Phylogenetic Networks

1
Phylogenetic Networks

• Anna Tholse
• MS Thesis Defense
• Department of Computer Science
• July 10, 2003

2
Outline

• Background
• Network generation
• Distance measure for networks
• Network reconstruction
• Conclusion

3
Phylogenetic Trees

• Mathematical model for representing evolutionary
  histories among taxa
• Rooted or unrooted
• Leaves taxa for which we have sampled data
• Internal nodes hypothetical ancestors

4
Model Trees

• Not enough biological datasets exists
• Algorithms for simulating the true phylogeny have
  been developed
• Underlying model of topology
• uniform random all topologies are equally likely
  
• birth-death well balanced topologies,
  biologically meaningful

5
Sequence Evolution

• The model tree itself does not provide us with
  all the information, we need sequence data
• Mutational changes on the sequence (nucleotide
  substitution, insertion and deletions, and
  recombination)
• Seq-gen (Rambaut and Grassly, 1997)

6
Distance Measure

• Assess the performance of a reconstruction method
  by computing the distance between the inferred
  phylogeny and the model phylogeny
• Robinson-Foulds
• Every edge e in a leaf-labeled tree T defines a
  bipartition be
• T is encoded by C(T) be e IN E(T)
• n-3 internal edges in an unrooted tree

7
Robinson-Foulds Cont.

• False Positive rate (C(T2) - C(T1)) / (n-3)
• False Negative rate (C(T1) - C(T2)) / (n-3)
• RF value (FP FN) / 2

8
Reconstruction Methods

• Maximum parsimony optimization method
• Produces the tree (or trees) that needs the
  fewest evolutionary changes between sequences
• Maximum likelihood optimization method
• Produces the tree (or trees) that is most likely
  to give rise to the given sequences
• Neighbor-joining distance method
• Produces the tree (or trees) that minimizes the
  total branch lengths

9
Simulations

• Important for testing the performance of
  phylogeny reconstruction methods
• Can generate test sets in arbitrary large numbers
  with different settings
• Parameter space is large
• Test a large range of parameters and do many runs
  for each setting to estimate the variance

10
Simulation Flow

• Create model topology
• Evolve sequences on the topology
• Feed resulting leaf sequences to the studied
  reconstruction method
• Compute distance between inferred phylogeny and
  model phylogeny

11
Outline

• Background
• Network generation
• Distance measure for networks
• Network reconstruction
• Conclusion

12
Related Work

• SplitsTree (Huson, 1998) and NeighborNet (Bryant
  and Moulton, 2002). Representing incompatible
  splits.
• Ancestral Recombination Graphs (Hudson, 1983 and
  Griffiths Marjoram, 1996). Extension of the
  coalescent model.
• Lateral Gene Transfer (Hallett et al. 2001,
  2003). Detection and representation.

13
Non-treelike Evolutionary Events

• Not all evolutionary events can be captured by a
  tree
• Hybridization two lineages (edges) combine and
  create a new lineage (edge)
• Lateral gene transfer genetic material from one
  lineage (edge) is transferred to another lineage
• Definition homolog - a member of a chromosome
  pair

14
Hybridization

• A network (a) and its two induced trees (b,c)
• Different kinds of hybridization
• Diploid same of homologs as its 2 parents
• Polyploid double of homologs as its 2 parents
• Auto-polyploid double of homologs as parent
  lineage

15
Network Representation

• Rooted directed acyclic graphs (DAGs)
• Three kinds of nodes
• Root node indegree 0 and outdegree 2
• Tree node
• indegree 1 and outdegree 2 (internal node)
• indegree 1 and outdegree 0 (leaf node)
• Network node
• indegree 2 and outdegree 1 (diploid or
  polyploid)
• indegree 1 and outdegree 1 (auto-polyploid)

16
Network Representation Cont.

• tree node

• network node

• tree edge

--- network edge

• Two kinds directed edges
• e(u,v) is a tree edge iff v is a tree node
• e(u,v) is a network edge iff v is a network node

17
Evolutionary Events

• Extinction A new node u is created at the end of
  a lineage, no new lineage is started from u
• Speciation A new node u is created at the end of
  a lineage, and two new lineages are started from
  u
• Hybridization A new node u is created
• when two lineages combine (diploid or polyploid)
• when one lineage creates u and the new lineage
  from u has double the number of homologs
  (auto-polyploid)

18
Network Generation I

• Start with one node (the root), and two sequences
  (the homologs), setup an initial speciation that
  starts two lineages
• Consider, at any time t, all existing lineages
  and with probability p an evolutionary events
  takes place
• hybridization find a coexisting lineage that
  also seeks to hybridize (the evolutionary
  distance between the two lineages cannot be too
  large)
• Evolve sequences at each new node created

19
Network Generation II

• Generate a birth-death tree, let time on the root
  be 0 and time at the last generated leaf be tl
  and let ti be in the range 0, tl
• Find all nodes who do not exceed time ti but
  whose children do
• Calculate evolutionary distance between the found
  nodes

20
Network Sequence Evolution

• In our simpler model we evolve sequences after
  the phylogeny is created.
• Seq-gen2, evolves the two homologs
  simultaneously. Similar to Seq-gen, but at each
  network node, the node randomly inherits one of
  the parents two homologs.
• Output the evolved pairs of sequences for each
  leaf in the network.

21
Outline

• Background
• Network generation
• Distance measure for networks
• Network reconstruction
• Conclusion

22
Network Distance Measure
u
v

• Each edge e, in a rooted network induces a
  tripartition on the leaves
• e (u,v) X(e) A,B, Y(e) C,D, Z(e)
  E,F

23
Robinson-Foulds Extended

• FP(N1,N2) e2 IN E(N2) not ? e1 IN E(N1), e1
  ? e2 / E(N2)
• FN(N1,N2) e1 IN E(N1) not ? e2 IN E(N2), e1
  ? e2 / E(N1)
• RF(N1,N2) (FN(N1,N2) FP(N1,N2) / 2

24
Convergence

• Convergence might cause the metric to return 0 in
  cases where N1 and N2 do NOT have the same
  topology X Y make up a convergent set in both
  networks

25
Class I and Class II Networks

• Class I network does not contain a convergent
  set
• Class II network contains a convergent set
• Low probability of a class II network

26
Measure is a Provable Metric

• The pair (N,m), where N is the space of Class I
  phylogenetic networks and m(.,.) is our error
  measure, is a metric space.
• For more details and proofs see Thesis or An
  Error Metric for Phylogenetic Networks. Linder et
  al. Department of Computer Science. Technical
  Report. 2003.

27
Evaluating the Metric Experimental Setup

• Number of network nodes 0, 1, 2, 3, 4, and 5
• Number of taxa 10, 20, 40, and 80
• Sequence lengths 25, 50, 100, 250 and 500
• Scaling 0.1, 0.5, 1 and 2
• SplitsTree, neighbor-joining, and greedy maximum
  parsimony (using PAUP)

28
Experimental Results
80 taxa, edge scaling 0.5, sequence length 500

• SplitsTree introduces too many network nodes

29
Experimental Results Cont.
40 taxa, edge scaling 0.5, sequence length 1000

• Error rate grows as a function of the number of
  network nodes present in model network

30
Experimental Results Cont.
80 taxa, edge scaling 0.5 , 1 network node in
model network

• MP and NJ Slow decrease in error as sequence
  length increases
• Metric performance Performs as expected, it does
  neither under- nor overemphasize the importance
  of network nodes

31
Outline

• Background
• Network generation
• Distance measure for networks
• Network reconstruction
• Conclusion

32
Network Reconstruction

• Inferred phylogeny might look significantly
  different from model phylogeny due to
• Extinction
• Missing data in taxon sampling
• Lineage has undergone two or more simultaneous
  hybridization events

33
Related Work

• Most parsimonious network (Fitch, 1997)
• Parsimony for reconstructing evolutionary
  histories when recombination is present (Hein,
  1990)

34
Parsimony on Phylogenetic Networks

• The evolutionary history of a site i in a set S
  of sequences that evolved on a network N is
  captured by one of the trees induced by N.
• Parsimony score of a network N leaf-labeled by a
  set of taxa S is

NCost(N,S) ?i Cost(N,i) where
Cost(N,i) minT IN T(N) TCost(T,i)
35
Fixed-tree Maximum Parsimony on Phylogenetic
Networks (FTMPPN)

• Input A tree T, leaf-labeled by a set of aligned
  sequences, S, and a bound B
• Output A phylogenetic network N (containing T)
  with at most B network nodes, with leaves labeled
  by S and internal nodes labeled by additional
  sequences that minimizes NCost(N,S)

36
FTMPPN Investigated

• Determine if the best scoring phylogenetic
  network shows a bias towards fewer, equivalent,
  or larger number of network nodes than present in
  the model network
• Assess if the inferred topology is accurate
  compared to the model topology

37
FTMPPN Investigated Cont.

• Take a network, N, leaf-labeled by a set of
  sequences, S
• Find all the trees that are contained within N
• Introduce at most B network nodes to N to
  minimize NCost

38
Experimental Setup

• Used a subset of the generated data from previous
  experiments
• Used model networks directly
• Added at most 5 network nodes to each tree of the
  network

39
Number of Network Nodes (inferred vs. model)
80 taxa, edge scaling 0.5, sequence length 500

• The heuristic infers too many network nodes

40
Topological Accuracy
40 taxa, edge scaling 0.5, sequence length 1000

• Poor, the inferred network nodes do not
  correspond to the ones in the model network

41
Conclusions

• Computational tools for phylogenetic network
  generation and sequence evolution on the networks
• Metric for the evaluation of the performance of
  phylogenetic network reconstruction methods
• Reconstructed network topologies might look
  different from model network

42
Conclusions Cont.

• Reconstruction using maximum parsimony where the
  minimum of each site is taken appears ill-suited.
  A better way might be to take the average of each
  site over all trees?

43
Acknowledgements

• Bernard Moret
• UT Austin Randy Linder, Luay Nakhleh, Anneke
  Padolina, Jerry Sun, Ruth Timme, and Tandy Warnow