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# NAME

Bio::PhyloNetwork - Module to compute with Phylogenetic Networks

# SYNOPSIS

`````` use Bio::PhyloNetwork;

# Create a PhyloNetwork object from a eNewick string
my \$net1=Bio::PhyloNetwork->new(
-eNewick=>'t0:((H1,(H2,l2)),H2); H1:((H3,l1)); H2:((H3,(l3,H1))); H3:(l4);'
);

# Print all available data
print \$net1;

# Rebuild \$net1 from its mu_data
my %mudata=\$net1->mudata();
my \$net2=Bio::PhyloNetwork->new(-mudata=>\%mudata,-numleaves=>4);
print \$net2;
print "d=".\$net1->mu_distance(\$net2)."\n";

# Get another one and compute distance
my \$net3=Bio::PhyloNetwork->new(
-eNewick=>'(l2,((l1,(H1,l4)),H1))r; (l3)H1;'
);
print "d=".\$net1->mu_distance(\$net3)."\n";

# ...and find an optimal alignment w.r.t. the Manhattan distance (default)
my (\$weight,%alignment)=\$net1->optimal_alignment(\$net3);
print "weight:\$weight\n";
foreach my \$node1 (keys %alignment) {
print "\$node1 => ".\$alignment{\$node1}."\n";
}
# ...or the Hamming distance

my (\$weightH,%alignmentH)=\$net1->optimal_alignment(\$net3,-metric=>'Hamming');
print "weight:\$weightH\n";
foreach my \$node1 (keys %alignmentH) {
print "\$node1 => ".\$alignmentH{\$node1}."\n";
}

# Test for time consistency of \$net1
if (\$net1->is_time_consistent) {
print "net1 is time consistent\n"
}
else {
print "net1 is not time consistent\n"
}

# create a network from the list of edges
my \$net4=Bio::PhyloNetwork->new(-edges=>
[qw(r s r t s u s c t c t v u b u l3 u b v b v l4 b l2 c l1)]);

# Test for time consistency of \$net3
if (\$net4->is_time_consistent) {
print "net4 is time consistent\n"
}
else {
print "net4 is not time consistent\n"
}

# And print all information on net4
print \$net4;

# Compute some tripartitions
my %triparts=\$net1->tripartitions();

# Now these are stored
print \$net1;

# And can compute the tripartition error
print "dtr=".\$net1->tripartition_error(\$net3)."\n";``````

# DESCRIPTION

## Phylogenetic Networks

This is a module to work with phylogenetic networks. Phylogenetic networks have been studied over the last years as a richer model of the evolutionary history of sets of organisms than phylogenetic trees, because they take not only mutation events but also recombination and horizontal gene transfer events into account.

The natural model for describing the evolutionary history of a set of sequences under recombination events is a DAG, hence this package relies on the package Graph::Directed to represent the underlying graph of a phylogenetic network. We refer the reader to [CRV1,CRV2] for formal definitions related to phylogenetic networks.

## eNewick description

With this package, phylogenetic networks can be given by its eNewick string. This description appeared in other packages related to phylogenetic networks (see [PhyloNet] and [NetGen]); in fact, these two packages use different descriptions. The Bio::PhyloNetwork package allows both of them, but uses the second one in its output.

The first approach [PhyloNet] goes as follows: For each hybrid node H, say with parents u_1,u_2,...,u_k and children v_1,v_2,...v_l: split H in k+1 different nodes; let each of the first k copies be a child of one of the u_1,...,u_k (one for each) and have no children (hence we will have k extra leaves); as for the last copy, let it have no parents and have v_1,...,v_l be its children. This way we get a forest; each of the trees will be rooted at either one root of the phylogenetic network or a hybrid node of it; the set of leaves (of the whole forest) will be the set of leaves of the original network together with the set of hybrid nodes (each of them repeated as many times as its in-degree). Then, the eNewick representation of the phylogenetic network will be the Newick representation of all the trees in the obtained forest, each of them with its root labeled.

The second approach [NetGen] goes as follows: For each hybrid node H, say with parents u_1,u_2,...,u_k and children v_1,v_2,...v_l: split H in k different nodes; let the first copy be a child of u_1 and have all v_1,v_2,...v_l as its children; let the other copies be child of u_2,...,u_k (one for each) and have no children. This way, we get a tree whose set of leaves is the set of leaves of the original network together with the set of hybrid nodes (possibly repeated). Then the Newick string of the obtained tree (note that some internal nodes will be labeled and some leaves will be repeated) is the eNewick string of the phylogenetic network.

For example, consider the network depicted below:

``````       r
/ \
/   \
U     V
/ \   / \
1   \ /   3
H
|
2``````

If the first approach is taken, we get the forest:

``````       r
/ \
/   \
U     V
/ \   / \
1   H H   3
|
H
|
2``````

Hence, the eNewick string is '((1,H),(H,3))r; (2)H;'.

As for the second one, one gets the tree:

``````       r
/ \
/   \
U     V
/ \   / \
1   H |   3
H
|
2``````

Hence, the eNewick string is '((1,H),((2)H,3))r;'.

Note: when rooting a tree, this package allows the notations '(subtree,subtree,...)root' as well as 'root:(subtree,subtree,...)', but the first one is used when writing eNewick strings.

## Tree-child phylogenetic networks

Tree-child (TC) phylogenetic networks are a special class of phylogenetic networks for which a distance, called mu-distance, is defined [CRV2] based on certain data (mu-data) associated to every node. Moreover, this distance extends the Robinson-Foulds on phylogenetic trees. This package allows testing for a phylogenetic network if it is TC and computes mu-distances between networks over the same set of leaves.

Moreover, the mu-data allows one to define the optimal (in some precise sense) alignment between networks over the same set of leaves. This package also computes this optimal alignment.

## Tripartitions

Although tripartitions (see [CRV1] and the references therein) do not allow to define distances, this package outputs tripartitions and computes a weak form of the tripartition error.

## Time-consistency

Another useful property of Phylogenetic Networks that appears in the literature is that of time-consistency or real-time hybrids [BSS]. Roughly speaking, a network admits a temporal representation if it can be drawn in such a way that tree arcs (those whose end is a tree node) are inclined downwards, while hybridization arcs (those whose end is a hybrid node) are horizontal. This package checks for time-consistency and, if so, a temporal representation is provided.

# AUTHOR

`````` Gabriel Cardona, gabriel(dot)cardona(at)uib(dot)es
Gabriel Valiente, valiente(at)lsi(dot)upc(dot)edu``````

[CRV1]

G. Cardona, F. Rossello, G. Valiente. Tripartitions do not always discriminate phylogenetic networks. arXiv:0707.2376v1 [q-bio.PE]

[CRV2]

G. Cardona, F. Rossello, G. Valiente. A Distance Measure for Tree-Child Phylogenetic Networks. Preprint.

[NetGen]

M.M. Morin, and B.M.E. Moret. NetGen: generating phylogenetic networks with diploid hybrids. Bioinformatics 22 (2006), 1921-1923

[PhyloNet]

PhyloNet: "Phylogenetic Networks Toolkit". http://bioinfo.cs.rice.edu/phylonet

[BSS]

M. Baroni, C. Semple, and M. Steel. Hybrids in Real Time. Syst. Biol. 55(1):46-56, 2006

# APPENDIX

The rest of the documentation details each of the object methods.

## new

`````` Title   : new
Usage   : my \$obj = new Bio::PhyloNetwork();
Function: Creates a new Bio::PhyloNetwork object
Returns : Bio::PhyloNetwork
Args    : none
OR
-eNewick => string
OR
-graph => Graph::Directed object
OR
-edges => reference to an array
OR
-tree => Bio::Tree::Tree object
OR
-mudata => reference to a hash,
-leaves => reference to an array
OR
-mudata => reference to a hash,
-numleaves => integer``````

Returns a Bio::PhyloNetwork object, created according to the data given:

new()

creates an empty network.

new(-eNewick => \$str)

creates the network whose Extended Newick representation (see description above) is the string \$str.

new(-graph => \$graph)

creates the network with underlying graph given by the Graph::Directed object \$graph

new(-tree => \$tree)

creates a network as a copy of the Bio::Tree::Tree object in \$tree

new(-mudata => \%mudata, -leaves => \@leaves)

creates the network by reconstructing it from its mu-data stored in \%mudata and with set of leaves in \@leaves.

new(-mudata => \%mudata, -numleaves => \$numleaves)

creates the network by reconstructing it from its mu-data stored in \%mudata and with set of leaves in ("l1".."l\$numleaves").

## is_leaf

`````` Title   : is_leaf
Usage   : my \$b=\$net->is_leaf(\$u)
Function: tests if \$u is a leaf in \$net
Returns : boolean
Args    : scalar``````

## is_root

`````` Title   : is_root
Usage   : my \$b=\$net->is_root(\$u)
Function: tests if \$u is the root of \$net
Returns : boolean
Args    : scalar``````

## is_tree_node

`````` Title   : is_tree_node
Usage   : my \$b=\$net->is_tree_node(\$u)
Function: tests if \$u is a tree node in \$net
Returns : boolean
Args    : scalar``````

## is_hybrid_node

`````` Title   : is_hybrid_node
Usage   : my \$b=\$net->is_hybrid_node(\$u)
Function: tests if \$u is a hybrid node in \$net
Returns : boolean
Args    : scalar``````

## is_tree_child

`````` Title   : is_tree_child
Usage   : my \$b=\$net->is_tree_child()
Function: tests if \$net is a Tree-Child phylogenetic network
Returns : boolean
Args    : Bio::PhyloNetwork``````

## nodes

`````` Title   : nodes
Usage   : my @nodes=\$net->nodes()
Function: returns the set of nodes of \$net
Returns : array
Args    : none``````

## leaves

`````` Title   : leaves
Usage   : my @leaves=\$net->leaves()
Function: returns the set of leaves of \$net
Returns : array
Args    : none``````

## roots

`````` Title   : roots
Usage   : my @roots=\$net->roots()
Function: returns the set of roots of \$net
Returns : array
Args    : none``````

## internal_nodes

`````` Title   : internal_nodes
Usage   : my @internal_nodes=\$net->internal_nodes()
Function: returns the set of internal nodes of \$net
Returns : array
Args    : none``````

## tree_nodes

`````` Title   : tree_nodes
Usage   : my @tree_nodes=\$net->tree_nodes()
Function: returns the set of tree nodes of \$net
Returns : array
Args    : none``````

## hybrid_nodes

`````` Title   : hybrid_nodes
Usage   : my @hybrid_nodes=\$net->hybrid_nodes()
Function: returns the set of hybrid nodes of \$net
Returns : array
Args    : none``````

## graph

`````` Title   : graph
Usage   : my \$graph=\$net->graph()
Function: returns the underlying graph of \$net
Returns : Graph::Directed
Args    : none``````

## edges

`````` Title   : edges
Usage   : my @edges=\$net->edges()
Function: returns the set of edges of \$net
Returns : array
Args    : none``````

Each element in the array is an anonimous array whose first element is the head of the edge and the second one is the tail.

## tree_edges

`````` Title   : tree_edges
Usage   : my @tree_edges=\$net->tree_edges()
Function: returns the set of tree edges of \$net
(those whose tail is a tree node)
Returns : array
Args    : none``````

## hybrid_edges

`````` Title   : hybrid_edges
Usage   : my @hybrid_edges=\$net->hybrid_edges()
Function: returns the set of hybrid edges of \$net
(those whose tail is a hybrid node)
Returns : array
Args    : none``````

## explode

`````` Title   : explode
Usage   : my @trees=\$net->explode()
Function: returns the representation of \$net by a set of
Bio::Tree:Tree objects
Returns : array
Args    : none``````

## mudata

`````` Title   : mudata
Usage   : my %mudata=\$net->mudata()
Function: returns the representation of \$net by its mu-data
Returns : hash
Args    : none``````

\$net->mudata() returns a hash with keys the nodes of \$net and each value is a muVector object holding its mu-vector.

## heights

`````` Title   : heights
Usage   : my %heights=\$net->heights()
Function: returns the heights of the nodes of \$net
Returns : hash
Args    : none``````

\$net->heights() returns a hash with keys the nodes of \$net and each value is its height.

## mu_distance

`````` Title   : mu_distance
Usage   : my \$dist=\$net1->mu_distance(\$net2)
Function: Computes the mu-distance between the networks \$net1 and \$net2 on
the same set of leaves
Returns : scalar
Args    : Bio::PhyloNetwork``````

## mu_distance_generalized

`````` Title   : mu_distance_generalized
Usage   : my \$dist=\$net1->mu_distance(\$net2)
Function: Computes the mu-distance between the topological restrictions of
networks \$net1 and \$net2 on its common set of leaves
Returns : scalar
Args    : Bio::PhyloNetwork``````

## tripartitions

`````` Title   : tripartitions
Usage   : my %tripartitions=\$net->tripartitions()
Function: returns the set of tripartitions of \$net
Returns : hash
Args    : none``````

\$net->tripartitions() returns a hash with keys the nodes of \$net and each value is a string representing the tripartition of the leaves induced by the node. A string "BCA..." associated with a node u (e.g.) means, the first leaf is in the set B(u), the second one in C(u), the third one in A(u), and so on.

## is_time_consistent

`````` Title   : is_time_consistent
Usage   : my \$b=\$net->is_time_consistent()
Function: tests if \$net is (strong) time-consistent
Returns : boolean
Args    : none``````

## temporal_representation

`````` Title   : temporal_representation
Usage   : my %time=\$net->temporal_representation()
Function: returns a hash containing a temporal representation of \$net, or 0
if \$net is not time-consistent
Returns : hash
Args    : none``````

## contract_elementary

`````` Title   : contract_elementary
Usage   : my (\$contracted,\$blocks)=\$net->contract_elementary();
Function: Returns the network \$contracted, obtained by contracting elementary
paths of \$net into edges. The reference \$blocks points to a hash
where, for each node of \$contracted, gives the corresponding nodes
of \$net that have been deleted.
Returns : Bio::PhyloNetwork,reference to hash
Args    : none``````

## optimal_alignment

`````` Title   : optimal_alignment
Usage   : my (\$weight,\$alignment,\$wgts)=\$net->optimal_alignment(\$net2)
Function: returns the total weight of an optimal alignment,
the alignment itself, and partial weights
between the networks \$net1 and \$net2 on the same set of leaves.
An optional argument allows one to use the Manhattan (default) or the
Hamming distance between mu-vectors.
Returns : scalar,reference to hash,reference to hash
Args    : Bio::PhyloNetwork,
-metric => string (optional)``````

Supported strings for the -metric parameter are 'Manhattan' or 'Hamming'.

## optimal_alignment_generalized

`````` Title   : optimal_alignment_generalized
Usage   : my (\$weight,%alignment)=\$net->optimal_alignment_generalized(\$net2)
Function: returns the wieght of an optimal alignment, and the alignment itself,
between the topological restriction of the networks \$net1 and \$net2
on the set of common leaves.
An optional argument allows one to use the Manhattan (default) or the
Hamming distance between mu-vectors.
Returns : scalar,hash
Args    : Bio::PhyloNetwork,
-metric => string (optional)``````

Supported strings for the -metric parameter are 'Manhattan' or 'Hamming'.

## topological_restriction

`````` Title   : topological_restriction
Usage   : my (\$netr1,\$netr2)=\$net1->topological_restriction(\$net2)
Function: returns the topological restriction of \$net1 and \$net2 on its
common set of leaves
Returns : Bio::PhyloNetwork, Bio::PhyloNetwork
Args    : Bio::PhyloNetwork``````

## eNewick

`````` Title   : eNewick
Usage   : my \$str=\$net->eNewick()
Function: returns the eNewick representation of \$net without labeling
internal tree nodes
Returns : string
Args    : none``````

## eNewick_full

`````` Title   : eNewick_full
Usage   : my \$str=\$net->eNewick_full()
Function: returns the eNewick representation of \$net labeling
internal tree nodes
Returns : string
Args    : none``````

## display

`````` Title   : display
Usage   : my \$str=\$net->display()
Function: returns a string containing all the available information on \$net
Returns : string
Args    : none``````