Comparative Genomics Via Phylogenetic Invariants For Jukes-cantor Semigroups

We review the theory of invariants as it has been developed for comparing the DNA sequences of homologous genes from phylogenetically re-lated species, with particular attention to the semigroups used to model se-quence evolution. We also outline the computational theory of genome rear-rangements, including the optimization problems in calculating edit distances between genomes and the simpler notion of breakpoint distance. The combi-natorics of rearrangements, involving non-local changes in the relative order of genes in the genome, are more complex than the base substitutions responsi-ble for gene sequence evolution. Nevertheless we can construct models of gene order evolution through symmetry assumptions about disruptions of gene ad-jacencies. Based on the extended Jukes-Cantor semigroup that emerges from this modeling, we derive a complete set of linear phylogenetic invariants. We use these invariants to relate mitochondrial genomes from a number of an-imal phyla and compare the results to parsimony trees also based on gene adjacencies and to minimal breakpoint trees