table 4.3 K80ΒΆ
For a K80 model of molecular evolution along a fixed evolutionary tree shape, use EM for maximum likelihood estimation of branch lengths and of the K80 kappa parameter given an observed alignment with IUPAC nucleotide ambiguity.
The output includes the results of 8 iterations of EM, enough to converge to the maximum log likelihood -6,113.86 and the maximum likelihood kappa parameter estimate 3.561 given in Table 4.3 of Ziheng Yang’s 2014 textbook.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 | from __future__ import print_function, division, absolute_import
import copy
import json
import pyparsing
import numpy as np
from numpy.testing import assert_equal
import jsonctmctree.interface
s_tree = """(kiwi_fruit, ((((agave, garlic), rice), black_pepper),
((cabbage, cotton), (cucumber, walnut))), (sunflower, (tomato, tobacco)))"""
def _help_build_tree(parent, root, node, name_to_node, edges):
if parent is not None:
edges.append((parent, node))
neo = node + 1
if isinstance(root, basestring):
name_to_node[root] = node
else:
for element in root:
neo = _help_build_tree(node, element, neo, name_to_node, edges)
return neo
def get_tree_info():
# Return a dictionary mapping name to node index,
# and return a list of edges as ordered pairs of node indices.
tree = s_tree.replace(',', ' ')
nestedItems = pyparsing.nestedExpr(opener='(', closer=')')
tree = (nestedItems + pyparsing.stringEnd).parseString(tree).asList()[0]
name_to_node = {}
edges = []
_help_build_tree(None, tree, 0, name_to_node, edges)
return name_to_node, edges
def get_nucleotide_alignment_info(name_to_node):
# Return an ordered list of observable node indices,
# and return the array of iid observations.
# An observed state of -1 means completely missing data.
nt_to_state = {
'A' : [1, 0, 0, 0],
'C' : [0, 1, 0, 0],
'G' : [0, 0, 1, 0],
'T' : [0, 0, 0, 1],
'?' : [-1, -1, -1, -1],
'-' : [-1, -1, -1, -1],
'N' : [-1, -1, -1, -1],
'M' : [-1, -1, 0, 0],
'R' : [-1, 0, -1, 0],
'W' : [-1, 0, 0, -1],
'S' : [0, -1, -1, 0],
'Y' : [0, -1, 0, -1],
'K' : [0, 0, -1, -1],
}
sequences = []
nodes = []
variables = []
with open('vegetables.rbcL.txt') as fin:
lines = fin.readlines()
header = lines[0]
for line in lines[1:]:
name, sequence = line.strip().split()
node = name_to_node[name]
nodes.extend([node]*4)
sequences.append([nt_to_state[c] for c in sequence])
variables.extend([0, 1, 2, 3])
# arr[node, site, variable]
arr = np.array(sequences, dtype=int)
arr = np.transpose(arr, (1, 0, 2))
iid_observations = np.reshape(arr, (arr.shape[0], -1))
iid_observations = iid_observations.tolist()
return nodes, variables, iid_observations
def get_process_definition(kappa):
# Get the structure of the rate matrix.
info = get_transition_components()
ts_row_states, ts_column_states, tv_row_states, tv_column_states = info
# Put together the rate matrix.
rate = 2 + kappa
row_states = ts_row_states + tv_row_states
column_states = ts_column_states + tv_column_states
rates = [kappa/rate]*len(ts_row_states) + [1/rate]*len(tv_row_states)
# Assemble and return the process definition.
process_definition = dict(
row_states = row_states,
column_states = column_states,
transition_rates = rates)
return process_definition
def get_transition_components():
# Return ts_row_states, ts_col_states, tv_row_states, tv_col_states
ts_row_states = []
ts_column_states = []
tv_row_states = []
tv_column_states = []
ident = np.identity(4, dtype=int).tolist()
# ts: A<->G, C<->T
ts = ((0, 2), (2, 0), (1, 3), (3, 1))
for i in range(4):
for j in range(4):
if i != j:
rs = ident[i]
cs = ident[j]
if (i, j) in ts:
ts_row_states.append(rs)
ts_column_states.append(cs)
else:
tv_row_states.append(rs)
tv_column_states.append(cs)
return ts_row_states, ts_column_states, tv_row_states, tv_column_states
def main():
# Read the tree.
name_to_node, edges = get_tree_info()
edge_count = len(edges)
node_count = edge_count + 1
# Read the alignment.
info = get_nucleotide_alignment_info(name_to_node)
nodes, variables, iid_observations = info
nsites = len(iid_observations)
# Define the tree component of the scene
row_nodes, column_nodes = zip(*edges)
tree = dict(
row_nodes = list(row_nodes),
column_nodes = list(column_nodes),
edge_rate_scaling_factors = [0.01] * edge_count,
edge_processes = [0] * edge_count)
# Get the structure of the rate matrix.
info = get_transition_components()
ts_row_states, ts_column_states, tv_row_states, tv_column_states = info
row_states = ts_row_states + tv_row_states
column_states = ts_column_states + tv_column_states
# Define the root distribution.
ident = np.identity(4, dtype=int).tolist()
root_prior = dict(
states = ident,
probabilities = [0.25, 0.25, 0.25, 0.25])
# Define the observed data.
observed_data = dict(
nodes = nodes,
variables = variables,
iid_observations = iid_observations)
# Assemble the scene.
scene = dict(
node_count = node_count,
process_count = 1,
state_space_shape = [2, 2, 2, 2],
tree = tree,
root_prior = root_prior,
observed_data = observed_data)
# Define some requests.
# These include the log likelihood
# and the sum of transition count expectations.
requests = [
{"property" : "SNNLOGL"},
{
"property" : "SDNTRAN",
"transition_reduction" : {
"row_states" : row_states,
"column_states" : column_states,
"weights" : [1 / nsites] * len(row_states)
}
},
{
"property" : "SSNTRAN",
"transition_reduction" : {
"row_states" : ts_row_states,
"column_states" : ts_column_states,
"weights" : [1] * len(ts_row_states)
}
},
{
"property" : "SSNTRAN",
"transition_reduction" : {
"row_states" : tv_row_states,
"column_states" : tv_column_states,
"weights" : [1] * len(tv_row_states)
}
}]
# Request some stuff.
j_in = {
"scene" : scene,
"requests" : requests
}
arr = []
j_out = None
kappa = 2.0
for i in range(8):
# if j_out is available, recompute kappa and edge rates
if j_out is not None:
ll, edge_rates, ts, tv = j_out['responses']
kappa = 2 * (ts / tv)
j_in['scene']['tree']['edge_rate_scaling_factors'] = edge_rates
j_in['scene']['process_definitions'] = [get_process_definition(kappa)]
j_out = jsonctmctree.interface.process_json_in(j_in)
arr.append(copy.deepcopy(j_out))
print(json.dumps(arr, indent=4))
print('kappa estimate:', kappa)
main()
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{
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],
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304.23134098972497
]
},
{
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],
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]
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{
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{
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]
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{
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{
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]
},
{
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]
|