How to Infer Ancestral Genome Features by Parsimony: Dynamic Programming over an Evolutionary Tree

Abstract

We review mathematical and algorithmic problems of reconstructing evolutionary features at ancestors in a known phylogeny. In particular, we revisit a generic framework for the problem that was introduced by Sankoff and Rousseau ["Locating the vertices of a Steiner tree in an arbitrary metric space," Mathematical Programming, 9: [240][241][242][243][244][245][246] 1975].

Ancestral Reconstruction: Theory and Practice

“…The computations have a quadratic complexity with respect to the state space size k, which makes dynamic programming a weak tool for large or infinite state spaces. If the state space is the integer set, it is possible to see the cost function C u (i) as an affine function of i and to propagate only the coefficients of the function along the nodes, instead of every value, to reach a complexity that does not depend on the size of the state space (Csűrös, 2014), making parsimony calculations feasible. When the state space is large but without a good structure to order it, as with gene orders (Section 4, there can be n!…”

“…When the state space Ω is a continuous set of numbers, the parsimony cost function d ij is usually defined as the absolute value or the square of the difference between i and j. The cost C cannot be computed for all values i ∈ Ω, and the coefficients of a linear or quadratic function of i is computed at each node, following the same dynamic programming principle (for an exhaustive review on parsimony methods see Csűrös (2014)). If d ij = (i − j) 2 , then the parsimony solution is also the ML one under a Brownian motion (BM) with a constant rate, which is the most commonly used Markovian process under continuous characters.…”

Evolution of genes neighborhood within reconciled phylogenies: an ensemble approach

“…From a methodological point of view, most existing algorithms to reconstruct evolutionary scenarios along a species tree in a parsimony framework rely on dynamicprogramming along this tree, whose introduction can be traced back to Sankoff in the 1970s (see [9] for a recent retrospective on this topic). Recently, several works considered more general approaches for such parsimony problems that either explore a wider range of values for combinatorial parameters of parsimonious models [10] or consider several alternate histories for a given instance, chosen for example from the set of all possible co-optimal scenarios or from the whole solution space, including suboptimal solutions (see [11,12,13] for examples of this approach for the gene tree/species tree reconciliation problem).…”

Evolution of genes neighborhood within reconciled phylogenies: an ensemble approach

“…From a methodological point of view, most existing algorithms to reconstruct evolutionary scenarios along a species tree in a parsimony framework rely on dynamic-programming along this tree, whose introduction can be traced back to Sankoff in the 1970s (see [ 9 ] for a recent retrospective on this topic). Recently, several works considered more general approaches for such parsimony problems that either explore a wider range of values for combinatorial parameters of parsimonious models [ 10 ] or consider several alternate histories for a given instance, chosen for example from the set of all possible co-optimal scenarios or from the whole solution space, including suboptimal solutions (see [ 11 - 13 ] for examples of this approach for the gene tree/species tree reconciliation problem).…”