def prob_birth_death(genes1, genes2, t, birth, death): """Probability of 'genes1' genes at time 0 give rise to 'genes2' genes at time 't' with 'birth' and 'death' rates. """ # special cases if birth == 0.0 and death == 0.0: if genes1 == genes2: return 1.0 else: return 0.0 l = birth u = death elut = exp((l - u) * t) a = u * (elut - 1.0) / (l * elut - u) # alpha b = l * (elut - 1.0) / (l * elut - u) # beta n = genes1 i = genes2 if genes1 < 1: return 0.0 if genes2 == 0: return a**n else: return sum(stats.choose(n,j) * stats.choose(n+i-j-1, n-1) *\ a**(n-j) * b**(i-j) * (1.0 - a - b)**j for j in xrange(min(n, i)+1))
def prob_birth_death(genes1, genes2, t, birth, death): """Probability of 'genes1' genes at time 0 give rise to 'genes2' genes at time 't' with 'birth' and 'death' rates. """ # special cases if birth == 0.0 and death == 0.0: if genes1 == genes2: return 1.0 else: return 0.0 l = birth u = death elut = exp((l-u)*t) a = u * (elut - 1.0) / (l*elut - u) # alpha b = l * (elut - 1.0) / (l*elut - u) # beta n = genes1 i = genes2 if genes1 < 1: return 0.0 if genes2 == 0: return a ** n else: return sum(stats.choose(n,j) * stats.choose(n+i-j-1, n-1) *\ a**(n-j) * b**(i-j) * (1.0 - a - b)**j for j in xrange(min(n, i)+1))
def walk(node): if node in leaves: return 0 else: internals = map(walk, node.children) prod[0] *= stats.choose(sum(internals), internals[0]) return 1 + sum(internals)
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 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