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  FJOURNAL = {Notices of the American Mathematical Society},
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  FJOURNAL = {Advances in Applied Mathematics},
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     PAGES = {75--95},
      ISSN = {0196-8858},
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  MRNUMBER = {3339033},
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      YEAR = {2015},
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author = {Huson, Daniel H. and Bryant, David},
title = {Application of Phylogenetic Networks in Evolutionary Studies},
volume = {23},
number = {2},
pages = {254-267},
year = {2006},
doi = {10.1093/molbev/msj030},
abstract ={The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.},
URL = {http://mbe.oxfordjournals.org/content/23/2/254.abstract},
eprint = {http://mbe.oxfordjournals.org/content/23/2/254.full.pdf+html},
journal = {Molecular Biology and Evolution}
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    AUTHOR = {Mikhalkin, Grigory},
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 BOOKTITLE = {Proceedings of {G}\"okova {G}eometry-{T}opology {C}onference
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 PUBLISHER = {G\"okova Geometry/Topology Conference (GGT), G\"okova},
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@misc{gasquel2015stochastic,
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notes={http://arxiv.org/abs/1411.4106}
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abstract ={FastME provides distance algorithms to infer phylogenies. FastME is based on balanced
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 topological moves using fast, sophisticated algorithms. The first version of FastME only
 included Nearest Neighbor Interchange (NNI). The new 2.0 version also includes Subtree Pruning and Regrafting (SPR),
 while remaining as fast as NJ and providing a number of facilities: distance estimation for
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 FastME is available using several interfaces: command-line (to be integrated in pipelines),
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URL = {http://mbe.oxfordjournals.org/content/early/2015/06/29/molbev.msv150.abstract},
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h

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journal={Molecular Biology and Evolution},
volume={11},
year= {1994},
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}
@article{Pachter2009,
author={R. Mihaescu and D. Levy and L. Pachter},
title={Why neighbor-joining works},
journal={Algorithmica},
year=2009,
Volume= 54,
number= 1,
pages= {1--24}
}
@article{Roch2014,
journal={Theor Popul Biol.},
year=2014,
title={Likelihood-based tree reconstruction on a concatenation of aligned sequence data sets can be statistically inconsistent},
author={Roch, S. and Steel, M.},
pages={56--62}
}
@article{KDETrees,
journal={Bioinformatics},
year=2014,
volume=30,
number=16,
pages={2280--2287},
title={kdetrees: non-parametric estimation of phylogenetic tree distributions},
author={Weyenberg, G. and Huggins, P.M. and Schardl, C.L. and Howe, D.K. and Yoshida, R.},
}
@article{nye2008,
year = 2008,
title = {Trees of Trees: An Approach to Comparing Multiple Alternative Phylogenies},
author = {Tom M. Nye},
volume = 57,
number = 5,
pages = {785--794},
journal = {Systematic Biology}
}
@misc{nei2003,
author={Zhang, J. and M. Nei},
year=2003,
title={Evolutionary distance: estimation},
notes={In: Encyclopedia of the Human Genome}
}



@article{xi2015,
author={Xi, Jing and Xie, Jin and Yoshida, Ruriko and Forcey, Stefan},
year=2015,
title={Stochastic safety radius on Neighbor-Joining method and Balanced Minimal Evolution on small trees},
journal={http://arxiv.org/abs/1507.08734}
}

@article{williams2013,
author= {Williams, JS  and Niedzwiecki, JH  and Weisrock, DW},
title={Species tree reconstruction of a poorly resolved clade of salamanders {({\it Ambystomatidae})} using multiple nuclear loci},
journal={Molecular phylogenetics and evolution},
volume=68,
number=3,
year=2013,
pages={671--82},
}

@article{Eickmeyer2008,
title={On the optimality of the neighbor-joining algorithm},
author={K. Eickmeyer and P. Huggins and L. Pachter and R. Yoshida},
journal={Algorithms for Molecular Biology},
Volume =3,
number= 5,
year=2008,
url={http://www.almob.org/content/3/1/5}
}

@article{Gascuel2009,
    Author = {M. Bordewich and O. Gascuel and {K. T.} Huber and V. Moulton},
    Journal = {IEEE/ACM Trans. Comput. Biology Bioinform.},
    Number = 1,
    Pages = {110--117},
    Title = {Consistency of Topological Moves Based on the Balanced Minimum Evolution Principle of Phylogenetic Inference},
    Volume = 6,
    Year = 2009}
@article{Pauplin,
    Author = {Pauplin, Y.},
    Journal = {J. Mol. Evol.},
    Pages = {41--47},
    Title = {Direct calculation of a tree length using a distance matrix},
    Volume = 51,
    Year = 2000}

@article{Gascuel2003,
    Author = {F. Denis and O. Gascuel},
    Journal = {Discrete Applied Mathematics},
    Number = 1,
    Pages = {63--77},
    Title = {On the consistency of the minimum evolution principle of phylogenetic inference},
    Volume = 127,
    Year = 2003}
@article{Bryant2005,
    Author = {D Bryant},
    Journal = {J. Classif.},
    Pages = {3--15},
    Title = {On the uniqueness of the selection criterion in neighbor-joining},
    Volume = {22},
    Year = 2005}

@article{consis,
    Author = {Ronald W. DeBry},
    Journal = {Mol Biol Evol},
    Number = 3,
    Pages = {537--551},
    Title = {The Consistency of Several Phylogeny-Inference Methods under Varying Evolutionary Rates},
    Volume = 9,
    Year = 1992}

@article{Felsenstein1978,
    Author = {J. Felsenstein},
    Journal = {Syst. Zool.},
    Pages = {240-249},
    Title = {Cases in which parsimony or compatibility methods will be positively misleading},
    Volume = {22},
    Year = {1978}}

@misc{steel2014,
author={O. Gasquel and M. Steel},
title={A 'stochastic safety radius' for distance-based tree reconstruction},
year=2014,
notes={http://arxiv.org/abs/1411.4106}
}

@article {AguBerSot:2006,
    AUTHOR = {Aguiar, Marcelo and Bergeron, Nantel and Sottile, Frank},
     TITLE = {Combinatorial {H}opf algebras and generalized
              {D}ehn-{S}ommerville relations},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {142},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {1--30},
      ISSN = {0010-437X},
}

@article {Billera,
    AUTHOR = {Billera, Louis J. and Sarangarajan, A.},
     TITLE = {All {$0$}-{$1$} polytopes are traveling salesman polytopes},
   JOURNAL = {Combinatorica},
  FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
              the Theory of Computing},
    VOLUME = {16},
      YEAR = {1996},
    NUMBER = {2},
     PAGES = {175--188},
      ISSN = {0209-9683},
     CODEN = {COMBDI},
   MRCLASS = {52B12 (05C45 90C27)},
  MRNUMBER = {1401891 (97j:52016)},
MRREVIEWER = {Alexander I. Barvinok},
       DOI = {10.1007/BF01844844},
       URL = {http://dx.doi.org/10.1007/BF01844844},
}


@techreport{ReinerZiegler1993,
  author      = {Victor Reiner and G{\"u}nter M. Ziegler},
  title       = {Coxeter-associahedra.},
  institution = {ZIB},
  address     = {Takustr.7, 14195 Berlin},
  number      = {SC-93-11},
  language    = {eng},
  urn         = {urn:nbn:de:0297-zib-1075},
  year        = {1993}
}

@article {Catan,
    AUTHOR = {Catanzaro, Daniele and Labb{\'e}, Martine and Pesenti,
              Raffaele and Salazar-Gonz{\'a}lez, Juan-Jos{\'e}},
     TITLE = {The balanced minimum evolution problem},
   JOURNAL = {INFORMS J. Comput.},
  FJOURNAL = {INFORMS Journal on Computing},
    VOLUME = {24},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {276--294},
      ISSN = {1091-9856},
   MRCLASS = {92D15 (90C11)},
  MRNUMBER = {2924705},
       DOI = {10.1287/ijoc.1110.0455},
       URL = {http://dx.doi.org/10.1287/ijoc.1110.0455},
}


@article {Cueto,
    AUTHOR = {Cueto, Mar{\'{\i}}a Ang{\'e}lica and Matsen, Frederick A.},
     TITLE = {Polyhedral geometry of phylogenetic rogue taxa},
   JOURNAL = {Bull. Math. Biol.},
  FJOURNAL = {Bulletin of Mathematical Biology},
    VOLUME = {73},
      YEAR = {2011},
    NUMBER = {6},
     PAGES = {1202--1226},
      ISSN = {0092-8240},
   MRCLASS = {92B10},
  MRNUMBER = {2799936 (2012b:92007)},
       DOI = {10.1007/s11538-010-9556-x},
       URL = {http://dx.doi.org/10.1007/s11538-010-9556-x},
}

@article {Day,
    AUTHOR = {Day, William H. E.},
     TITLE = {Computational complexity of inferring phylogenies from
              dissimilarity matrices},
   JOURNAL = {Bull. Math. Biol.},
  FJOURNAL = {Bulletin of Mathematical Biology},
    VOLUME = {49},
      YEAR = {1987},
    NUMBER = {4},
     PAGES = {461--467},
      ISSN = {0092-8240},
     CODEN = {BMBTAP},
   MRCLASS = {92A10 (68Q25 92A05)},
  MRNUMBER = {908160 (88j:92041)},
       DOI = {10.1016/S0092-8240(87)80007-1},
       URL = {http://dx.doi.org/10.1016/S0092-8240(87)80007-1},
}

@article {fastme,
    AUTHOR = {Desper, R. and Gascuel, O.},
     TITLE = {Fast and accurate phylogeny reconstruction algorithms based on the minimum-evolution principle},
   JOURNAL = {J. Comp. Biol.},
  FJOURNAL = {Journal of Computational Biology},
    VOLUME = {9},
      YEAR = {2002},
    NUMBER = {5},
     PAGES = {687--705},
}

@article{Despernew,
author = {Desper, R. and Gascuel, O.},
title = {Theoretical Foundation of the Balanced Minimum Evolution Method of Phylogenetic Inference and Its Relationship to Weighted Least-Squares Tree Fitting},
volume = {21},
number = {3},
pages = {587-598},
year = {2004},
doi = {10.1093/molbev/msh049},
eprint = {http://mbe.oxfordjournals.org/content/21/3/587.full.pdf+html},
journal = {Molecular Biology and Evolution}
}

@article {Eickmeyer,
    AUTHOR = {Eickmeyer, K. and Huggins, P. and Pachter, L. and Yoshida, R.},
     TITLE = {On the optimality of the neighbor-joining algorithm},
   JOURNAL = {Alg. Mol. Biol.},
  FJOURNAL = {Algorithms for Molecular Biology},
    VOLUME = {3},
      YEAR = {2008},
}


 @article {Fiorini,
    AUTHOR = {Fiorini, Samuel and Joret, Gwena{\"e}l},
     TITLE = {Approximating the balanced minimum evolution problem},
   JOURNAL = {Oper. Res. Lett.},
  FJOURNAL = {Operations Research Letters},
    VOLUME = {40},
      YEAR = {2012},
    NUMBER = {1},
     PAGES = {31--35},
      ISSN = {0167-6377},
     CODEN = {ORLED5},
   MRCLASS = {05C90 (05C05 90C35 90C60 92D15)},
  MRNUMBER = {2877448},
MRREVIEWER = {Peter Lochhead Ralph},
       DOI = {10.1016/j.orl.2011.10.003},
       URL = {http://dx.doi.org/10.1016/j.orl.2011.10.003},
}

@article {freedom,
    AUTHOR = {Forcey, S.},
     TITLE = {Dear {N}{S}{A}: Long-Term Security Depends on Freedom},
   JOURNAL = {Notices of the AMS},
  FJOURNAL = {Notices of the American Math Society},
  VOLUME = {61},
      YEAR = {2014},
    NUMBER = {1},
    PAGES = {7},
}

@article {Gascuel,
    AUTHOR = {Gascuel, O. and Steel, M.},
     TITLE = {Neighbor-joining revealed},
   JOURNAL = {Mol. Biol. and Evol.},
  FJOURNAL = {Molecular Biology and Evolution},
    VOLUME = {23},
      YEAR = {2006},
     PAGES = {1997--2000},
}

@article {Huggins,
AUTHOR = {Huggins, P.},
     TITLE = {Polytopes in computational biology},
   JOURNAL = {Ph.D. Dissertation, U.C. Berkeley},
      YEAR = {2008},
}

@book {RobevaHodge,
     TITLE = {Mathematical concepts and methods in modern biology},
    EDITOR = {Robeva, Raina and Hodge, Terrell L.},
      NOTE = {Using modern discrete models},
 PUBLISHER = {Elsevier/Academic Press, Amsterdam},
      YEAR = {2013},
     PAGES = {xxi+349},
      ISBN = {978-0-12-415780-4},
   MRCLASS = {92-01 (92Dxx)},
  MRNUMBER = {3295938},
       DOI = {10.1016/B978-0-12-415780-4.00001-6},
       URL = {http://dx.doi.org/10.1016/B978-0-12-415780-4.00001-6},
}

@book {Robeva,
     TITLE = {Algebraic and Discrete Mathematical Methods for Modern Biology 1st Edition},
    EDITOR = {Robeva, Raina},
 PUBLISHER = {Elsevier/Academic Press},
      YEAR = {2015},
     }


@article{Rudy2008,
title={On the optimality of the neighbor-joining algorithm},
author={K. Eickmeyer and P. Huggins and L. Pachter and R. Yoshida},
journal={Algorithms for Molecular Biology},
Volume =3,
number= 5,
year=2008,
url={http://www.almob.org/content/3/1/5}
}
@article {Rudy,
    AUTHOR = {Haws, D. and Hodge, T. and Yoshida, R.},
     TITLE = {Optimality of the neighbor joining algorithm and faces of the
              balanced minimum evolution polytope},
   JOURNAL = {Bull. Math. Biol.},
  FJOURNAL = {Bulletin of Mathematical Biology},
    VOLUME = {73},
      YEAR = {2011},
    NUMBER = {11},
     PAGES = {2627--2648},
      ISSN = {0092-8240},
   MRCLASS = {92D15 (05C05 05C90 52B12)},
  MRNUMBER = {2855185 (2012h:92108)},
       DOI = {10.1007/s11538-011-9640-x},
       URL = {http://dx.doi.org/10.1007/s11538-011-9640-x},
}

@article {pachter,
    AUTHOR = {Mihaescu, Radu and Levy, Dan and Pachter, Lior},
     TITLE = {Why neighbor-joining works},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {54},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {1--24},
      ISSN = {0178-4617},
     CODEN = {ALGOEJ},
   MRCLASS = {05C85 (68W40 92D15)},
  MRNUMBER = {2496663 (2010c:05132)},
MRREVIEWER = {Hua Wang},
       DOI = {10.1007/s00453-007-9116-4},
       URL = {http://dx.doi.org/10.1007/s00453-007-9116-4},
}

@article {Saitou,
    AUTHOR = {Saitou, N. and Nei, M.},
     TITLE = {The neighbor joining method: a new method
for reconstructing phylogenetic trees},
   JOURNAL = {Mol. Biol. and Evol.},
  FJOURNAL = {Molecular Biology and Evolution},
    VOLUME = {4},
      YEAR = {1987},
     PAGES = {406--425},
}

@article {Steel,
    AUTHOR = {Semple, Charles and Steel, Mike},
     TITLE = {Cyclic permutations and evolutionary trees},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {32},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {669--680},
      ISSN = {0196-8858},
   MRCLASS = {05C05 (05A05 92D15)},
  MRNUMBER = {2053839 (2005g:05042)},
MRREVIEWER = {Vincent L. Moulton},
       DOI = {10.1016/S0196-8858(03)00098-8},
       URL = {http://dx.doi.org/10.1016/S0196-8858(03)00098-8},
}

@article {Pauplin,
    AUTHOR = {Pauplin, Yves},
     TITLE = {Direct calculation of a tree length using a distance matrix},
   JOURNAL = {J. of Mol. Evol.},
  FJOURNAL = {Journal of Molecular Evolution},
    VOLUME = {51},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {41--47},
}


@incollection {polymake,
  author =       {Ewgenij Gawrilow and Michael Joswig},
  title =        {polymake: a Framework for Analyzing Convex Polytopes},
  pages =        {43-74},
  editor =       {Gil Kalai and G\"unter M. Ziegler},
  booktitle =    {Polytopes --- Combinatorics and Computation},
  publisher =    {Birkh\"auser},
  year =         {2000},
}

@article{Gomez,
author = {Gomez, Bernard and Daviero-Gomez, V鲯nique and Coiffard, Cl魥nt and Mart�Closas, Carles and Dilcher, David L.},
title = {Montsechia, an ancient aquatic angiosperm},
volume = {112},
number = {35},
pages = {10985-10988},
year = {2015},
doi = {10.1073/pnas.1509241112},
abstract ={The early diversification of angiosperms in diverse ecological niches is poorly understood.
 Some have proposed an origin in a darkened forest habitat and others an open aquatic or near aquatic habitat. The research presented
 here centers on Montsechia vidalii, first recovered from lithographic limestone deposits in the Pyrenees of Spain more than 100 y ago.
 This fossil material has been poorly understood and misinterpreted in the past. Now, based upon the study of more than 1,000 carefully
  prepared specimens, a detailed analysis of Montsechia is presented. The morphology and anatomy of the plant, including aspects of its
  reproduction, suggest that Montsechia is sister to Ceratophyllum (whenever cladistic analyses are made with or without a backbone).
   Montsechia was an aquatic angiosperm living and reproducing below the surface of the water, similar to Ceratophyllum. Montsechia is
   Barremian in age, raising questions about the very early divergence of the Ceratophyllum clade compared with its position as sister to
   eudicots in many cladistic analyses. Lower Cretaceous aquatic angiosperms, such as Archaefructus and Montsechia, open the possibility
   that aquatic plants were locally common at a very early stage of angiosperm evolution and that aquatic habitats may have played a major
   role in the diversification of some early angiosperm lineages.},
URL = {http://www.pnas.org/content/112/35/10985.abstract},
eprint = {http://www.pnas.org/content/112/35/10985.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}

@article{Goremykin2015,
author = {Goremykin, V. V. and Nikiforova, S. V. and Cavalieri, D. and Pindo, M. and Lockhart, Peter},
title = {The Root of Flowering Plants and Total Evidence},
volume = {64},
number = {5},
pages = {879-891},
year = {2015},
doi = {10.1093/sysbio/syv028},
abstract ={Support for Amborella as the sole survivor of an evolutionary lineage that
is sister to all other angiosperms comes from positions in DNA multiple-sequence alignments that have a poor fit to
 time-reversible substitution models. These sites exhibit significant levels of homoplasy, compositional heterogeneity,
 and strong heterotachy. We report phylogenetic analyses with observed, randomized, and simulated data which show there is
  little or no expectation that these sites provide useful information for understanding relationships among basal angiosperms.
   Their inclusion in phylogenetic analyses leads to a long-branch attraction artifact that favors Amborella as sister to other angiosperms
    in reconstructed phylogenies. Using parametric simulations, we show that sites in chloroplast sequences that exhibit less homoplasy
     between angiosperms and gymnosperms provide more reliable information for inferring basal angiosperm relationships. We confirm our
      earlier findings that the basal angiosperm Amborella is most closely related to aquatic herbs. Our current and previously reported
       (Goremykin et al. 2013) analyses highlight an essential aspect of the total evidence approach to phylogenetic inference. They suggest
        that data partitioning aimed at identifying components of the data that better fit evolutionary models is a more reliable approach
         to phylogeny reconstruction at deep taxonomic levels.},
URL = {http://sysbio.oxfordjournals.org/content/64/5/879.abstract},
eprint = {http://sysbio.oxfordjournals.org/content/64/5/879.full.pdf+html},
journal = {Systematic Biology}
}

@article{Xi2014,
author = {Xi, Zhenxiang and Liu, Liang and Rest, Joshua S. and Davis, Charles C.},
title = {Coalescent versus Concatenation Methods and the Placement of Amborella as Sister to Water Lilies},
volume = {63},
number = {6},
pages = {919-932},
year = {2014},
doi = {10.1093/sysbio/syu055},
abstract ={The molecular era has fundamentally reshaped our knowledge of the evolution and diversification of angiosperms.
 One outstanding question is the phylogenetic placement of Amborella trichopoda Baill., commonly thought to represent the
  first lineage of extant angiosperms. Here, we leverage publicly available data and provide a broad coalescent-based species
   tree estimation of 45 seed plants. By incorporating 310 nuclear genes, our coalescent analyses strongly support a clade
    containing Amborella plus water lilies (i.e., Nymphaeales) that is sister to all other angiosperms across different
     nucleotide rate partitions. Our results also show that commonly applied concatenation methods produce strongly supported,
     but incongruent placements of Amborella: slow-evolving nucleotide sites corroborate results from coalescent analyses,
      whereas fast-evolving sites place Amborella alone as the first lineage of extant angiosperms. We further explored the
       performance of coalescent versus concatenation methods using nucleotide sequences simulated on (i) the two alternate
        placements of Amborella with branch lengths and substitution model parameters estimated from each of the 310 nuclear
         genes and (ii) three hypothetical species trees that are topologically identical except with respect to the degree of
          deep coalescence and branch lengths. Our results collectively suggest that the Amborella alone placement inferred using
           concatenation methods is likely misled by fast-evolving sites. This appears to be exacerbated by the combination of long
            branches in stem group angiosperms, Amborella, and Nymphaeales with the short internal branch separating Amborella and
            Nymphaeales. In contrast, coalescent methods appear to be more robust to elevated substitution rates.},
URL = {http://sysbio.oxfordjournals.org/content/63/6/919.abstract},
eprint = {http://sysbio.oxfordjournals.org/content/63/6/919.full.pdf+html},
journal = {Systematic Biology}
}
@article{Drew,
author = {Drew, Bryan T. and Ruhfel, Brad R. and Smith, Stephen A. and Moore, Michael J. and Briggs, Barbara G. and Gitzendanner, Matthew A. and Soltis, Pamela S. and Soltis, Douglas E.},
title = {Another Look at the Root of the Angiosperms Reveals a Familiar Tale},
volume = {63},
number = {3},
pages = {368-382},
year = {2014},
doi = {10.1093/sysbio/syt108},
abstract ={Since the advent of molecular phylogenetics more than 25 years ago, a major goal of plant systematists has been
 to discern the root of the angiosperms. Although most studies indicate that Amborella trichopoda is sister to all remaining
 extant flowering plants, support for this position has varied with respect to both the sequence data sets and analyses employed.
  Recently, Goremykin et al. (2013) questioned the ねborella-sister hypothesis䠵sing a 㮯ise-reduction䠡pproach and reported
   a topology with Amborella?+?Nymphaeales (water lilies) sister to all remaining angiosperms. Through a series of analyses of both
   plastid genomes and mitochondrial genes, we continue to find mostly strong support for the Amborella-sister hypothesis and offer a
   rebuttal of Goremykin et al. (2013). The major tenet of Goremykin et al. is that the Amborella-sister position is determined by noisy
    data紨at is, characters with high rates of change and lacking true phylogenetic signal. To investigate the signal in these noisy data
     further, we analyzed the discarded characters from their noise-reduced alignments. We recovered a tree identical to that of the currently
      accepted angiosperm framework, including the position of Amborella as sister to all other angiosperms, as well as all other major clades.
       Thus, the signal in the 㮯isy䠤ata is consistent with that of our complete data sets硲guing against the use of their noise-reduction approach.
        We also determined that one of the alignments presented by Goremykin et al. yields results at odds with their central claim紨eir data set
         actually supports Amborella as sister to all other angiosperms, as do larger plastid data sets we present here that possess more complete
          taxon sampling both within the monocots and for angiosperms in general. Previous unpartitioned, multilocus analyses of mitochondrial DNA
          (mtDNA) data have provided the strongest support for Amborella?+?Nymphaeales as sister to other angiosperms. However, our analysis
           of third codon positions from mtDNA sequence data also supports the Amborella-sister hypothesis. Finally, we challenge the conclusion
           of Goremykin et al. that the first flowering plants were aquatic and herbaceous, reasserting that even if Amborella?+?water lilies,
            or water lilies alone, are sister to the rest of the angiosperms, the earliest angiosperms were not necessarily aquatic and/or herbaceous.
             [Angiosperms; Amborella; Nymphaeales; plastid genome; water lilies.]},
URL = {http://sysbio.oxfordjournals.org/content/63/3/368.abstract},
eprint = {http://sysbio.oxfordjournals.org/content/63/3/368.full.pdf+html},
journal = {Systematic Biology}
}
@article{Goremykin2013,
author = {Goremykin, Vadim V. and Nikiforova, Svetlana V. and Biggs, Patrick J. and Zhong, Bojian and Delange, Peter and Martin, William and Woetzel, Stefan and Atherton, Robin A. and Mclenachan, Patricia A. and Lockhart, Peter J.},
title = {The Evolutionary Root of Flowering Plants},
volume = {62},
number = {1},
pages = {50-61},
year = {2013},
doi = {10.1093/sysbio/sys070},
abstract ={Correct rooting of the angiosperm radiation is both challenging and necessary for understanding the
origins and evolution of physiological and phenotypic traits in flowering plants. The problem is known to be difficult
due to the large genetic distance separating flowering plants from other seed plants and the sparse taxon sampling among
basal angiosperms. Here, we provide further evidence for concern over substitution model misspecification in analyses of
 chloroplast DNA sequences. We show that support for Amborella as the sole representative of the most basal angiosperm lineage
  is founded on sequence site patterns poorly described by time-reversible substitution models. Improving the fit between sequence
   data and substitution model identifies Trithuria, Nymphaeaceae, and Amborella as surviving relatives of the most basal lineage
    of flowering plants. This finding indicates that aquatic and herbaceous species dominate the earliest extant lineage of flowering plants. [; ; ; ; ; .]},
URL = {http://sysbio.oxfordjournals.org/content/62/1/50.abstract},
eprint = {http://sysbio.oxfordjournals.org/content/62/1/50.full.pdf+html},
journal = {Systematic Biology}
}

@article{Leebens-Mack,
author = {Leebens-Mack, Jim and Raubeson, Linda A. and Cui, Liying and Kuehl, Jennifer V. and Fourcade, Matthew H. and Chumley, Timothy W. and Boore, Jeffrey L. and Jansen, Robert K. and dePamphilis, Claude W.},
title = {Identifying the Basal Angiosperm Node in Chloroplast Genome Phylogenies: Sampling One's Way Out of the Felsenstein Zone},
volume = {22},
number = {10},
pages = {1948-1963},
year = {2005},
doi = {10.1093/molbev/msi191},
abstract ={While there has been strong support for Amborella and Nymphaeales (water lilies) as branching from basal-most nodes
in the angiosperm phylogeny, this hypothesis has recently been challenged by phylogenetic analyses of 61 protein-coding genes
extracted from the chloroplast genome sequences of Amborella, Nymphaea, and 12 other available land plant chloroplast genomes.
 These character-rich analyses placed the monocots, represented by three grasses (Poaceae), as sister to all other extant angiosperm
 lineages. We have extracted protein-coding regions from draft sequences for six additional chloroplast genomes to test whether this
  surprising result could be an artifact of long-branch attraction due to limited taxon sampling. The added taxa include three monocots
   (Acorus, Yucca, and Typha), a water lily (Nuphar), a ranunculid (Ranunculus), and a gymnosperm (Ginkgo). Phylogenetic analyses
    of the expanded DNA and protein data sets together with microstructural characters (indels) provided unambiguous support for
     Amborella and the Nymphaeales as branching from the basal-most nodes in the angiosperm phylogeny. However, their relative
      positions proved to be dependent on the method of analysis, with parsimony favoring Amborella as sister to all other
       angiosperms and maximum likelihood (ML) and neighbor-joining methods favoring an Amborella + Nymphaeales clade as sister.
        The ML phylogeny supported the later hypothesis, but the likelihood for the former hypothesis was not significantly different.
         Parametric bootstrap analysis, single-gene phylogenies, estimated divergence dates, and conflicting indel characters all help to
          illuminate the nature of the conflict in resolution of the most basal nodes in the angiosperm phylogeny. Molecular dating analyses
           provided median age estimates of 161 MYA for the most recent common ancestor (MRCA) of all extant angiosperms and 145 MYA for the
            MRCA of monocots, magnoliids, and eudicots. Whereas long sequences reduce variance in branch lengths and molecular dating estimates,
             the impact of improved taxon sampling on the rooting of the angiosperm phylogeny together with the results of parametric bootstrap
              analyses demonstrate how long-branch attraction might mislead genome-scale phylogenetic analyses.},
URL = {http://mbe.oxfordjournals.org/content/22/10/1948.abstract},
eprint = {http://mbe.oxfordjournals.org/content/22/10/1948.full.pdf+html},
journal = {Molecular Biology and Evolution}
}


@article {Simmons,
    AUTHOR = {Simmons, Mark P. and Gatesy, John},
     TITLE = {Coalescence vs. concatenation: Sophisticated analyses vs. first principles applied to rooting the angiosperms},
   JOURNAL = {Mol. Phyl. and Evol.},
  FJOURNAL = {Molecular Phylogenetics and Evolution},
    VOLUME = {91},
      YEAR = {2015},
     PAGES = {98--122},
}

@article{Wickett,
author = {Wickett, Norman J. and Mirarab, Siavash and Nguyen, Nam and Warnow, Tandy and Carpenter, Eric and Matasci, Naim and Ayyampalayam, Saravanaraj and Barker, Michael S. and Burleigh, J. Gordon and Gitzendanner, Matthew A. and Ruhfel, Brad R. and Wafula, Eric and Der, Joshua P. and Graham, Sean W. and Mathews, Sarah and Melkonian, Michael and Soltis, Douglas E. and Soltis, Pamela S. and Miles, Nicholas W. and Rothfels, Carl J. and Pokorny, Lisa and Shaw, A. Jonathan and DeGironimo, Lisa and Stevenson, Dennis W. and Surek, Barbara and Villarreal, Juan Carlos and Roure, B顴rice and Philippe, Herv頡nd dePamphilis, Claude W. and Chen, Tao and Deyholos, Michael K. and Baucom, Regina S. and Kutchan, Toni M. and Augustin, Megan M. and Wang, Jun and Zhang, Yong and Tian, Zhijian and Yan, Zhixiang and Wu, Xiaolei and Sun, Xiao and Wong, Gane Ka-Shu and Leebens-Mack, James},
title = {Phylotranscriptomic analysis of the origin and early diversification of land plants},
volume = {111},
number = {45},
pages = {E4859-E4868},
year = {2014},
doi = {10.1073/pnas.1323926111},
abstract ={Reconstructing the origin and evolution of
land plants and their algal relatives is a fundamental problem in plant phylogenetics, and is essential for understanding how
 critical adaptations arose, including the embryo, vascular tissue, seeds, and flowers. Despite advances in molecular systematics,
 some hypotheses of relationships remain weakly resolved. Inferring deep phylogenies with bouts of rapid diversification can be problematic;
  however, genome-scale data should significantly increase the number of informative characters for analyses. Recent phylogenomic reconstructions
   focused on the major divergences of plants have resulted in promising but inconsistent results. One limitation is sparse taxon sampling, likely
   resulting from the difficulty and cost of data generation. To address this limitation, transcriptome data for 92 streptophyte taxa were generated
    and analyzed along with 11 published plant genome sequences. Phylogenetic reconstructions were conducted using up to 852 nuclear genes and 1,701,170 aligned
     sites. Sixty-nine analyses were performed to test the robustness of phylogenetic inferences to permutations of the data matrix or to phylogenetic method,
     including supermatrix, supertree, and coalescent-based approaches, maximum-likelihood and Bayesian methods, partitioned and unpartitioned analyses,
     and amino acid versus DNA alignments. Among other results, we find robust support for a sister-group relationship between land plants
     and one group of streptophyte green algae, the Zygnematophyceae. Strong and robust support for a clade comprising liverworts and mosses
      is inconsistent with a widely accepted view of early land plant evolution,
 and suggests that phylogenetic hypotheses used to understand the evolution of fundamental plant traits should be reevaluated.},
URL = {http://www.pnas.org/content/111/45/E4859.abstract},
eprint = {http://www.pnas.org/content/111/45/E4859.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}

@article {Morton,
    AUTHOR = {Morton, Cynthia M.},
     TITLE = {Newly Sequenced Nuclear Gene (Xdh) for Inferring Angiosperm Phylogeny},
   JOURNAL = {Ann. of Missouri Botanical Garden},
  FJOURNAL = {Annals of the Missouri Botanical Garden},
    VOLUME = {98},
      YEAR = {2011},
      NUMBER = {1},
     PAGES = {63--89},
}

@article {Ruhfel,
    AUTHOR = {Ruhfel, B.R. and Gitzendanner, M.A. and Soltis, P.S. and Soltis, D.E. and Burleigh, J.G.},
     TITLE = {From algae to angiosperms-inferring the phylogeny of green plants (Viridiplantae) from 360 plastid genomes.},
   JOURNAL = {BMC Evol. Biol.},
  FJOURNAL = {BMC Evolutionary Biology},
    VOLUME = {14},
      YEAR = {2014},
      NUMBER = {23},
     PAGES = {online},
}


@article {Huang,
    AUTHOR = {Huang, Ruiqi and  Hippauf, Frank and Rohrbeck, Diana and Haustein, Maria and Wenke, Katrin and  Feike, Janie and  Sorrelle, Noah and  Piechulla, Birgit and Barkman, Todd J.},
     TITLE = {Enzyme functional evolution through improved
catalysis of ancestrally non-preferred substrates.},
   JOURNAL = {Proc. Nat. Acad. Sci.},
  FJOURNAL = {Proceedings of
the National Academy of Sciences},
    VOLUME = {109},
      YEAR = {2012},
     PAGES = {2966--2971},
}

@article{Barkman2000,
author = {Barkman, Todd J. and Chenery, Gordon and McNeal, Joel R. and Lyons-Weiler, James and Ellisens, Wayne J. and Moore, Gerry and Wolfe, Andrea D. and dePamphilis, Claude W.},
title = {Independent and combined analyses of sequences from all three genomic compartments converge on the root of flowering plant phylogeny},
volume = {97},
number = {24},
pages = {13166-13171},
year = {2000},
doi = {10.1073/pnas.220427497},
abstract ={Plant phylogenetic estimates are most likely to be reliable when
 congruent evidence is obtained independently from the mitochondrial,
 plastid, and nuclear genomes with all methods of analysis. Here,
 results are presented from separate and combined genomic analyses of
 new and previously published data, including six and nine genes (8,911
 bp and 12,010 bp, respectively) for different subsets of taxa that
 suggest Amborella + Nymphaeales (water lilies) are the
 first-branching angiosperm lineage. Before and after tree-independent
 noise reduction, most individual genomic compartments and methods of
 analysis estimated the Amborella + Nymphaeales basal
 topology with high support. Previous phylogenetic estimates placing
 Amborella alone as the first extant angiosperm branch
 may have been misled because of a series of specific problems with
 paralogy, suboptimal outgroups, long-branch taxa, and method
 dependence. Ancestral character state reconstructions differ between
 the two topologies and affect inferences about the features of early
 angiosperms.},
URL = {http://www.pnas.org/content/97/24/13166.abstract},
eprint = {http://www.pnas.org/content/97/24/13166.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}

@article {Skippington,
    AUTHOR = {Skippington, Elizabeth and  Barkman, Todd J. and Rice, Danny W. and Palmer, Jeff D.},
     TITLE = {The miniaturized mitogenome of the parasitic plant
Viscum scurruloideum is extremely divergent and dynamic and has lost
all nad genes.},
   JOURNAL = {Proc. Nat. Acad. Sci.},
  FJOURNAL = {Proceedings of the National Academy of Sciences},
    VOLUME = {112},
      YEAR = {2015},
     PAGES = {E3515--E3524},
}

@article{weisrock2013, author={Weisrock, DW and Smith, SD  and Chan,
LM  and Biebouw, K. and Kappeler, PM  and Yoder, AD},
title={Concatenation and concordance in the reconstruction of mouse
lemur phylogeny: an empirical demonstration of the effect of allele
sampling in phylogenetics}, journal={Molecular biology and
evolution}, volume=29, number=6, year=2012, pages= {1615--30} }
@article{weisrock2012, author={Weisrock, DW}, title={Concordance
analysis in mitogenomic phylogenetics}, journal={Molecular
phylogenetics and evolution}, volume=65, number=1, year=2012,
pages={194--202} } @article{kajita2013, author={Kajita, Y. and
O'Neill, EM  and Zheng, Y. and Obrycki, JJ  and Weisrock, DW},
title={A population genetic signature of human releases in an
invasive ladybeetle}, journal={Molecular ecology}, volume=21,
number=22, year= 2012, pages={5473--83} } @article{oneill2013,
author={O'Neill, EM  and Schwartz, R. and Bullock, CT  and Williams,
JS  and Shaffer, HB  and Aguilar-Miguel, X. and Parra-Olea, G. and
Weisrock, DW}, title={Parallel tagged amplicon sequencing reveals
major lineages and phylogenetic structure in the North American
tiger salamander ({{\it Ambystoma tigrinum}}) species complex},
journal={Molecular ecology}, volume=22, number=1, year=2013,
pages={111--29} }

@incollection{hoy, title={First steps toward the geometry of
cophylogeny}, author={P. Huggins and M. Owen and R. Yoshida},
Booktitle={the Proceedings of the Second CREST--SBM International
Conference ``Harmony of Gr��r Bases and the Modern Industrial
Society.''}, year=2012, pages={99--116}, publisher={World Scientific
Publishing Company}, address={Hackensack, NJ}, } @article{svn,
    Author = {D. Haws and P. Huggins and E. M. O'Neill and D. W. Weisrock and R. Yoshida},
    Date-Modified = {2011-10-24 21:41:02 -0400},
    Note = {doi:10.1186/1471-2105-13-210},
Volume = 13, Number = 210,
    Title = {A support vector machine based test for incongruence between sets of trees in tree space},
journal = {BMC Bioinformatics},
    Year = 2012}
@article{diffmean, title = {Statistical Phylogenetic Tree Analysis
Using Differences of Means}, author = {E. Arnaoudova and D. Haws and
P. Huggins and J. W. Jaromczyk and N. Moore and C. Schardl and R.
Yoshida}, journal = {Front. Psychiatry}, volume = 1, number = 47,
year = 2010, note = {doi:10.3389/fnins.2010.0004} }

@article{bayes, title = {Bayes estimators for phylogenetic
reconstruction}, author = {P. Huggins and W. Li and D. Haws and T.
Friedrich and J. Liu and R. Yoshida}, Volume = 60, number = 4, Pages
= {528--540}, journal = {Systematic Biology}, year = 2010, }
@article{weisrock2013b, title={Molecular phylogenetic reconstruction
of the endemic Asian salamander family {Hynobiidae (Amphibia,
Caudata)}}, author={D. Weisrock and JR Macey and M. Matsui and DG
Malcahy and TJ Papenfuss}, year= 2013, journal={Zootaxa}, volume =
1, pages={77--93} }

@article{layne2012nested,
  title={Nested canalyzing depth and network stability},
  author={Layne, L. and Dimitrova, E. and Macauley, M.},
  journal={Bull. Math. Biol.},
  volume={74},
  number={2},
  pages={422--433},
  year={2012},
  publisher={Springer}
}

@article{Macauley:13,
  title={An atlas of limit set dynamics for asynchronous elementary cellular automata},
  author={Macauley, M. and Mortveit, H.S.},
  journal={Theor. Comput. Sci.},
  volume={504},
  pages={26--37},
  year={2013},
  publisher={Elsevier}
}

@inproceedings{macauley2014cycle,
  title = {Cycle equivalence of finite dynamical systems containing symmetries},
  author = {Macauley, M. and Mortveit, H.},
  booktitle = {Proceedings of the 20th International Workshop, AUTOMATA},
  pages = {64--76},
  location = {Himeji, Japan},
  year = {2014}
}

@inproceedings{macauley2014analysis,
  title = {Analysis and dynamics of bi-threshold functions},
  author = {Macauley, M. and Thomas, G.},
  booktitle = {Proceedings of the 20th International Workshop, AUTOMATA},
  pages = {170--177},
  location = {Himeji, Japan},
  year = {2014}
}

@misc{develin2015toric,
  author = {Develin, M. and Macauley, M. and Reiner, V.},
  title = {Toric partial orders},
  journal = {Trans. Amer. Math. Soc.},
  note = {Trans. Amer. Math. Soc. In press. arXiv:1211.4247},
  year = {2015}
}

@misc{he2015stratification,
  author = {He, Q. and Macauley, M.},
  title = {Stratification and enumerate of Boolean functions by canalizing depth},
  journal = {Trans. Amer. Math. Soc.},
  note = {Submitted to Physica D. arXiv:1504.07591},
  year = {2015}
}