Abstract
BackgroundRecent coevolutionary analysis has considered tree topology as a means to reduce the asymptotic complexity associated with inferring the complex coevolutionary interrelationships that arise between phylogenetic trees. Targeted algorithmic design for specific tree topologies has to date been highly successful, with one recent formulation providing a logarithmic space complexity reduction for the dated tree reconciliation problem.MethodsIn this work we build on this prior analysis providing a further asymptotic space reduction, by providing a new formulation for the dynamic programming table used by a number of popular coevolutionary analysis techniques. This model gives rise to a sub quadratic running time solution for the dated tree reconciliation problem for selected tree topologies, and is shown to be, in practice, the fastest method for solving the dated tree reconciliation problem for expected evolutionary trees. This result is achieved through the analysis of not only the topology of the trees considered for coevolutionary analysis, but also the underlying structure of the dynamic programming algorithms that are traditionally applied to such analysis.ConclusionThe newly inferred theoretical complexity bounds introduced herein are then validated using a combination of synthetic and biological data sets, where the proposed model is shown to provide an O(sqrt{n}) space saving, while it is observed to run in half the time compared to the fastest known algorithm for solving the dated tree reconciliation problem. What is even more significant is that the algorithm derived herein is able to guarantee the optimality of its inferred solution, something that algorithms of comparable speed have to date been unable to achieve.
Highlights
Recent coevolutionary analysis has considered tree topology as a means to reduce the asymptotic complexity associated with inferring the complex coevolutionary interrelationships that arise between phylogenetic trees
Within the field of phylogenetics only a small subset of these topologies are of interest, that is, the tree topologies which represent biological data
We argue that this is a very crude estimation, it does demonstrate that the set of trees corresponding to the heights that we expect to see under realistic biological conditions represents only a very small fraction of all tree topologies
Summary
Recent coevolutionary analysis has considered tree topology as a means to reduce the asymptotic complexity associated with inferring the complex coevolutionary interrelationships that arise between phylogenetic trees. Selective pressures and the adaptations that they give rise to, have provided almost a limitless diversity within the natural world [1]. These adaptations are often represented using bifurcating trees, where each internal node represents a divergence of a species lineage. Drinkwater and Charleston Algorithms Mol Biol (2016) 11:15 topologies as a means to optimise phylogenetic analysis techniques for expected evolutionary data [9]. Ignoring branch lengths when selecting the node for speciation has been shown to produce trees that represent the most balanced evolutionary trees within the tree of life [11, 12]
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