Ancestral reconstruction over continuous characters and distributions

CREATED: 200810140800 TITLE: Ancestral reconstruction by asymmetric Wagner parsimony over continuous characters and squared parsimony over distributions SPEAKER: Miklos Csuros ** Squared parsimony

• Evolutionary character may be over real values, for example probability values
• Parsimony labeling (steiner tree labeling), can be solved by DP in the discrete case (Sankoff and Rousseau 1975)
• Squared parsimony, $\Delta(x,y) = (x - y)^2$
• SquaP for a distribution can be computed by Maddison’s algorithm in each position independently ** Gene family evolution using Wagner parsimony
• events: duplication, speciation, gene gain/loss
• character is the size of the gene family, eg COG0247 (Kinesin-like protein)
• Wagner parsimony: $\Delta(x,y) = |x - y|$
• Asymmetric Wagner parsimony with gain loss penalty: $\Delta(x,y) = (y > x) ? a(y - x) : b(x - y)$
• For a tree of n nodes and height h, can be computed in $O(nh)$
• symmetric Wagner is like a cup, asymmetric Wagner parsimony is a piece-wise linear, continuous convex function
• can be computed in postorder traversal ** Gene content evolution in Archaea
• arCOG data set: 7538 gene families (Makarova et al. 2007)
• gains followed by specialization