We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under consideration. In particular, for the symmetric four-state substitution model which is also known as Jukes-Cantor model, we answer affirmatively a conjecture of...

Changes of gene ordering under rearrangements have been extensively used as a signal to reconstruct phylogenies and ancestral genomes. Inferring the gene order of an extinct species has the potential in revealing a more detailed evolutionary history of species descended from it. Current tools used in ancestral reconstruction may fall into parsimonious and probabilistic methods according to the ...

Various phylogenetic problems (such as DNA, protein and genome reconstruction) involve estimating the ancestral states at the root of a tree from data at the tips (leaves). A better understanding of various methods of ancestral reconstruction would help us determine their reliability and credibility. This project investigates the upper and lower bound for the correct probability of reconstructi...

We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition under which maximum parsimony, a common reconstruction method requiring only the knowledge of the tree, succeeds better than random guessing uniformly in the...

Changes in parity mode between egg-laying (oviparity) and live-bearing (viviparity) have occurred repeatedly throughout vertebrate evolution. Oviparity is the ancestral amniote state, and viviparity has evolved many times independently within amniotes (especially in lizards and snakes), with possibly a few reversions to oviparity. In amniotes, the shelled egg is considered a complex structure t...

In this paper we investigate mathematical questions concerning the reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm for reconstructing the ancestral state given a phylogenetic tree and a character. In particular, we consider the question whether the maximum parsimony method applied to a subset of taxa can reconstruct the ancestral state of the root more accurately th...