## Bioconsensus: DIMACS Working Group Meetings on Bioconsensus : October 25-26, 2000 and October 2-5, 2001, DIMACS CenterThis volume is based on two DIMACS working group meetings on ''Bioconsensus''. It provides a valuable introduction and reference to the various aspects of this rapidly developing field. The meetings brought together mathematical and biological scientists to discuss the uses in the biological sciences of methods of consensus and social choice. These two lively meetings contributed much toward establishing the new field of ''bioconsensus''. Yet this book is much more than just a report of two meetings. It includes some historical background, as well as a substantial introduction to the axiomatic foundations of the field of bioconsensus and some practical applications of consensus methods to real data. Also included are contributed papers from experts who were not at the meetings. The book is intended for mathematical biologists, evolutionary biologists, and computer scientists. |

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### Contents

Axiomatics in group choice and bioconsensus | 5 |

The Arrovian program from weak orders to hierarchical and treelike | 37 |

Consensus ntrees weak independence and veto power | 47 |

The size of a maximum agreement subtree for random binary trees | 55 |

An injective set representation of closed systems of sets | 67 |

Consensus list colorings of graphs and physical mapping of | 83 |

A topdown method for building genome classification trees with linear | 97 |

A genetic | 113 |

Achieving consensus of long genomic sequences with the Wcurve | 123 |

A supertree construction method | 135 |

A classification of consensus methods for phylogenetics | 163 |

A view of supertree methods | 185 |

How good can a consensus get? Assessing the reliability of consensus trees | 205 |

Increasing phylogenetic accuracy with global congruence | 218 |

MRP supertree construction in the consensus setting | 231 |

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### Common terms and phrases

Adams consensus tree agent algorithm analysis Arrow's theorem average consensus axioms binary relation branch lengths character characterization clades cladistic Classification closed weak hierarchy co-Pareto COGs combined Computer Science consensus function consensus methods consensus rule consensus tree data sets defined denote evolutionary example F. R. McMorris Figure gene genomes global congruence graph coloring impossibility theorem incidence matrix input trees interval graph leaf set Lemma list coloring majority rule tree Math Mathematical matrix representation maximum parsimony median rule model tree Molecular MRP supertree n-trees node NP-complete number of source obtained Pareto optimal parsimony partitions permutation phylogenetic trees phylogenies physical mapping problem proper cluster R. C. Powers reduced consensus rooted trees rooted triples satisfies semi-strict semilattice sequences simulations social choice source trees species splits strict consensus tree subset supertree methods Systematic Biology taxa taxonomic congruence tuple unrooted trees vertex vertices W-curve weak orders