Drawing Phylogenetic
Networks
Daniel H. Huson
joint work with Tobias Kloepper and Regula Rupp
1Future Directions in Phylogenetics, Cambridge, December 2007
Split Networks and Cluster Networks
Split network
Data: binary sequences (Kumar, 1998)
Cluster network
2
How to Draw Cluster Networks?
Data: 61 genes (Leebens-Mack et al, MBE, 2005)
3
Cladograms For Trees
4
Phylograms and Radial Diagrams
5
Drawing a Cladogram for a Tree
Assign x-coords
in a postorder
traversal of N:
if v is a leaf:
x(v) = 0
4
else:
x(v) = max x of
children + 1
1
0
0
3
0
2
1
0
0
0
7
Drawing a Cladogram for a Tree
1
Assign y-coords
in a postorder
traversal:
if v is a leaf:
y(v) = number
of leaves visited
else:
y(v) = mean
y of children
1.5
2
2.625
3
3.75
4.125
4.5
4
5
6
8
Naïve Algorithm for Drawing Networks
Network N:
p



q
p
Choose a guide tree T
Compute coordinates for T
Draw network using tree coordinates
9
Naïve Algorithm for Drawing Networks
Q
R
P
Problems:

x-coordinates: P and Q have different x-coordinates

y-coordinates: R isn‘t placed between P and Q

Unnecessary edge crossings
10
Better x-Coordinates
Assign x-coords
in a postorder
traversal of N:
if v is a leaf:
x(v) = 0
else:
x(v) = max x of
children + 1
2
1
0
0
1
4
0
0
3
2
0
11
Better y-Coordinates?

Need to introduce:
–
–
LSA guide tree
topological embedding 
12
Lowest Single Ancestor

The LSA of a node v is the last node ( v)
on all paths from  to v:
v

lsa(v)
13
LSA Guide Tree

Connect each reticulate node to its LSA
and remove all reticulate edges:
LSA tree T
cladogram
14
Topological Embedding


A topological embedding  is given by an
ordering of the children of each node v:
v e
q v
d
r
q
r

r
w
p b
p
w a
Any  gives rise to a planar drawing of T
15
Better y-Coordinates


Choose  so that reticulate nodes are
placed between their sources:
Order subtrees in preorder traversal of T
16
Resulting Cladogram

Use diagonal or curved lines for
reticulate edges
17
Additional Twist for y-Coordinates


LSA guide tree has true and false leaves:
Network N
LSA tree T
A leaf is false if it is only a leaf in T
18
Additional Twist for y-Coordinates

False leaves produce uneven spacing of
leaves in N:
19
Additional Twist for y-Coordinates

Assign integer coordinates to true
leaves, fractional to false ones:
1
2
3
3½
4
5
6
20
Circular Cladograms

Compute polar coordinates in similar way:
21
Phylograms and Radial Diagrams


y-coordinates: as for cladogram
x-coordinates: preorder traversal
22
Example 1




Multiple gene trees
Leebens-Mack et al,
MBE, 2005
61 chloroplast
genes for 26 plants
Filtered cluster
networks
–
–
–
–
50%
30%
20%
10%
23
Example 2: Splits vs Clusters
Split network of consensus splits
from 106 maximum-parsimony
trees (Rokas et al, 2003)
(Holland et al, 2004)
Weighted cluster network
24
Weights for Reticulate Edges?

Use LSA to determine weight of
reticulate edge:
1,2,3,4,5

1,3,4
v
lsa(v)
2,5

Use average weight on paths to lsa(v)
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Example 3


Arndt von Haeseler
over 12,000 trees

76.5 %

11.4 %

11.4 %
Weighted cluster network
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Outlook



All algorithms discussed have been
implemented and will be made available in
Dendroscope2
Dendroscope2 will be released in first
half of 2008
Dendroscope 1 (for trees only) is
available from:
www-ab.informatik.uni-tuebingen.de/software
27