Beispiel #1
0
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))
Beispiel #2
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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))
Beispiel #3
0
 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)
Beispiel #4
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 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)
Beispiel #5
0
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
Beispiel #6
0
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