def sample_dsmc_sprs(k,
popsize,
rho,
recombmap=None,
start=0.0,
end=0.0,
times=None,
times2=None,
init_tree=None,
names=None,
make_names=True):
"""
Sample ARG using Discrete Sequentially Markovian Coalescent (SMC)
k -- chromosomes
popsize -- effective population size (haploid)
rho -- recombination rate (recombinations / site / generation)
recombmap -- map for variable recombination rate
start -- staring chromosome coordinate
end -- ending chromsome coordinate
t -- initial time (default: 0)
names -- names to use for leaves (default: None)
make_names -- make names using strings (default: True)
"""
assert times is not None
assert times2 is not None
ntimes = len(times) - 1
time_steps = [times[i] - times[i - 1] for i in range(1, ntimes + 1)]
# times2 = get_coal_times(times)
if hasattr(popsize, "__len__"):
popsizes = popsize
else:
popsizes = [popsize] * len(time_steps)
# yield initial tree first
if init_tree is None:
init_tree = sample_tree(k,
popsizes,
times,
start=start,
end=end,
names=names,
make_names=make_names)
argweaver.discretize_arg(init_tree, times2)
yield init_tree
# sample SPRs
pos = start
tree = init_tree.copy()
while True:
# sample next recomb point
treelen = sum(x.get_dist() for x in tree)
blocklen = int(
sample_next_recomb(treelen,
rho,
pos=pos,
recombmap=recombmap,
minlen=1))
pos += blocklen
if pos >= end - 1:
break
root_age_index = times.index(tree.root.age)
# choose time interval for recombination
states = set(argweaver.iter_coal_states(tree, times))
nbranches, nrecombs, ncoals = argweaver.get_nlineages_recomb_coal(
tree, times)
probs = [
nbranches[i] * time_steps[i] for i in range(root_age_index + 1)
]
recomb_time_index = stats.sample(probs)
recomb_time = times[recomb_time_index]
# choose branch for recombination
branches = [
x for x in states
if x[1] == recomb_time_index and x[0] != tree.root.name
]
recomb_node = tree[random.sample(branches, 1)[0][0]]
# choose coal time
j = recomb_time_index
last_kj = nbranches[max(j - 1, 0)]
while j < ntimes - 1:
kj = nbranches[j]
if ((recomb_node.name, j) in states
and recomb_node.parents[0].age > times[j]):
kj -= 1
assert kj > 0, (j, root_age_index, states)
A = (times2[2 * j + 1] - times2[2 * j]) * kj
if j > recomb_time_index:
A += (times2[2 * j] - times2[2 * j - 1]) * last_kj
coal_prob = 1.0 - exp(-A / float(popsizes[j]))
if random.random() < coal_prob:
break
j += 1
last_kj = kj
coal_time_index = j
coal_time = times[j]
# choose coal node
# since coal points collapse, exclude parent node, but allow sibling
exclude = []
def walk(node):
exclude.append(node.name)
if node.age == coal_time:
for child in node.children:
walk(child)
walk(recomb_node)
exclude2 = (recomb_node.parents[0].name,
times.index(recomb_node.parents[0].age))
branches = [
x for x in states if x[1] == coal_time_index
and x[0] not in exclude and x != exclude2
]
coal_node = tree[random.sample(branches, 1)[0][0]]
# yield SPR
rleaves = list(tree.leaf_names(recomb_node))
cleaves = list(tree.leaf_names(coal_node))
yield pos, (rleaves, recomb_time), (cleaves, coal_time)
# apply SPR to local tree
broken = recomb_node.parents[0]
recoal = tree.new_node(age=coal_time,
children=[recomb_node, coal_node])
# add recoal node to tree
recomb_node.parents[0] = recoal
broken.children.remove(recomb_node)
if coal_node.parents:
recoal.parents.append(coal_node.parents[0])
util.replace(coal_node.parents[0].children, coal_node, recoal)
coal_node.parents[0] = recoal
else:
coal_node.parents.append(recoal)
# remove broken node
broken_child = broken.children[0]
if broken.parents:
broken_child.parents[0] = broken.parents[0]
util.replace(broken.parents[0].children, broken, broken_child)
else:
broken_child.parents.remove(broken)
del tree.nodes[broken.name]
tree.set_root()
def sample_dsmc_sprs(
k, popsize, rho, recombmap=None, start=0.0, end=0.0, times=None,
times2=None, init_tree=None, names=None, make_names=True):
"""
Sample ARG using Discrete Sequentially Markovian Coalescent (SMC)
k -- chromosomes
popsize -- effective population size (haploid)
rho -- recombination rate (recombinations / site / generation)
recombmap -- map for variable recombination rate
start -- staring chromosome coordinate
end -- ending chromsome coordinate
t -- initial time (default: 0)
names -- names to use for leaves (default: None)
make_names -- make names using strings (default: True)
"""
assert times is not None
assert times2 is not None
ntimes = len(times) - 1
time_steps = [times[i] - times[i-1] for i in range(1, ntimes+1)]
# times2 = get_coal_times(times)
if hasattr(popsize, "__len__"):
popsizes = popsize
else:
popsizes = [popsize] * len(time_steps)
# yield initial tree first
if init_tree is None:
init_tree = sample_tree(k, popsizes, times, start=start, end=end,
names=names, make_names=make_names)
argweaver.discretize_arg(init_tree, times2)
yield init_tree
# sample SPRs
pos = start
tree = init_tree.copy()
while True:
# sample next recomb point
treelen = sum(x.get_dist() for x in tree)
blocklen = int(sample_next_recomb(treelen, rho, pos=pos,
recombmap=recombmap, minlen=1))
pos += blocklen
if pos >= end - 1:
break
root_age_index = times.index(tree.root.age)
# choose time interval for recombination
states = set(argweaver.iter_coal_states(tree, times))
nbranches, nrecombs, ncoals = argweaver.get_nlineages_recomb_coal(
tree, times)
probs = [nbranches[i] * time_steps[i]
for i in range(root_age_index+1)]
recomb_time_index = stats.sample(probs)
recomb_time = times[recomb_time_index]
# choose branch for recombination
branches = [x for x in states if x[1] == recomb_time_index and
x[0] != tree.root.name]
recomb_node = tree[random.sample(branches, 1)[0][0]]
# choose coal time
j = recomb_time_index
last_kj = nbranches[max(j-1, 0)]
while j < ntimes - 1:
kj = nbranches[j]
if ((recomb_node.name, j) in states and
recomb_node.parents[0].age > times[j]):
kj -= 1
assert kj > 0, (j, root_age_index, states)
A = (times2[2*j+1] - times2[2*j]) * kj
if j > recomb_time_index:
A += (times2[2*j] - times2[2*j-1]) * last_kj
coal_prob = 1.0 - exp(-A/float(popsizes[j]))
if random.random() < coal_prob:
break
j += 1
last_kj = kj
coal_time_index = j
coal_time = times[j]
# choose coal node
# since coal points collapse, exclude parent node, but allow sibling
exclude = []
def walk(node):
exclude.append(node.name)
if node.age == coal_time:
for child in node.children:
walk(child)
walk(recomb_node)
exclude2 = (recomb_node.parents[0].name,
times.index(recomb_node.parents[0].age))
branches = [x for x in states if x[1] == coal_time_index and
x[0] not in exclude and x != exclude2]
coal_node = tree[random.sample(branches, 1)[0][0]]
# yield SPR
rleaves = list(tree.leaf_names(recomb_node))
cleaves = list(tree.leaf_names(coal_node))
yield pos, (rleaves, recomb_time), (cleaves, coal_time)
# apply SPR to local tree
broken = recomb_node.parents[0]
recoal = tree.new_node(age=coal_time,
children=[recomb_node, coal_node])
# add recoal node to tree
recomb_node.parents[0] = recoal
broken.children.remove(recomb_node)
if coal_node.parents:
recoal.parents.append(coal_node.parents[0])
util.replace(coal_node.parents[0].children, coal_node, recoal)
coal_node.parents[0] = recoal
else:
coal_node.parents.append(recoal)
# remove broken node
broken_child = broken.children[0]
if broken.parents:
broken_child.parents[0] = broken.parents[0]
util.replace(broken.parents[0].children, broken, broken_child)
else:
broken_child.parents.remove(broken)
del tree.nodes[broken.name]
tree.set_root()
def test_trans_two():
"""
Calculate transition probabilities for k=2
Only calculate a single matrix
"""
k = 2
n = 1e4
rho = 1.5e-8 * 20
length = 1000
times = argweaver.get_time_points(ntimes=5, maxtime=200000)
time_steps = [times[i] - times[i - 1] for i in range(1, len(times))]
time_steps.append(200000 * 10000.0)
popsizes = [n] * len(times)
arg = arglib.sample_arg(k, 2 * n, rho, start=0, end=length)
argweaver.discretize_arg(arg, times)
print "recomb", arglib.get_recomb_pos(arg)
arg = argweaver.make_trunk_arg(0, length, "n0")
pos = 10
tree = arg.get_marginal_tree(pos)
nlineages = argweaver.get_nlineages_recomb_coal(tree, times)
states = list(argweaver.iter_coal_states(tree, times))
mat = argweaver.calc_transition_probs(tree, states, nlineages, times,
time_steps, popsizes, rho)
nstates = len(states)
def coal(j):
return 1.0 - exp(-time_steps[j] / (2.0 * n))
def recoal2(k, j):
p = coal(j)
for m in range(k, j):
p *= 1.0 - coal(m)
return p
def recoal(k, j):
if j == nstates - 1:
return exp(-sum(time_steps[m] / (2.0 * n) for m in range(k, j)))
else:
return ((1.0 - exp(-time_steps[j] / (2.0 * n))) *
exp(-sum(time_steps[m] / (2.0 * n) for m in range(k, j))))
def isrecomb(i):
return 1.0 - exp(-max(rho * 2.0 * times[i], rho))
def recomb(i, k):
treelen = 2 * times[i] + time_steps[i]
if k < i:
return 2.0 * time_steps[k] / treelen / 2.0
else:
return time_steps[k] / treelen / 2.0
def trans(i, j):
a = states[i][1]
b = states[j][1]
p = sum(recoal(k, b) * recomb(a, k) for k in range(0, min(a, b) + 1))
p += sum(recoal(k, b) * recomb(a, k) for k in range(0, min(a, b) + 1))
p *= isrecomb(a)
if i == j:
p += 1.0 - isrecomb(a)
return p
for i in range(len(states)):
for j in range(len(states)):
print isrecomb(states[i][1])
print states[i], states[j], mat[i][j], log(trans(i, j))
fequal(mat[i][j], log(trans(i, j)))
# recombs add up to 1
fequal(sum(recomb(i, k) for k in range(i + 1)), 0.5)
# recoal add up to 1
fequal(sum(recoal(i, j) for j in range(i, nstates)), 1.0)
# recomb * recoal add up to .5
fequal(
sum(
sum(
recoal(k, j) * recomb(i, k)
for k in range(0,
min(i, j) + 1))
for j in range(0, nstates)), 0.5)
fequal(sum(trans(i, j) for j in range(len(states))), 1.0)
def test_trans_two():
"""
Calculate transition probabilities for k=2
Only calculate a single matrix
"""
k = 2
n = 1e4
rho = 1.5e-8 * 20
length = 1000
times = argweaver.get_time_points(ntimes=5, maxtime=200000)
time_steps = [times[i] - times[i-1]
for i in range(1, len(times))]
time_steps.append(200000*10000.0)
popsizes = [n] * len(times)
arg = arglib.sample_arg(k, 2*n, rho, start=0, end=length)
argweaver.discretize_arg(arg, times)
print "recomb", arglib.get_recombs(arg)
arg = argweaver.make_trunk_arg(0, length, "n0")
pos = 10
tree = arg.get_marginal_tree(pos)
nlineages = argweaver.get_nlineages_recomb_coal(tree, times)
states = list(argweaver.iter_coal_states(tree, times))
mat = argweaver.calc_transition_probs(
tree, states, nlineages,
times, time_steps, popsizes, rho)
nstates = len(states)
def coal(j):
return 1.0 - exp(-time_steps[j]/(2.0 * n))
def recoal2(k, j):
p = coal(j)
for m in range(k, j):
p *= 1.0 - coal(m)
return p
def recoal(k, j):
if j == nstates-1:
return exp(- sum(time_steps[m] / (2.0 * n)
for m in range(k, j)))
else:
return ((1.0 - exp(-time_steps[j]/(2.0 * n))) *
exp(- sum(time_steps[m] / (2.0 * n)
for m in range(k, j))))
def isrecomb(i):
return 1.0 - exp(-max(rho * 2.0 * times[i], rho))
def recomb(i, k):
treelen = 2*times[i] + time_steps[i]
if k < i:
return 2.0 * time_steps[k] / treelen / 2.0
else:
return time_steps[k] / treelen / 2.0
def trans(i, j):
a = states[i][1]
b = states[j][1]
p = sum(recoal(k, b) * recomb(a, k)
for k in range(0, min(a, b)+1))
p += sum(recoal(k, b) * recomb(a, k)
for k in range(0, min(a, b)+1))
p *= isrecomb(a)
if i == j:
p += 1.0 - isrecomb(a)
return p
for i in range(len(states)):
for j in range(len(states)):
print isrecomb(states[i][1])
print states[i], states[j], mat[i][j], log(trans(i, j))
fequal(mat[i][j], log(trans(i, j)))
# recombs add up to 1
fequal(sum(recomb(i, k) for k in range(i+1)), 0.5)
# recoal add up to 1
fequal(sum(recoal(i, j) for j in range(i, nstates)), 1.0)
# recomb * recoal add up to .5
fequal(sum(sum(recoal(k, j) * recomb(i, k)
for k in range(0, min(i, j)+1))
for j in range(0, nstates)), 0.5)
fequal(sum(trans(i, j) for j in range(len(states))), 1.0)