The prevalence of terraced treescapes in analyses of phylogenetic data sets

Barbara H Dobrin,Michael J Sanderson,Derrick J Zwickl

doi:10.1186/s12862-018-1162-9

Abstract

BackgroundThe pattern of data availability in a phylogenetic data set may lead to the formation of terraces, collections of equally optimal trees. Terraces can arise in tree space if trees are scored with parsimony or with partitioned, edge-unlinked maximum likelihood. Theory predicts that terraces can be large, but their prevalence in contemporary data sets has never been surveyed. We selected 26 data sets and phylogenetic trees reported in recent literature and investigated the terraces to which the trees would belong, under a common set of inference assumptions. We examined terrace size as a function of the sampling properties of the data sets, including taxon coverage density (the proportion of taxon-by-gene positions with any data present) and a measure of gene sampling “sufficiency”. We evaluated each data set in relation to the theoretical minimum gene sampling depth needed to reduce terrace size to a single tree, and explored the impact of the terraces found in replicate trees in bootstrap methods.ResultsTerraces were identified in nearly all data sets with taxon coverage densities < 0.90. They were not found, however, in high-coverage-density (i.e., ≥ 0.94) transcriptomic and genomic data sets. The terraces could be very large, and size varied inversely with taxon coverage density and with gene sampling sufficiency. Few data sets achieved a theoretical minimum gene sampling depth needed to reduce terrace size to a single tree. Terraces found during bootstrap resampling reduced overall support.ConclusionsIf certain inference assumptions apply, trees estimated from empirical data sets often belong to large terraces of equally optimal trees. Terrace size correlates to data set sampling properties. Data sets seldom include enough genes to reduce terrace size to one tree. When bootstrap replicate trees lie on a terrace, statistical support for phylogenetic hypotheses may be reduced. Although some of the published analyses surveyed were conducted with edge-linked inference models (which do not induce terraces), unlinked models have been used and advocated. The present study describes the potential impact of that inference assumption on phylogenetic inference in the context of the kinds of multigene data sets now widely assembled for large-scale tree construction.

Highlights

The pattern of data availability in a phylogenetic data set may lead to the formation of terraces, collections of optimal trees
We were more interested in the impact of the structure of the data than the particular inference assumptions of the published papers, and we investigated the terraces that would have arisen had the reported trees been recovered with parsi- be broken and their subtended partial trees placed elsemony or with some form of maximum likelihood (ML)-EUL inference model. where, forming optimal alternative topologies
Size of terraces; relationship to taxon coverage percentage We succeeded in measuring the terraces present in 25 data sets; the sizes ranged from one tree to an astonishing 10388 trees (Fig. 3a, Table 1)

Summary

Introduction

The pattern of data availability in a phylogenetic data set may lead to the formation of terraces, collections of optimal trees. Problems tied to incomplete data sets first emerged in the context of paleontological data matrices [1,2,3], from which character states may be missing because of inapplicable characters or fossil incompleteness, leading to parsimony reconstruction (used widely for morphological data sets) recovering multiple, good trees. A large literature (e.g., [4,5,6,7,8,9,10,11,12,13,14,15,16]) has since assessed the risks and identified advantages linked to the use of incomplete data sets for inference, and the issues remain salient in the modern phylogenetics context because few data sets are fully sampled (i.e., include data at every taxon-by-gene position). For example, that abundant or nonrandom missing data can bias estimates of model parameters [21] promote the emergence of support artifacts [22, 23]; and worsen biases built into heuristic search procedures [24, 25], leading to artifactual tree search outcomes [25].

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Conclusion