - 1.5 / (4*N)
h = get_two_allele_distribution(N_big_haploid, N_small, f0, f1,
f_subsample)
arr.append(h.tolist())
# Get frequencies for the other two configurations
for hist in allele_histograms:
# Get probabilities conditional on dimorphism.
hist[0] = 0
hist[-1] = 0
hist /= np.sum(hist)
# Get the subsampled pmf.
distn = f_subsample(hist, N_small)
MatrixUtil.assert_distribution(distn)
# Get probabiities conditional on dimorphism of the sample.
distn[0] = 0
distn[-1] = 0
distn /= np.sum(distn)
# Add to the table of densities.
arr.append(distn[1:-1].tolist())
# Get a large population approximation
# when there is mutational bias.
params = (0.008, 2, 1, fs.gamma_0, fs.gamma_1, fs.gamma_2)
mutation, fitness = kaizeng.params_to_mutation_fitness(
N_big_haploid, params)
gammas = np.array([fs.gamma_0, fs.gamma_1, fs.gamma_2, 0])
h = kaizeng.get_large_population_approximation(N_small, k, gammas,
mutation)
arr.append(h.tolist())
# define the r script
out = StringIO()
print >> out, 'title.string <- "allele 1 vs allele 2"'
print >> out, 'mdat <-', RUtil.matrix_to_R_string(arr)
print >> out, mk_call_str(
'barplot',
'mdat',
'legend.text=' + mk_call_str(
'c',
'"two-allele large N limit"',
'"two-allele"',
'"four-allele without mutational bias"',
'"four-allele with mutational bias (kappa_{1,2}=2)"',
'"four-allele with mutational bias, large N limit"',
),
'args.legend = list(x="topleft", bty="n")',
'names.arg = c(1,2,3,4,5,6,7,8,9)',
main='title.string',
xlab='"frequency of allele 1"',
ylab='"frequency"',
col=mk_call_str(
'c',
'"red"',
'"white"',
'"black"',
'"gray"',
'"blue"',
),
beside='TRUE',
)
#print >> out, 'box()'
script = out.getvalue().rstrip()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter_no_table(
script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
return out.getvalue()
if __name__ == '__main__':
k = 4
nsamples = 100
settings_list = [
[15, 50000, [0.002, 1, 1, 0, 0, 0]],
[15, 50000, [0.002, 1, 2, 0.4, -1.2, 2]],
[10, 10000, [0.008, 1, 1, 0.5, 1, 1.5]],
[6, 5000, [0.01, 1, 2, 0, 0, 0]]]
for N_diploid, nsites, params in settings_list:
N = 2*N_diploid
print 'diploid population size = %s, sequence length = %s' % (
N_diploid, nsites)
print '\t'.join(str(x) for x in ['Input'] + params)
mutation, fitnesses = kaizeng.params_to_mutation_fitness(N, params)
P = kaizeng.get_transition_matrix(N, k, mutation, fitnesses)
v = MatrixUtil.get_stationary_distribution(P)
arr = []
for i in range(nsamples):
counts = np.random.multinomial(nsites, v)
X0 = np.array(params)
g = G(N, counts)
Xopt = optimize.fmin(g, X0)
arr.append(Xopt.tolist())
means = []
cis = []
for mles in zip(*arr):
means.append(np.mean(mles))
x = sorted(mles)
cis.append([x[2], x[-2]])
return out.getvalue()
if __name__ == '__main__':
k = 4
nsamples = 100
settings_list = [[15, 50000, [0.002, 1, 1, 0, 0, 0]],
[15, 50000, [0.002, 1, 2, 0.4, -1.2, 2]],
[10, 10000, [0.008, 1, 1, 0.5, 1, 1.5]],
[6, 5000, [0.01, 1, 2, 0, 0, 0]]]
for N_diploid, nsites, params in settings_list:
N = 2 * N_diploid
print 'diploid population size = %s, sequence length = %s' % (
N_diploid, nsites)
print '\t'.join(str(x) for x in ['Input'] + params)
mutation, fitnesses = kaizeng.params_to_mutation_fitness(N, params)
P = kaizeng.get_transition_matrix(N, k, mutation, fitnesses)
v = MatrixUtil.get_stationary_distribution(P)
arr = []
for i in range(nsamples):
counts = np.random.multinomial(nsites, v)
X0 = np.array(params)
g = G(N, counts)
Xopt = optimize.fmin(g, X0)
arr.append(Xopt.tolist())
means = []
cis = []
for mles in zip(*arr):
means.append(np.mean(mles))
x = sorted(mles)
cis.append([x[2], x[-2]])
def get_response_content(fs):
N_diploid = 5
N_haploid = N_diploid * 2
k = 4
gamma = 1.5
params_list = [
(0.008, 1, 1, 0, gamma, 1),
(0.008, 2, 1, 0, gamma, 1)]
allele_histograms = np.zeros((2, N_haploid+1))
for i, params in enumerate(params_list):
mutation, fitnesses = kaizeng.params_to_mutation_fitness(
N_haploid, params)
P = kaizeng.get_transition_matrix(
N_diploid, k, mutation, fitnesses)
v = MatrixUtil.get_stationary_distribution(P)
for state_index, counts in enumerate(kaizeng.gen_states(N_haploid, k)):
if counts[0] and counts[1]:
allele_histograms[i, counts[0]] += v[state_index]
# Define the r table.
# There are nine columns each corresponding to an allele frequency.
# There are three rows each corresponding to a configuration.
arr = []
# Use the exact two allele distribution.
# Well, it is exact if I understand the right scaling
# of the population size and fitnesses.
f0 = 1.0
f1 = 1.0 - gamma / N_haploid
#f0 = 1.0 + gamma / N
#f1 = 1.0
#f0 = 1.0 + 1.5 / (4*N)
#f1 = 1.0 - 1.5 / (4*N)
h = get_two_allele_distribution(N_diploid, f0, f1)
arr.append(h.tolist())
# Use the two allele approximation
# from mcvean and charlesworth 1999 referred to by zeng 2011.
# I'm not sure if I am using the right equation.
"""
gamma_0 = 0
gamma_1 = 1.5
s_0 = -gamma_0 / float(N)
s_1 = -gamma_1 / float(N)
hist = np.zeros(N+1)
for i in range(1, N):
x = i / float(N)
hist[i] = math.exp(1*N*(s_0 - s_1)*x) / (x*(1-x))
h = hist[1:-1]
h /= np.sum(h)
arr.append(h.tolist())
"""
# Get frequencies for the other two configurations
for hist in allele_histograms:
h = hist[1:-1]
h /= np.sum(h)
arr.append(h.tolist())
# define the r script
out = StringIO()
print >> out, 'title.string <- "allele 1 vs allele 2, gamma = 1.5"'
print >> out, 'mdat <-', RUtil.matrix_to_R_string(arr)
print >> out, mk_call_str(
'barplot',
'mdat',
'legend.text=' + mk_call_str(
'c',
'"two-allele"',
'"four-allele without mutational bias"',
'"four-allele with mutational bias kappa_{1,2}=2"',
),
'args.legend = list(x="topleft", bty="n")',
'names.arg = c(1,2,3,4,5,6,7,8,9)',
main='title.string',
xlab='"frequency of allele 1"',
ylab='"frequency"',
col=mk_call_str(
'c',
#'"red"',
'"white"',
'"black"',
'"gray"',
),
beside='TRUE',
)
#print >> out, 'box()'
script = out.getvalue().rstrip()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter_no_table(
script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
def get_response_content(fs):
N_diploid = 5
N_haploid = N_diploid * 2
k = 4
gamma = 1.5
params_list = [(0.008, 1, 1, 0, gamma, 1), (0.008, 2, 1, 0, gamma, 1)]
allele_histograms = np.zeros((2, N_haploid + 1))
for i, params in enumerate(params_list):
mutation, fitnesses = kaizeng.params_to_mutation_fitness(
N_haploid, params)
P = kaizeng.get_transition_matrix(N_diploid, k, mutation, fitnesses)
v = MatrixUtil.get_stationary_distribution(P)
for state_index, counts in enumerate(kaizeng.gen_states(N_haploid, k)):
if counts[0] and counts[1]:
allele_histograms[i, counts[0]] += v[state_index]
# Define the r table.
# There are nine columns each corresponding to an allele frequency.
# There are three rows each corresponding to a configuration.
arr = []
# Use the exact two allele distribution.
# Well, it is exact if I understand the right scaling
# of the population size and fitnesses.
f0 = 1.0
f1 = 1.0 - gamma / N_haploid
#f0 = 1.0 + gamma / N
#f1 = 1.0
#f0 = 1.0 + 1.5 / (4*N)
#f1 = 1.0 - 1.5 / (4*N)
h = get_two_allele_distribution(N_diploid, f0, f1)
arr.append(h.tolist())
# Use the two allele approximation
# from mcvean and charlesworth 1999 referred to by zeng 2011.
# I'm not sure if I am using the right equation.
"""
gamma_0 = 0
gamma_1 = 1.5
s_0 = -gamma_0 / float(N)
s_1 = -gamma_1 / float(N)
hist = np.zeros(N+1)
for i in range(1, N):
x = i / float(N)
hist[i] = math.exp(1*N*(s_0 - s_1)*x) / (x*(1-x))
h = hist[1:-1]
h /= np.sum(h)
arr.append(h.tolist())
"""
# Get frequencies for the other two configurations
for hist in allele_histograms:
h = hist[1:-1]
h /= np.sum(h)
arr.append(h.tolist())
# define the r script
out = StringIO()
print >> out, 'title.string <- "allele 1 vs allele 2, gamma = 1.5"'
print >> out, 'mdat <-', RUtil.matrix_to_R_string(arr)
print >> out, mk_call_str(
'barplot',
'mdat',
'legend.text=' + mk_call_str(
'c',
'"two-allele"',
'"four-allele without mutational bias"',
'"four-allele with mutational bias kappa_{1,2}=2"',
),
'args.legend = list(x="topleft", bty="n")',
'names.arg = c(1,2,3,4,5,6,7,8,9)',
main='title.string',
xlab='"frequency of allele 1"',
ylab='"frequency"',
col=mk_call_str(
'c',
#'"red"',
'"white"',
'"black"',
'"gray"',
),
beside='TRUE',
)
#print >> out, 'box()'
script = out.getvalue().rstrip()
# create the R plot image
device_name = Form.g_imageformat_to_r_function[fs.imageformat]
retcode, r_out, r_err, image_data = RUtil.run_plotter_no_table(
script, device_name)
if retcode:
raise RUtil.RError(r_err)
return image_data
