Source code for dendropy.model.birthdeath

#! /usr/bin/env python
# -*- coding: utf-8 -*-

##############################################################################
##  DendroPy Phylogenetic Computing Library.
##
##  Copyright 2010-2015 Jeet Sukumaran and Mark T. Holder.
##  All rights reserved.
##
##  See "LICENSE.rst" for terms and conditions of usage.
##
##  If you use this work or any portion thereof in published work,
##  please cite it as:
##
##     Sukumaran, J. and M. T. Holder. 2010. DendroPy: a Python library
##     for phylogenetic computing. Bioinformatics 26: 1569-1571.
##
##############################################################################

##############################################################################
## Parts of this code were adapted from:
##
##  -   TESS
##
##          https://github.com/hoehna/TESS
##
##          H{"o}hna S. 2013. Fast simulation of reconstructed phylogenies under
##          global time-dependent birth--death processes. Bioinformatics, 29(11)
##          1367-1374.
##
##          Copyright (c) 2012- Sebastian Hoehna
##
##          TESS is free software; you can redistribute it and/or modify
##          it under the terms of the GNU Lesser General Public License as
##          published by the Free Software Foundation; either version 2
##          of the License, or (at your option) any later version.
##
##############################################################################

"""
Models, modeling and model-fitting of birth-death processes.

-   Nee, S.  2001.  Inferring speciation rates from phylogenies.
    Evolution 55:661-668.
-   Yule, G. U. 1924. A mathematical theory of evolution based on the
    conclusions of Dr.  J. C. Willis. Phil. Trans. R. Soc. Lond. B
    213:21-87.
-   Hoehna, S. (2015). The time-dependent reconstructed evolutionary process
    with a key-role for mass-extinction events. Journal of theoretical biology,
    380, 321-331.

"""

import sys
import math
import collections
import itertools
from dendropy.calculate import combinatorics
from dendropy.calculate import probability
from dendropy.utility import GLOBAL_RNG
from dendropy.utility.error import TreeSimTotalExtinctionException
from dendropy.utility import constants
from dendropy.utility import deprecate

import dendropy

[docs]def birth_death_tree(birth_rate, death_rate, birth_rate_sd=0.0, death_rate_sd=0.0, **kwargs): """ Returns a birth-death tree with birth rate specified by ``birth_rate``, and death rate specified by ``death_rate``, with edge lengths in continuous (real) units. Tree growth is controlled by one or more of the following arguments, of which at least one must be specified: - If ``num_extant_tips`` is given as a keyword argument, tree is grown until the number of EXTANT tips equals this number. - If ``num_extinct_tips`` is given as a keyword argument, tree is grown until the number of EXTINCT tips equals this number. - If ``num_total_tips`` is given as a keyword argument, tree is grown until the number of EXTANT plus EXTINCT tips equals this number. - If 'max_time' is given as a keyword argument, tree is grown for a maximum of ``max_time``. - If ``gsa_ntax`` is given then the tree will be simulated up to this number of EXTANT tips (or 0 tips), then a tree will be randomly selected from the intervals which corresond to times at which the tree had exactly ``num_extant_tips`` leaves. This allows for simulations according to the "General Sampling Approach" of Hartmann et al. (2010). If this option is specified, then ``num_extant_tips`` MUST be specified and ``num_extinct_tips`` and ``num_total_tips`` CANNOT be specified. If more than one of the above is given, then tree growth will terminate when *any* one of the termination conditions are met. Parameters ---------- birth_rate : float The birth rate. death_rate : float The death rate. birth_rate_sd : float The standard deviation of the normally-distributed mutation added to the birth rate as it is inherited by daughter nodes; if 0, birth rate does not evolve on the tree. death_rate_sd : float The standard deviation of the normally-distributed mutation added to the death rate as it is inherited by daughter nodes; if 0, death rate does not evolve on the tree. Keyword Arguments ----------------- num_extant_tips: int If specified, branching process is terminated when number of EXTANT tips equals this number. num_extinct_tips: int If specified, branching process is terminated when number of EXTINCT tips equals this number. num_total_tips: int If specified, branching process is terminated when number of EXTINCT plus EXTANT tips equals this number. max_time: float If specified, branching process is terminated when time reaches or exceeds this value. gsa_ntax: int The General Sampling Approach threshold for number of taxa. See above for details. tree : Tree instance If given, then this tree will be used; otherwise a new one will be created. taxon_namespace : TaxonNamespace instance If given, then this will be assigned to the new tree, and, in addition, taxa assigned to tips will be sourced from or otherwise created with reference to this. is_assign_extant_taxa : bool [default: True] If False, then taxa will not be assigned to extant tips. If True (default), then taxa will be assigned to extant tips. Taxa will be assigned from the specified ``taxon_namespace`` or ``tree.taxon_namespace``. If the number of taxa required exceeds the number of taxa existing in the taxon namespace, new |Taxon| objects will be created as needed and added to the taxon namespace. is_assign_extinct_taxa : bool [default: True] If False, then taxa will not be assigned to extant tips. If True (default), then taxa will be assigned to extant tips. Taxa will be assigned from the specified ``taxon_namespace`` or ``tree.taxon_namespace``. If the number of taxa required exceeds the number of taxa existing in the taxon namespace, new |Taxon| objects will be created as needed and added to the taxon namespace. Note that this option only makes sense if extinct tips are retained (specified via 'is_retain_extinct_tips' option), and will otherwise be ignored. is_add_extinct_attr: bool [default: True] If True (default), add an boolean attribute indicating whether or not a node is an extinct tip or not. False will skip this. Name of attribute is set by 'extinct_attr_name' argument, defaulting to 'is_extinct'. Note that this option only makes sense if extinct tips are retained (specified via 'is_retain_extinct_tips' option), and will otherwise be ignored. extinct_attr_name: str [default: 'is_extinct'] Name of attribute to add to nodes indicating whether or not tip is extinct. Note that this option only makes sense if extinct tips are retained (specified via 'is_retain_extinct_tips' option), and will otherwise be ignored. is_retain_extinct_tips : bool [default: False] If True, extinct tips will be retained on tree. Defaults to False: extinct lineages removed from tree. repeat_until_success: bool [default: True] Under some conditions, it is possible for all lineages on a tree to go extinct. In this case, if this argument is given as |True| (the default), then a new branching process is initiated. If |False| (default), then a TreeSimTotalExtinctionException is raised. rng: random.Random() or equivalent instance A Random() object or equivalent can be passed using the ``rng`` keyword; otherwise GLOBAL_RNG is used. References ---------- Hartmann, Wong, and Stadler "Sampling Trees from Evolutionary Models" Systematic Biology. 2010. 59(4). 465-476 """ if "assign_taxa" in kwargs: deprecate.dendropy_deprecation_warning( message="Deprecated: 'assign_taxa' will no longer be supported as an argument to this function. Use 'is_assign_extant_taxa' and/or 'is_assign_extinct_taxa' instead", stacklevel=3) a = kwargs.pop("assign_taxa") kwargs["is_assign_extant_taxa"] = a kwargs["is_assign_extant_taxa"] = a if "ntax" in kwargs: deprecate.dendropy_deprecation_warning( message="Deprecated: 'ntax' is no longer supported as an argument to this function. Use one or more of the following instead: 'num_extant_tips', 'num_extinct_tips', 'num_total_tips', or 'max_time'", stacklevel=3) kwargs["num_extant_tips"] = kwargs.pop("ntax") if (("num_extant_tips" not in kwargs) and ("num_extinct_tips" not in kwargs) and ("num_total_tips" not in kwargs) and ("max_time" not in kwargs) ): if "taxon_namespace" in kwargs: ### cannot support legacy approach, b/c ``taxon_namespace`` may grow during function, leading to unpredictable behavior # deprecate.dendropy_deprecation_warning( # preamble="Deprecated: The 'taxon_namespace' argument can no longer be used to specify a termination condition as a side-effect. Use one or more of the following instead with the length of the taxon namespace instance as a value: 'num_extant_tips', 'num_extinct_tips', or 'num_total_tips'", # old_construct="tree = birth_death_tree(\n ...\n taxon_namespace=taxon_namespace,\n ...\n)", # new_construct="tree = birth_death_tree(\n ...\n taxon_namespace=taxon_namespace,\n num_extant_tips=len(taxon_namespace),\n ...\n)") # kwargs["num_extant_tips"] = len(kwargs["taxon_namespace"]) raise ValueError("The 'taxon_namespace' argument can no longer be used to specify a termination condition as a side-effect." "Use one or more of the following instead with the length of the taxon namespace instance as a value: " "'num_extant_tips', 'num_extinct_tips', or 'num_total_tips'.\n" "That is, instead of:\n\n" " tree = birth_death_tree(\n ...\n taxon_namespace=taxon_namespace,\n ...\n )\n\n" "Use:\n\n" " ntax = len(taxon_namespace)\n tree = birth_death_tree(\n ...\n taxon_namespace=taxon_namespace,\n num_extant_tips=ntax,\n ...\n )\n" "\nOr (recommended):\n\n" " tree = birth_death_tree(\n ...\n taxon_namespace=taxon_namespace,\n num_extant_tips=100,\n ...\n )\n" "\nNote that the taxon namespace instance size may grow during any particular call of the function depending on taxon assignment/creation settings, so" " for stable and predictable behavor it is important to take a snapshot of the desired taxon namespace size before any call of the function, or, better yet" " simply pass in a constant value." ) else: raise ValueError("One or more of the following must be specified: 'num_extant_tips', 'num_extinct_tips', or 'max_time'") target_num_extant_tips = kwargs.pop("num_extant_tips", None) target_num_extinct_tips = kwargs.pop("num_extinct_tips", None) target_num_total_tips = kwargs.pop("num_total_tips", None) max_time = kwargs.pop('max_time', None) gsa_ntax = kwargs.pop('gsa_ntax', None) is_add_extinct_attr = kwargs.pop('is_add_extinct_attr', True) extinct_attr_name = kwargs.pop('extinct_attr_name', 'is_extinct') is_retain_extinct_tips = kwargs.pop('is_retain_extinct_tips', False) is_assign_extant_taxa = kwargs.pop('is_assign_extant_taxa', True) is_assign_extinct_taxa = kwargs.pop('is_assign_extinct_taxa', True) repeat_until_success = kwargs.pop('repeat_until_success', True) tree = kwargs.pop("tree", None) taxon_namespace = kwargs.pop("taxon_namespace", None) rng = kwargs.pop('rng', GLOBAL_RNG) ignore_unrecognized_keyword_arguments = kwargs.pop('ignore_unrecognized_keyword_arguments', False) if kwargs and not ignore_unrecognized_keyword_arguments: raise ValueError("Unsupported keyword arguments: {}".format(kwargs.keys())) terminate_at_full_tree = False if gsa_ntax is None: terminate_at_full_tree = True # gsa_ntax = 1 + target_num_taxa elif target_num_extant_tips is None: raise ValueError("If 'gsa_ntax' is specified, 'num_extant_tips' must be specified") elif target_num_extinct_tips is not None: raise ValueError("If 'gsa_ntax' is specified, 'num_extinct_tups' cannot be specified") elif target_num_total_tips is not None: raise ValueError("If 'gsa_ntax' is specified, 'num_total_tips' cannot be specified") elif gsa_ntax < target_num_extant_tips: raise ValueError("'gsa_ntax' ({}) must be greater than 'num_extant_tips' ({})".format(gsa_ntax, target_num_extant_tips)) # initialize tree if tree is not None: if taxon_namespace is not None: assert tree.taxon_namespace is taxon_namespace else: taxon_namespace = tree.taxon_namespace extant_tips = set() extinct_tips = set() for nd in tree: if not nd._child_nodes: if getattr(nd, extinct_attr_name, False): extant_tips.add(nd) if is_add_extinct_attr: setattr(nd, extinct_attr_name, False) else: extinct_tips.add(nd) if is_add_extinct_attr: setattr(nd, extinct_attr_name, True) elif is_add_extinct_attr: setattr(nd, extinct_attr_name, None) else: if taxon_namespace is None: taxon_namespace = dendropy.TaxonNamespace() tree = dendropy.Tree(taxon_namespace=taxon_namespace) tree.is_rooted = True tree.seed_node.edge.length = 0.0 tree.seed_node.birth_rate = birth_rate tree.seed_node.death_rate = death_rate if is_add_extinct_attr: setattr(tree.seed_node, extinct_attr_name, False) extant_tips = set([tree.seed_node]) extinct_tips = set() initial_extant_tip_set = set(extant_tips) initial_extinct_tip_set = set(extinct_tips) total_time = 0 # for the GSA simulations targetted_time_slices is a list of tuple # the first element in the tuple is the duration of the amount # that the simulation spent at the (targetted) number of taxa # and a list of edge information. The list of edge information includes # a list of terminal edges in the tree and the length for that edge # that marks the beginning of the time slice that corresponds to the # targetted number of taxa. targetted_time_slices = [] while True: if gsa_ntax is None: if target_num_extant_tips is not None and len(extant_tips) >= target_num_extant_tips: break if target_num_extinct_tips is not None and len(extinct_tips) >= target_num_extinct_tips: break if target_num_total_tips is not None and (len(extant_tips) + len(extinct_tips)) >= target_num_total_tips: break if max_time is not None and total_time >= max_time: break elif len(extant_tips) >= gsa_ntax: break # get vector of birth/death probabilities, and # associate with nodes/events event_rates = [] event_nodes = [] for nd in extant_tips: if not hasattr(nd, 'birth_rate'): nd.birth_rate = birth_rate if not hasattr(nd, 'death_rate'): nd.death_rate = death_rate event_rates.append(nd.birth_rate) event_nodes.append((nd, True)) # birth event = True event_rates.append(nd.death_rate) event_nodes.append((nd, False)) # birth event = False; i.e. death # get total probability of any birth/death rate_of_any_event = sum(event_rates) # waiting time based on above probability waiting_time = rng.expovariate(rate_of_any_event) if ( (gsa_ntax is not None) and (len(extant_tips) == target_num_extant_tips) ): edge_and_start_length = [] for nd in extant_tips: e = nd.edge edge_and_start_length.append((e, e.length)) targetted_time_slices.append((waiting_time, edge_and_start_length)) if terminate_at_full_tree: break # add waiting time to nodes for nd in extant_tips: try: nd.edge.length += waiting_time except TypeError: nd.edge.length = waiting_time total_time += waiting_time # if event occurs within time constraints if max_time is None or total_time <= max_time: # normalize probability for i in range(len(event_rates)): event_rates[i] = event_rates[i]/rate_of_any_event # select node/event and process nd, birth_event = probability.weighted_choice(event_nodes, event_rates, rng=rng) extant_tips.remove(nd) if birth_event: if is_add_extinct_attr: setattr(nd, extinct_attr_name, None) c1 = nd.new_child() c2 = nd.new_child() c1.edge.length = 0 c2.edge.length = 0 c1.birth_rate = nd.birth_rate + rng.gauss(0, birth_rate_sd) c1.death_rate = nd.death_rate + rng.gauss(0, death_rate_sd) c2.birth_rate = nd.birth_rate + rng.gauss(0, birth_rate_sd) c2.death_rate = nd.death_rate + rng.gauss(0, death_rate_sd) extant_tips.add(c1) extant_tips.add(c2) else: if len(extant_tips) > 0: extinct_tips.add(nd) if is_add_extinct_attr: setattr(nd, extinct_attr_name, None) else: # total extinction if (gsa_ntax is not None): if (len(targetted_time_slices) > 0): break if not repeat_until_success: raise TreeSimTotalExtinctionException() # We are going to basically restart the simulation because # the tree has gone extinct (without reaching the specified # ntax) extant_tips = set(initial_extant_tip_set) extinct_tips = set(initial_extinct_tip_set) for nd in extant_tips: if is_add_extinct_attr: setattr(nd, extinct_attr_name, False) nd.clear_child_nodes() total_time = 0 if gsa_ntax is not None: total_duration_at_target_n_tax = 0.0 for i in targetted_time_slices: total_duration_at_target_n_tax += i[0] r = rng.random()*total_duration_at_target_n_tax selected_slice = None for n, i in enumerate(targetted_time_slices): r -= i[0] if r < 0.0: selected_slice = i assert(selected_slice is not None) edges_at_slice = selected_slice[1] last_waiting_time = selected_slice[0] for e, prev_length in edges_at_slice: daughter_nd = e.head_node for nd in daughter_nd.child_nodes(): nd._parent_node = None extinct_tips.discard(nd) extant_tips.discard(nd) for desc in nd.preorder_iter(): extinct_tips.discard(desc) extant_tips.discard(desc) daughter_nd.clear_child_nodes() extinct_tips.discard(daughter_nd) extant_tips.add(daughter_nd) if is_add_extinct_attr: setattr(daughter_nd, extinct_attr_name, False) e.length = prev_length + last_waiting_time if not is_retain_extinct_tips: processed_nodes = set() for nd in list(extinct_tips): if nd in processed_nodes: continue processed_nodes.add(nd) extinct_tips.discard(nd) assert not nd._child_nodes while (nd.parent_node is not None) and (len(nd.parent_node._child_nodes) == 1): nd = nd.parent_node processed_nodes.add(nd) tree.prune_subtree(nd, suppress_unifurcations=False) tree.suppress_unifurcations() if is_assign_extant_taxa or is_assign_extinct_taxa: taxon_pool = [t for t in taxon_namespace] rng.shuffle(taxon_pool) taxon_pool_labels = set([t.label for t in taxon_pool]) ### ONLY works if in GSA sub-section we remove ALL extant and ### extinct nodes beyond time slice: expensive ### Furthermore, main reason to use this approach is to have different ### label prefixes for extinct vs. extant lineages, but the second time ### this function is called with the same taxon namespace or any time ### this function is called with a populated taxon namespace, that ### aesthetic is lost. # node_pool_labels = ("T", "X") # for node_pool_idx, node_pool in enumerate((extant_tips, extinct_tips)): # for node_idx, nd in enumerate(node_pool): # if taxon_pool: # taxon = taxon_pool.pop() # else: # taxon = taxon_namespace.require_taxon("{}{}".format(node_pool_labels[node_pool_idx], node_idx+1)) # nd.taxon = taxon # assert not nd._child_nodes tlabel_counter = 0 leaf_nodes = tree.leaf_nodes() rng.shuffle(leaf_nodes) for nd_idx, nd in enumerate(leaf_nodes): if not is_assign_extant_taxa and nd in extant_tips: continue if not is_assign_extant_taxa and nd in extinct_tips: continue if taxon_pool: taxon = taxon_pool.pop() else: while True: tlabel_counter += 1 label = "{}{}".format("T", tlabel_counter) if label not in taxon_pool_labels: break taxon = taxon_namespace.require_taxon(label=label) taxon_pool_labels.add(label) nd.taxon = taxon
return tree
[docs]def discrete_birth_death_tree(birth_rate, death_rate, birth_rate_sd=0.0, death_rate_sd=0.0, **kwargs): """ Returns a birth-death tree with birth rate specified by ``birth_rate``, and death rate specified by ``death_rate``, with edge lengths in discrete (integer) units. ``birth_rate_sd`` is the standard deviation of the normally-distributed mutation added to the birth rate as it is inherited by daughter nodes; if 0, birth rate does not evolve on the tree. ``death_rate_sd`` is the standard deviation of the normally-distributed mutation added to the death rate as it is inherited by daughter nodes; if 0, death rate does not evolve on the tree. Tree growth is controlled by one or more of the following arguments, of which at least one must be specified: - If ``ntax`` is given as a keyword argument, tree is grown until the number of tips == ntax. - If ``taxon_namespace`` is given as a keyword argument, tree is grown until the number of tips == len(taxon_namespace), and the taxa are assigned randomly to the tips. - If 'max_time' is given as a keyword argument, tree is grown for ``max_time`` number of generations. If more than one of the above is given, then tree growth will terminate when *any* of the termination conditions (i.e., number of tips == ``ntax``, or number of tips == len(taxon_namespace) or number of generations = ``max_time``) are met. Also accepts a Tree object (with valid branch lengths) as an argument passed using the keyword ``tree``: if given, then this tree will be used; otherwise a new one will be created. If ``assign_taxa`` is False, then taxa will *not* be assigned to the tips; otherwise (default), taxa will be assigned. If ``taxon_namespace`` is given (``tree.taxon_namespace``, if ``tree`` is given), and the final number of tips on the tree after the termination condition is reached is less then the number of taxa in ``taxon_namespace`` (as will be the case, for example, when ``ntax`` < len(``taxon_namespace``)), then a random subset of taxa in ``taxon_namespace`` will be assigned to the tips of tree. If the number of tips is more than the number of taxa in the ``taxon_namespace``, new Taxon objects will be created and added to the ``taxon_namespace`` if the keyword argument ``create_required_taxa`` is not given as False. Under some conditions, it is possible for all lineages on a tree to go extinct. In this case, if the keyword argument ``repeat_until_success`` is |True|, then a new branching process is initiated. If |False| (default), then a TreeSimTotalExtinctionException is raised. A Random() object or equivalent can be passed using the ``rng`` keyword; otherwise GLOBAL_RNG is used. """ if 'ntax' not in kwargs \ and 'taxon_namespace' not in kwargs \ and 'max_time' not in kwargs: raise ValueError("At least one of the following must be specified: 'ntax', 'taxon_namespace', or 'max_time'") target_num_taxa = None taxon_namespace = None target_num_gens = kwargs.get('max_time', None) if 'taxon_namespace' in kwargs: taxon_namespace = kwargs.get('taxon_namespace') target_num_taxa = kwargs.get('ntax', len(taxon_namespace)) elif 'ntax' in kwargs: target_num_taxa = kwargs['ntax'] if taxon_namespace is None: taxon_namespace = dendropy.TaxonNamespace() repeat_until_success = kwargs.get('repeat_until_success', False) rng = kwargs.get('rng', GLOBAL_RNG) # grow tree if "tree" in kwargs: tree = kwargs['tree'] if "taxon_namespace" in kwargs and kwargs['taxon_namespace'] is not tree.taxon_namespace: raise ValueError("Cannot specify both ``tree`` and ``taxon_namespace``") else: tree = dendropy.Tree(taxon_namespace=taxon_namespace) tree.is_rooted = True tree.seed_node.edge.length = 0 tree.seed_node.birth_rate = birth_rate tree.seed_node.death_rate = death_rate leaf_nodes = tree.leaf_nodes() num_gens = 0 while (target_num_taxa is None or len(leaf_nodes) < target_num_taxa) \ and (target_num_gens is None or num_gens < target_num_gens): for nd in leaf_nodes: if not hasattr(nd, 'birth_rate'): nd.birth_rate = birth_rate if not hasattr(nd, 'death_rate'): nd.death_rate = death_rate try: nd.edge.length += 1 except TypeError: nd.edge.length = 1 u = rng.uniform(0, 1) if u < nd.birth_rate: c1 = nd.new_child() c2 = nd.new_child() c1.edge.length = 0 c2.edge.length = 0 c1.birth_rate = nd.birth_rate + rng.gauss(0, birth_rate_sd) c1.death_rate = nd.death_rate + rng.gauss(0, death_rate_sd) c2.birth_rate = nd.birth_rate + rng.gauss(0, birth_rate_sd) c2.death_rate = nd.death_rate + rng.gauss(0, death_rate_sd) elif u > nd.birth_rate and u < (nd.birth_rate + nd.death_rate): if nd is not tree.seed_node: tree.prune_subtree(nd) elif not repeat_until_success: # all lineages are extinct: raise exception raise TreeSimTotalExtinctionException() else: # all lineages are extinct: repeat num_gens = 0 num_gens += 1 leaf_nodes = tree.leaf_nodes() # If termination condition specified by ntax or taxon_namespace, then the last # split will have a daughter edges of length == 0; # so we continue growing the edges until the next birth/death event *or* # the max number of generations condition is given and met gens_to_add = 0 while (target_num_gens is None or num_gens < target_num_gens): u = rng.uniform(0, 1) if u < (birth_rate + death_rate): break gens_to_add += 1 for nd in tree.leaf_nodes(): nd.edge.length += gens_to_add if kwargs.get("assign_taxa", True): tree.randomly_assign_taxa(create_required_taxa=True, rng=rng) # return
return tree
[docs]def uniform_pure_birth_tree(taxon_namespace, birth_rate=1.0, rng=None): "Generates a uniform-rate pure-birth process tree. " if rng is None: rng = GLOBAL_RNG # use the global rng by default tree = dendropy.Tree(taxon_namespace=taxon_namespace) tree.seed_node.edge.length = 0.0 leaf_nodes = tree.leaf_nodes() while len(leaf_nodes) < len(taxon_namespace): waiting_time = rng.expovariate(len(leaf_nodes)/birth_rate) for nd in leaf_nodes: nd.edge.length += waiting_time parent_node = rng.choice(leaf_nodes) c1 = parent_node.new_child() c2 = parent_node.new_child() c1.edge.length = 0.0 c2.edge.length = 0.0 leaf_nodes = tree.leaf_nodes() leaf_nodes = tree.leaf_nodes() waiting_time = rng.expovariate(len(leaf_nodes)/birth_rate) for nd in leaf_nodes: nd.edge.length += waiting_time for idx, leaf in enumerate(leaf_nodes): leaf.taxon = taxon_namespace[idx] tree.is_rooted = True
return tree
[docs]def fit_pure_birth_model(**kwargs): """ Calculates the maximum-likelihood estimate of the birth rate of a set of *internal* node ages under a Yule (pure-birth) model. Requires either a |Tree| object or an interable of *internal* node ages to be passed in via keyword arguments ``tree`` or ``internal_node_ages``, respectively. The former is more convenient when doing one-off calculations, while the latter is more efficient if the list of internal node ages needs to be used in other places and you already have it calculated and want to avoid re-calculating it here. Parameters ---------- \*\*kwargs : keyword arguments, mandatory Exactly *one* of the following *must* be specified: tree : a |Tree| object. A |Tree| object. The tree needs to be ultrametric for the internal node ages (time from each internal node to the tips) to make sense. The precision by which the ultrametricity is checked can be specified using the ``ultrametricity_precision`` keyword argument (see below). If ``tree`` is given, then ``internal_node_ages`` cannot be given, and vice versa. If ``tree`` is not given, then ``internal_node_ages`` must be given. internal_node_ages : iterable (of numerical values) Iterable of node ages of the internal nodes of a tree, i.e., the list of sum of the edge lengths between each internal node and the tips of the tree. If ``internal_node_ages`` is given, then ``tree`` cannot be given, and vice versa. If ``internal_node_ages`` is not given, then ``tree`` must be given. The following are optional, and are only used if internal node ages are specified (i.e., 'internal_node_ages' are passed in): is_node_ages_presorted : bool By default, the vector of node ages are sorted. If this argument is specified as ``True``, then this sorting will be skipped, in which case it is the client code's responsibility to make sure that the node ages are given in REVERSE order (i.e., oldest nodes -- nodes closer to the root -- given first). Returns ------- m : dictionary A dictionary with keys being parameter names and values being estimates: "birth_rate" The birth rate. "log_likelihood" The log-likelihood of the model and given birth rate. Examples -------- Birth rates can be estimated by passing in trees directly:: for idx, tree in enumerate(trees): m = birthdeath.fit_pure_birth_model(tree=tree) print("Tree {}: birth rate = {} (logL = {})".format( idx+1, m["birth_rate"], m["log_likelihood"])) Or by pre-calculating and passing in a list of node ages:: for idx, tree in enumerate(trees): m = birthdeath.fit_pure_birth_model( internal_node_ages=tree.internal_node_ages()) print("Tree {}: birth rate = {} (logL = {})".format( idx+1, m["birth_rate"], m["log_likelihood"])) Notes ----- Adapted from the laser package for R: - Dan Rabosky and Klaus Schliep (2013). laser: Likelihood Analysis of Speciation/Extinction Rates from Phylogenies. R package version 2.4-1. http://CRAN.R-project.org/package=laser """ tree = kwargs.get("tree", None) if tree is not None: internal_node_ages = tree.internal_node_ages(ultrametricity_precision=kwargs.get("ultrametricity_precision", 1e-6)) else: try: internal_node_ages = kwargs["internal_node_ages"] except KeyError: raise TypeError("Need to specify 'tree' or 'internal_node_ages'") x = internal_node_ages if tree is not None or not kwargs.get("is_node_ages_presorted", False): x = sorted(internal_node_ages, reverse=True) st1 = x[0] st2 = 0 nvec = range(2, len(x)+2) nv = [i for i in x if (i < st1) and (i >= st2)] lo = max(nvec[idx] for idx, i in enumerate(x) if i >= st1) up = max(nvec[idx] for idx, i in enumerate(x) if i >= st2) if st1 <= x[0]: nv.insert(0, st1) nv = [i - st2 for i in nv] else: nv = [i - st2 for i in nv] t1 = (up-lo) t2 = (lo*nv[0]) t3 = sum( nv[1:(up-lo+1)] ) smax = t1/(t2 + t3) try: s1 = sum(map(math.log, range(lo,up))) s2 = (up-lo) * math.log(smax) s3 = lo - up lh = s1 + s2 + s3 except ValueError: if kwargs.get("ignore_likelihood_calculation_failure", False): raise ValueError("Likelihood estimation failure") else: lh = float("-inf") result = { "birth_rate" : smax, "log_likelihood" : lh, }
return result
[docs]def fit_pure_birth_model_to_tree(tree, ultrametricity_precision=constants.DEFAULT_ULTRAMETRICITY_PRECISION): """ Calculates the maximum-likelihood estimate of the birth rate a tree under a Yule (pure-birth) model. Parameters ---------- tree : |Tree| object A tree to be fitted. Returns ------- m : dictionary A dictionary with keys being parameter names and values being estimates: - "birth_rate" The birth rate. - "log_likelihood" The log-likelihood of the model and given birth rate. Examples -------- :: import dendropy from dendropy.model import birthdeath trees = dendropy.TreeList.get_from_path( "pythonidae.nex", "nexus") for idx, tree in enumerate(trees): m = birthdeath.fit_pure_birth_model_to_tree(tree) print("Tree {}: birth rate = {} (logL = {})".format( idx+1, m["birth_rate"], m["log_likelihood"])) """
return fit_pure_birth_model(tree=tree, ultrametricity_precision=ultrametricity_precision)
[docs]def birth_death_likelihood(**kwargs): """ Calculates the log-likelihood of a tree (or a set of internal nodes) under a birth death model. Requires either a |Tree| object or an interable of *internal* node ages to be passed in via keyword arguments ``tree`` or ``internal_node_ages``, respectively. The former is more convenient when doing one-off calculations, while the latter is more efficient if the list of internal node ages needs to be used in other places and you already have it calculated and want to avoid re-calculating it here. Parameters ---------- \*\*kwargs : keyword arguments, mandatory Exactly *one* of the following *must* be specified: tree : a |Tree| object. A |Tree| object. The tree needs to be ultrametric for the internal node ages (time from each internal node to the tips) to make sense. The precision by which the ultrametricity is checked can be specified using the ``ultrametricity_precision`` keyword argument (see below). If ``tree`` is given, then ``internal_node_ages`` cannot be given, and vice versa. If ``tree`` is not given, then ``internal_node_ages`` must be given. internal_node_ages : iterable (of numerical values) Iterable of node ages of the internal nodes of a tree, i.e., the list of sum of the edge lengths between each internal node and the tips of the tree. If ``internal_node_ages`` is given, then ``tree`` cannot be given, and vice versa. If ``internal_node_ages`` is not given, then ``tree`` must be given. The following keyword parameters are mandatory: birth_rate : float The birth rate. death_rate : float The death rate. The following keyword parameters are optional: sampling_probability The probability for a species to be included in the sample. Defaults to 1.0 (all species sampled). sampling_strategy The strategy how samples were obtained. Options are: uniform|diversified|age. is_mrca_included Does the process start with the most recent common ancestor? condition_on : string Do we condition the process on: "time", "survival", or "taxa"? The following are optional, and are only used if internal node ages need to be calculated (i.e., 'tree' is passed in). ultrametricity_precision : float When calculating the node ages, an error will be raised if the tree in o ultrametric. This error may be due to floating-point or numerical imprecision. You can set the precision of the ultrametricity validation by setting the ``ultrametricity_precision`` parameter. E.g., use ``ultrametricity_precision=0.01`` for a more relaxed precision, down to 2 decimal places. Use ``ultrametricity_precision=False`` to disable checking of ultrametricity precision. ignore_likelihood_calculation_failure: bool (default: False) In some cases (typically, abnormal trees, e.g., 1-tip), the likelihood estimation will fail. In this case a ValueError will be raised. If ``ignore_likelihood_calculation_failure`` is |True|, then the function call will still succeed, with the likelihood set to -``inf``. The following are optional, and are only used if internal node ages are specified (i.e., 'internal_node_ages' are passed in): is_node_ages_presorted : bool By default, the vector of node ages are sorted. If this argument is specified as ``True``, then this sorting will be skipped, in which case it is the client code's responsibility to make sure that the node ages are given in REVERSE order (i.e., oldest nodes -- nodes closer to the root -- given first). Notes ----- Lifted directly from the (fantastic!) TESS package for R: H{"o}hna S. 2013. Fast simulation of reconstructed phylogenies under global time-dependent birth--death processes. Bioinformatics, 29(11) 1367-1374. Returns ------- lnl : float The log-likehood of the tree under the birth-death model. """ tree = kwargs.get("tree", None) if tree is not None: internal_node_ages = tree.internal_node_ages(ultrametricity_precision=kwargs.get("ultrametricity_precision", 1e-6)) else: try: internal_node_ages = kwargs["internal_node_ages"] except KeyError: raise TypeError("Need to specify 'tree' or 'internal_node_ages'") if tree is not None or not kwargs.get("is_node_ages_presorted", False): internal_node_ages = sorted(internal_node_ages, reverse=True) # check for sensible parameter values # if ( lambda <= 0 || mu < 0 || sampling_probability <= 0 || sampling_probability > 1.0) { # stop("Invalid parameter values for lambda and mu!") # } # massExtinctionTimes=c(), # massExtinctionSurvivalProbabilities=c(), # missingSpecies = c(), # timesMissingSpecies = c(), # tess.likelihood 11 # samplingProbability=1.0, # samplingStrategy="uniform", # MRCA=TRUE, # CONDITION="survival", birth_rate = kwargs.get("birth_rate") death_rate = kwargs.get("death_rate") massExtinctionTimes = None massExtinctionSurvivalProbabilities = None sampling_probability = kwargs.get("sampling_probability", 1.0) sampling_strategy = kwargs.get("sampling_strategy", "uniform") is_mrca_included = kwargs.get("is_mrca_included", True) condition_on = kwargs.get("condition_on", "survival") ntax = len(internal_node_ages) + 1 PRESENT = max(internal_node_ages) times = [(PRESENT - t) for t in internal_node_ages] # if we condition on the MRCA, then we need to remove the root speciation event if is_mrca_included: times = times[1:] # set the uniform taxon sampling probability if sampling_strategy == "uniform": rho = sampling_probability else: rho = 1.0 # initialize the log likelihood lnl = 0.0 # what do we condition on? # did we condition on survival? if condition_on == "survival": lnl = - _p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,rho,0,PRESENT,PRESENT) # death_rateltiply the probability of a descendant of the initial species lnl = lnl + _p1_constant( birth_rate=birth_rate, death_rate=death_rate, massExtinctionTimes=massExtinctionTimes, massExtinctionSurvivalProbabilities=massExtinctionSurvivalProbabilities, sampling_probability=rho, t=0, T=PRESENT) # add the survival of a second species if we condition on the MRCA if is_mrca_included: lnl = 2 * lnl # did we condition on observing n species today if condition_on == "taxa": lnl = lnl - _p_N_constant( birth_rate=birth_rate, death_rate=death_rate, massExtinctionTimes=massExtinctionTimes, massExtinctionSurvivalProbabilities=massExtinctionSurvivalProbabilities, sampling_probability=sampling_probability, i=ntax, s=0, t=PRESENT, SURVIVAL=False, MRCA=is_mrca_included) # if we assume diversified sampling, we need to death_rateltiply with the # probability that all missing species happened after the last speciation # event if sampling_strategy == "diversified": # We use equation (5) of Hoehna et al. "Inferring Speciation and Extinction Rates under Different Sampling Schemes" lastEvent = times[-1] p_0_T = 1.0 - math.exp(_p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,1.0,0,PRESENT,PRESENT)) * math.exp((death_rate-birth_rate)*PRESENT) p_0_t = 1.0 - math.exp(_p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,1.0,lastEvent,PRESENT,PRESENT)) * math.exp((death_rate-birth_rate)*(PRESENT-lastEvent)) F_t = p_0_t / p_0_T # get an estimate of the actual number of taxa m = round(float(ntax) / sampling_probability) # remove the number of species that we started with if is_mrca_included: k = 2 else: k = 1 lnl = lnl + (m-ntax) * math.log(F_t) + math.log(combinatorics.choose(int(m-k),int(ntax-k))) # multiply the probability for the missing species # if len(missing_species) > 0: # # We use equation (5) of Hoehna et al. "Inferring Speciation and Extinction Rates under Different Sampling Schemes" # # now iterate over the vector of missing species per interval # lastEvent = timesMissingSpecies # p_0_T = 1.0 - math.exp( _p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,1.0,0,PRESENT,PRESENT,log=TRUE) + ((death_rate-birth_rate)*PRESENT) ) # p_0_t = 1.0 - math.exp( _p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,1.0,lastEvent,PRESENT,PRESENT,log=TRUE) + ((death_rate-birth_rate)*(PRESENT-lastEvent)) ) # log_F_t = math.log(p_0_t) - math.log(p_0_T) # # get an estimate of the actual number of taxa # m = missingSpecies # # remove the number of species that we started with # lnl = lnl + sum( m * log_F_t ) #+ lchoose(m-k,ntax-k) # multiply the probability for each speciation time if len(times) > 0: # lnl = lnl + len(times)*math.log(birth_rate) + sum(tess.equations.p1.constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,rho,times,PRESENT,log=TRUE)) lnl += (len(times) * math.log(birth_rate)) for time in times: lnl += _p1_constant( birth_rate=birth_rate, death_rate=death_rate, massExtinctionTimes=massExtinctionTimes, massExtinctionSurvivalProbabilities=massExtinctionSurvivalProbabilities, sampling_probability=rho, t=time, T=PRESENT)
return lnl ################################################################################ # From: TESS # # https://github.com/hoehna/TESS # # H{"o}hna S. 2013. Fast simulation of reconstructed phylogenies under # global time-dependent birth--death processes. Bioinformatics, 29(11) # 1367-1374. # # Copyright (c) 2012- Sebastian Hoehna # # TESS is free software; you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as # published by the Free Software Foundation; either version 2 # of the License, or (at your option) any later version. # # @brief Calculate the probability of n lineage existing at time t # if we started with 1 (or 2) lineage at time s. # # # @see Equation (3), (5) and (12) in Hoehna, S.: Fast simulation of reconstructed phylogenies # under global, time-dependent birth-death processes. 2013, Bioinformatics # # @date Last modified: 2013-01-30 # @author Sebastian Hoehna # @version 1.1 # @since 2012-09-11, version 1.0 # # @param lambda scalar speciation rate # @param mu scalar extinction rate # @param massExtinctionTimes vector timse at which mass-extinctions happen # @param massExtinctionSurvivalProbabilities vector survival probability of a mass extinction event # @param samplingProbability scalar probability of uniform sampling at present # @param i scalar number of lineages # @param s scalar start time # @param t scalar stop time # @param MRCA boolean does the tree start at the mrca? # @param log bool if in log-scale # @return scalar log-probability # ################################################################################ # tess.equations.pN.constant = function(lambda,mu,massExtinctionTimes,massExtinctionSurvivalProbabilities,samplingProbability,i,s,t,SURVIVAL=FALSE,MRCA=FALSE,log=FALSE) { def _p_N_constant( birth_rate, death_rate, massExtinctionTimes, massExtinctionSurvivalProbabilities, sampling_probability, i, s, t, SURVIVAL=False, MRCA=False,): if i < 1: # we assume conditioning on survival p = 0 elif i == 1: if MRCA: # we assume conditioning on survival of the two species p = 0 else: if SURVIVAL: p = _p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,sampling_probability,s,t,t) + (death_rate-birth_rate)*(t-s) - math.log(sampling_probability) else: p = 2*_p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,sampling_probability,s,t,t) + (death_rate-birth_rate)*(t-s) - math.log(sampling_probability) else: p_s = math.exp(_p_survival_constant(birth_rate,death_rate,massExtinctionTimes,massExtinctionSurvivalProbabilities,sampling_probability,s,t,t)) r = (death_rate-birth_rate)*(t-s) - math.log(sampling_probability) # for (j in seq_len(length(massExtinctionTimes)) ) { # cond = (s < massExtinctionTimes[j]) & (t >= massExtinctionTimes[j]) # r = r - ifelse(cond, log(massExtinctionSurvivalProbabilities[j]), 0.0) e = p_s * math.exp(r) if e > 1: e = 1.0 if not MRCA: if SURVIVAL: p = math.log(p_s) + r + math.log( 1 - e) * (i-1) else: p = 2*math.log(p_s) + r + math.log( 1 - e) * (i-1) else: if SURVIVAL: p = math.log(i-1) + 2*math.log(p_s) + 2*r + math.log( 1 - e) * (i-2) else: p = math.log(i-1) + 4*math.log(p_s) + 2*r + math.log( 1 - e) * (i-2) return p ################################################################################ # From: TESS # # https://github.com/hoehna/TESS # # H{"o}hna S. 2013. Fast simulation of reconstructed phylogenies under # global time-dependent birth--death processes. Bioinformatics, 29(11) # 1367-1374. # # Copyright (c) 2012- Sebastian Hoehna # # TESS is free software; you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as # published by the Free Software Foundation; either version 2 # of the License, or (at your option) any later version. # # @brief Calculate the probability of survival in the interval [t_low,t_high]. # # See Equation (2) from Hoehna, S., 2013, Fast simulation of reconstructed phylogenies under global, time-dependent birth-death processes # # # @date Last modified: 2013-01-30 # @author Sebastian Hoehna # @version 1.1 # @since 2012-09-11, version 1.0 # # @param lambda scalar speciation rate # @param mu scalar extinction rate # @param massExtinctionTimes vector timse at which mass-extinctions happen # @param massExtinctionSurvivalProbabilities vector survival probability of a mass extinction event # @param samplingProbability scalar probability of uniform sampling at present # @param t_low scalar starting time # @param t_high scalar end time # @param T scalar present time (time goes forward and the origin/MRCA might be 0) # @param log bool if in log-scale # @return scalar probability of survival in [t,tau] # ################################################################################ # tess.equations.pSurvival.constant = function(lambda,mu,massExtinctionTimes,massExtinctionSurvivalProbabilities,samplingProbability,t_low,t_high,T,log=FALSE) { def _p_survival_constant( birth_rate, death_rate, massExtinctionTimes, massExtinctionSurvivalProbabilities, sampling_probability, t_low, t_high, T): # compute the rate rate = death_rate - birth_rate # do the integration of int_{t_low}^{t_high} ( death_rate(s) exp(rate(t,s)) ds ) # where rate(t,s) = int_{t}^{s} ( death_rate(x)-birth_rate(x) dx ) - sum_{for all t < m_i < s in massExtinctionTimes }( log(massExtinctionSurvivalProbability[i]) ) # we compute the integral stepwise for each epoch between mass-extinction events # add mass-extinction accudeath_ratelatedMassExtinction = 1.0 prev_time = t_low den = 1.0 # if ( length(massExtinctionTimes) > 0 ) { # for (j in 1:length(massExtinctionTimes) ) { # cond = (t_low < massExtinctionTimes[j]) & (t_high >= massExtinctionTimes[j]) # # compute the integral for this time episode until the mass-extinction event # # den = den + ifelse(cond, exp(-rate*t_low) * death_rate / (rate * accudeath_ratelatedMassExtinction ) * ( exp(rate* massExtinctionTimes[j]) - exp(rate*prev_time)) , 0 ) # den = den + cond * exp(-rate*t_low) * death_rate / (rate * accudeath_ratelatedMassExtinction ) * ( exp(rate* massExtinctionTimes[j]) - exp(rate*prev_time)) # # store the current time so that we remember from which episode we need to integrate next # # prev_time = ifelse(cond, massExtinctionTimes[j], prev_time) # prev_time[cond] = massExtinctionTimes[j] # accudeath_ratelatedMassExtinction = accudeath_ratelatedMassExtinction * ifelse(cond, massExtinctionSurvivalProbabilities[j], 1.0) # # integrate over the tiny time interval of the mass-extinction event itself and add it to the integral # # den = den - ifelse(cond, (massExtinctionSurvivalProbabilities[j]-1) / accudeath_ratelatedMassExtinction * exp( rate*(massExtinctionTimes[j] - t_low) ), 0.0 ) # den = den - cond * (massExtinctionSurvivalProbabilities[j]-1) / accudeath_ratelatedMassExtinction * exp( rate*(massExtinctionTimes[j] - t_low) ) # } # } # add the integral of the final epoch until the present time den = den + math.exp(-rate*t_low) * death_rate / (rate * accudeath_ratelatedMassExtinction ) * ( math.exp(rate*t_high) - math.exp(rate*prev_time)) # add sampling if (sampling_probability < 1) and (t_low < T) and (t_high >= T): accudeath_ratelatedMassExtinction = accudeath_ratelatedMassExtinction * sampling_probability cond = 1 else: cond = 0 # den = den - ifelse(cond, (sampling_probability-1)*math.exp( rate*(T-t_low) ) / accudeath_ratelatedMassExtinction, 0.0) den = den - cond * (sampling_probability-1)*math.exp( rate*(T-t_low) ) / accudeath_ratelatedMassExtinction res = 1.0 / den res = math.log(res) return (res) ################################################################################ # From: TESS # # https://github.com/hoehna/TESS # # H{"o}hna S. 2013. Fast simulation of reconstructed phylogenies under # global time-dependent birth--death processes. Bioinformatics, 29(11) # 1367-1374. # # Copyright (c) 2012- Sebastian Hoehna # # TESS is free software; you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as # published by the Free Software Foundation; either version 2 # of the License, or (at your option) any later version. # # @brief Calculate the probability of exactly 1 lineage surviving until time T # if we started with 1 lineage at time t. # # @see Equation (4) in Hoehna, S.: Fast simulation of reconstructed phylogenies # under global, time-dependent birth-death processes. 2013, Bioinformatics # # @date Last modified: 2013-01-30 # @author Sebastian Hoehna # @version 1.1 # @since 2012-09-11, version 1.0 # # @param lambda scalar speciation rate # @param mu scalar extinction rate # @param massExtinctionTimes vector timse at which mass-extinctions happen # @param massExtinctionSurvivalProbabilities vector survival probability of a mass extinction event # @param samplingProbability scalar probability of uniform sampling at present # @param t scalar time # @param T scalar present time # @param log bool if in log-scale # @return scalar ln-probability # ################################################################################ # tess.equations.p1.constant = function(lambda,mu,massExtinctionTimes,massExtinctionSurvivalProbabilities,samplingProbability,t,T,log=FALSE) { def _p1_constant( birth_rate, death_rate, massExtinctionTimes, massExtinctionSurvivalProbabilities, sampling_probability, t, T): # compute the survival probability a = _p_survival_constant( birth_rate=birth_rate, death_rate=death_rate, massExtinctionTimes=massExtinctionTimes, massExtinctionSurvivalProbabilities=massExtinctionSurvivalProbabilities, sampling_probability=sampling_probability, t_low=t, t_high=T, T=T) # compute the rate rate = (death_rate - birth_rate)*(T-t) # add mass-extinction # for (j in range(len(massExtinctionTimes)) ) : # rate = rate - ifelse( t < massExtinctionTimes[j] & T >= massExtinctionTimes[j], log(massExtinctionSurvivalProbabilities[j]), 0 ) # add sampling rate = rate - math.log(sampling_probability) p = 2*a + rate return p