Minimal ancestral recombination graphs
Meeting Room 2, CMS
Finding the ancestral recombination graph (ARG) that explains a data set with the least number of recombination is the parsimony-ARG analogue to finding parsimonious phylogenies. This is a hard computational problem and two main approaches will be discussed. Firstly, a "scan along sequences dynamic programming approach that works up to 10 sequences of any length. Secondly, a "trace history back in time" branch and bound approach that can work very fast for much larger number of sequences, but can also fail totally dependent on data". The second approach can also be extended to include gene conversion. Finally, the number of ancestral states that could be encountered for a given data set it counted for small number of sequences and segregating sites. It is also illustrated how likelihood calculations can be done on a restricted graph that contains close to minimal histories of a set of sequences
Allen, B. and Steel, M., Subtree transfer operations and their induced metrics on evolutionary trees,Annals of Combinatorics 5, 1-13 (2001)
Baroni, M., Grunewald, S., Moulton, V., and Semple, C. Bounding the number of hybridisation events for a consistent evolutionary history. Journal of Mathematical Biology 51 (2005), 171-182
Bordewich, M. and Semple, C. On the computational complexity of the rooted subtree prune and regraft distance. Annals of Combintorics 8 (2004), 409-423
Hein,J.J., T.Jiang, L.Wang & K.Zhang (1996): "On the complexity of comparing evolutionary trees" Discrete Applied Mathematics 71.153-169.
Hein, J., Schierup, M. & Wiuf, C. (2004) Gene Genealogies, Variation and Evolution, Oxford University Press
Lyngsø, R.B., Song, Y.S. & Hein, J. (2005) Minimum Recombination Histories by Branch and Bound. Lecture Notes in Bioinformatics: Proceedings of WABI 2005 3692: 239250.
Myers, S. R. and Griffiths, R. C. (2003). Bounds on the minimum number of recombination events in a sample history. Genetics 163, 375-394.
Song, Y.S., Lyngsø, R.B. & Hein, J. (2005) Counting Ancestral States in Population Genetics. Submitted.
Song, Y.S. & Hein, J. (2005) Constructing Minimal Ancestral Recombination Graphs. J. Comp. Biol., 12:147169
Song, Y.S. & Hein, J. (2004) On the minimum number of recombination events in the evolutionary history of DNA sequences. J. Math. Biol., 48:160186.
Song, Y.S. & Hein, J. (2003) Parsimonious reconstruction of sequence evolution and haplotype blocks: finding the minimum number of recombination events, Lecture Notes in Bioinformatics, Proceedings of WABI'03, 2812:287302.