Small Phylogeny Problem: Character Evolution Trees

Phylogenetics is a science of determining connections between groups of organisms in terms of ancestor/descendent relationships, usually expressed by phylogenetic trees, also called “trees of life”, cladograms, or dendograms. In parsimony approach to reconstruct the phylogenetic trees, the goal is to find the most parsimonious tree, i.e., the tree requiring the smallest number/score of evolutionary steps. For all reasonable measures this problem is NP-hard. Assuming the structure of the tree is given, we are left with, in some cases tractable, problem of “small phylogeny”: how to assign characters to the internal nodes representing extinct species. We propose a new approach together with the corresponding parsimony criteria for working with nonlinear transformation series of states of a character: a character evolution trees. We use tools of structural graph theory to reconcile a character tree with a phylogenetic tree. For this purpose, we introduce two new scoring metrics: the bag cost, analogous to unweighted parsimony, and the arc cost, analogous to weighted parsimony. We will provide several linear time algorithms solving small phylogeny problem while minimizing the above scoring functions.