def dup_loss_topology_prior(tree, stree, recon, birth, death, maxdoom=20, events=None):
"""
Returns the log prior of a gene tree topology according to dup-loss model
"""
def gene2species(gene):
return recon[tree.nodes[gene]].name
if events is None:
events = phylo.label_events(tree, recon)
leaves = set(tree.leaves())
phylo.add_implied_spec_nodes(tree, stree, recon, events)
pstree, snodes, snodelookup = spidir.make_ptree(stree)
# get doomtable
doomtable = calc_doom_table(stree, birth, death, maxdoom)
prod = 0.0
for node in tree:
if events[node] == "spec":
for schild in recon[node].children:
nodes2 = [x for x in node.children if recon[x] == schild]
if len(nodes2) > 0:
node2 = nodes2[0]
subleaves = get_sub_tree(node2, schild, recon, events)
nhist = birthdeath.num_topology_histories(node2, subleaves)
s = len(subleaves)
thist = stats.factorial(s) * stats.factorial(s - 1) / 2 ** (s - 1)
if len(set(subleaves) & leaves) == 0:
# internal
prod += log(num_redundant_topology(node2, gene2species, subleaves, True))
else:
# leaves
prod += log(num_redundant_topology(node2, gene2species, subleaves, False))
else:
nhist = 1.0
thist = 1.0
s = 0
t = sum(
stats.choose(s + i, i)
* birthdeath.prob_birth_death1(s + i, schild.dist, birth, death)
* exp(doomtable[snodelookup[schild]]) ** i
for i in range(maxdoom + 1)
)
prod += log(nhist) - log(thist) + log(t)
# correct for renumbering
nt = num_redundant_topology(tree.root, gene2species)
prod -= log(nt)
# phylo.removeImpliedSpecNodes(tree, recon, events)
treelib.remove_single_children(tree)
return prod
def gegenbauer3(n, a, z):
tot = 0
for k in xrange(int(n/2)+1):
tot += ((-1)**k * stats.gamma(n - k + a) / (
stats.gamma(a) * stats.factorial(k) * stats.factorial(n - 2*k))
* ((2*z) ** (n - 2*k)))
return tot
def prob_coal_counts(u, v, t, n):
"""
The probabiluty of going from 'u' lineages to 'v' lineages in time 't'
with population size 'n'
"""
T = t / n
s = 0.0
for k in xrange(v, u+1):
a = exp(-k*(k-1)*T/2.0) * (2*k-1)*(-1)**(k-v) / stats.factorial(v) / \
stats.factorial(k-v) / (k+v-1) * \
stats.prod((v+y)*(u-y)/(u+y) for y in xrange(k))
s += a
return s
def prob_coal_counts_slow(a, b, t, n):
"""
The probabiluty of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
Implemented more directly, but slower. Good for testing against.
"""
s = 0.0
for k in range(b, a + 1):
i = exp(-k*(k-1)*t/2.0/n) * \
float(2*k-1)*(-1)**(k-b) / stats.factorial(b) / \
stats.factorial(k-b) / (k+b-1) * \
stats.prod((b+y)*(a-y)/float(a+y) for y in range(k))
s += i
return s
def legendre_poly(n):
""" \frac{1}{2^n n!} d^n/dx^n [(x^2 - 1)^n] """
return simplify(('mult', ('scalar', 1.0 / (2 ** n * stats.factorial(n))),
derivate(('power', ('add', ('power', ('var', 'x'),
('scalar', 2)),
('scalar', -1)),
('scalar', n)),
'x', n)))
def prob_coal_counts_slow(a, b, t, n):
"""
The probabiluty of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
Implemented more directly, but slower. Good for testing against.
"""
s = 0.0
for k in xrange(b, a + 1):
i = (
exp(-k * (k - 1) * t / 2.0 / n)
* float(2 * k - 1)
* (-1) ** (k - b)
/ stats.factorial(b)
/ stats.factorial(k - b)
/ (k + b - 1)
* stats.prod((b + y) * (a - y) / float(a + y) for y in xrange(k))
)
s += i
return s
def num_redundant_topology(node, gene2species, leaves=None, all_leaves=False):
"""Returns the number of 'redundant' topologies"""
if leaves is None:
leaves = node.leaves()
leaves = set(leaves)
colors = {}
nmirrors = [0]
def walk(node):
if node in leaves:
colors[node] = phylo.hash_tree(node, gene2species)
else:
# recurse
for child in node.children:
walk(child)
childHashes = util.mget(colors, node.children)
if len(childHashes) > 1 and util.equal(*childHashes):
nmirrors[0] += 1
childHashes.sort()
colors[node] = phylo.hash_tree_compose(childHashes)
walk(node)
colorsizes = util.hist_dict(util.mget(colors, leaves)).values()
if all_leaves:
val = stats.factorial(len(leaves))
else:
val = 1
for s in colorsizes:
if s > 1:
val *= stats.factorial(s)
# print "py val=", val, "nmirrors=", nmirrors[0]
return val / (2 ** nmirrors[0])
def num_redundant_topology(node, gene2species, leaves=None, all_leaves=False):
"""Returns the number of 'redundant' topologies"""
if leaves is None:
leaves = node.leaves()
leaves = set(leaves)
colors = {}
nmirrors = [0]
def walk(node):
if node in leaves:
colors[node] = phylo.hash_tree(node, gene2species)
else:
# recurse
for child in node.children:
walk(child)
childHashes = util.mget(colors, node.children)
if len(childHashes) > 1 and util.equal(*childHashes):
nmirrors[0] += 1
childHashes.sort()
colors[node] = phylo.hash_tree_compose(childHashes)
walk(node)
colorsizes = util.hist_dict(util.mget(colors, leaves)).values()
if all_leaves:
val = stats.factorial(len(leaves))
else:
val = 1
for s in colorsizes:
if s > 1:
val *= stats.factorial(s)
#print "py val=", val, "nmirrors=", nmirrors[0]
return val / (2**nmirrors[0])
def prob_coal_counts(a, b, t, n):
"""
The probability of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
"""
try:
terms = []
C = stats.prod((b + y) * (a - y) / float(a + y) for y in xrange(b)) / float(stats.factorial(b))
terms.append(exp(-b * (b - 1) * t / 2.0 / n) * C)
for k in xrange(b + 1, a + 1):
k1 = k - 1
C = (b + k1) * (a - k1) / float(a + k1) / float(b - k) * C
terms.append(exp(-k * k1 * t / 2.0 / n) * (2 * k - 1) / float(k1 + b) * C)
terms.sort(key=abs)
return kahan_sum(terms)
except:
print a, b, t, n
raise
def prob_coal_counts(a, b, t, n):
"""
The probability of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
"""
try:
terms = []
C = stats.prod((b+y)*(a-y)/float(a+y) for y in range(b)) \
/ float(stats.factorial(b))
terms.append(exp(-b * (b - 1) * t / 2.0 / n) * C)
for k in range(b + 1, a + 1):
k1 = k - 1
C = (b + k1) * (a - k1) / float(a + k1) / float(b - k) * C
terms.append(
exp(-k * k1 * t / 2.0 / n) * (2 * k - 1) / float(k1 + b) * C)
terms.sort(key=abs)
return kahan_sum(terms)
except:
print(a, b, t, n)
raise
def dup_loss_topology_prior(tree,
stree,
recon,
birth,
death,
maxdoom=20,
events=None):
"""
Returns the log prior of a gene tree topology according to dup-loss model
"""
def gene2species(gene):
return recon[tree.nodes[gene]].name
if events is None:
events = phylo.label_events(tree, recon)
leaves = set(tree.leaves())
phylo.add_implied_spec_nodes(tree, stree, recon, events)
pstree, snodes, snodelookup = spidir.make_ptree(stree)
# get doomtable
doomtable = calc_doom_table(stree, birth, death, maxdoom)
prod = 0.0
for node in tree:
if events[node] == "spec":
for schild in recon[node].children:
nodes2 = [x for x in node.children if recon[x] == schild]
if len(nodes2) > 0:
node2 = nodes2[0]
subleaves = get_sub_tree(node2, schild, recon, events)
nhist = birthdeath.num_topology_histories(node2, subleaves)
s = len(subleaves)
thist = stats.factorial(s) * stats.factorial(s - 1) / 2**(
s - 1)
if len(set(subleaves) & leaves) == 0:
# internal
prod += log(
num_redundant_topology(node2, gene2species,
subleaves, True))
else:
# leaves
prod += log(
num_redundant_topology(node2, gene2species,
subleaves, False))
else:
nhist = 1.0
thist = 1.0
s = 0
t = sum(
stats.choose(s + i, i) * birthdeath.prob_birth_death1(
s + i, schild.dist, birth, death) *
exp(doomtable[snodelookup[schild]])**i
for i in range(maxdoom + 1))
prod += log(nhist) - log(thist) + log(t)
# correct for renumbering
nt = num_redundant_topology(tree.root, gene2species)
prod -= log(nt)
#phylo.removeImpliedSpecNodes(tree, recon, events)
treelib.remove_single_children(tree)
return prod
