Phylogenetic Algebraic Geometry

Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover classical geometric objects, such as toric and determinantal varieties and their secant varieties, but larger trees lead to new and largely unexplored territory. This paper gives a self-contained introduction to this subject and offers numerous open problems for algebraic geometers.Comment: 15 pages, 7 figure

A new phylogenetic reconstruction method based on invariants

An attempt to use phylogenetic invariants for tree reconstruction was made at the end of the 80s and the beginning of the 90s by several authors (the initial idea due to Lake [Lake, 1987] and Cavender and Felsenstein [Cavender and Felsenstein, 1987]). However, the e±ciency of methods based on invariants is still in doubt ([Huelsenbeck, 1995], [Jin and Nei, 1990]), probably because these methods only used few generators of the set of phylogenetic invariants. The method studied in this paper was first introduced in [Casanellas et al., 2005] and it is the first method based on invariants that uses the whole set of generators for DNA data. The simulation studies performed in this paper prove that it is a very competitive and highly e±cient phylogenetic reconstruction method, especially for non-homogeneous phylogenetic trees

Alignments of mitochondrial genome arrangements: Applications to metazoan phylogeny

Mitochondrial genomes provide a valuable dataset for phylogenetic studies, in particular of metazoan phylogeny because of the extensive taxon sample that is available. Beyond the traditional sequence-based analysis it is possible to extract phylogenetic information from the gene order. Here we present a novel approach utilizing these data based on cyclic list alignments of the gene orders. A progressive alignment approach is used to combine pairwise list alignments into a multiple alignment of gene orders. Parsimony methods are used to reconstruct phylogenetic trees, ancestral gene orders, and consensus patterns in a straightforward approach. We apply this method to study the phylogeny of protostomes based exclusively on mitochondrial genome arrangements. We, furthermore, demonstrate that our approach is also applicable to the much larger genomes of chloroplasts

Sequencing and Comparing Whole Mitochondrial Genomes of Animals

Comparing complete animal mitochondrial genome sequences is becoming increasingly common for phylogenetic reconstruction and as a model for genome evolution. Not only are they much more informative than shorter sequences of individual genes for inferring evolutionary relatedness, but these data also provide sets of genome-level characters, such as the relative arrangements of genes, that can be especially powerful. We describe here the protocols commonly used for physically isolating mtDNA, for amplifying these by PCR or RCA, for cloning,sequencing, assembly, validation, and gene annotation, and for comparing both sequences and gene arrangements. On several topics, we offer general observations based on our experiences to date with determining and comparing complete mtDNA sequences

Phylogenetic Invariants for Genome Rearrangements

We review the combinatorial optimization problems in calculating edit distances between genomes and phylogenetic inference based on minimizing gene order changes. With a view to avoiding the computational cost and the "long branches attract" artifact of some treebuilding methods, we explore the probabilization of genome rearrangement models prior to developing a methodology based on branch-length invariants. We characterize probabilistically the evolution of the structure of the gene adjacency set for reversals on unsigned circular genomes and, using a nontrivial recurrence relation, reversals on signed genomes. Concepts from the theory of invariants developed for the phylogenetics of homologous gene sequences can be used to derive a complete set of linear invariants for unsigned reversals, as well as for a mixed rearrangement model for signed genomes, though not for pure transposition or pure signed reversal models. The invariants are based on an extended Jukes-Cantor semigroup. We i..