def get_response_content(fs):
parental_state = multiline_state_to_ndarray(fs.parental_state)
nchromosomes, npositions = parental_state.shape
if nchromosomes * npositions > 10:
raise ValueError('at most 2^10 states are allowed')
#
mutation = 0.5 * fs.mutation_param
recombination = 0.5 * fs.recombination_param
selection = fs.selection_param
#
out = StringIO()
print >> out, 'number of chromosomes:'
print >> out, nchromosomes
print >> out
print >> out, 'number of positions per chromosome:'
print >> out, npositions
print >> out
# define the transition matrix
P = get_transition_matrix(
selection, mutation, recombination, nchromosomes, npositions)
# sample the endpoint conditioned path
initial_integer_state = popgenmarkov.bin2d_to_int(initial_state)
final_integer_state = popgenmarkov.bin2d_to_int(final_state)
path = sample_endpoint_conditioned_path(
initial_integer_state, final_integer_state,
fs.ngenerations, P)
print >> out, 'sampled endpoint conditioned path, including endpoints:'
print >> out
for integer_state in path:
# print integer_state
print >> out, ndarray_to_multiline_state(
popgenmarkov.int_to_bin2d(
integer_state, nchromosomes, npositions))
print >> out
return out.getvalue()
def get_transition_matrix(
selection, mutation, recombination,
nchromosomes, npositions):
"""
This factors into the product of two transition matrices.
The first transition matrix accounts for selection and recombination.
The second transition matrix independently accounts for mutation.
@param selection: a fitness ratio
@param mutation: a state change probability
@param recombination: a linkage phase change probability
@param nchromosomes: number of chromosomes in the population
@param npositions: number of positions per chromosome
@return: a numpy array
"""
nstates = 1 << (nchromosomes * npositions)
# define the mutation transition matrix
P_mutation = np.zeros((nstates, nstates))
for source in range(nstates):
for sink in range(nstates):
ndiff = gmpy.hamdist(source, sink)
nsame = nchromosomes * npositions - ndiff
P_mutation[source, sink] = (mutation**ndiff)*((1-mutation)**nsame)
"""
print 'mutation transition matrix row sums:'
for value in np.sum(P_mutation, axis=1):
print value
print
"""
# init the unnormalized selection and recombination transition matrix
M = np.zeros((nstates, nstates))
for source_index in range(nstates):
K_source = popgenmarkov.int_to_bin2d(
source_index, nchromosomes, npositions)
chromosome_distn = popgenmarkov.get_chromosome_distn(
selection, recombination, K_source)
for x in product(range(1<<npositions), repeat=nchromosomes):
weight = 1
for index in x:
weight *= chromosome_distn[index]
sink_index = 0
for i, index in enumerate(x):
sink_index <<= npositions
sink_index |= index
M[source_index, sink_index] = weight
M_row_sums = np.sum(M, axis=1)
P_selection_recombination = (M.T / M_row_sums).T
"""
print 'selection-recombination matrix row sums:'
for value in np.sum(P_selection_recombination, axis=1):
print value
print
"""
# define the state transition probability matrix
P = np.dot(P_selection_recombination, P_mutation)
return P
