1. Why use phylogenetic networks?
to visualize data when the evolutionary model is assumed to be bifurcating
to visualize data when the evolutionary model may not be bifurcating
to provide an analytical framework for studying processes that cause phylogenetic incongruence
to build reticulate evolutionary models

2. - to identify phylogenetic relationships that are uncertain

3. -to ask whether data are suitable for tree building

4. another example: do Noppadon’s inversion distances give tree-like distances?

5. -to help us understand why some phylogenetic problems are hard
NNET splits graph of angiosperm & gymnosperm sequences
Qui et al. 1999
[Mt: matR, atpI, Cp: atpB, rbcL, Nuc. 18sRNA]

6. to study complex processes (where sequence evolution at an individual locus has not been tree like)

7. - to study complex processes (where phylogenetic information from different gene loci is incongruent)

8. - to study complex processes (where phylogenetic information from different gene loci is incongruent)

9. - to reconstruct reticulate evolutionary models
R.nivicola
origins of diploid and polyploid hybrids

10. Overview of phylogenetic network methods

11. Median, split decomposition, NeighborNet
Distance
matrix
Median network splits graph
Split decomposition & NeighborNet network splits graph
Aligned sequences
ACGACCTACGACTGCATCAGCATCGCATCAGCTACGCTCGCTCAGACTATCGGATTAAAAGCATCAGCATCGACATCAGCATCAGCGGCGCCATCGATCGCAATCAAGGGGGGGCCCTACCGCATTCAGCATCACGCTCGCCCAATCGCATCACGCATCGCATCGCATCGCATCGCATCGACTCGCAT
We have recently published on biogeographic interpretation of median networks and split decomposition, and I no going to talk about these methods today. Median networks build splits graphs directly from sequences. Split decomposition and NeighborNet build splitsgraphs from distances. These distances can be derived from sequences.

12. Consensus Networks and Super-Networks
Tree 1
Tree 2
Tree 3
I want to introduce to you two newer approaches that we have been working with. These methods build Consensus networks and Supernetworks.
Unlike Median networks, splitdecomposition and Neighbor Net, these methods visualise incongruence between gene trees.
I would like to introduce these methods to you in the context of New alpine Ranunculus.

13. site patterns, splits, splits graph
site patterns observed splits splits graph

14. calculated splits NJ
8 site patterns
SD, NNET, MEDIAN network

15. extra site pattern
added

17. nodes in splits graphs

18. Different splits graphs – same splits

19. summary
Different reasons why you might want to build a phylogenetic network
Some network methods identify more splits in the data than other methods
there may be more than one splits graph representation for a set of splits
Nodes in splits graph are not equivalent to the nodes in trees

20. Splits graphs and reticulate evolutionary models
explicit model of reticulate evolution
splits graphs

21. Building a reticulate evolutionary model
Z-closure Supernetwork
Hybridisation network

22. Daniel Huson and David Bryant
You can also undertake the anlayses I have carried out here yourself on your own data - Daniel and David have cowritten a new version of SplitsTree that carries out all of the methods that I have mentioned today.

23. Split decomposition
Identify weakly compatible splits for all possible combinations of quartets
Define split lengths for all splits in split system
Build splits graph

24. An example of using distances to calculate the length of internal splits

25. distance matrix calculated from sequences
B 3
C 6 5
D 5 6 9
AB|CD
AC|BD
AD|BC

26. An example of using distances to calculate
the length of external splits

27. example A
B 3
C 6 5
D 5 6 9
A|CD
A|BD
A|BC

29. NeighborNet (NNET)
Use NeighborJoining like algorithms to determine the order in which sequences (nodes) can be joined to give a circular ordering.
Once you have the circular ordering, use least squares to identify all splits with positive (non zero) lengths
Build splits graph

30. All splits that have a circular ordering can be displayed in a plane

31. Median networks
Perform the median operation on all combinations of 3 sequences
Identify all the splits between median and extant sequences – built a splits graph

32. Consensus networks
Extends idea of median networks to splits calculated from trees

34. 106 random trees with 8 taxa

35. Combining gene trees for 106 loci

36. Supernetworks

37. More detail about building a splits graph…..

38. Adding the Trivial Splits
The set O of all trivial splits on X is represented by a star:
(Embedded graph: fixed circular ordering) x1 x4 x2 x3 x5 x7 x6

39. Adding a Circular Split
Want to add split
{x2,x3,x4} vs {x1,x5,x6,x7}
Determine a path from x2 to x4 along the fontier of G
Separate components
Insert new split edges x4 x3 x2 x3 x2 x4 x1 x6 x5 x7 x1 x5 x6 x7

40. Adding a Circular Splitx3 x2
Want to add split
{x2,x3,x4} vs {x1,x5,x6,x7}
Determine a path from x2 to x4 along the frontier of G
Separate components
Insert new split edges
Done! x4 x1 x5 x6 x7

41. Adding a Non-Circular Splitx6 x5 x3 x1 x7 x4 x2 x3 x2
Want to add split
{x3,x5,x6} vs {x1,x2,x6,x7}
Convex hull {x3,x5,x6}
Convex hull {x1,x2,x6,x7}
Determine intersection 3 2 1 1 x4 3 1 2 2 4 x1 3 4 2 4 x5 3 x6 x7

42. Adding a Non-Circular Splitx3 x1 x7 x4 x2 x2
Want to add split
{x3,x5,x6} vs {x1,x2,x6,x7}
Convex hull {x3,x5,x6}
Convex hull {x1,x2,x6,x7}
Determine intersection
Duplicate intersection
Insert new split edges x4 x1 x5 x6 x7

43. Adding a Non-Circular Splitx3 x1 x7 x4 x2 x2
Want to add split
{x3,x5,x6} vs {x1,x2,x6,x7}
Convex hull {x3,x5,x6}
Convex hull {x1,x2,x6,x7}
Determine intersection
Duplicate intersection
Insert new split edges
Done! x4 x1 x5 x6 x7