Scaling of Accuracy in Extremely Large Phylogenetic Trees

Abstract

The accuracy of phylogenetic inference was examined in simulated data sets up to nearly 10,000 taxa, the size of the largest set of homologous genes in existing molecular sequence databases. Even with a simple search algorithm (maximum parsimony without branch swapping), the number of characters needed to estimate 80% of a tree correctly can scale remarkably well at optimal substitution rates (on the order of log N, where N is the number of taxa). In other words, the number of taxa in an analysis can be doubled and only an arithmetic increase in the number of characters is required to maintain the same level of accuracy. Even substitution rates that are much higher than normally used in phylogenetic studies did not affect the scaling too adversely. However, scaling is usually worse than log N for more stringent levels of accuracy. Moreover, errors are not distributed randomly throughout the tree. Shallow nodes are remarkably easy to reconstruct and display favourable log-linear scaling. The deepest nodes are extremely difficult to reconstruct accurately, even with branch swapping, and the scaling is poor. Therefore, the strategy of sequencing large numbers of homologous genes may not always provide global solutions to extreme phylogenetic problems and alternative strategies may be required.

Taxon Sampling versus Computational Complexity and Their Impact on Obtaining the Tree of Life

“…Thus, the analysis of larger data sets requires a disproportionately longer time (or disproportionately more computer resources) and/or the use of increasingly less efficient heuristic search strategies, with both factors impacting negatively on our ability to recover the best solution for that given data set. Fortunately, several studies using empirical and/or simulated data have shown that even phylogenetic analyses at the high end of the scale currently examined are both tractable and show acceptable, if not surprising, accuracy with shorter sequence lengths than might be expected [11][12][13] , thereby reinforcing some theoretical work in the latter area 14,15 . Additionally, advances in computer technology and architecture such as parallel and distributed computing and programs that exploit them efficiently in combination with the continual development of faster search strategies promise to make even larger phylogenetic problems increasingly tractable.…”

“…The simulation protocol used was modelled on that followed by Bininda-Emonds et al 13 to examine the scaling of accuracy in very large phylogenetic trees. For each run, a model tree of 4,096 taxa was generated according to a stochastic Yule birth process using the default parameters of the YULE_C procedure in the program r8s v1.60 25 .…”

“…A model data set was then created by evolving a nucleotide sequence down the model tree using a standard Markov process model as implemented in Seq-Gen v.1.2.7 26 . The sequence length was 2,000 bp, which is of sufficient length for simulated data with its stronger signal to achieve good accuracy for even the largest tree examined herein 13 , but is also short enough to keep running times within acceptable limits. Sequences were generated under a Kimura 2-parameter model 27 with a transition/transversion ratio (ti:tv) of 2.0, site-to-site rate heterogeneity (that is, Gamma model) with shape parameter of 0.5, and an overall average rate of evolution of 0.1 substitutions/site, measured along a path from the root to a tip of the tree.…”

“…This procedure differs substantially from that used by Bininda-Emonds et al 13 , in which model trees of the desired problem size were generated (that is, there was no sampling performed). Additionally, for each subproblem size and sampling strategy, the same alignment was analysed by each of MP, NJ, ML and where appropriate ML-DCM3.…”

“…Although it is widely accepted that larger phylogenetic problems are more difficult to solve and should therefore show decreased accuracy, there is now accumulating evidence to suggest that the performance dropoff is not as severe as many would believe, at least up to problem sizes of about 10,000 taxa 11,13 . Our finding that accuracy is essentially flat with respect to tree size ( Figure 6.2A and Figure 6.2B) lends further support to these latter findings, indicating that good accuracy is achievable even for very large phylogenetic problems and within a reasonable timeframe.…”