Missing Data in Phylogenetic Analysis: Reconciling Results from Simulations and Empirical Data

Abstract

This paper will attempt to resolve some controversies about the effects of missing data on phylogenetic analysis. Whether missing data are generally problematic is a critical issue in modern phylogenetics, especially as wildly different amounts of molecular data become available for different taxa, ranging from entire genomes, to single genes, to none (e.g., fossils). Our perception of the impact of missing data (or lack thereof) may strongly influence which taxa and characters we include in a phylogenetic analysis (Wiens 2006) and may lead to a diversity of serious errors. For example, if we think that missing data are problematic when they are not, then we may exclude taxa and characters that would otherwise benefit our analyses, given the abundant evidence that increasing numbers of both taxa and characters can potentially improve the accuracy of phylogenetic analyses (e.g., Huelsenbeck 1995; Rannala et al. 1998; Poe 2003), where accuracy is generally defined as the similarity between the estimated tree and the correct, known phylogeny. In contrast, if missing data cells are themselves intrinsically problematic (e.g., Huelsenbeck 1991), including taxa or characters with many missing data cells may lead to inaccurate phylogenetic estimates. Several studies have explored how missing data may impact phylogenetic analyses, using both empirical and simulated data. Many simulation and empirical studies now suggest that it is often possible to include taxa that have large amounts of missing data without ill effects (e.g., Wiens 2003b; Driskell et al. 2004; Philippe et al. 2004; Wiens et al. 2005; Wiens and Moen 2008; Lynch and Wagner 2010; Thomson and Shaffer 2010; Wiens, Kuczynski, Townsend, et al. 2010). However, a recent simulation study (Lemmon et al. 2009) suggested instead that missing (“ambiguous”) data are generally problematic for phylogenetic analysis and implied that these previous simulation and empirical studies are therefore incorrect. They justified their study based on the grounds that previous studies were supposedly in conflict about the impacts of missing data (p. 131). In this paper, we will show that the paper by Lemmon et al. (2009; LEA hereafter) is problematic for several reasons. First, despite their statement that previous studies are in conflict, most simulation and empirical results on missing data can be easily explained within an existing theoretical framework (Wiens 2003b). Furthermore, many contradictory studies suggesting that missing data are not generally problematic for Bayesian and likelihood analyses (given some assumptions) were not addressed by LEA. Second, the sweeping negative conclusions of LEA are not necessarily supported by their results. LEA find missing data to be problematic primarily when using sets of invariant or saturated characters and/or when obvious rate heterogeneity is ignored. Their results do not support the idea that missing data generally lead to incorrect inferences about topology when informative data are analyzed with appropriate methods. We conduct new simulations under more realistic conditions, and these results show no evidence that missing data generally lead to inaccurate Bayesian estimates of phylogeny. In fact, we show that the practice of excluding characters simply because they contain missing data cells may itself reduce accuracy. We reanalyze the “manipulated” empirical example from LEA and find that, without these artificial “manipulations” of the data, their conclusions are not supported. We also analyze eight empirical data sets, each containing many taxa with extensive missing data. We show that these incomplete taxa are consistently placed into the expected higher taxa, often with very strong support. Overall, our results confirm previous simulation and empirical studies showing that taxa with extensive missing data can be accurately placed in phylogenetic analyses and that adding characters with missing data can be beneficial (at least under some conditions). We conclude by pointing out important areas for future research on the topic of missing data and phylogenetic analysis. There are two main ways that missing data might be added to a phylogenetic analysis, either through the addition of incomplete characters or incomplete taxa. For example, imagine having data from two genes for a given genus of organisms, in which the first gene has been sequenced for all 10 species and the second gene has been sequenced for only 5 species. Given this situation, one might (a) analyze only the first gene for all 10 species and then decide whether or not to (b) add the second gene (adding incomplete characters that are missing data for 5 of the species). Or, one might (c) analyze only the 5 species having data for both genes, and then decide whether or not to (d) add the 5 species lacking data for the second gene (adding incomplete taxa that are lacking data for the first gene). Note that (b) and (d) are effectively identical. Most of the lite