On the Accuracy of Ancestral Sequence Reconstruction for Ultrametric Trees with Parsimony
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 Li, Steel and Zhang which states that for any ultrametric phylogenetic tree and a symmetric model, the Fitch parsimony method using all terminal taxa is more accurate, or at least as accurate, for ancestral state reconstruction than using any particular terminal taxon or any particular pair of taxa. This conjecture had so far only been answered for two-state data by Fischer and Thatte. Here, we focus on answering the biologically more relevant case with four states, which corresponds to ancestral sequence reconstruction from DNA or RNA data.
KeywordsMaximum parsimony Ancestral sequence reconstruction Reconstruction accuracy Symmetric four-state model
- Jukes T, Cantor C (1969) Evolution of protein molecules. Mamm Protein Metab 3:21–132. https://doi.org/10.1016/B978-1-4832-3211-9.50009-7 CrossRefGoogle Scholar
- Liberles (ed) DA (2007) Ancestral Sequence Reconstruction. Oxford University Press, NY. https://doi.org/10.1093/acprof:oso/9780199299188.001.0001
- Regner P (2012) Phylogenetic trees-selected combinatorial problems. Diplomarbeit, Technical University of Vienna, ViennaGoogle Scholar
- Semple C, Steel M (2003) Phylogenetics. Oxford Lecture Series in Mathematics and its ApplicationGoogle Scholar
- Yang J, Li J, Dong L, Grünewald S (2011) Analysis on the reconstruction accuracy of the fitch method for inferring ancestral states. BMC Bioinform 12(18). https://doi.org/10.1186/1471-2105-12-18