Markov Katana: a Novel Method for Bayesian Resampling of Parameter Space Applied to Phylogenetic Trees

Abstract

14Phylogenetic inference requires a means to search phylogenetic tree space. This is usually 15 achieved using progressive algorithms that propose and test small alterations in the current tree 16 topology and branch lengths. Current programs search tree topology space using branch-17 swapping algorithms, but proposals do not discriminate well between swaps likely to succeed or 18 fail. When applied to datasets with many taxa, the huge number of possible topologies slows 19 these programs dramatically. To overcome this, we developed a statistical approach for proposal 20 generation in Bayesian analysis, and evaluated its applicability for the problem of searching 21 phylogenetic tree space. The general idea of the approach, which we call 'Markov katana', is to 22 make proposals based on a heuristic algorithm using bootstrapped subsets of the data. Such 23 proposals induce an unintended sampling distribution that must be determined and removed to 24 generate posterior estimates, but the cost of this extra step can in principle be small compared to 25 the added value of more efficient parameter exploration in Markov chain Monte Carlo analyses. 26Our prototype application uses the simple neighbor-joining distance heuristic on data subsets to 27propose new reasonably likely phylogenetic trees (including topologies and branch lengths). The 28 evolutionary model used to generate distances in our prototype was far simpler than the more 29 complex model used to evaluate the likelihood of phylogenies based on the full dataset. This 30 prototype implementation indicates that the Markov katana approach could be easily 31 incorporated into existing phylogenetic search programs and may prove a useful alternative in 32 conjunction with existing methods. The general features of this statistical approach may also 33 prove useful in disciplines other than phylogenetics. We demonstrate that this method can be 34 used to efficiently estimate a Bayesian posterior. 35

Systematic Exploration of the High Likelihood Set of Phylogenetic Tree Topologies

“…We have recently developed efficient such methods (Fourment et al, 2018) that we show work well for common models, and hope to show that they work well for more complex phylogenetic models in the future. One could also develop proposal distributions for MCMC samplers which draw topologies directly from the HLS set (Pollard et al, 2018), or use an importance-sampling approach.…”

“…Our work is distinguished from this previous work by our goal of approximating tree topology posterior distributions using likelihood methods, and by our methods of parallelized systematic exploration of suboptimal topologies. Another vein of work uses a collection of trees obtained using bootstrapping as a proxy for a posterior distribution (Rodrigo et al, 2009;Syme and Oakley, 2012;Pankey et al, 2014;Pollard et al, 2018). That work uses different methods and has not shown the level of agreement that we obtain between our approximation and the true posterior.…”