Refined Buneman Trees

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Chapter 1 Introduction Although much remains obscure, and will long remain obscure, I can entertain no doubt, after the most deliberate study and dispassionate judgement of which I am capable, that the view which most naturalists entertain, and which I formerly entertained — namely, that each species has been independently created — is erroneous. I am fully convinced that species are not immutable; but that those belonging to what are called the same genera are lineal descendants of some other and generally extinct species, in the same manner as the acknowledged varieties of any one species are the descendants of that species. Charles Darwin: “The Origin of Species” Charles Darwin published his theory of evolution in 1859, roughly 150 years ago at the time of writing. He was opposed by a majority of his age, where the great majority of naturalists believed that species were immutable productions, and had been separately created. 150 years later, the theory is widely accepted and has given rise to much scientific research and new philosophy. Controversy still lurks, particularly in some school systems where creationism and evolutionism compete for the role as the “theory of life”. Luckily, the battle is heavily favoured by the latter, and religious sensibilities are being forced to subside. All in all, the theory of evolution has gone from victory to victory as many scientific achievements have turned out to support it. The discovery of DNA by Crick & Watson in 1953 solved a big part of the puzzle, showing how genetic information is stored, copied and propagated, thus creating evolutionary history through inheritance. The appearance of modern day computers also contributes significantly to the success of evolutionary biology. As huge amounts of data is being sequenced in labs all over the world, computer programs implementing mathematical models of evolution are giving us new information on a daily basis, information that gives us increasingly greater understanding of nature and life itself. 7
The theory of evolution has also become a cornerstone in philosophy and modern thinking, to a point where it is almost religious. The phrase survival of the fittest is the guideline for businesses in the capitalist economy, and playing God through genetic experiments is one of the most popular scenarios in modern science fiction. In this work we shall look at a specific method for inferring evolutionary history from a set of species, the refined Buneman tree algorithm. 1.1 Document structure This work is organized into three major parts. Part 1 Overview of Evolutionary Trees In the first part we look at evolutionary trees, their applications and some of the most important tree reconstruction methods and method classes. We introduce evolutionary principles and mechanisms, and establish how these may be modelled mathematically. Part 2 Implementing Refined Buneman Trees In this part we will concern ourselves with the implementation of the refined Buneman tree algorithms described in [BFÖ+ 03]. This algorithm is the first algorithm that runs in time O(n 3 )andspaceO(n 2 )—the previous best algorithm would use time O(n 5 )andspaceO(n 4 ). This implementation is the first of its kind and the first that is practical to run on larger scale data sets. We will also see how the implementation is integrated into the widely used JSplits tree visualizing tool. Part 3 Tests and Experiments In this part we test the implementation of the refined Buneman tree algorithm to see if it performs as specified, and we also perform experiments that demonstrate the applicability of the method, relating it to the well known Neighbor-Joining method. 8
Page 1 and 2: Refined Buneman Trees Lasse Westh-N
Page 3 and 4: This thesis is dedicated to my fami
Page 5 and 6: Contents 1 Introduction 7 1.1 Docum
Page 7: 13.3 Correctness of the reference i
Page 11 and 12: Chapter 2 Definitions This chapter
Page 13 and 14: A C B Figure 2.1: An evolutionary t
Page 15 and 16: 2.4 Quartets To every set of four s
Page 17 and 18: 2.6 Splits The partition of a finit
Page 19 and 20: evolutionary tree gives an invaluab
Page 21 and 22: time in the algorithm. In [BFÖ+ 03
Page 23 and 24: Figure 3.1: A tree of life. 22
Page 25 and 26: knowing its origins, but how does h
Page 27 and 28: anging from huge time complexity to
Page 29 and 30: Algorithm 2 The Neighbor-Joining al
Page 31 and 32: A, C, T 1 2 3 T A, C, T T C, T A, T
Page 33 and 34: Part II Implementing Refined Bunema
Page 35 and 36: Algorithm 3 Overapproximating the r
Page 37 and 38: 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
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6000 Quad Tree performance characte
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30000 Quad Tree performance charact
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sets A, B, C and D by scanning the
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Chapter 10 The Selection Algorithm
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is O(n 2 ). The algorithm uses a di
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Chapter 11 JSplits Figure 11.1: A s
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implementing an algorithm with a hi
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Chapter 12 Source Code The source c
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Chapter 13 The Reference Implementa
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• the splits that are generated.
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Chapter 14 Correctness This chapter
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The best possible way of testing wo
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100000 90000 Performance of the ref
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of the size of the heap during the
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140000 Space complexity best fit: x
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Chapter 16 Comparing Evolutionary T
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Figure 16.1: The size of the set B(
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Figure 16.2: The total number of sp
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that it over-induces splits, and th
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efined Buneman therefore suffers a
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Speedups might be achieved using op
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Appendix A Correctness of the Refer
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Quartet: 0 0 | 1 4 -0.1263501163396
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Appendix B Garbage Collector Log 0.
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Bibliography [AJL + 02] Bruce Alber
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[Kim80] M. Kimura. A simple model f
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