def get_sample_distn(M_large, M_small, mut_ratio, fit_ratio, h):
"""
@param M_large: an array of microstate counts
@param M_small: an array of microstate counts
@param mut_ratio: positive mutation rate ratio
@param fit_ratio: positive fitness ratio
@param h: recessiveness or dominance between 0 and 1
@return: a distribution over polymorphic samples
"""
# N is the population haploid count
# n is the sample count
N = sum(M_large[0])
n = sum(M_small[0])
nstates_large = len(M_large)
nstates_small = len(M_small)
if N-1 != nstates_large:
raise Exception('internal error unexpected population state space')
if N % 2:
raise Exception('expected an even number of haploids in the population')
if n-1 != nstates_small:
raise Exception('internal error unexpected sample state space')
# Get the value of s to construct the diallelic transition matrix.
# It is positive when the lowercase allele is less fit.
s = 1.0 - fit_ratio
# Get the diallelic transition matrix.
# The first state is allele A fixation
# and the last state is allele a fixation.
N_diploid = N // 2
P = np.exp(wfengine.create_diallelic_recessive(N_diploid, s, h))
MatrixUtil.assert_transition_matrix(P)
# Get the expected number of visits
# to polymorphic states, starting from (1, N-1) and from (N-1, 1),
# assuming that fixed states are absorbing.
I = np.eye(N - 1)
Q = P[1:-1, 1:-1]
B = np.zeros((N - 1, 2))
B[0,0] = 1
B[-1,-1] = 1
X = linalg.solve((I - Q).T, B)
# At this point X has two columns, each giving an array of expectations.
# The first column gives expectations starting from a single A allele.
# The second column gives expectations starting from a single a allele.
# To get the expectations defined by the mixture,
# take the weighted sum of the columns.
e_large = X[:,0] * mut_ratio + X[:,1]
# Compute a multivariate hypergeometric reduction
# from the population state space expectations
# to the sample state space expectations.
e_small = wfengine.reduce_hypergeometric(M_large, M_small, e_large)
# Compute the distribution.
return e_small / e_small.sum()
def get_response_content(fs):
out = StringIO()
print >> out, '<html><body><table border="1" cellpadding="10">'
#
headers = ('N', 's', '2Ns', 'h', 'f00', 'f01', 'f11', '2Nsh', 'NP01',
'NP10')
print >> out, get_html_table_row(headers)
# In this web script, N is a diploid population size.
# get the transition matrix
for x2Nsh in (0.075, 0.75):
for h in (0.25, 0.5, 0.75):
for N in (50, 200):
x2N = 2 * N
x2Ns = x2Nsh / float(h)
s = x2Ns / float(x2N)
#
P = np.exp(wfengine.create_diallelic_recessive(N, s, 1 - h))
#print P
MatrixUtil.assert_transition_matrix(P)
P01, P10 = get_fixation_probabilities(P)
NP01 = N * P01
NP10 = N * P10
#
f00 = 1.0
f11 = 1.0 - s
f01 = (1 - h) * f00 + h * f11
#
values = (
N,
s,
x2Ns,
h,
f00,
f01,
f11,
x2Nsh,
NP01,
NP10,
)
print >> out, get_html_table_row(values)
print >> out, '</table></body></html>'
return out.getvalue()
def get_sample_distn(N, n, mutation_rate, fitness_ratio, h):
"""
@param N: haploid pop size
@param n: allele sample size
@param mutation_rate: mutation rate
@param fitness_ratio: fitness ratio
@param h: dominance parameter 0.5 when additive
@return: a distribution over n+1 mono-/di-morphic sample states
"""
s = 1.0 - fitness_ratio
P = np.exp(wfengine.create_diallelic_recessive(N // 2, s, h))
MatrixUtil.assert_transition_matrix(P)
# allow mutation out of the fixed states
P[0, 0] = 1.0 - mutation_rate
P[0, 1] = mutation_rate
P[-1, -1] = 1.0 - mutation_rate
P[-1, -2] = mutation_rate
MatrixUtil.assert_transition_matrix(P)
# get the population stationary distribution
v_large = MatrixUtil.get_stationary_distribution(P)
# get the allele distribution
v_small = StatsUtil.subsample_pmf_without_replacement(v_large, n)
return v_small
def get_sample_distn(N, n, mutation_rate, fitness_ratio, h):
"""
@param N: haploid pop size
@param n: allele sample size
@param mutation_rate: mutation rate
@param fitness_ratio: fitness ratio
@param h: dominance parameter 0.5 when additive
@return: a distribution over n+1 mono-/di-morphic sample states
"""
s = 1.0 - fitness_ratio
P = np.exp(wfengine.create_diallelic_recessive(N // 2, s, h))
MatrixUtil.assert_transition_matrix(P)
# allow mutation out of the fixed states
P[0, 0] = 1.0 - mutation_rate
P[0, 1] = mutation_rate
P[-1, -1] = 1.0 - mutation_rate
P[-1, -2] = mutation_rate
MatrixUtil.assert_transition_matrix(P)
# get the population stationary distribution
v_large = MatrixUtil.get_stationary_distribution(P)
# get the allele distribution
v_small = StatsUtil.subsample_pmf_without_replacement(v_large, n)
return v_small
def get_response_content(fs):
out = StringIO()
print >> out, '<html><body><table border="1" cellpadding="10">'
#
headers = (
'N', 's', '2Ns', 'h',
'f00', 'f01', 'f11',
'2Nsh', 'NP01', 'NP10')
print >> out, get_html_table_row(headers)
# In this web script, N is a diploid population size.
# get the transition matrix
for x2Nsh in (0.075, 0.75):
for h in (0.25, 0.5, 0.75):
for N in (50, 200):
x2N = 2*N
x2Ns = x2Nsh / float(h)
s = x2Ns / float(x2N)
#
P = np.exp(wfengine.create_diallelic_recessive(N, s, 1-h))
#print P
MatrixUtil.assert_transition_matrix(P)
P01, P10 = get_fixation_probabilities(P)
NP01 = N * P01
NP10 = N * P10
#
f00 = 1.0
f11 = 1.0 - s
f01 = (1-h) * f00 + h * f11
#
values = (
N, s, x2Ns, h,
f00, f01, f11,
x2Nsh, NP01, NP10,
)
print >> out, get_html_table_row(values)
print >> out, '</table></body></html>'
return out.getvalue()
