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      Calibration uncertainty in molecular dating analyses: there is no substitute for the prior evaluation of time priors

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          Abstract

          Calibration is the rate-determining step in every molecular clock analysis and, hence, considerable effort has been expended in the development of approaches to distinguish good from bad calibrations. These can be categorized into a priori evaluation of the intrinsic fossil evidence, and a posteriori evaluation of congruence through cross-validation. We contrasted these competing approaches and explored the impact of different interpretations of the fossil evidence upon Bayesian divergence time estimation. The results demonstrate that a posteriori approaches can lead to the selection of erroneous calibrations. Bayesian posterior estimates are also shown to be extremely sensitive to the probabilistic interpretation of temporal constraints. Furthermore, the effective time priors implemented within an analysis differ for individual calibrations when employed alone and in differing combination with others. This compromises the implicit assumption of all calibration consistency methods, that the impact of an individual calibration is the same when used alone or in unison with others. Thus, the most effective means of establishing the quality of fossil-based calibrations is through a priori evaluation of the intrinsic palaeontological, stratigraphic, geochronological and phylogenetic data. However, effort expended in establishing calibrations will not be rewarded unless they are implemented faithfully in divergence time analyses.

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          A Total-Evidence Approach to Dating with Fossils, Applied to the Early Radiation of the Hymenoptera

          Phylogenies are usually dated by calibrating interior nodes against the fossil record. This relies on indirect methods that, in the worst case, misrepresent the fossil information. Here, we contrast such node dating with an approach that includes fossils along with the extant taxa in a Bayesian total-evidence analysis. As a test case, we focus on the early radiation of the Hymenoptera, mostly documented by poorly preserved impression fossils that are difficult to place phylogenetically. Specifically, we compare node dating using nine calibration points derived from the fossil record with total-evidence dating based on 343 morphological characters scored for 45 fossil (4--20 complete) and 68 extant taxa. In both cases we use molecular data from seven markers (∼5 kb) for the extant taxa. Because it is difficult to model speciation, extinction, sampling, and fossil preservation realistically, we develop a simple uniform prior for clock trees with fossils, and we use relaxed clock models to accommodate rate variation across the tree. Despite considerable uncertainty in the placement of most fossils, we find that they contribute significantly to the estimation of divergence times in the total-evidence analysis. In particular, the posterior distributions on divergence times are less sensitive to prior assumptions and tend to be more precise than in node dating. The total-evidence analysis also shows that four of the seven Hymenoptera calibration points used in node dating are likely to be based on erroneous or doubtful assumptions about the fossil placement. With respect to the early radiation of Hymenoptera, our results suggest that the crown group dates back to the Carboniferous, ∼309 Ma (95% interval: 291--347 Ma), and diversified into major extant lineages much earlier than previously thought, well before the Triassic. [Bayesian inference; fossil dating; morphological evolution; relaxed clock; statistical phylogenetics.]
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            Paleontological evidence to date the tree of life.

            The role of fossils in dating the tree of life has been misunderstood. Fossils can provide good "minimum" age estimates for branches in the tree, but "maximum" constraints on those ages are poorer. Current debates about which are the "best" fossil dates for calibration move to consideration of the most appropriate constraints on the ages of tree nodes. Because fossil-based dates are constraints, and because molecular evolution is not perfectly clock-like, analysts should use more rather than fewer dates, but there has to be a balance between many genes and few dates versus many dates and few genes. We provide "hard" minimum and "soft" maximum age constraints for 30 divergences among key genome model organisms; these should contribute to better understanding of the dating of the animal tree of life.
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              Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds.

              We implement a Bayesian Markov chain Monte Carlo algorithm for estimating species divergence times that uses heterogeneous data from multiple gene loci and accommodates multiple fossil calibration nodes. A birth-death process with species sampling is used to specify a prior for divergence times, which allows easy assessment of the effects of that prior on posterior time estimates. We propose a new approach for specifying calibration points on the phylogeny, which allows the use of arbitrary and flexible statistical distributions to describe uncertainties in fossil dates. In particular, we use soft bounds, so that the probability that the true divergence time is outside the bounds is small but nonzero. A strict molecular clock is assumed in the current implementation, although this assumption may be relaxed. We apply our new algorithm to two data sets concerning divergences of several primate species, to examine the effects of the substitution model and of the prior for divergence times on Bayesian time estimation. We also conduct computer simulation to examine the differences between soft and hard bounds. We demonstrate that divergence time estimation is intrinsically hampered by uncertainties in fossil calibrations, and the error in Bayesian time estimates will not go to zero with increased amounts of sequence data. Our analyses of both real and simulated data demonstrate potentially large differences between divergence time estimates obtained using soft versus hard bounds and a general superiority of soft bounds. Our main findings are as follows. (1) When the fossils are consistent with each other and with the molecular data, and the posterior time estimates are well within the prior bounds, soft and hard bounds produce similar results. (2) When the fossils are in conflict with each other or with the molecules, soft and hard bounds behave very differently; soft bounds allow sequence data to correct poor calibrations, while poor hard bounds are impossible to overcome by any amount of data. (3) Soft bounds eliminate the need for "safe" but unrealistically high upper bounds, which may bias posterior time estimates. (4) Soft bounds allow more reliable assessment of estimation errors, while hard bounds generate misleadingly high precisions when fossils and molecules are in conflict.
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                Author and article information

                Journal
                Proc Biol Sci
                Proc. Biol. Sci
                RSPB
                royprsb
                Proceedings of the Royal Society B: Biological Sciences
                The Royal Society
                0962-8452
                1471-2954
                7 January 2015
                7 January 2015
                : 282
                : 1798
                : 20141013
                Affiliations
                [1 ]School of Earth Sciences, University of Bristol , Bristol, UK
                [2 ]National Evolutionary Synthesis Center , Durham, NC, USA
                [3 ]Department of Paleobiology, Smithsonian Institution , Washington DC, USA
                [4 ]John D. Cooper Archaeological and Paleontological Center, Department of Geological Sciences, California State University , Fullerton, CA, USA
                [5 ]Department of Geosciences, University of Fribourg/Freiburg , Switzerland
                [6 ]Denver Museum of Nature and Science , Denver, CO, USA
                Author notes
                Article
                rspb20141013
                10.1098/rspb.2014.1013
                4262156
                25429012
                4dee1c46-8166-4166-85e0-3ad7c7f8312b

                © 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

                History
                : 26 April 2014
                : 23 October 2014
                Categories
                1001
                144
                70
                22
                Research Articles
                Custom metadata
                January 7, 2015

                Life sciences
                molecular clock,calibration,cross-validation,fossil record,bayesian,priors
                Life sciences
                molecular clock, calibration, cross-validation, fossil record, bayesian, priors

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