def test_regress_mutation_probability_endpoint_conditioning(self):
ngenerations = 10
selection = 2.0
mutation = 0.0001
recombination = 0.001
nchromosomes = 2
npositions = 4
K_initial = np.array([
[1,1,1,1],
[0,0,0,0]], dtype=np.int8)
K_final = np.array([
[1,1,0,0],
[0,0,1,1]], dtype=np.int8)
#
ngenboundaries = ngenerations - 1
no_mutation_prior = (1 - mutation)**(
npositions*ngenboundaries*nchromosomes)
#
initial_long = popgenmarkov.bin2d_to_int(K_initial)
final_long = popgenmarkov.bin2d_to_int(K_final)
ci_to_short, short_to_count, sorted_chrom_lists = get_state_space_info(
nchromosomes, npositions)
initial_ci = chroms_to_index(
sorted(popgenmarkov.bin_to_int(row) for row in K_initial),
npositions)
initial_short = ci_to_short[initial_ci]
final_ci = chroms_to_index(
sorted(popgenmarkov.bin_to_int(row) for row in K_final),
npositions)
final_short = ci_to_short[final_ci]
# get an answer using the less efficient methods
P_sr = popgenmarkov.get_selection_recombination_transition_matrix(
selection, recombination, nchromosomes, npositions)
P_m = popgenmarkov.get_mutation_transition_matrix(
mutation, nchromosomes, npositions)
p_b_given_a = linalg.matrix_power(np.dot(P_sr, P_m), ngenerations-1)[
initial_long, final_long]
p_b_given_a_no_mutation = linalg.matrix_power(P_sr, ngenerations-1)[
initial_long, final_long]
no_mutation_posterior = (
no_mutation_prior * p_b_given_a_no_mutation) / p_b_given_a
# get an answer using the more efficient methods
P_sr_s = get_selection_recombination_transition_matrix_s(
ci_to_short, short_to_count, sorted_chrom_lists,
selection, recombination, nchromosomes, npositions)
P_m_s = get_mutation_transition_matrix_s(
ci_to_short, short_to_count, sorted_chrom_lists,
mutation, nchromosomes, npositions)
p_b_given_a_s = linalg.matrix_power(
np.dot(P_sr_s, P_m_s), ngenerations-1)[
initial_short, final_short]
p_b_given_a_no_mutation_s = linalg.matrix_power(
P_sr_s, ngenerations-1)[
initial_short, final_short]
no_mutation_posterior_s = (
no_mutation_prior * p_b_given_a_no_mutation_s) / p_b_given_a_s
#
self.assertTrue(
np.allclose(no_mutation_posterior, no_mutation_posterior_s))
def test_regress_mutation_probability_endpoint_conditioning(self):
ngenerations = 10
selection = 2.0
mutation = 0.0001
recombination = 0.001
nchromosomes = 2
npositions = 4
K_initial = np.array([[1, 1, 1, 1], [0, 0, 0, 0]], dtype=np.int8)
K_final = np.array([[1, 1, 0, 0], [0, 0, 1, 1]], dtype=np.int8)
#
ngenboundaries = ngenerations - 1
no_mutation_prior = (1 - mutation)**(npositions * ngenboundaries *
nchromosomes)
#
initial_long = popgenmarkov.bin2d_to_int(K_initial)
final_long = popgenmarkov.bin2d_to_int(K_final)
ci_to_short, short_to_count, sorted_chrom_lists = get_state_space_info(
nchromosomes, npositions)
initial_ci = chroms_to_index(
sorted(popgenmarkov.bin_to_int(row) for row in K_initial),
npositions)
initial_short = ci_to_short[initial_ci]
final_ci = chroms_to_index(
sorted(popgenmarkov.bin_to_int(row) for row in K_final),
npositions)
final_short = ci_to_short[final_ci]
# get an answer using the less efficient methods
P_sr = popgenmarkov.get_selection_recombination_transition_matrix(
selection, recombination, nchromosomes, npositions)
P_m = popgenmarkov.get_mutation_transition_matrix(
mutation, nchromosomes, npositions)
p_b_given_a = linalg.matrix_power(np.dot(P_sr, P_m),
ngenerations - 1)[initial_long,
final_long]
p_b_given_a_no_mutation = linalg.matrix_power(
P_sr, ngenerations - 1)[initial_long, final_long]
no_mutation_posterior = (no_mutation_prior *
p_b_given_a_no_mutation) / p_b_given_a
# get an answer using the more efficient methods
P_sr_s = get_selection_recombination_transition_matrix_s(
ci_to_short, short_to_count, sorted_chrom_lists, selection,
recombination, nchromosomes, npositions)
P_m_s = get_mutation_transition_matrix_s(ci_to_short, short_to_count,
sorted_chrom_lists, mutation,
nchromosomes, npositions)
p_b_given_a_s = linalg.matrix_power(np.dot(P_sr_s, P_m_s),
ngenerations - 1)[initial_short,
final_short]
p_b_given_a_no_mutation_s = linalg.matrix_power(
P_sr_s, ngenerations - 1)[initial_short, final_short]
no_mutation_posterior_s = (no_mutation_prior *
p_b_given_a_no_mutation_s) / p_b_given_a_s
#
self.assertTrue(
np.allclose(no_mutation_posterior, no_mutation_posterior_s))
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
"""
P_mutation = popgenmarkov.get_mutation_transition_matrix(
mutation, nchromosomes, npositions)
P_selection_recombination = popgenmarkov.get_selection_recombination_transition_matrix(
selection, recombination, nchromosomes, npositions)
P = np.dot(P_selection_recombination, P_mutation)
return P
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
"""
P_mutation = popgenmarkov.get_mutation_transition_matrix(
mutation, nchromosomes, npositions)
P_selection_recombination = popgenmarkov.get_selection_recombination_transition_matrix(
selection, recombination, nchromosomes, npositions)
P = np.dot(P_selection_recombination, P_mutation)
return P
