rnni_convexity.bib

@ARTICLE{Whidden2018-fw,
  title    = "Calculating the Unrooted Subtree {Prune-and-Regraft} Distance",
  author   = "Whidden, Chris and Matsen, Frederick",
  abstract = "The subtree prune-and-regraft (SPR) distance metric is a
              fundamental way of comparing evolutionary trees. It has
              wide-ranging applications, such as to study lateral genetic
              transfer, viral recombination, and Markov chain Monte Carlo
              phylogenetic inference. Although the rooted version of SPR
              distance can be computed relatively efficiently between rooted
              trees using fixed-parameter-tractable maximum agreement forest
              (MAF) algorithms, no MAF formulation is known for the unrooted
              case. Correspondingly, previous algorithms are unable to compute
              unrooted SPR distances larger than 7.",
  journal  = "IEEE/ACM Trans. Comput. Biol. Bioinform.",
  month    =  feb,
  year     =  2018,
}

@INCOLLECTION{Whidden2010-bw,
  title       = "Fast {FPT} Algorithms for Computing Rooted Agreement Forests:
                 Theory and Experiments",
  booktitle   = "Experimental Algorithms",
  author      = "Whidden, Chris and Beiko, Robert G and Zeh, Norbert",
  abstract    = "We improve on earlier FPT algorithms for computing a rooted
                 maximum agreement forest (MAF) or a maximum acyclic agreement
                 forest (MAAF) of a pair of phylogenetic trees. Their sizes
                 give the subtree-prune-and-regraft (SPR) distance and the
                 hybridization number of the trees, respectively. We introduce
                 new branching rules that reduce the running time of the
                 algorithms from O(3 k n) and O(3 k n logn) to O(2.42 k n) and
                 O(2.42 k n logn), respectively. In practice, the speed up may
                 be much more than predicted by the worst-case analysis. We
                 confirm this intuition experimentally by computing MAFs for
                 simulated trees and trees inferred from protein sequence data.
                 We show that our algorithm is orders of magnitude faster and
                 can handle much larger trees and SPR distances than the best
                 previous methods, treeSAT and sprdist.",
  publisher   = "Springer Berlin Heidelberg",
  pages       = "141--153",
  series      = "Lecture Notes in Computer Science",
  year        =  2010,
  original_id = "1d576390-41d4-094a-ab1f-abc6999f4d83"
}

@INCOLLECTION{Whidden2016-kl,
  title       = "{Ricci-Ollivier} Curvature of the Rooted Phylogenetic
                 {Subtree-Prune-Regraft} Graph",
  booktitle   = "Proceedings of the Thirteenth Workshop on Analytic
                 Algorithmics and Combinatorics ({ANALCO16})",
  author      = "Whidden, Chris and Matsen, IV, Frederick A",
  abstract    = "Abstract Statistical phylogenetic inference methods use tree
                 rearrangement operations such as subtree-prune-regraft (SPR)
                 to perform Markov chain Monte Carlo (MCMC) across tree
                 topologies. These methods are known to mix quickly when
                 sampling from the simple uniform distribution of trees but may
                 become stuck in the local optima of multi-modal posterior
                 distributions for real data induced by non-uniform
                 likelihoods. The structure of the graph induced by tree
                 rearrangement operations is an important determinant of the
                 mixing properties of MCMC, motivating study of the underlying
                 rSPR graph in greater detail. In this paper, we investigate
                 the rSPR graph in a new way: by calculating Ricci-Ollivier
                 curvature with respect to uniform and Metropolis-Hastings
                 random walks. We confirm using simulation that mean access
                 time distributions depend on distance, degree, and curvature,
                 showing the relevance of these curvature results to stochastic
                 tree search. These calculations require fast new algorithms
                 for constructing and sampling these graphs, reducing the time
                 required to compute an rSPR graph from O(m2n)-time to O(mn3),
                 where m is the (often large) number of trees in the graph and
                 n their number of leaves, and reducing the time required to
                 select an SPR neighbor of a tree uniformly at random to O(n)
                 time. We then develop a closed form solution to characterize
                 how the number of SPR neighbors of a tree changes after an SPR
                 operation is applied to that tree. This gives bounds on the
                 curvature, as well as a flatness-in-the-limit theorem
                 indicating that paths of small topology changes are easy to
                 traverse. However, we find that large topology changes (i.e.
                 moving a large subtree) gives pairs of trees with negative
                 curvature. Although these pairs of trees with negative
                 curvature do not impede mixing in this simple well-connected
                 space, they may manifest as bottlenecks in the much smaller
                 credible sets induced by phylogenetic posteriors with a
                 likelihood function. This work extends our knowledge of the
                 rSPR graph, in particular properties that are relevant for
                 investigation of sampling the rSPR graph.",
  pages       = "106--120",
  year        =  2016,
  original_id = "298654fa-992a-09d8-aeb3-d8cb2926fe89"
}

@BOOK{Steel2016-ye,
  title     = "Phylogeny: Discrete and Random Processes in Evolution",
  author    = "Steel, Mike",
  publisher = "SIAM-Society for Industrial and Applied Mathematics",
  month     =  sep,
  year      =  2016,
}

@BOOK{Semple2003-nj,
  title       = "Phylogenetics",
  author      = "Semple, C and Steel, M",
  publisher   = "Oxford University Press",
  year        =  2003,
  keywords    = "algorithms; methods",
  original_id = "7f9dcea0-5361-0d3b-ae10-3b0f12c98f1c"
}

@BOOK{Felsenstein2004-of,
  title       = "Inferring phylogenies",
  author      = "Felsenstein, Joseph",
  publisher   = "Sinauer associates Sunderland",
  year        =  2004,
  original_id = "97f64136-7543-0b8c-bd51-954e67661ac9"
}

@ARTICLE{Gavryushkin2018-ol,
  title       = "The combinatorics of discrete time-trees: theory and open
                 problems",
  author      = "Gavryushkin, Alex and Whidden, Chris and Matsen, IV,
                 Frederick A",
  abstract    = "A time-tree is a rooted phylogenetic tree such that all
                 internal nodes are equipped with absolute divergence dates and
                 all leaf nodes are equipped with sampling dates. Such
                 time-trees have become a central object of study in
                 phylogenetics but little is known about the parameter space of
                 such objects. Here we introduce and study a hierarchy of
                 discrete approximations of the space of time-trees from the
                 graph-theoretic and algorithmic point of view. One of the
                 basic and widely used phylogenetic graphs, the [Formula: see
                 text] graph, is the roughest approximation and bottom level of
                 our hierarchy. More refined approximations discretize the
                 relative timing of evolutionary divergence and sampling dates.
                 We study basic graph-theoretic questions for these graphs,
                 including the size of neighborhoods, diameter upper and lower
                 bounds, and the problem of finding shortest paths. We settle
                 many of these questions by extending the concept of graph
                 grammars introduced by Sleator, Tarjan, and Thurston to our
                 graphs. Although time values greatly increase the number of
                 possible trees, we show that 1-neighborhood sizes remain
                 linear, allowing for efficient local exploration and
                 construction of these graphs. We also obtain upper bounds on
                 the r-neighborhood sizes of these graphs, including a smaller
                 bound than was previously known for [Formula: see text]. Our
                 results open up a number of possible directions for
                 theoretical investigation of graph-theoretic and algorithmic
                 properties of the time-tree graphs. We discuss the directions
                 that are most valuable for phylogenetic applications and give
                 a list of prominent open problems for those applications. In
                 particular, we conjecture that the split theorem applies to
                 shortest paths in time-tree graphs, a property not shared in
                 the general [Formula: see text] case.",
  journal     = "J. Math. Biol.",
  volume      =  76,
  number      =  5,
  pages       = "1101--1121",
  month       =  apr,
  year        =  2018,
  keywords    = "Nearest neighbor interchange graph; Phylogenetic inference
                 methods; Phylogenetic time-tree",
  original_id = "b0300412-d0c5-0352-aa50-b6554f976dfc"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@INCOLLECTION{Li1996-zw,
  title       = "Some notes on the nearest neighbour interchange distance",
  booktitle   = "Computing and Combinatorics",
  author      = "Li, Ming and Tromp, John and Zhang, Louxin",
  abstract    = "We present some new results on a well known distance measure
                 between evolutionary trees. The trees we consider are free
                 3-trees having n leaves labeled 0,..., n − 1 (representing
                 species), and n − 2 internal nodes of degree 3. The distance
                 between two trees is the minimum number of nearest neighbour
                 interchange (NNI) operations required to transform one into
                 the other. First, we improve an upper bound on the
                 nni-distance between two arbitrary n-node trees from 4n log n
                 [2] to n log n. Second, we present a counterexample disproving
                 several theorems in [13]. Roughly speaking, finding an equal
                 partition between two trees doesn't imply decomposability of
                 the distance finding problem. Third, we present a
                 polynomial-time approximation algorithm that, given two trees,
                 finds a transformation between them of length O(log n) times
                 their distance. We also present some results of computations
                 we performed on small size trees.",
  publisher   = "Springer Berlin Heidelberg",
  pages       = "343--351",
  series      = "Lecture Notes in Computer Science",
  month       =  jun,
  year        =  1996,
  original_id = "459e31cd-1c71-05d1-b545-e5a31b8eb62e"
}

@INPROCEEDINGS{Dasgupta2000-xa,
  title       = "On computing the nearest neighbor interchange distance",
  booktitle   = "Discrete Mathematical Problems with Medical Applications:
                 {DIMACS} Workshop Discrete Mathematical Problems with Medical
                 Applications, December 8-10, 1999, {DIMACS} Center",
  author      = "Dasgupta, Bhaskar and He, Xin and Jiang, Tao and Li, Ming and
                 Tromp, John and Zhang, Louxin",
  abstract    = "ABSTRACT. In the practice of molecular evolution, different
                 phylogenetic trees for the same group of species are often
                 produced either by procedures that use diverse optimality
                 criteria [24] or from different genes [15, 16, 17, 18, 14].
                 Comparing these trees to find their ...",
  publisher   = "American Mathematical Soc.",
  volume      =  55,
  pages       = "19",
  year        =  2000,
  original_id = "b5ce2683-2f0b-07c3-8c11-2331b1331f28"
}

@BOOK{Knuth1997-pi,
  title     = "The art of computer programming",
  author    = "Knuth, Donald Ervin",
  publisher = "Pearson Education",
  volume    =  3,
  year      =  1997
}

@ARTICLE{Bordewich2005-nx,
  title       = "On the Computational Complexity of the Rooted Subtree Prune
                 and Regraft Distance",
  author      = "Bordewich, Magnus and Semple, Charles",
  abstract    = "The graph-theoretic operation of rooted subtree prune and
                 regraft is increasingly being used as a tool for understanding
                 and modelling reticulation events in evolutionary biology. In
                 this paper, we show that computing the rooted subtree prune
                 and regraft distance between two rooted binary phylogenetic
                 trees on the same label set is NP-hard. This resolves a
                 longstanding open problem. Furthermore, we show that this
                 distance is fixed parameter tractable when parameterised by
                 the distance between the two trees.",
  journal     = "Ann. Comb.",
  publisher   = "Birkh{\"a}user-Verlag",
  volume      =  8,
  number      =  4,
  pages       = "409--423",
  year        =  2005,
  original_id = "6fa5db83-c29d-04de-8d40-c801cffa029d"
}

@ARTICLE{Allen2001-ky,
  title       = "Subtree Transfer Operations and Their Induced Metrics on
                 Evolutionary Trees",
  author      = "Allen, Benjamin L and Steel, Mike",
  abstract    = "Leaf-labelled trees are widely used to describe evolutionary
                 relationships, particularly in biology. In this setting,
                 extant species label the leaves of the tree, while the
                 internal vertices correspon",
  journal     = "Ann. Comb.",
  publisher   = "Birkh{\"a}user Verlag",
  volume      =  5,
  number      =  1,
  pages       = "1--15",
  month       =  jun,
  year        =  2001,
  original_id = "bc656618-5e16-057b-ae6b-2a3c819fd4ad"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Floyd1962-ew,
  title     = "Algorithm 97: Shortest Path",
  author    = "Floyd, Robert W",
  abstract  = "\textcent{} onlment This procedure will perform different order
               arithmetic operations with b and c, putting the result in a. The
               order of the operation is given by op. For op= 1 addition is
               performed. For op= 2 multiplicaLion, repeated addition, is done.
               Beyond these the operations are non-commutative. For op= 3
               exponentiation, repeated multiplication, is done, raising b to
               the power c. Beyond these the question of grouping is important.
               The innermost implied parentheses are at the right. The
               hyper-exponent is always c. For op= 4 tetration …",
  journal   = "Commun. ACM",
  publisher = "ACM",
  volume    =  5,
  number    =  6,
  pages     = "345--",
  month     =  jun,
  year      =  1962,
  address   = "New York, NY, USA"
}

@article{seidel_all-pairs-shortest-path_1995,
	title = {On the All-Pairs-Shortest-Path Problem in Unweighted Undirected Graphs},
	volume = {51},
	issn = {0022-0000},
	doi = {10.1006/jcss.1995.1078},
	abstract = {We present an algorithm, {APD}, that solves the distance version of the all-pairs-shortest-path problem for undirected, unweighted n-vertex graphs in time O(M(n) log n), where M(n) denotes the time necessary to multiply two n × n matrices of small integers (which is currently known to be o(n2.376)). We also address the problem of actually finding a shortest path between each pair of vertices and present a randomized algorithm that matches {APD} in its simplicity and in its expected running time.},
	pages = {400--403},
	number = {3},
	journaltitle = {Journal of Computer and System Sciences},
	shortjournal = {Journal of Computer and System Sciences},
	author = {Seidel, R.},
	urldate = {2019-12-08},
	date = {1995-12-01},
	langid = {english},
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Dijkstra1959-ph,
  title     = "A note on two problems in connexion with graphs",
  author    = "Dijkstra, E W",
  abstract  = "III. the remaining branches (rejected or not yet considered).
               The nodes are subdivided into two sets: A. the nodes connected
               by the branches of set I, B. the remaining nodes (one and only
               one branch of set II will lead to each of these nodes), We start
               the construction by …",
  journal   = "Numer. Math.",
  publisher = "Springer-Verlag",
  volume    =  1,
  number    =  1,
  pages     = "269--271",
  month     =  dec,
  year      =  1959,
}

@ARTICLE{Robinson1971-ql,
  title     = "Comparison of labeled trees with valency three",
  author    = "Robinson, D F",
  abstract  = "This paper is concerned with the sets of trees with all interior
               vertices of valency three and the terminal vertices labeled from
               a given set. Some of the properties of such trees are
               investigated and a ``crossover'' operation defined, leading to a
               distance between trees. Results towards the calculation of the
               probability of two trees being at most a certain distance apart
               are produced. Finally a connection with manipulation in
               semigroups is pointed out.",
  journal   = "J. Combin. Theory Ser. B",
  publisher = "Elsevier",
  volume    =  11,
  number    =  2,
  pages     = "105--119",
  month     =  oct,
  year      =  1971
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Moore1973-kk,
  title     = "An iterative approach from the standpoint of the additive
               hypothesis to the dendrogram problem posed by molecular data
               sets",
  author    = "Moore, G W and Goodman, M and Barnabas, J",
  abstract  = "The problem of constructing a dendrogram depicting phylogenetic
               relationships for a collection of contemporary species is
               considered. An approach was developed based on the additive
               hypothesis in which each ``length'' between two species can be
               described by the shortest sum of lengths for the individual
               links on the dendrogram topology which connect the two species.
               The additive hypothesis holds equally well if the dendro gram is
               replaced by its corresponding (rootless) network. Network
               topologies are defined set theoretically in …",
  journal   = "J. Theor. Biol.",
  publisher = "Elsevier",
  volume    =  38,
  number    =  3,
  pages     = "423--457",
  month     =  mar,
  year      =  1973,
}

@ARTICLE{Gordon2013-fw,
  title     = "Hamiltonian walks of phylogenetic treespaces",
  author    = "Gordon, Kevaughn and Ford, Eric and St John, Katherine",
  abstract  = "We answer Bryant's combinatorial challenge on minimal walks of
               phylogenetic treespace under the nearest-neighbor interchange
               (NNI) metric. We show that the shortest path through the
               NNI-treespace of n-leaf trees is Hamiltonian for all n. That is,
               there is a minimal path that visits all binary trees exactly
               once, under NNI moves.",
  journal   = "IEEE/ACM Trans. Comput. Biol. Bioinform.",
  publisher = "ieeexplore.ieee.org",
  volume    =  10,
  number    =  4,
  pages     = "1076--1079",
  month     =  jul,
  year      =  2013,
}

@ARTICLE{De_Jong2016-al,
  title     = "Neighborhoods of Phylogenetic Trees: Exact and Asymptotic Counts",
  author    = "de Jong, J V and McLeod, J C and Steel, M",
  abstract  = "A central theme in phylogenetics is the reconstruction and
               analysis of evolutionary trees from a given set of data. To
               determine the optimal search methods for reconstructing trees,
               it is crucial to understand the size and structure of the
               neighborhoods of trees under tree rearrangement operations. The
               diameter and size of the immediate neighborhood of a tree have
               been well-studied; however, little is known about the number of
               trees at distance two, three, or (more generally) $k$ from a
               given tree. In this paper we provide a number of exact and
               asymptotic results concerning these quantities and identify some
               key aspects of tree shape that play a role in determining these
               quantities. We obtain several new results for two of the main
               tree rearrangement operations---nearest neighbor interchange and
               subtree prune and regraft---as well as for the Robinson--Foulds
               metric on trees.",
  journal   = "SIAM J. Discrete Math.",
  publisher = "Society for Industrial and Applied Mathematics",
  volume    =  30,
  number    =  4,
  pages     = "2265--2287",
  month     =  jan,
  year      =  2016
}

@ARTICLE{Gavryushkin2016-uu,
  title    = "The space of ultrametric phylogenetic trees",
  author   = "Gavryushkin, Alex and Drummond, Alexei J",
  abstract = "The reliability of a phylogenetic inference method from genomic
              sequence data is ensured by its statistical consistency. Bayesian
              inference methods produce a sample of phylogenetic trees from the
              posterior distribution given sequence data. Hence the question of
              statistical consistency of such methods is equivalent to the
              consistency of the summary of the sample. More generally,
              statistical consistency is ensured by the tree space used to
              analyse the sample. In this paper, we consider two standard
              parameterisations of phylogenetic time-trees used in evolutionary
              models: inter-coalescent interval lengths and absolute times of
              divergence events. For each of these parameterisations we
              introduce a natural metric space on ultrametric phylogenetic
              trees. We compare the introduced spaces with existing models of
              tree space and formulate several formal requirements that a
              metric space on phylogenetic trees must possess in order to be a
              satisfactory space for statistical analysis, and justify them. We
              show that only a few known constructions of the space of
              phylogenetic trees satisfy these requirements. However, our
              results suggest that these basic requirements are not enough to
              distinguish between the two metric spaces we introduce and that
              the choice between metric spaces requires additional properties
              to be considered. Particularly, that the summary tree minimising
              the square distance to the trees from the sample might be
              different for different parameterisations. This suggests that
              further fundamental insight is needed into the problem of
              statistical consistency of phylogenetic inference methods.",
  journal  = "J. Theor. Biol.",
  volume   =  403,
  pages    = "197--208",
  month    =  aug,
  year     =  2016,
  keywords = "CAT(0); Curvature; Geodesic; Phylogenetic inference; Phylogenetic
              tree; Posterior distribution summary; Simplicial complex;
              Time-tree; Ultrametric tree",
}


@ARTICLE{Drummond2010-yf,
  title     = "Bayesian random local clocks, or one rate to rule them all",
  author    = "Drummond, Alexei J and Suchard, Marc A",
  abstract  = "BACKGROUND: Relaxed molecular clock models allow divergence time
               dating and ``relaxed phylogenetic'' inference, in which a time
               tree is estimated in the face of unequal rates across lineages.
               We present a new method for relaxing the assumption of a strict
               molecular clock using Markov chain Monte Carlo to implement
               Bayesian modeling averaging over random local molecular clocks.
               The new method approaches the problem of rate variation among
               lineages by proposing a series of local molecular clocks, each
               extending over a subregion of the full phylogeny. Each branch in
               a phylogeny (subtending a clade) is a possible location for a
               change of rate from one local clock to a new one. Thus,
               including both the global molecular clock and the unconstrained
               model results, there are a total of 2(2n-2) possible rate models
               available for averaging with 1, 2, ..., 2n - 2 different rate
               categories. RESULTS: We propose an efficient method to sample
               this model space while simultaneously estimating the phylogeny.
               The new method conveniently allows a direct test of the strict
               molecular clock, in which one rate rules them all, against a
               large array of alternative local molecular clock models. We
               illustrate the method's utility on three example data sets
               involving mammal, primate and influenza evolution. Finally, we
               explore methods to visualize the complex posterior distribution
               that results from inference under such models. CONCLUSIONS: The
               examples suggest that large sequence datasets may only require a
               small number of local molecular clocks to reconcile their branch
               lengths with a time scale. All of the analyses described here
               are implemented in the open access software package BEAST 1.5.4
               (http://beast-mcmc.googlecode.com/).",
  journal   = "BMC Biol.",
  publisher = "bmcbiol.biomedcentral.com",
  volume    =  8,
  pages     = "114",
  month     =  aug,
  year      =  2010,
}


@ARTICLE{Drummond2006-nl,
  title     = "Relaxed phylogenetics and dating with confidence",
  author    = "Drummond, Alexei J and Ho, Simon Y W and Phillips, Matthew J and
               Rambaut, Andrew",
  abstract  = "In phylogenetics, the unrooted model of phylogeny and the strict
               molecular clock model are two extremes of a continuum. Despite
               their dominance in phylogenetic inference, it is evident that
               both are biologically unrealistic and that the real evolutionary
               process lies between these two extremes. Fortunately,
               intermediate models employing relaxed molecular clocks have been
               described. These models open the gate to a new field of
               ``relaxed phylogenetics.'' Here we introduce a new approach to
               performing relaxed phylogenetic analysis. We describe how it can
               be used to estimate phylogenies and divergence times in the face
               of uncertainty in evolutionary rates and calibration times. Our
               approach also provides a means for measuring the clocklikeness
               of datasets and comparing this measure between different genes
               and phylogenies. We find no significant rate autocorrelation
               among branches in three large datasets, suggesting that
               autocorrelated models are not necessarily suitable for these
               data. In addition, we place these datasets on the continuum of
               clocklikeness between a strict molecular clock and the
               alternative unrooted extreme. Finally, we present analyses of
               102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate
               alignments. From these we conclude that our method is
               phylogenetically more accurate and precise than the traditional
               unrooted model while adding the ability to infer a timescale to
               evolution.",
  journal   = "PLoS Biol.",
  publisher = "journals.plos.org",
  volume    =  4,
  number    =  5,
  pages     = "e88",
  month     =  may,
  year      =  2006,
}


@ARTICLE{Yoder2000-ks,
  title     = "Estimation of primate speciation dates using local molecular
               clocks",
  author    = "Yoder, A D and Yang, Z",
  abstract  = "Protein-coding genes of the mitochondrial genomes from 31
               mammalian species were analyzed to estimate the speciation dates
               within primates and also between rats and mice. Three
               calibration points were used based on paleontological data: one
               at 20-25 MYA for the hominoid/cercopithecoid divergence, one at
               53-57 MYA for the cetacean/artiodactyl divergence, and the third
               at 110-130 MYA for the metatherian/eutherian divergence. Both
               the nucleotide and the amino acid sequences were analyzed,
               producing conflicting results. The global molecular clock was
               clearly violated for both the nucleotide and the amino acid
               data. Models of local clocks were implemented using maximum
               likelihood, allowing different evolutionary rates for some
               lineages while assuming rate constancy in others. Surprisingly,
               the highly divergent third codon positions appeared to contain
               phylogenetic information and produced more sensible estimates of
               primate divergence dates than did the amino acid sequences.
               Estimated dates varied considerably depending on the data type,
               the calibration point, and the substitution model but differed
               little among the four tree topologies used. We conclude that the
               calibration derived from the primate fossil record is too recent
               to be reliable; we also point out a number of problems in date
               estimation when the molecular clock does not hold. Despite these
               obstacles, we derived estimates of primate divergence dates that
               were well supported by the data and were generally consistent
               with the paleontological record. Estimation of the mouse-rat
               divergence date, however, was problematic.",
  journal   = "Mol. Biol. Evol.",
  publisher = "academic.oup.com",
  volume    =  17,
  number    =  7,
  pages     = "1081--1090",
  month     =  jul,
  year      =  2000,
}

@ARTICLE{Ronquist2003-eq,
  title       = "{MrBayes} 3: Bayesian phylogenetic inference under mixed
                 models",
  author      = "Ronquist, Fredrik and Huelsenbeck, John P",
  abstract    = "MrBayes 3 performs Bayesian phylogenetic analysis combining
                 information from different data partitions or subsets evolving
                 under different stochastic evolutionary models. This allows
                 the user to analyze heterogeneous data sets consisting of
                 different data types-e.g. morphological, nucleotide, and
                 protein-and to explore a wide variety of structured models
                 mixing partition-unique and shared parameters. The program
                 employs MPI to parallelize Metropolis coupling on Macintosh or
                 UNIX clusters.",
  journal     = "Bioinformatics",
  publisher   = "Oxford Univ Press",
  volume      =  19,
  number      =  12,
  pages       = "1572--1574",
  month       =  aug,
  year        =  2003,
  original_id = "cbde3d79-17bc-0795-a58b-9fac91428887"
}

@UNPUBLISHED{Bouckaert2018-yr,
  title    = "{BEAST} 2.5: An Advanced Software Platform for Bayesian
              Evolutionary Analysis",
  author   = "Bouckaert, Remco and Vaughan, Timothy G and Barido-Sottani,
              Joelle and Duchene, Sebastian and Fourment, Mathieu and
              Gavryushkina, Alexandra and Heled, Joseph and Jones, Graham and
              Kuhnert, Denise and de Maio, Nicola and Matschiner, Michael and
              Mendes, Fabio K and Muller, Nicola and Ogilvie, Huw A and du
              Plessis, Louis and Popinga, Alex and Rambaut, Andrew and
              Rasmussen, David and Siveroni, Igor and Suchard, Marc and Wu,
              Chieh-Hsi and Xie, Dong and Zhang, Chi and Stadler, Tanja and
              Drummond, Alexei J",
  abstract = "Elaboration of Bayesian phylogenetic inference methods has
              continued at pace in recent years with major new advances in
              nearly all aspects of the joint modelling of evolutionary data.
              It is increasingly appreciated that some evolutionary questions
              can only be adequately answered by combining evidence from
              multiple independent sources of data, including genome sequences,
              sampling dates, phenotypic data, radiocarbon dates, fossil
              occurrences, and biogeographic range information among others.
              Including all relevant data into a single joint model is very
              challenging both conceptually and computationally. Advanced
              computational software packages that allow robust development of
              compatible (sub-)models which can be composed into a full model
              hierarchy have played a key role in these developments.
              Developing such software frameworks is increasingly a major
              scientific activity in its own right, and comes with specific
              challenges, from practical software design, development and
              engineering challenges to statistical and conceptual modelling
              challenges. BEAST 2 is one such computational software platform,
              and was first announced over 4 years ago. Here we describe a
              series of major new developments in the BEAST 2 core platform and
              model hierarchy that have occurred since the first release of the
              software, culminating in the recent 2.5 release.",
  journal  = "bioRxiv",
  pages    = "474296",
  month    =  nov,
  year     =  2018,
}

@ARTICLE{Hadfield2018-xp,
  title     = "Nextstrain: real-time tracking of pathogen evolution",
  author    = "Hadfield, James and Megill, Colin and Bell, Sidney M and
               Huddleston, John and Potter, Barney and Callender, Charlton and
               Sagulenko, Pavel and Bedford, Trevor and Neher, Richard A",
  abstract  = "Summary: Understanding the spread and evolution of pathogens is
               important for effective public health measures and surveillance.
               Nextstrain consists of a database of viral genomes, a
               bioinformatics pipeline for phylodynamics analysis, and an
               interactive visualization platform. Together these present a
               real-time view into the evolution and spread of a range of viral
               pathogens of high public health importance. The visualization
               integrates sequence data with other data types such as
               geographic information, serology, or host species. Nextstrain
               compiles our current understanding into a single accessible
               location, open to health professionals, epidemiologists,
               virologists and the public alike. Availability and
               implementation: All code (predominantly JavaScript and Python)
               is freely available from github.com/nextstrain and the
               web-application is available at nextstrain.org.",
  journal   = "Bioinformatics",
  publisher = "academic.oup.com",
  volume    =  34,
  number    =  23,
  pages     = "4121--4123",
  month     =  dec,
  year      =  2018,
}

@ARTICLE{Whidden2018-tk,
  title         = "Systematic Exploration of the High Likelihood Set of
                   Phylogenetic Tree Topologies",
  author        = "Whidden, Chris and Claywell, Brian C and Fisher, Thayer and
                   Magee, Andrew F and Fourment, Mathieu and Matsen, IV,
                   Frederick A",
  abstract      = "Bayesian Markov chain Monte Carlo explores tree space
                   slowly, in part because it frequently returns to the same
                   tree topology. An alternative strategy would be to explore
                   tree space systematically, and never return to the same
                   topology. In this paper, we present an efficient
                   parallelized method to map out the high likelihood set of
                   phylogenetic tree topologies via systematic search, which we
                   show to be a good approximation of the high posterior set of
                   tree topologies. Here `likelihood' of a topology refers to
                   the tree likelihood for the corresponding tree with
                   optimized branch lengths. We call this method `phylogenetic
                   topographer' (PT). The PT strategy is very simple: starting
                   in a number of local topology maxima (obtained by
                   hill-climbing from random starting points), explore out
                   using local topology rearrangements, only continuing through
                   topologies that are better than than some likelihood
                   threshold below the best observed topology. We show that the
                   normalized topology likelihoods are a useful proxy for the
                   Bayesian posterior probability of those topologies. By using
                   a non-blocking hash table keyed on unique representations of
                   tree topologies, we avoid visiting topologies more than once
                   across all concurrent threads exploring tree space. We
                   demonstrate that PT can be used directly to approximate a
                   Bayesian consensus tree topology. When combined with an
                   accurate means of evaluating per-topology marginal
                   likelihoods, PT gives an alternative procedure for obtaining
                   Bayesian posterior distributions on phylogenetic tree
                   topologies.",
  month         =  nov,
  year          =  2018,
  archivePrefix = "arXiv",
  primaryClass  = "q-bio.PE",
  eprint        = "1811.11007"
}

@misc{Collienne2019,
  author = {Collienne, Lena and Elmes, Kieran and Gavryushkin, Alex},
  title = {RNNI code},
  year = {2019},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/bioDS/RNNI_code}}
}

@ARTICLE{Kendall1948-tx,
  title     = "Rank correlation methods",
  author    = "Kendall, M G",
  publisher = "Griffin Rank correlation methods.",
  year      =  1948,
  address   = "Oxford, England"
}