Our results show that it is best to avoid stem branch time, because the length of any (stem) branch in the tree should not be related to the time depth of the descendant node (crown age; fig. 5 d and e). Therefore, the use of stem branch time will introduce large statistical noise and make the test extremely conservative. For example, when considering every node in a timetree of species, the coefficient of variation of stem branch length relative to crown age is over 200% in the best sampled groups, mammals (208%) and birds (224%). That noise is further weighted by the pull of the present ( Nee et al. 1994), which, we determined, adds 40% time (median) to crown age at any given node (if stem age is used instead of crown age), in separate analyses of birds, mammals, and all eukaryotes. This is because the pull of the present creates longer internal branches deeper in a tree, as more lineages are pruned by extinction. Therefore, the use of stem branches in diversification analyses adds noise (variance) and gives increased weight to that noise. We believe that the stronger signal of constant expansion in our results, compared with earlier studies that have supported hypo-expansion and saturation, is in part because we have identified and avoided some biases (e.g., sampling effort, clade size, and stem age) that can impact diversification analyses. Speciation Costello MJ, May RM, Stork NE. Can we name Earth's species before they go extinct? Science. 2013; 339(6118):413–416. [ PubMed] [ Google Scholar] Gogarten, J. P., Murphey, R. D. & Olendzenski, L. Horizontal gene transfer: pitfalls and promises. Biol. Bull. 196, 359–362 (1999). Szöllősi, G. J., Rosikiewicz, W., Boussau, B., Tannier, E. & Daubin, V. Efficient exploration of the space of reconciled gene trees. Syst. Biol. 62, 901–912 (2013). Our diversification results for birds are similar to an earlier analysis ( Jetz et al. 2012), with a strong increase in diversification from ∼45 Ma to the present. The mammal results are also generally similar to past mammal analyses in showing the absence of any rate increase immediately after the end-Cretaceous extinctions ( Bininda-Emonds et al. 2007; Meredith et al. 2011). We did not find a sharp mid-Cenozoic increase in rate that was found in one other analysis ( Stadler 2011), although we determined that the cause of that rate increase was from a polytomy in the mammal timetree used in that study ( Stadler 2011); otherwise our results are comparable.

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For the bird tree ( supplementary fig. S4a, Supplementary Material online), the models with zero, one, two, three, four, and five rate shifts are rejected in favor of a model with six rate shifts ( P< 0.05) ( supplementary table S9, Supplementary Material online). A model with six rate shifts is not rejected in favor of a model with seven rate shifts ( P = 0.091). The 6 shifts are detected at 1, 3.4, 14.4, 48.2, 73.3, and 84.4 Ma ( supplementary table S10, Supplementary Material online). The parameters obtained for the 6 shifts model between 73.3 and 48.2 Ma (λ−μ = 0.04058 and μ/λ = 0.0395) were used to plot the confidence interval of the null distribution ( supplementary fig. S4a, Supplementary Material online). The large TTOL afforded us the opportunity to examine patterns of lineage splitting across the diversity of eukaryotes (we omit prokaryotes in our TTOL analyses because they have an arbitrary species definition). Under models of “expansion,” diversity will continue to expand, either at an increasing diversification rate (hyper-expansion), the same rate (constant expansion), or decreasing rate (hypo-expansion). Saturation, on the other hand, refers to a drop in rate to zero as diversity reaches a plateau (equilibrium), possibly because of density-dependent biotic factors such as species interactions ( Morlon 2014). Most recent analyses, but not all ( Venditti et al. 2010; Jetz et al. 2012), have suggested that hypo-expansion is the predominant pattern in the tree of life, although there has been considerable debate as to the importance of timescales, biotic or abiotic factors, and potential biases in the analyses ( Sepkoski 1984; Benton 2009; Morlon et al. 2010; Rabosky et al. 2012; Cornell 2013; Rabosky 2013). For the TTOL, we estimated node time uncertainty in both the LTT curve and rate test by producing 500 replicates of the TTOL, sampling a time between the confidence intervals at each node under a uniform distribution. These replicates were then used in the TREEPAR analysis to estimate and test rate change, with the uncertainty shown in figure 4 and the significant shifts by time interval (20 My) shown in supplementary table S8, Supplementary Material online. Here, we have taken an approach to build a global TTOL by means of a data-driven synthesis of published timetrees into a large hierarchy. We have synthesized timetrees and related information in 2,274 molecular studies, which we collected and curated in a knowledgebase ( Hedges et al. 2006) ( supplementary Materials and Methods, Supplementary Material online). We mapped timetrees and divergence data from those studies on a robust and conservative guidetree based on community consensus ( National Center for Biotechnology Information 2013) and used those times to resolve polytomies and derive nodal times in the TTOL ( supplementary fig. S2, Supplementary Material online). We present this synthesis here, for use by the community, and explore how it bears on evolutionary hypotheses and mechanisms of speciation and diversification. Results A Global Timetree of Species

There are challenges in synthesizing a global TTOL. The most common approach for constructing a large timetree using a sequence alignment or super alignment is possible ( Smith and O'Meara 2012; Tamura et al. 2012), but not generally practical because of data matrix sparseness. For example, genes appropriate for closely related species are unalignable at higher levels, and those appropriate for higher levels are too conserved for resolving relationships of species. Disproportionate attention to some species, such as model organisms and groups of general interest (e.g., mammals and birds), also results in an uneven distribution of knowledge. In addition, computational limits are reached for Bayesian timing methods involving more than a few hundred species ( Battistuzzi et al. 2011; Jetz et al. 2012). Tamura K, Battistuzzi FU, Billing-Ross P, Murillo O, Filipski A, Kumar S. Estimating divergence times in large molecular phylogenies. Proc Natl Acad Sci U S A. 2012; 109(47):19333–19338. [ PMC free article] [ PubMed] [ Google Scholar] A unique collection of thousands of videos, images and fact-files illustrating the world's species. Szöllősi, G. J., Tannier, E., Lartillot, N. & Daubin, V. Lateral gene transfer from the dead. Syst. Biol. 62, 386–397 (2013). Wolfe, J. M. & Fournier, G. P. Tunneling through time: horizontal gene transfer constrains the timing of methanogen evolution. Preprint at https://www.biorxiv.org/content/early/2017/04/21/129494 (2017).Dufresne, A., Garczarek, L. & Partensky, F. Accelerated evolution associated with genome reduction in a free-living prokaryote. Genome Biol. 6, R14 (2005). Morlon H. Phylogenetic approaches for studying diversification. Ecol Lett. 2014; 17:508–525. [ PubMed] [ Google Scholar] Spatafora, J. W. et al. A phylum-level phylogenetic classification of zygomycete fungi based on genome-scale data. Mycologia 108, 1028–1046 (2016). We used a hierarchical average linkage method of estimating divergence times ( T s) of clade pairs to build a Super Timetree, along with a procedure for testing and updating topological partitions to ensure the highest degree of consistency with individual timetrees in every study. For the TTOL, uncertainty derived from individual studies is available for each node ( supplementary table S2, Supplementary Material online). Branch time modes of different Linnaean categories were estimated ( supplementary table S3, Supplementary Material online). Diversification Analyses