Why use phylogenetic networks?

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

- to identify phylogenetic

relationships that are uncertain

-to ask whether data are suitable for tree building

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

NNET splits graph of angiosperm & gymnosperm sequences

Qui et al. 1999

[Mt: matR, atpI, Cp: atpB, rbcL, Nuc. 18sRNA]

-to help us understand why

some phylogenetic problems are hard

-to study complex processes (where sequence evolution at an individual

locus has not been tree like)

- to study complex processes (where phylogenetic information from

different gene loci is incongruent)

- to study complex processes (where phylogenetic information from

different gene loci is incongruent)

R.nivicola

- to reconstruct reticulate

evolutionary models

origins of diploid and polyploid

hybrids

Overview of phylogenetic network methods

Median, split decomposition, NeighborNet

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Aligned sequencesAligned sequences

DistanceDistancematrixmatrix

Median network Median network splits graphsplits graph

Split decomposition & Split decomposition & NeighborNet network NeighborNet network splits graphsplits graph

Consensus Networks and Super-Consensus Networks and Super-NetworksNetworks

Tree 1Tree 1 Tree 2Tree 2 Tree 3Tree 3

site patterns, splits, splits graph

site patterns observed splits splits graph

NJ

SD, NNET, MEDIAN network

calculated splits

8 site patterns

extra site pattern

added

nodes in splits graphs

Different splits graphs – same splits

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

Splits graphs and reticulate evolutionary models

splits graphs explicit model of reticulate evolution

A H B CA H B C

Building a reticulate evolutionary model

Z-closure Supernetwork

Hybridisation network

Daniel Huson and David Bryant

Split decomposition

• Identify weakly compatible splits for all possible combinations of quartets

• Define split lengths for all splits in split system

• Build splits graph

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

distance matrix calculated from sequences

• A• B 3 • C 6 5• D 5 6 9

AB|CD

AC|BD

AD|BC

An example of using distances to calculate

the length of external splits

example• A• B 3 • C 6 5• D 5 6 9

A|CD

A|BD

A|BC

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

All splits that have a circular ordering can be displayed in a

plane

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

Consensus networks

• Extends idea of median networks to splits calculated from trees

106 random trees with 8 taxa

Combining gene trees for 106 loci

Supernetworks

More detail about building a splits graph…..

Adding the Trivial Splits

• The set O of all trivial splits on X is represented by a star:

(Embedded graph: fixed circular ordering)

xx11

xx44

xx22xx33

xx55 xx77xx66

xx11

xx66

xx55

xx77

Adding a Circular Split

Want to add split Want to add split {{xx22,x,x33,x,x44} vs {} vs {xx11,x,x55,x,x66,x,x77}}

•Determine a path from Determine a path from xx22 to to xx44 along the fontier along the fontier of Gof G

•Separate componentsSeparate components

•Insert new split edgesInsert new split edgesxx44

xx33 xx22

xx44

xx33 xx22

xx11

xx66

xx55

xx77

Adding a Circular Split

xx66

xx55

xx33

xx11

xx77

xx44

xx22Want to add split Want to add split {{xx22,x,x33,x,x44} vs {} vs {xx11,x,x55,x,x66,x,x77}}

•Determine a path from Determine a path from xx22 to to xx44 along the frontier of along the frontier of GG

•Separate componentsSeparate components

•Insert new split edgesInsert new split edges

•Done!Done!

Adding a Non-Circular Split

xx66

xx55

xx33Want to add split Want to add split {{xx33,x,x55,x,x66} vs {} vs {xx11,x,x22,x,x66,x,x77}}

•Convex hull Convex hull {{xx33,x,x55,x,x66} }

•Convex hull {Convex hull {xx11,x,x22,x,x66,x,x77}}

•Determine intersectionDetermine intersection xx11

xx77

xx44

xx22

xx66

xx55

xx33

xx11

xx77

xx44

xx22

1111 1122

22 22

22

33

33

33

3344 44

44

Adding a Non-Circular Split

Want to add split Want to add split {{xx33,x,x55,x,x66} vs {} vs {xx11,x,x22,x,x66,x,x77}}

•Convex hull Convex hull {{xx33,x,x55,x,x66} }

•Convex hull {Convex hull {xx11,x,x22,x,x66,x,x77}}

•Determine intersectionDetermine intersection

•Duplicate intersectionDuplicate intersection

•Insert new split edgesInsert new split edges

xx11

xx77

xx44

xx22

xx66

xx55

xx33

xx11

xx77

xx44

xx22

Adding a Non-Circular Split

Want to add split Want to add split {{xx33,x,x55,x,x66} vs {} vs {xx11,x,x22,x,x66,x,x77}}

•Convex hull Convex hull {{xx33,x,x55,x,x66} }

•Convex hull {Convex hull {xx11,x,x22,x,x66,x,x77}}

•Determine intersectionDetermine intersection

•Duplicate intersectionDuplicate intersection

•Insert new split edgesInsert new split edges

•Done!Done!

xx11

xx77

xx44

xx22

xx66

xx55

xx33

xx11

xx77

xx44

xx22