ReCombinatorics: The Algorithmics of Ancestral Recombination Graphs and Explicit Phylogenetic Networks

600 Pages·2014·5.7 MB·English

by  Dan Gusfield

ReCombinatorics
Dan Gusfield
withcontributionsfrom
CharlesH.Langley
YunS.Songand
YufengWu
ReCombinatorics
TheAlgorithmicsofAncestralRecombinationGraphs
andExplicitPhylogeneticNetworks
TheMITPress
Cambridge,Massachusetts London,England
(cid:2)c 2014MassachusettsInstituteofTechnology
Allrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicormechanicalmeans
(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthe
publisher.
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ThisbookwassetinTimesRomanusingLATEXbyTEXnologyInc.andwasprintedandboundinthe
UnitedStatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Gusfield,Dan.
ReCombinatorics:thealgorithmicsofancestralrecombinationgraphsandexplicit
phylogeneticnetworks/DanGusfield.
p.cm
Includesbibliographicalreferencesandindex.
ISBN978-0-262-02752-6(hardcover:alk.paper)
1.Geneticrecombination.2.Evolution(Biology)I.Title.II.Title:Recombinatorics.
QH443.G872014
572.8’77dc23
2013043434
10 9 8 7 6 5 4 3 2 1
Contents ix
8.3 AnEfficientAlgorithmfortheRoot-KnownGalled-TreeProblem 244
8.4 TheEssentialUniquenessofReducedGalledTrees 250
8.5 AnEfficientAlgorithmfortheRoot-UnknownGalled-TreeProblem 252
8.6 ExtensionstoOtherBiologicalPhenomenaandStructured
Recombination 260
8.7 ACommentonGalledTreesandLowerBounds 262
8.8 AdvancedTopic:FurtherSpeedingUptheGalled-TreeAlgorithms 263
8.9 AdvancedTopic:FurtherLimitationsontheNumberofSite
ArrangementsonaGall 268
8.10 AdvancedTopic:AConciseNecessaryandSufficientCondition
foraGalledTree 270
8.11 AdvancedTopic:TheCharacter-Removal,Site-Compatibility
ProblemonGalledTrees 279
8.12 AdvancedTopic:RelationofGalledTreestotheBack-Mutation
Model 281
9 GeneralARGConstructionMethods 285
9.1 ARGConstructionMethodsthatDestroyM 285
9.2 ARGBuildingbyTree-Scanning 328
9.3 AdvancedMaterial:TheFastest(inWorst-Case)MinARGAlgorithm 354
10 TheHistoryandForestLowerBounds 361
10.1 TheHistoryLowerBound 361
10.2 TheForestBound 375
11 ConditionstoGuaranteeaFullyDecomposedMinARG 381
11.1 Introduction 381
11.2 SufficientConditionsforaFullyDecomposedMinARG 382
11.3 TheMostGeneralResult 387
11.4 AdditionalApplications 387
12 TreeandARG-BasedHaplotyping 389
12.1 Introduction 389
12.2 TheHaplotypeInference(HI)Problem 391
Idedicatethisbook
tothememoryofmymother
IrmaGusfield,
andtothefutureofmydaughters
TaliaandShira

Contents
Preface xi
Acknowledgments xix
1 Introduction 1
1.1 CombinatorialGenomesandtheGrandChallenge 1
1.2 GenealogicalandPhylogeneticNetworks 2
1.3 TheCentralThesisoftheBook 14
1.4 FundamentalDefinitions 14
1.5 TheObservedData 22
1.6 AFewGraphDefinitions 23
1.7 TheBook 33
2 TreesFirst 35
2.1 TheRootedPerfect-PhylogenyProblem 35
2.2 TheCaseofaKnown,Non-ZeroAncestralSequence 47
2.3 TheRoot-UnknownPerfect-PhylogenyProblem 49
2.4 TheSplits-EquivalenceTheorem:TheFundamentalTheoremof
Trees 54
2.5 GeneralReferencesonPhylogeneticTrees 59
3 ADeeperIntroductiontoRecombinationandNetworks 61
3.1 TheBiologicalandPhysicalContextofRecombination 61
3.2 TheAlgorithmicandMathematicalContextofRecombination 67

viii Contents
3.3 TheCoreAlgorithmicProblem:RecombinationMinimization 82
3.4 WhyDoWeCareaboutRmin(M)andMinARGs? 84
3.5 Non-MeioticRecombination,andanExtensionoftheModel
beyondAnimalsandPlants 87
3.6 MindtheGap 88
4 ExploitingRecombination 97
4.1 HaplotypesandGenotypes 98
4.2 Problem/Solution1:GeneticMappingbyLinkage 99
4.3 Problem/Solution2:LocatingSignaturesofRecentPositiveSelection 110
4.4 Problem/Solution3:AnIdealizedIntroductiontoAssociation
Mapping 118
5 FirstBounds 127
5.1 IntroductiontoBounds 127
5.2 LowerBoundsonRmin 128
5.3 AdvancedMaterial:ASharpAnalyticalUpperBoundonRmin(M) 173
6 FundamentalCombinatorialStructureandTools 177
6.1 IncompatibilityandConflictGraphs 177
6.2 ConnectedComponentsandtheStructureofM 179
6.3 SurprisinglyFastIdentificationoftheComponentsoftheConflict
andIncompatibilityGraphs 186
7 FirstUsesofFundamentalStructure 197
7.1 TheConnected-ComponentLowerBoundonRmin 197
7.2 TheARGFull-DecompositionTheory 201
7.3 ProofoftheFull-DecompositionTheoremandItsReverse 208
7.4 TheUtilityofFullDecomposition 228
7.5 BroaderImplicationsandApplications 231
8 GalledTrees 235
8.1 IntroductiontoGalledTrees 235
8.2 FirstMajorResults 241