David Bapst

A stochastic rate‐calibrated method for time‐scaling phylogenies of fossil taxa

Summary Applying phylogeny-based analyses of trait evolution and diversification in the fossil record generally involves transforming an unscaled cladogram into a phylogeny scaled to geologic time. Current methods produce single time-scaled phylogenies with no indication of the uncertainty in the temporal relationships and, under some methods, artificial zero-length branches. Here, I present a stochastic algorithm for time-scaling phylogenies of fossil taxa by randomly sampling node ages from a constrained distribution, with the ultimate goal of producing large samples of time-scaled phylogenies for a given data set as the basis for phylogeny-based analyses. I describe how this stochastic approach can be extended to consider potential ancestral relationships and resolve polytomies. The stochastic selection of node ages in this algorithm is weighted by the probability density of the total inferable unobserved evolutionary history at single divergence events in a tree, a distribution dependent on rates of branching, extinction and sampling in the fossil record. The combined time-scaling method must be calibrated with explicit estimates of three rates: branching, extinction and sampling, and thus is named the cal3 time-scaling method, included in the r library paleotree. I test the time-scaling capabilities of the cal3 and older time-scaling methods in simulations. cal3 produces samples of time-scaled trees that better bracket the uncertainty in the true node ages than existing time-scaling methods. This is true even in simulations under a ‘terminal-taxon’ model of differentiation that violates many of the assumptions of the cal3 method. The cal3 method provides a new approach for time-scaling palaeontological cladograms, calibrated to estimated sampling and diversification rates, allowing for better estimates of uncertainty in the phylogenetic time-scaling. The cal3 method is robust to relaxation of at least some model assumptions. Additional work is needed to analyse the impact of time-scaling approaches on macroevolutionary analyses and to integrate time-scaling with phylogenetic inference.

Graptoloid diversity and disparity became decoupled during the Ordovician mass extinction

The morphological study of extinct taxa allows for analysis of a diverse set of macroevolutionary hypotheses, including testing for change in the magnitude of morphological divergence, extinction selectivity on form, and the ecological context of radiations. Late Ordovician graptoloids experienced a phylogenetic bottleneck at the Hirnantian mass extinction (∼445 Ma), when a major clade of graptoloids was driven to extinction while another clade simultaneously radiated. In this study, we developed a dataset of 49 ecologically relevant characters for 183 species with which we tested two main hypotheses: (i) could the biased survival of one graptoloid clade over another have resulted from morphological selectivity alone and (ii) are the temporal patterns of morphological disparity and innovation during the recovery consistent with an interpretation as an adaptive radiation resulting from ecological release? We find that a general model of morphological selectivity has a low probability of producing the observed pattern of taxonomic selectivity. Contrary to predictions from theory on adaptive radiations and ecological speciation, changes in disparity and species richness are uncoupled. We also find that the early recovery is unexpectedly characterized by relatively low morphological disparity and innovation, despite also being an interval of elevated speciation. Because it is necessary to invoke factors other than ecology to explain the graptoloid recovery, more complex models may be needed to explain recovery dynamics after mass extinctions.

Assessing the effect of time-scaling methods on phylogeny-based analyses in the fossil record

Abstract Phylogeny-based approaches can be used to infer diversification dynamics and the rate and pattern of trait change. Applying these analyses to fossil data often requires time-scaling a cladogram of morphotaxon relationships. Although several time-scaling methods have been developed for this purpose, the incomplete sampling of the fossil record can distort the apparent timing of branching. It is unclear how well different time-scaling methods reconstruct the true temporal relationships or how any such inaccuracy could affect tree-based evolutionary analyses. I developed process-based simulations of the fossil record that allow the comparison of approximated time-scaled trees to true time-scaled trees. I used this simulation framework to test the effect of time-scaling methods on the fidelity of several commonly applied tree-based analyses, across a range of simulation conditions. When the fidelity of time-scaling methods differed, the stochastic “cal3” time-scaling method with ancestral assignment produced preferable results. Estimating rates and models of continuous trait evolution was particularly sensitive to bias from scenarios that forced the insertion of many short branch lengths, a bias that is not solved by any of the considered time-scaling methods in all scenarios. The cal3 method of time-scaling can be recommended as the preferred time-scaling method among those tested, but caution must be exercised because tree-based analyses are prone to easily overlooked biases.

Topology, divergence dates, and macroevolutionary inferences vary between different tip-dating approaches applied to fossil theropods (Dinosauria).

Dated phylogenies of fossil taxa allow palaeobiologists to estimate the timing of major divergences and placement of extinct lineages, and to test macroevolutionary hypotheses. Recently developed Bayesian ‘tip-dating’ methods simultaneously infer and date the branching relationships among fossil taxa, and infer putative ancestral relationships. Using a previously published dataset for extinct theropod dinosaurs, we contrast the dated relationships inferred by several tip-dating approaches and evaluate potential downstream effects on phylogenetic comparative methods. We also compare tip-dating analyses to maximum-parsimony trees time-scaled via alternative a posteriori approaches including via the probabilistic cal3 method. Among tip-dating analyses, we find opposing but strongly supported relationships, despite similarity in inferred ancestors. Overall, tip-dating methods infer divergence dates often millions (or tens of millions) of years older than the earliest stratigraphic appearance of that clade. Model-comparison analyses of the pattern of body-size evolution found that the support for evolutionary mode can vary across and between tree samples from cal3 and tip-dating approaches. These differences suggest that model and software choice in dating analyses can have a substantial impact on the dated phylogenies obtained and broader evolutionary inferences.

When can clades be potentially resolved with morphology

Morphology-based phylogenetic analyses are the only option for reconstructing relationships among extinct lineages, but often find support for conflicting hypotheses of relationships. The resulting lack of phylogenetic resolution is generally explained in terms of data quality and methodological issues, such as character selection. A previous suggestion is that sampling ancestral morphotaxa or sampling multiple taxa descended from a long-lived, unchanging lineage can also yield clades which have no opportunity to share synapomorphies. This lack of character information leads to a lack of ‘intrinsic’ resolution, an issue that cannot be solved with additional morphological data. It is unclear how often we should expect clades to be intrinsically resolvable in realistic circumstances, as intrinsic resolution must increase as taxonomic sampling decreases. Using branching simulations, I quantify intrinsic resolution across several models of morphological differentiation and taxonomic sampling. Intrinsically unresolvable clades are found to be relatively frequent in simulations of both extinct and living taxa under realistic sampling scenarios, implying that intrinsic resolution is an issue for morphology-based analyses of phylogeny. Simulations which vary the rates of sampling and differentiation were tested for their agreement to observed distributions of durations from well-sampled fossil records and also having high intrinsic resolution. This combination only occurs in those datasets when differentiation and sampling rates are both unrealistically high relative to branching and extinction rates. Thus, the poor phylogenetic resolution occasionally observed in morphological phylogenetics may result from a lack of intrinsic resolvability within groups.

Probabilistic divergence time estimation without branch lengths: dating the origins of dinosaurs, avian flight and crown birds

Branch lengths—measured in character changes—are an essential requirement of clock-based divergence estimation, regardless of whether the fossil calibrations used represent nodes or tips. However, a separate set of divergence time approaches are typically used to date palaeontological trees, which may lack such branch lengths. Among these methods, sophisticated probabilistic approaches have recently emerged, in contrast with simpler algorithms relying on minimum node ages. Here, using a novel phylogenetic hypothesis for Mesozoic dinosaurs, we apply two such approaches to estimate divergence times for: (i) Dinosauria, (ii) Avialae (the earliest birds) and (iii) Neornithes (crown birds). We find: (i) the plausibility of a Permian origin for dinosaurs to be dependent on whether Nyasasaurus is the oldest dinosaur, (ii) a Middle to Late Jurassic origin of avian flight regardless of whether Archaeopteryx or Aurornis is considered the first bird and (iii) a Late Cretaceous origin for Neornithes that is broadly congruent with other node- and tip-dating estimates. Demonstrating the feasibility of probabilistic time-scaling further opens up divergence estimation to the rich histories of extinct biodiversity in the fossil record, even in the absence of detailed character data.

Comparing cal3 and other a posteriori time-scaling approaches in a case study with the pterocephaliid trilobites

Abstract. Reconstructing the tree of life involvesmore than identifying relationships among lineages; it also entails accurately estimating when lineages diverged. Paleontologists typically scale cladograms to time a posteriori by direct reference to first appearances of taxa in the stratigraphic record. Some approaches use probabilistic models of branching, extinction, and sampling processes to date samples of trees, such as the recently developed cal3 method, which stochastically draws divergence dates given a set of rates for those processes. However, these models require estimates of the rates of those processes, which may be hard to obtain, particularly for sampling. Here, we contrast the use of cal3 and other a posteriori time-scaling approaches by examining a previous study that documented a decelerating rate of morphological evolution in pterocephaliid trilobites. Although aspects of the data set make estimation of branching, extinction, and sampling rates difficult, we use a multifaceted approach to calculate and evaluate the rate estimates needed for applying cal3. In agreement with previous simulation studies, we find that the choice of phylogenetic dating method impacts downstream macroevolutionary conclusions. We also find contradictory evolutionary inferences between analyses on ancestor—descendant contrasts (based on ancestor trait reconstruction methods) and maximum-likelihood parameter estimates. Ancestral taxon inference in cal3 corroborates previously hypothesized ancestor—descendant sequences, but cal3 suggests greater support for budding cladogenesis than anagenesis. This case study demonstrates the potential and wide applicability of the cal3 method and the benefits afforded by choosing cal3 over simpler a posteriori time-scaling approaches.

Preparing Paleontological Datasets for Phylogenetic Comparative Methods

The fossil record holds considerable promise for furthering our understanding of macroevolutionary patterns, particularly allowing us to analyze hypotheses which cannot be tested with phylogenies of extant taxa alone. However, although there is a growing number of paleontological studies that use phylogenetic comparative methods to address questions of trait evolution, there is little documentation on obtaining the timescaled phylogenies of fossil taxa required for such analyses. This chapter is an attempt to introduce interested readers to the issues involved with that process, including the uncertainties and biases involved with fossil data, which some might inadvertently overlook. In addition, I illustrate how the fossil records of different groups can be very different in terms of the datasets available, including the issues of that data, and stress that there is no ‘one size fits all’ solution. Instead, for several hypothetical examples, I recommend several approaches that explicitly consider potential uncertainties, unavailable data, and biasing factors.

Combined Analysis of Extant Rhynchonellida (Brachiopoda) using Morphological and Molecular Data

Abstract. Independent molecular and morphological phylogenetic analyses have often produced discordant results for certain groups which, for fossil‐rich groups, raises the possibility that morphological data might mislead in those groups for which we depend upon morphology the most. Rhynchonellide brachiopods, with more than 500 extinct genera but only 19 extant genera represented today, provide an opportunity to explore the factors that produce contentious phylogenetic signal across datasets, as previous phylogenetic hypotheses generated from molecular sequence data bear little agreement with those constructed using morphological characters. Using a revised matrix of 66 morphological characters, and published ribosomal DNA sequences, we performed a series of combined phylogenetic analyses to identify conflicting phylogenetic signals. We completed a series of parsimony‐based and Bayesian analyses, varying the data used, the taxa included, and the models used in the Bayesian analyses. We also performed simulation‐based sensitivity analyses to assess whether the small size of the morphological data partition relative to the molecular data influenced the results of the combined analyses. In order to compare and contrast a large number of phylogenetic analyses and their resulting summary trees, we developed a measure for the incongruence between two topologies and simultaneously ignore any differences in phylogenetic resolution. Phylogenetic hypotheses generated using only morphological characters differed among each other, and with previous analyses, whereas molecular‐only and combined Bayesian analyses produced extremely similar topologies. Characters historically associated with traditional classification in the Rhynchonellida have very low consistency indices on the topology preferred by the combined Bayesian analyses. Overall, this casts doubt on the use of morphological systematics to resolve relationships among the crown rhynchonellide brachiopods. However, expanding our dataset to a larger number of extinct taxa with intermediate morphologies is necessary to exclude the possibility that the morphology of extant taxa is not dominated by convergence along long branches.

The inseparability of sampling and time and its influence on attempts to unify the molecular and fossil records

Abstract. The two major approaches to studying macroevolution in deep time are the fossil record and reconstructed relationships among extant taxa from molecular data. Results based on one approach sometimes conflict with those based on the other, with inconsistencies often attributed to inherent flaws of one (or the other) data source. Any contradiction between the molecular and fossil records represents a failure of our ability to understand the imperfections of our data, as both are limited reflections of the same evolutionary history. We therefore need to develop conceptual and mathematical models that jointly explain our observations in both records. Fortunately, the different limitations of each record provide an opportunity to test or calibrate the other, and new methodological developments leverage both records simultaneously. However, we must reckon with the distinct relationships between sampling and time in the fossil record and molecular phylogenies. These differences impact our recognition of baselines and the analytical incorporation of age estimate uncertainty.