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Several authors have argued recently that extensive taxon sampling has a positive and important effect on the accuracy of phylogenetic estimates. However, other authors have argued that there is little benefit of extensive taxon sampling, and so phylogenetic problems can or should be reduced to a few exemplar taxa as a means of reducing the computational complexity of the phylogenetic analysis. In this paper we examined five aspects of study design that may have led to these different perspectives. First, we considered the measurement of phylogenetic error across a wide range of taxon sample sizes, and conclude that the expected error based on randomly selecting trees (which varies by taxon sample size) must be considered in evaluating error in studies of the effects of taxon sampling. Second, we addressed the scope of the phylogenetic problems defined by different samples of taxa, and argue that phylogenetic scope needs to be considered in evaluating the importance of taxon-sampling strategies. Third, we examined the claim that fast and simple tree searches are as effective as more thorough searches at finding near-optimal trees that minimize error. We show that a more complete search of tree space reduces phylogenetic error, especially as the taxon sample size increases. Fourth, we examined the effects of simple versus complex simulation models on taxonomic sampling studies. Although benefits of taxon sampling are apparent for all models, data generated under more complex models of evolution produce higher overall levels of error and show greater positive effects of increased taxon sampling. Fifth, we asked if different phylogenetic optimality criteria show different effects of taxon sampling. Although we found strong differences in effectiveness of different optimality criteria as a function of taxon sample size, increased taxon sampling improved the results from all the common optimality criteria. Nonetheless, the method that showed the lowest overall performance (minimum evolution) also showed the least improvement from increased taxon sampling. Taking each of these results into account re-enforces the conclusion that increased sampling of taxa is one of the most important ways to increase overall phylogenetic accuracy.

Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software.

BackgroundHigher-level relationships within the Lepidoptera, and particularly within the species-rich subclade Ditrysia, are generally not well understood, although recent studies have yielded progress. We present the most comprehensive molecular analysis of lepidopteran phylogeny to date, focusing on relationships among superfamilies.Methodology / Principal Findings483 taxa spanning 115 of 124 families were sampled for 19 protein-coding nuclear genes, from which maximum likelihood tree estimates and bootstrap percentages were obtained using GARLI. Assessment of heuristic search effectiveness showed that better trees and higher bootstrap percentages probably remain to be discovered even after 1000 or more search replicates, but further search proved impractical even with grid computing. Other analyses explored the effects of sampling nonsynonymous change only versus partitioned and unpartitioned total nucleotide change; deletion of rogue taxa; and compositional heterogeneity. Relationships among the non-ditrysian lineages previously inferred from morphology were largely confirmed, plus some new ones, with strong support. Robust support was also found for divergences among non-apoditrysian lineages of Ditrysia, but only rarely so within Apoditrysia. Paraphyly for Tineoidea is strongly supported by analysis of nonsynonymous-only signal; conflicting, strong support for tineoid monophyly when synonymous signal was added back is shown to result from compositional heterogeneity.Conclusions / SignificanceSupport for among-superfamily relationships outside the Apoditrysia is now generally strong. Comparable support is mostly lacking within Apoditrysia, but dramatically increased bootstrap percentages for some nodes after rogue taxon removal, and concordance with other evidence, strongly suggest that our picture of apoditrysian phylogeny is approximately correct. This study highlights the challenge of finding optimal topologies when analyzing hundreds of taxa. It also shows that some nodes get strong support only when analysis is restricted to nonsynonymous change, while total change is necessary for strong support of others. Thus, multiple types of analyses will be necessary to fully resolve lepidopteran phylogeny.

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