Towards sub-quadratic time and space complexity solutions for the dated tree reconciliation problem

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 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.

Cophylogenetic signal is detectable in pollination interactions across ecological scales

“…Both approaches have limitations (Balbuena et al. , Drinkwater and Charleston ) and we take a global‐fit approach here because it is the most amenable to the data we have and network‐centric questions we explore.…”

“…Currently, there are a range of tools available for undertaking cophylogenetic analysis, and these methods can mainly be sorted into event-based and global-fit methods. Event-based methods reconcile one phylogenetic tree with the other by directly assessing evolutionary events (i.e., cospeciation, duplication, host switches) that are explicit in the tree topology (Conow et al 2010, Drinkwater andCharleston 2016). Conversely, global-fit methods, such as ParaFit and PACo, aim to assess cophylogeny based on the congruence of observed interactions relative to the phylogenies rather than with the specifics of the phylogenetic topologies (Legendre et al 2002, Balbuena et al 2013).…”

“…Conversely, event-based methods such as Jane (Conow et al 2010) and CoRe-PA Merkle et al 2010) instead permute the topology of the phylogenies due to their explicit focus on specific events. Both approaches have limitations (Balbuena et al 2013, Drinkwater andCharleston 2016) and we take a global-fit approach here because it is the most amenable to the data we have and network-centric questions we explore.…”

The dynamics of preferential host switching: host phylogeny as a key predictor of parasite prevalence and distribution

“…Most of the previous theoretical work on host-shifts has focused on reconciling host and parasite phylogenetic trees, identifying host-shift vs. cospeciation events, and inferring parameters underlying these processes (older literature reviewed in de Vienne et al 2013;newer work includes Baudet et al 2015;Wieseke et al 2015;Drinkwater & Charleston 2016;Alcala et al 2017). Mathematically speaking, these are very hard problems and most of the developed algorithms are computationally expensive.…”

The dynamics of preferential host switching: Host phylogeny as a key predictor of parasite distribution*

“…Most of the previous theoretical work on host shifts has focused on reconciling host and parasite phylogenetic trees, identifying host shift versus cospeciation events, and inferring parameters underlying these processes (older literature reviewed in de Vienne et al 2013;Baudet et al 2015;Wieseke et al 2015;Drinkwater and Charleston 2016;Alcala et al 2017). Mathematically speaking, these are very hard problems and most of the developed algorithms are computationally expensive.…”