Parsimonious identification of evolutionary shifts for quantitative characters

Detecting shifts in the rate or the trend of a character evolution is an important question which has been widely addressed. To our knowledge, all the approaches developed so far for detecting such shifts from a quantitative character strongly involved stochastic models of evolution.\n\nWe propose here a novel method based on an asymmetric version of the linear parsimony (aka Wagner parsimony) for identifying the most parsimonious split of a tree into two parts between which the evolution of the character is allowed to differ. To this end, we evaluate the cost of splitting a phylogenetic tree at a given node as the integral, over all pairs of asymmetry parameters, of the most parsimonious cost which can be achieved by using the first parameter on the subtree pending from this node and the second parameter elsewhere. By testing all the nodes, we then get the most parsimonious split of a tree with regard to the character values at its tips.\n\nA study of the partial costs of the tree enabled us to develop a polynomial algorithm for determining the most parsimonious splits and their evolutionary costs. Applying this algorithm on two toy examples shows that using more than one asymmetry parameter does not always lower parsimonious costs. By using the approach on biological datasets, we obtained splits consistent with those identified by previous stochastic approaches.