Refined Buneman Trees

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worst case time and space complexity. However, with respect to performance in terms of reconstructing accurate phylogenetic trees, the refined Buneman method might demonstrate unknown strengths. 16.1 Test setup In the following section we will test the refined Buneman tree algorithm against two other known algorithms, the Buneman method ([Bun71]) and the Neighbor- Joining ([SN87]) method. All experiments have been run on test data from the PFAM database of protein sequence families. The data consists of distance matrices with sizes ranging from 10–50 (30), 100–200 (50) and 500–700 (50), for a total of 130 test matrices. Matrices with larger sizes are available, but they will be disregarded due to time constraints. Distance data is given in the common Phylip format. 16.2 Buneman and refined Buneman The implementation of the refined Buneman tree algorithm can easily be adapted to mark those splits which are both in B(δ) andinRB(δ). Since we have the n − 3 least scoring quartets used to calculate the refined Buneman index for a split, it is easy to find the least scoring quartet among them. If that quartet has positive Buneman score, we can mark the split as belonging in B(δ). This first experiment consists of running the (modified) refined Buneman tree algorithm on examples from the set of PFAM distance matrices, counting for each one the number of splits in B(δ) andinRB(δ). The results from the experiment are given in Figure 16.1, sorted according to increasing distance matrix size and plotted in percentage (the size of RB(δ) is 100%). Figure 16.1 shows that the size of B(δ) fluctuates quite a bit, especially when the size of the distance matrix increases, where more and more datasets do not infer any Buneman splits at all. The refined Buneman method is clearly much less restrictive then the Buneman method, as expected. Regarding the quality of the splits that are in RB(δ) but not in B(δ), further studies would need to be undertaken — one could study either the specific dataset for which the Buneman method produces few splits, or use simulated data which would provide a key to which splits are well-supported and which are unsupported. 16.3 Refined Buneman and Neighbor-Joining To test the refined Buneman tree method against the Neighbor-Joining method, the author has run the implementation of the refined Buneman tree algorithm described in this paper, against the Quick-Join algorithm described in [BFM + 03]. The Quick-Join software is available from this website: http://www.birc.dk/Software/QuickJoin/ 89
Figure 16.1: The size of the set B(δ) as a percentage of the set RB(δ) onPFAM data. The two artifacts are due to two datasets where neither method produces any splits. 90
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Refined Buneman Trees Lasse Westh-N
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This thesis is dedicated to my fami
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Contents 1 Introduction 7 1.1 Docum
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13.3 Correctness of the reference i
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The theory of evolution has also be
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Chapter 2 Definitions This chapter
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A C B Figure 2.1: An evolutionary t
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2.4 Quartets To every set of four s
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2.6 Splits The partition of a finit
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evolutionary tree gives an invaluab
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time in the algorithm. In [BFÖ+ 03
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Figure 3.1: A tree of life. 22
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knowing its origins, but how does h
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anging from huge time complexity to
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Algorithm 2 The Neighbor-Joining al
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A, C, T 1 2 3 T A, C, T T C, T A, T
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Part II Implementing Refined Bunema
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Algorithm 3 Overapproximating the r
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the pseudo-code for the algorithm i
Page 39 and 40: AE DE D B e E BC A C BE AC Figure 5
Page 41 and 42: construction, but we still have to
Page 43 and 44: Chapter 6 TheTreeDataStructure This
Page 45 and 46: incidentedge Figure 6.2: The world
Page 47 and 48: interface EdgeIterator { boolean ha
Page 49 and 50: Figure 6.7: An example a node which
Page 51 and 52: So how do we find σ ′ We start
Page 53 and 54: Algorithm 5. Offhand, the algorithm
Page 55 and 56: Algorithm 6 The algorithm that calc
Page 57 and 58: a b c d root ab cd Figure 8.2: Upda
Page 59 and 60: 6000 Quad Tree performance characte
Page 61 and 62: 30000 Quad Tree performance charact
Page 63 and 64: sets A, B, C and D by scanning the
Page 65 and 66: Chapter 10 The Selection Algorithm
Page 67 and 68: is O(n 2 ). The algorithm uses a di
Page 69 and 70: Chapter 11 JSplits Figure 11.1: A s
Page 71 and 72: implementing an algorithm with a hi
Page 73 and 74: Chapter 12 Source Code The source c
Page 75 and 76: Chapter 13 The Reference Implementa
Page 77 and 78: • the splits that are generated.
Page 79 and 80: Chapter 14 Correctness This chapter
Page 81 and 82: The best possible way of testing wo
Page 83 and 84: 100000 90000 Performance of the ref
Page 85 and 86: of the size of the heap during the
Page 87 and 88: 140000 Space complexity best fit: x
Page 89: Chapter 16 Comparing Evolutionary T
Page 93 and 94: Figure 16.2: The total number of sp
Page 95 and 96: that it over-induces splits, and th
Page 97 and 98: efined Buneman therefore suffers a
Page 99 and 100: Speedups might be achieved using op
Page 101 and 102: Appendix A Correctness of the Refer
Page 103 and 104: Quartet: 0 0 | 1 4 -0.1263501163396
Page 105 and 106: Appendix B Garbage Collector Log 0.
Page 107 and 108: Bibliography [AJL + 02] Bruce Alber
Page 109: [Kim80] M. Kimura. A simple model f
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Refined Buneman Trees

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